Ca Final Ama Written Notes-mt Educare

AMA-Notes

Contents 0.

INTRODCUCITON TO AMA....................................................................................................................... 6

1.

LEARNING CURVE....................................................................................................................................... 7

1.1.

Logarithm and Anti-Logarithm ................................................................................................................ 7

1.2.

Introduction to Learning Curve ............................................................................................................... 7

1.3.

Learning Curve formula ............................................................................................................................ 8

2.

LINEAR PROGRAMMING......................................................................................................................... 25

2.1.

Learning Objectives .................................................................................................................................. 25

2.2.

Introduction ............................................................................................................................................... 25

2.3.

Maximization Linear Programming Problem (LPP)............................................................................ 26

2.3.1.

Graphical Approach ............................................................................................................................. 26

2.3.2.

Simplex Method .................................................................................................................................... 27

2.3.3.

Steps in solving a maximization problem using Simplex Method ................................................ 31

2.4.

Minimization Linear Programming Problem (LPP) ............................................................................ 32

2.4.1.

Graphical Approach ............................................................................................................................. 33

2.4.2.

Simplex Method .................................................................................................................................... 34

2.5.

Infeasible Solution .................................................................................................................................... 36

2.6.

Unbounded Solution ................................................................................................................................ 37

2.7.

Multiple Optimal Solution ...................................................................................................................... 39

2.8.

Degeneracy ................................................................................................................................................ 40

2.9.

Interpretation of final simplex table....................................................................................................... 42

2.10.

Primal and Dual .................................................................................................................................... 42

2.10.1.

Conversion of Primal to Dual ............................................................................................................. 42

2.10.2.

Interpretation of dual problem and Comparison of simplex tables .............................................. 46

2.11.

Formulation types................................................................................................................................. 50

3.

ASSIGNMENT PROBLEMS ........................................................................................................................ 56

3.1.

Introduction ............................................................................................................................................... 56

3.2.

Minimization balanced assignment problem – Hungarian Method ................................................. 56

3.3.

Maximization balanced assignment problem – Hungarian Method ................................................ 58

3.4.

Minimization unbalanced assignment problem – Hungarian Method & Degeneracy .................. 59

3.5.

Maximization unbalanced assignment problem – Hungarian Method ............................................ 63

3.6.

Multiple Optimal Solution ...................................................................................................................... 69

4.

TRANSPORTATION ................................................................................................................................... 76

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AMA-Notes 4.1.

Introduction ............................................................................................................................................... 76

4.2.

Minimization Balanced ............................................................................................................................ 76

4.2.1.

Northwest Corner Method .................................................................................................................. 76

4.2.2.

Least Cost Method ................................................................................................................................ 77

4.2.3.

Vogel’s approximation method .......................................................................................................... 77

4.3.

Minimization Balanced - Degeneracy .................................................................................................... 79

4.4.

Maximization Unbalanced and Improvement through Looping ...................................................... 81

4.5.

Multiple Optimal Solution ...................................................................................................................... 87

4.6.

Formulation ............................................................................................................................................... 92

5.

STANDARD COSTING or VARIANCE ANALYSIS: ........................................................................... 101

5.1.

Learning Objectives ................................................................................................................................ 101

5.2.

Introduction ............................................................................................................................................. 101

5.3.

Understanding Standard Cost .............................................................................................................. 102

5.4.

Cost Variances ......................................................................................................................................... 103

5.4.1.

Material Cost Variances – Single Raw Material Input .................................................................. 103

5.4.2.

Material Cost Variances – Mix of Raw Materials ........................................................................... 105

5.4.3.

Labour Variances – without mix ...................................................................................................... 109

5.4.4.

Labour Variances – with mix ............................................................................................................ 109

5.4.5.

Labour Variance – Idle time .............................................................................................................. 111

5.4.6.

Variable Overhead Variances ........................................................................................................... 112

5.4.7.

Fixed Overhead Variances – With Calendar .................................................................................. 114

5.4.8.

Fixed Overhead Variances – Without Calendar............................................................................. 118

5.4.9.

Cost Variances Reconciliation ........................................................................................................... 120

5.5.

Marginal Costing vs. Absorption Costing .......................................................................................... 124

5.6.

Sales Variances ........................................................................................................................................ 127

5.7.

Types of Reconciliation Problems ........................................................................................................ 132

5.7.1.

Standard Reconciliation Statement .................................................................................................. 132

5.8.

Concept of Standard Profit .................................................................................................................... 138

5.9.

Reconciliation with Work in Progress ................................................................................................. 140

5.10.

Opportunity Cost Method of Reconciliation .................................................................................. 146

5.11.

Planning Variance vs. Operating Variance ..................................................................................... 154

5.12.

Planning vs. Operating Variance – Market Size and Market Share Variance ............................ 163

5.13.

Balance Score Card Method of Reconciliation ................................................................................ 166

5.14.

Miscellaneous Concepts – Standard Costing Ratios ...................................................................... 171

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AMA-Notes 5.15.

Partial Plan vs. Single Plan ................................................................................................................ 175

5.16.

Reverse Working Problems ............................................................................................................... 191

5.17.

Investigation of Variances ................................................................................................................. 196

6.

RELEVANT COSTING .............................................................................................................................. 199

6.1.

Learning Objectives ................................................................................................................................ 199

6.2.

Relevant Cost of Materials .................................................................................................................... 199

6.3.

Relevant Cost of Labour ........................................................................................................................ 201

6.4.

Relevant Cost of Overheads .................................................................................................................. 202

6.5.

Comprehensive Problems ..................................................................................................................... 203

6.6.

Limiting Factor and Relevant Costing ................................................................................................. 208

6.7.

Joint product and Relevant Costing ..................................................................................................... 211

6.8.

Relevant Costing under Uncertainty ................................................................................................... 214

7.

MARGINAL COSTING ............................................................................................................................. 220

7.1.

Learning Objectives ................................................................................................................................ 220

7.2.

Basics in Marginal Costing .................................................................................................................... 220

7.2.1.

Income Statement ............................................................................................................................... 221

7.2.2.

PV Ratio ............................................................................................................................................... 221

7.2.3.

Breakeven Point .................................................................................................................................. 221

7.2.4.

Margin of Safety .................................................................................................................................. 221

7.2.5.

Profit ..................................................................................................................................................... 222

7.3.

Issues in the concept of Break-even point ........................................................................................... 222

7.3.1.

Multiple break-even points (Step fixed cost) .................................................................................. 222

7.3.2.

Break-even point with semi-variable cost ....................................................................................... 227

7.3.3.

Marginal Costing (vs.) Absorption Costing Break-even point..................................................... 229

7.3.4.

Break-even point with two products ............................................................................................... 234

7.4.

Indifference Point ................................................................................................................................... 235

7.4.1.

Introduction to Indifference point .................................................................................................... 235

7.4.2.

Indifference point as a state of demand .......................................................................................... 237

7.4.3.

Limiting Factor and Indifference Point ........................................................................................... 240

7.4.4.

Understanding how to analyze a semi-variable cost ..................................................................... 244

7.5.

Limiting Factor Problems ...................................................................................................................... 249

7.5.1.

Basic Limiting factor allocation problems ....................................................................................... 249

7.5.2.

Limiting factor in Make or Buy Situation........................................................................................ 251

7.5.3.

Multiple Limiting factors in Make or Buy Situation ...................................................................... 258

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AMA-Notes 7.5.4.

Limiting factor with Specific Fixed Cost ......................................................................................... 262

7.6.

Shut down (or) Continue decisions...................................................................................................... 268

7.7.

Differential Costing ................................................................................................................................ 270

8.

SIMULATION ............................................................................................................................................. 279

9.

MATERIALS REQUIREMENT PLANNING (MRP) ............................................................................. 289

9.1.

Introduction ............................................................................................................................................. 289

9.2.

Planning Order Release ......................................................................................................................... 289

9.3.

Construction of Product Tree ................................................................................................................ 291

9.4.

Preparation of MRP ................................................................................................................................ 292

9.5.

Preparation of MRP with safety stock ................................................................................................. 292

9.6.

Material Purchase Budget and Economic Order Quantity [EOQ]................................................... 293

10.

NETWORK ANALYSIS ......................................................................................................................... 296

10.1.

Learning Objectives ............................................................................................................................ 296

10.2.

Introduction ......................................................................................................................................... 296

10.3.

Understanding some basic terms used in Network ...................................................................... 296

10.3.1.

Activities & Events ............................................................................................................................. 296

10.3.2.

Errors in Networking ......................................................................................................................... 297

10.3.2.1.

Looping Error .................................................................................................................................. 297

10.3.2.2.

Dangling Error ................................................................................................................................ 298

10.3.2.3.

Mistake in Preceding, Succeeding relationship .......................................................................... 298

10.3.3.

Conventions in Network Drawing................................................................................................... 299

10.4.

Floats, Forward Pass, Backward Pass and Critical Path ............................................................... 299

10.5.

Network Crashing .............................................................................................................................. 303

10.6.

Program Evaluation Review Technique .......................................................................................... 310

10.7.

Resource Allocation ............................................................................................................................ 314

10.8.

Resource Leveling (or) Resource Smoothing .................................................................................. 316

10.9.

Understanding to draw a network & use dummy activities ........................................................ 320

10.10.

Network Updation ............................................................................................................................. 330

11.

TRANSFER PRICING ............................................................................................................................ 332

11.1.

Introduction ......................................................................................................................................... 332

11.2.

Transfer Price - Variable Cost ........................................................................................................... 332

11.3.

Transfer Price – Specific Fixed Cost ................................................................................................. 339

11.4.

Linear Programming Method of Transfer Price fixation .............................................................. 342

11.5.

Limiting Factor and Transfer Pricing............................................................................................... 347

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AMA-Notes 11.6.

Multi-Division range fixations .......................................................................................................... 352

11.7.

Lump Sum Consideration Method .................................................................................................. 354

11.8.

Transfer Pricing Fixation Chart ........................................................................................................ 358

12.

PRICING .................................................................................................................................................. 360

12.1.

Pricing Using Calculus....................................................................................................................... 360

12.2.

Pricing Under Uncertainty and Expected Value of Perfect Information (EVPI) ....................... 364

12.3.

ROI (Return on Investment) Pricing ................................................................................................ 367

13.

DEVELOPMENTS IN COST ACCOUNTING (STRAGETIC COST MANAGEMENT ................ 368

13.1.

Learning Objectives ............................................................................................................................ 368

13.2.

Through Put Costing .......................................................................................................................... 368

13.3.

Theory of Constraints......................................................................................................................... 370

13.3.1.

Theory of Constraints Measures (TOC Measures)......................................................................... 373

13.4.

Just-in-Time System (JIT)................................................................................................................... 377

13.5.

Backflush Costing ............................................................................................................................... 381

13.5.1.

Backflush Costing – Version 1 .......................................................................................................... 381

13.5.2.

Backflush Costing – Version 2 .......................................................................................................... 382

13.5.3.

Backflush Costing – Version 3 .......................................................................................................... 383

13.6.

Total Quality Management (TQM) .................................................................................................. 387

13.7.

Life Cycle Costing (LCC) ................................................................................................................... 393

13.8.

Target Costing ..................................................................................................................................... 395

13.9.

Activity Based Costing (ABC)........................................................................................................... 400

13.9.1.

Activity Based Costing (ABC) - Introduction ................................................................................. 400

13.9.2.

Activity Based Costing (ABC) & Target Costing ........................................................................... 412

13.9.3.

Activity Based Costing (ABC) with Variance Analysis................................................................. 417

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AMA-Notes 0. INTRODCUCITON TO AMA

1) Source for Preparation: i. Revision Test Papers ii. Practice Manual iii. Steady Material iv. Advance Management Accounting -CA-Final – By Saxena and Vasisht v. Callen Drury vi. Hongren 2) Examination Pattern i. 7 Questions a) Q1 – 20 Marks (4QX5M) – Compulsory question b) Q2 – Q7 – 96 Marks (6QX16M) – Should write 6 questions  Q7 – Theory question in most of the cases (5QX4M – 1Q Choice) – one theory from QT ii. 27 Marks – 33 Marks theory will be asked. Everyone has to compulsorily write 16 Marks of theory 3) Total Subject can be divided into two types broadly: i. Costing – 79 Marks ii. QT - Quantitative Techniques (Operations Research) – 37 Marks – 4 Marks theory (compulsory)

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AMA-Notes 1. LEARNING CURVE 1.1. Logarithm and Anti-Logarithm

1) Generally, we used to express numbers in decimal systems 2) In decimal system we generally do addition, subtraction, multiplication and division. In which multiplication and division are difficult to calculate in case of big numbers. 3) The another way to do multiplications (exponential -26 ) and divisions is using “logarithms”. 4) For every decimal number there exists a corresponding number in the log system and vice versa. This can be found using the log tables and anti-log tables respectively. 5) Log Computation – Converting a number in decimal system into Log system: Number No. of digits No. of digits – 1 Log Table Value Log Value 4000 4 4–1=3 0.6021 3.6021 400 3 3–1=2 0.6021 2.6021 40 2 2–1=1 0.6021 1.6021 4 1 1 – 1 =0 0.6021 0.6021 4568 4 4 – 1= 3 0.6598 3.6598 6) Anti-log Computation – Converting a number in Log system into a decimal number: Log Decimal Table Integer Integer+1 𝟏𝟎(𝐈𝐧𝐭𝐞𝐠𝐞𝐫+𝟏) Value Value Portion Value 3.6021 0.6021 0.4000 3 3+1 = 4 10000 4000 2.6021 0.6021 0.4000 2 2+1 = 3 1000 400 1.6021 0.6021 0.4000 1 1+1 = 2 100 40 0.6021 0.6021 0.4000 0 0+1 = 1 10 4 3.6598 0.6598 0.4568 3 3+1 = 4 10000 4568 7) Decimal function vs. Log function: Decimal Function Log Function AXB Log A + Log B A/B Log A − Log B B B Log A A A+B Log(A + B) A–B Log(A − B) 1.2. Introduction to Learning Curve

1) When a person performs the task repeatedly, the time taken to do it gradually reduces. 2) The above reduction in time happens because of learning effect. The learning effect occurs because: a) He becomes more familiar with the Job b) He develops better tooling methods to perform it c) He identifies and eliminates unwanted activities in performing the Job 3) The learning curve looks as follows:

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AMA-Notes

4) 5)

6)

7)

As the number of units increases, the average time per unit decreases. The rate at which it decreases is called “Learning Rate” and is always expresses as percentage (%). The other names given to learning curve are “Experience Curve”, “Improvement Curve” and “Progress Curve”. A learning of 80% means, every time the production doubles the average time per unit becomes 80% of the previous average. Example can be understood as follows: No. of Units Cumulative Average time per unit (Hours) 1 100 2 80 4 64 8 51.20 The learning curve can be applied by the management accountant in the following three areas: a) Price fixation b) Fixing Labour Standards for Variance analysis c) Volume determination for a given capacity Learning curve will not have impact in following situations: a) Where the production is automated involving lesser human element b) Where the Jobs are non-repetitive or User Specific or Customer Specific c) Where the job is performed by highly experienced persons who has reached saturation point or a state of steady point.

1.3. Learning Curve formula

Question no 1: Direct labour hours to assemble the first unit of new equipment were 400. Assuming that this type of assemble will experience a learning effect of 90%. Compute the average direct labour for the 3rd & the 4th units as also for the 5th to 8th units. Find also the average labour for the 6th & 7th units. And also calculate the time taken from the 1st unit to 8th Unit. B= -0.1520 Solution: Units (X)

Cumulative Average time per unit (Y)

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Total time in hours

Incremental Hours

Increme ntal Units

Average time for incremental unit Page | 8

AMA-Notes 1 2 4 8

400 400 x 90% = 360 360 x 90% = 324 324 x 90% = 291.6

400 x 1 = 400 360 x 2 = 720 324 x 4 = 1296 291.6 x 8 = 2332.8

400 720 – 400 = 320 1296 – 720 = 576 2332.8 – 1296 = 1036.8

1 1 2 4

400/1 = 400 320/1 = 320 576/2 = 288 1036.8/4 = 259.2

Conclusion: 1) Average direct labour for 3rd and 4th units = 288 Hours 2) Average direct labour for 5th to 8th units = 259.2 Hours A re-look into average time of 3rd and 4th units: TT(4)−TT(2) 2 Units

=

[Y4 x 4]−[Y2 x 2] 2 Units

Time taken for 4 units−Time taken for 2 units 2 Units

=

1296−720 2 Units

576

= 2 Units = 288

=

Cumulative average after producing 4 units X 4 −Cumulative average after producing 2 units X 2

=

[324 x 4]−[360 x 2]

2 Units 2 Units

=

1296−720 2 Units

576

= 2 Units = 288

A re-look into average time of 5th to 8th units: TT(8)−TT(4) 4 Units

=

[Y8 x 8]−[Y4 x 4] 4 Units

Time taken for 8 units−Time taken for 4 units 4 Units

=

2332.8−1296 4 Units

1036.8

= 4 Units = 259.2

=

Cumulative average after producing 8 units X 8 −Cumulative average after producing 4 units X 4

=

[291.6 x 8]−[324 x 4] 4 Units

=

2332.8−1296 4 Units

4 Units 1036.8

= 4 Units = 259.2

Average time of 6th and 7th units: TT(7)−TT(5) 2 Units

=

[Y7 x 7]−[Y5 x 5] 2 Units

Is Y5 and Y7 is available in the table? If average time is asked in between doublings (twice), the problem cannot be solved in the form of table as attempted above. One has to use the following formula: YX = a(X)b ; where YX → Cumulative Average time per unit for ‘X’ units a → time required for the first unit X →target units b→

Log of learning rate Log 2

Log P

= Log 2

Note: Learning rates should always be expresses in decimals. For example, if learning rate is 90%, it should be return as 0.90. Calculation ofY7 :

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AMA-Notes Y7 =a(X)b ; where Y7 → Cumulative Average time per unit for ‘7’ units a → 400 b→

Log of learning rate Log 2

=

Log 0.90 Log 2

X → 7 units Log Value Computations:

Function A X P Constant Base Log P

b = Log 2 =

Values 400 7 0.90 2

−0.0458 0.3010

No. of Digits 3 1 0 1

Base (No. of Digits – 1) 2 0 -1 0

Log Table Value 0.6021 0.8451 0.9542 0.3010

Log Value 2.6021 0.8451 -0.0458 0.3010

= - 0.1522

Y7 = 400 x (7)−0.1522 → Apply log on both Sides Log Y7 = Log 400 + Log 7−0.1522 Log Y7 = Log 400 – 0.1522 Log 7 = 2.6021 – (0.1522 X 0.8451) = 2.6021 – 0.1286 = 2.4735 Y7 = Antilog of 2.4735 = 297.50 Hours Calculation ofY5 : Y5 = 400 x (5)−0.1522 → Apply log on both Sides Log Y5 = Log 400 + Log 5−0.1522 Log Y5 = Log 400 – 0.1522 Log 5 = 2.6021 – (0.1522 X 0.6990) = 2.6021 – 0.1064 = 2.4957 Y5 = Antilog of 2.4957 = 313.10 Hours Average time of 6th and 7th units: TT(7)−TT(5) 2 Units

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=

[Y7 x 7]−[Y5 x 5] 2 Units

=

[297.50 X 7]−[313.50 X 5]

=

2082.5−1565.5

2 units

2 Units

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AMA-Notes = 258.8 Alternatively, the solution can be presented as follows: Unit s (X) 5 7

Cumulative Average time per unit (Y) 313.10 297.50

Total time in hours

Incremental Hours

313.1 x 5 = 1565.5 297.5 x 7 = 2082.5

2082.5 – 1565.5 = 517

Increme ntal Units 2

Average time for incremental unit 517/2 = 258.58

Calculation of time taken for each unit individually: Calculation of 𝑌3

Y3 = 400 x (3)−0.1522 → Apply log on both Sides Log Y3 = Log 400 + Log 3−0.1522 Log Y3 = Log 400 – 0.1522 Log 3 = 2.6021 – (0.1522 X 0.4771) = 2.6021 – 0.0726 = 2.5295 Y3 = Antilog of 2.5295 = 0.3385 X 10(2+1) = 338.50 Hours Time taken for 3rd unit =

TT(3)−TT(2) 1 Unit

=

[Y3 x 2]−[Y2 x 2]

=

[338.50 X 3]−[360 X 2]

=

1015.5−720

1 Unit

1 Unit

1 Unit

= 295.5 Hours Calculation of 𝑌6

Y6 = 400 x (6)−0.1522 → Apply log on both Sides Log Y6 = Log 400 + Log 6−0.1522 Log Y6 = Log 400 – 0.1522 Log 6 = 2.6021 – (0.1522 X 0.7781) = 2.6021 – 0.1184 = 2.4837 Y6 = Antilog of 2.4837 = 0.3046 X 10(2+1) = 304.60 Hours

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AMA-Notes Calculation of time taken for each unit: Units

Cumulative average time per unit Total Time (Hours)

1 2 3 4 5 6 7 8

400 360 338.50 324 313.10 304.60 297.50 291.60

400 x 1 = 400 360 x 2 = 720 338.50 x 2 = 1015.5 324 x 2 = 1296 313.10 x 2 = 1565.5 304.60 x 2 = 1827.6 297.50 x 2 = 2082.5 291.60 x 2 = 2332.8

Time taken for the Unit (Hours) 400 720 – 400 = 320 1015.5 – 720 = 295.5 1296 – 1015.5 = 280.5 1565.5 – 1015.5 = 269.5 1827.6 – 1565.5 = 262.1 2082.5 – 1827.6 = 254.9 2332.8 – 2082.5 = 250.3

Question no 2: First batch of 25 transistor radios took a total of 250 direct labour hours. It is proposed to assemble another 40 units. What will be the average labour per unit in this lot? Assuming that there is 85% learning rate. B=-0.23455 Solution: Facts: 1st Batch New Order Cumulative Production

25 Units 40 Units 65 Units

1 Batch 1.6 Batches 2.6 Batches

Log Computation: Function a X

Values 250 2.6

No. of Digits Base (No. of Digits – 1) 3 2 1 0

Log Table Value 0.3979 0.4150

Log Value 2.3979 0.4150

Calculation ofY2.6: YX Y2.6 Log Y2.6 Log Y2.6

Y5

= a(X)b = 250 x (2.6)−0.23455 → Apply log on both Sides = Log 250 + Log 2.6−0.23455 = Log 250 – 0.23455 Log 2.6 = 2.3979 – (0.23455 X 0.4150) = 2.3979 – 0.9733 = 2.3006 = Antilog of 2.3006 = 0.1998 X 10(2+1) = 0.1998 X 1000 = 199.80 Hours

Average time of 1.6 batches or 40 units: TT(2.6)−TT(1) 1.6 Batches or 40 Units

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=

[Y2.6 x 2.6]−[Y1 x 1] 40 Units

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AMA-Notes =

[199.8 X 2.6]−[250 X 1]

=

519.48−250

40 units

40 Units

= 6.74 Hours per unit Alternatively, can be presented as follows: Batc hes (X) 1 2.6

Cumulative Average time per batch (Y) 250 199.80

Total time in hours

Incremental Hours

250 X 1 = 250 199.8 x 2.6 = 519.48

519.48 – 250 = 269.48

Increme ntal Units 40

Average time for incremental unit 269.48/40 = 6.73

Notes: 1) While solving a problem, we should observe how “a-time per first unit” is given. If it is given as the time taken for the first unit, do the calculations in units but if it is given as the time taken for 1st batch, then convert the problem into batches and solve. Additional Calculation for learning: Calculation of “a-time taken for the first unit”:

YX = Y25 =

250 Hours 25 units

= 10 Hours

Y25 = a X 250.23455 10 = a X 250.23455 → Apply log on both Sides Log 10 = Log a -0.23455 x Log 25 1 = Log a – (0.23455 x 1.3979) 1 = Log a – 0.3279 Log a = 1+0.3279 Log a = 1.3279 → Apply anti log on both Sides a = Anti-log of 1.3279 = 0.2127 X 10(1+1) = 0.2127 X 100 = 21.27 Hours Calculation ofY65 :

YX Y65 Log Y65 Log Y65

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= a(X)b = 21.27 x (65)−0.23455 → Apply log on both Sides = Log 21.27 + Log 65−0.23455 = Log 21.27 – 0.23455 Log 65 = 1.3278 – (0.23455 X 1.8129) Page | 13

AMA-Notes = 1.3278 – 0.4252 = 0.9026 = Antilog of 0.9026 = 0.79909 X 10(0+1) = 0.79909 X 10 = 7.9909 Hours or 8 Hours

Y65

Average Time taken for 40 units

=

TT(65)−TT(25)

=

[Y65 x 65]−[Y25 x 25]

=

[8 x 65]−[10 x 25]

=

520−250

=

270

40 Units

40 Units

40 Units

40

40

= 6.75 Hours Question no 3: A company has found that the average direct labour just after completion of X units was 26.4 hours. The average at the end of the first unit was 52 hours. If there is learning curve effect of 85%. What would have been the total output to date? Solution: Units 1 X

Cumulative average time per unit 52 Hours 26.4 Hours

Learning Curve rate 85%. YX = a(X)b 26.4 = 52 x (X)−0.23455 → Apply log on both Sides Log 26.4 = Log 52 + Log X −0.23455 Log 26.4 = Log 52 – 0.23455 Log X 1.4216 = 1.7160 – (0.23455 x Log X) (0.23455 x Log X) = 1.7160 – 1.4216 Log X =

1.7160 – 1.4216 0.23455

Log X = 1.2549 → Apply anti log on both sides X = Antilog of 1.2549 = 0.1799 X 10(1+1) = 0.1799 X 1000 = 17.99 Units or 18 Units

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AMA-Notes Question no 4: Suraksha an electronic firm has designed a new model of fire lock system and assembled the first unit as a prototype for demonstration. The direct labour expended on this unit was 260 hours and the direct material cost was Rs. 37,000. The direct labour rate is Rs.30 per hour. Following successful demonstration to potential customers, confirm orders has been received for supply of 50 units during the first 6 months and the supply of 75 units during the following 6 months. The company wishes to set competitive prices for the supplies in each of the periods by passing on the benefits of learning curve effect of 80% i.e. normally applicable to this type of industry. Further the variable overhead in regular production runs is estimated to be 125% of the direct labour cost and the fixed overheads are charged at 75% of the direct labour cost. In view of the large production volumes it is expected that 5% discount can be got on the materials use for the first 6 months and 10% discount for the 2nd 6 months. The company sets selling prices with a 40% mark-up on cost. Determine the selling price per unit that should be set for the offer in each of the 6 months. B=-0.3220 Solution: Step 1: Calculation of Y51 YX Y51 Log Y51 Log Y51

Y51

= a(X)b = 260 x (51)−0.3220 → Apply log on both Sides = Log 260 + Log 51−0.3220 = Log 260 – 0.3220 Log 51 = 2.4150 – (0.3220 X 1.7076) = 2.4150 – 0.5498 = 1.8652 = Antilog of 1.8652 = 0.7333 X 10(1+1) = 0.7333 X 1000 = 73.33 Hours

Step 2: Calculation of Y126 YX Y126 Log Y126 Log Y126

Y51

= a(X)b = 260 x (126)−0.3220 → Apply log on both Sides = Log 260 + Log 126−0.3220 = Log 260 – 0.3220 Log 126 = 2.4150 – (0.3220 X 2.1004) = 2.4150 – 0.6763 = 1.7386 = Antilog of 1.7386 = 0.5481 X 10(1+1) = 0.5481 X 1000 = 54.81 Hours

Step 3: Average time per unit for each order

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AMA-Notes Units (X) 1 51

Cumulative Average time per unit (Y) 260 73.33

126

54.81

Total time in hours

Incremental Hours

260 x 1 = 260 73.33 x 51 = 3739.83 54.81 x 126 = 6906.06

260 3739.83 – 260 = 3479.83 6906.06 – 3739.83 = 3166.23

Increme ntal Units 1 50 75

Average time for incremental unit 260/1 = 260 3479.83/50 = 69.60 3166.23/75 = 42.22

Step 4: Fixation of selling price Particulars Units Material Cost per unit Labour Cost per unit Variable Overhead per unit Fixed Overhead per unit Total Cost per unit Margin per unit (40% of cost) Selling price per unit

1st Order 50 37,000 x 95% = Rs. 35,150 69.6 X 30 = Rs. 2088 2088 X 125% = Rs. 2,610 2088 X 75% = Rs. 1,566 Rs. 41,414 41,414 x 40% = Rs. 16,567 Rs. 57,981

2nd Order 75 37,000 x 90% = Rs. 33,300 42.2 X 30 = Rs. 1266 1266 X 125% = Rs. 1,583 1266 X 75% = Rs. 950 Rs. 37,099 37,099 x 40% = Rs. 14,840 Rs. 51,939

**Question no 5: EGM manufactures electrical goods on behalf of various clients as per their requirements. Currently having lost one major client, EGM is left with a large surplus of skilled labour. This labour cannot be retrenched nor can additional be recruited. EGM located HHDG a marketing firm in household goods, for whom it can offer manufacturing facilities to find gainful work for the skilled labour that may otherwise idle. EGM has compiled the following information so as to take decision whether to undertake manufacture on behalf of HHDG. Capital outlay on the special machinery Rs.2 lakhs (machine having no salvage value). Incremental overheads Rs.1 lakh per annum. Cost of Material Rs.180 per unit. Skilled labour rate Rs.30 per hour. The contract if entered into must be for a period of 3 years and HHDG will offer a unit price of Rs.260 valid for all the three years. A first unit trail run took 10 hours of direct labour of a skilled workman. It is expected that on repetitive production there will be learning effect of 82%. HHDG will accept all the production that EGM is capable of. It was also assured that the surplus skilled labour available will be adequate to manufacture of 3,000 units in the first year. The cost of capital for EGM is 18%. You may assume that all cash flows occur at the year-end. Except for the capital outlay that has to be at the start of year 1. What decision should EGM take with regard to acceptance of the contract for HHDG? B=-0.2864 Solution: Basic Details: Selling Price Material Cost Labour Cost Total Variable Cost Contribution per unit Fixed Cost E M Reddy

= Rs.260 = Rs.180 = Nil (As the labour cost is payable with order or without order also). = Rs.180 = Rs.80 = Rs.100000 Page | 16

AMA-Notes Step 1: Calculation of the annual labour capacity in hours a = 10 Hours p = 82% or 0.82 X = 3000 Units Log Values Computation:

Function a X

Values 10 3000

No. of digits 2 4

Base 1 3

Table Value 0 0.4771

Log Value 1 3.4771

Finding out no.of hours available to produce 3000 units in the first year: = 10 x (3000)−0.2864 → Apply log on both Sides = Log 10 + Log 3000−0.2864 = Log 10 – 0.2864 Log 3000 = 1 – (0.2864 X 3.4771) = 1 – 0.9958 = 0.0042 Y3000 = Antilog of 0.0042 = 0.10099 X 10(0+1) = 0.10099 X 10 = 1.0099 Hours per unit Total time for 3000 units = 1.0099 X 3000 = 3030 hours (approx.) In a given year 3030 hours are available for production. In 1st year with this capacity, we can produce 3000 units and in the subsequent years with the same capacity the production shall experience increase due to learning effect. Y3000 Log Y3000 Log Y3000

Step 2: Total time for 3 years Year 1 2 3

Total Time (Hours) 3030 6060 9090

Step 3: Calculation of Year 2 production Let cumulative units produced at the end of year 2 be ‘X’. Units x Cumulative average time per unit = Total time X * [a * X b ] = Total Time −0.2864 X * [10 * X ] = 6060 Hours 1 −0.2864 X *X * 10 = 6060 Hours 1−0.2864 X * 10 = 6060 Hours 0.7136 X * 10 = 6060 Hours X 0.7136

E M Reddy

=

6060 Hours 10

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AMA-Notes X 0.7136 Log X 0.7136 0.7136 Log X

= 606 Hours → Apply log on both sides = Log 606 = 2.7825

Log X

= 0.7136

2.7825

Log X X

Cumulative Units Year 2 Production

= 3.8992 → Apply anti log on both sides = Antilog of 3.8992 = 0.7929 X 10(3+1) = 0.7929 X 10000 = 7929 or 7300 (approx.) = 7930 Units = 7930 – 3000 = 4930

Step 4: Calculation of Year 3 production Let cumulative units produced at the end of year 3 be ‘X’. Units x Cumulative average time per unit = Total time X * [a * X b ] = Total Time −0.2864 X * [10 * X ] = 9090 Hours 1 −0.2864 X *X * 10 = 9090 Hours 1−0.2864 X * 10 = 9090 Hours 0.7136 X * 10 = 9090 Hours 9090 Hours

X 0.7136

=

X 0.7136 Log X 0.7136 0.7136 Log X

= 909 Hours → Apply log on both sides = Log 909 = 2.9590

Log X

= 0.7136

10

2.9590

Log X X

Cumulative Units Year 3 Production

= 4.1466 → Apply anti log on both sides = Antilog of 4.1466 = 0.1402 X 10(4+1) = 0.1402 X 100000 = 14020 or 14000 (approx.) = 14000 Units = 14000 – 7930 = 6090

Step 5: Operating Cash inflows Year

No. of Units

1 2 3

3000 4930 6070

E M Reddy

Contribution @ Rs.80 (Rs.) 3000 x 80 = 2,40,000 4930 x 80 = 3,94,400 6070 x 80 = 4,85,600

Incremental Overhead 1,00,000 1,00,000 1,00,000

Profit = Contribution – Overhead 1,40,000 2,94,400 3,85,600

Page | 18

AMA-Notes Step 6: Calculation of Net Present Value Year Cash Flow Present Value Factor @18% 1 1,40,000 0.8475 2 2,94,400 0.7182 3 3,85,600 0.6086 Present Value of Cash inflows Less: Fixed Asset cost Net Present Value

Discounted Cash Flow 1,18,650 2,11,438 2,34,676 5,64,764 2,00,000 3,64,764

The HHDG order can be accepted since the Net Present Value is positive. Question no 6: The following information is provided by a firm. The factory manager wants to use appropriate average learning rate on activities, so that he may forecast costs and prices for certain levels of activity. (i) A set of very experienced people feed data into the computer for processing inventory records in the factory. The manager wishes to apply 80% learning rate on data entry and calculation of inventory. (ii) A new type of machinery is to be installed in the factory. This is a patented process and the output may take a year for full-fledged production. The factor manager wants to use a learning rate on the workers at the new machine. (iii) An operation uses contract labour. The contractor shifts people among various jobs once in two days. The labour force performs on task in 3 days. The manager wants to apply an average learning rate for these workers. You are required to advice to the manager with reasons on the applicability of the learning curve theory on the above information. Solution: The learning curve does not apply to very experienced people for the same job, since time taken can never tend to become zero or reduce very considerably after a certain range of output. This is the limitation of the learning curve. (i) Data entry is a manual job so learning rate theory may be applied. Calculation of inventory is a computerized job. Learning rate applies only to manual labour. (ii) Learning rate should not be applied to a new process which the firm has never tried before. (iii) The workers are shifted even before completion of one unit of work. Hence learning rate will not apply. Question no 7: Bandookwala & Co., A firearms manufacturer has designed a new type of gun and a first lot of 25 guns assembled for test purposes had the following costs: Direct Materials Rs. 24,500 Direct Labour Rs. 22,500 Variable Overheads Rs. 16,875 Fixed Overheads Rs. 11,250 Total Costs Rs. 75,125 The Variable overheads and fixed overheads are charged to products in the proposition of direct labour cost. BSF being satisfied with this gun have asked the lowest bid for supply of 1,000 guns. The company

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AMA-Notes will pass on the benefit of learning of 85% to the client in setting the bid. The company will set a selling price to earn 40% gross profit margin. Determine the unit price that should be bid. Solution: 1 Lot 40 lots 41 lots

25 guns 1000 guns 1025 guns

Step 1: Calculation of “b” b= = =

Log of Learning ratio Log 2 Log 0.85 Log 2 −0.0706 0,3010

= -0.2346 Step 2: Calculation of Y41 = a(X)b = 22,500 x (41)−0.2346 → Apply log on both Sides = Log 22,500 + Log 41−0.2346 = Log 22,500 – 0.2346 Log 41 = 4.3522 – (0.2346 X 1.6128) = 4.3522 – 0.3784 = 3.9738 = Antilog of 3.9738 = 0.9414 X 10(3+1) = 0.9414 X 10000 = Rs. 9,414

YX Y41 Log Y41 Log Y41

Y41

Step 3: Calculation of Labour Cost per unit Lots (X) 1

Cumulative Average time per lot (Y) 22,500

41

9,414

Total cost in Rs.

Incremental Rs.

22,500 x 1 = 260 9,414 x 41 = 3,85,74

22,500 3,95,474 – 22,500 = 3,63,474

Increme Average cost ntal Lots for incremental lot 1 22,500/1 = 22,500 40 3,63,474/40 = 9087

Step 4: Calculation of selling price per lot Particulars Material Cost Labour Cost Variable Overhead

E M Reddy

Computation Given Given 16,875 x 9,087 22,500

Amount (Rs.) 24,500 9,087 6,815

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AMA-Notes Fixed Overhead

11,250 22,500

x 9,087

Total Cost per lot 44,946 Margin ( 60 x40) Selling price per lot Selling price per gun (74,910/25)

4,544 44,946 29,964 74,910 2,996

Notes: 1) “a” in the problem can be given in four ways: a) Time for 1st Unit - YX means ‘cumulative average time per unit’ b) Time for 1st Batch/Lot - YX means ‘cumulative average time per batch/lot’ c) Cost of 1st Unit - YX means ‘cumulative average cost per unit’ d) Cost of 1st Batch/Lot - YX means ‘cumulative average cost per batch/lot’ Question no 8: An electronics firm which has developed a new type of fire alarm system has been asked to quote for a prospective contract. The customer requires separate price quotations for each of the following possible orders. 1st Order 100 fire alarm Systems nd 2 Order 60 fire alarm Systems rd 3 Order 40 fire alarm Systems The firm estimates the following cost per unit for the first order. Direct Material Rs.500 Direct Labour Department A (Highly automatic) 20 hours @ Rs.10/Hour Department B (Skilled labour) 40 hours @ Rs.15/Hour Variable overheads 20% of direct labour Fixed Overheads absorbed Department A Rs.8 per Hour Department B Rs.5 per Hour Determine a price per unit for each of the three orders, assuming the firms uses a mark-up of 25% on total cost and allows for an 80% learning curve. Extract from 80% learning curve tables is given: X 1.0 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Y (%) 100.0 91.7 89.5 87.6 86.1 84.4 83.0 81.5 80.0 ‘X’ represents the cumulative volume produced to date expressed as a multiple of initial order and Y is the learning curve factor for a given ‘X’ value expressed as a percentage of the cost of initial order. Solution: Calculation of average time per unit for each order: Batches 𝐘𝐗 % (X) 1

100%

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Cumulative average time per batch (𝐘𝐗 ) 4000

Cumulative average time per unit 40

Total Time

Increm ental time

Incremen tal Units

Average time per incremental Unit

4000

4000

100

4000/100=40

Page | 21

AMA-Notes 1.6

86.1% 4000 x 86.1% = 3444 80% 4000 x 80.0% = 3444

2

3444/100 = 34.44 3200/100 = 32

3444 x 1.6 = 5510.4 3200 x 2 = 6400

1510.4

60

1510.4/60=25.17

889.6

40

889.6/40=22.24

Calculation of selling price per unit for each order: Particulars Material Cost Labour cost: Automated Labour cost: Skilled @ Rs.15 Variable overhead@20% of labour cost Fixed overheads Department A @ Rs.8 per hour Fixed overheads Department B @ Rs.5 per hour Total Cost Add: Margin 25% of cost Selling price per unit

First Order (Rs.) 500 200 40 x 15 = 600 [(200+600)] x 20% = 160 20 x 8 = 160 40 x 5 = 200 1820 455 2275

Second Order (Rs.) 500 200 25.17 x 15 = 377.55 [(200+377.55)] x 20% = 115.51 20 x 8 = 160

Third Order (Rs.) 500 200 22.24 x 15 = 333.60 [(200+333.60)] x 20% = 106.72 20 x 8 = 160

25.17 x 5 = 125.85 1478.91 369.73 1848.63

22.24 x 5 = 111.2 1411.52 352.88 1764.4

Question no 9: Sundaram products Ltd manufactures complex electronic measuring instruments for which highly skilled labour required. Conventional standard costing has been used for some time but problems have been experienced in setting nearest standards for labour costs. Analysis of production times has shown that there is a learning effect of 90%. During period 11 the following data were recorded: Cumulative production at start of period 526 Units Production in period 86 Units Wages Paid Rs. 71,823 for 6,861 actual hours Material actual cost Rs. 20,850 Actual overheads for period Rs. 1,52,600 Budget and standard cost for electronic meters. Budgeted Production 86 Units Budgeted Overhead Rs. 1,50,903 Standard labour cost Rs.10 per hour Standard Material cost per unit Rs.250 Hours for the first unit 200 Hours You are required to: (a) Calculate and analyze where possible the materials, labour and variable overhead cost variances; (b) Calculate a total standard cost for electrometers. Solution: Step 1: Computation of Y612

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AMA-Notes YX Y612 Log Y612 Log Y612

Y612

= a(X)b = 200 x (612)−0.1520 → Apply log on both Sides = Log 200 + Log 612−0.1520 = Log 200 – 0.1520 Log 612 = 2.3010 – (0.1520 X 2.7868) = 2.3010 – 0.4236 = 1.8774 = Antilog of 1.8774 = 0.7541 X 10(1+1) = 0.7541 X 100 = 75.41 Hours

Step 1: Computation of Y612 YX Y526 Log Y526 Log Y526

Y526

= a(X)b = 200 x (526)−0.1520 → Apply log on both Sides = Log 200 + Log 526−0.1520 = Log 200 – 0.1520 Log 526 = 2.3010 – (0.1520 X 2.7210) = 2.3010 – 0.4136 = 1.8874 = Antilog of 1.8874 = 0.7711 X 10(1+1) = 0.7716 X 100 = 77.16 Hours

Step 3: Calculation of Standard Hours Time allowed for 612 Units

Time allowed for 526 Units Time allowed for 86 Units (Standard Hours) (527th Unit – 612th Unit)

= Y612 x 612 Units + [Y526 x 526 Units] = 75.41 Hours x 612 Units + [77.16 Hours x 526 Units] = 46,151 Hours = Y526 x 526 Units = 77.16 Hours x 526 Units = 40,586 Hours = Time allowed for 612 Units – Time allowed for 526 units = 46,151 Hours – 40.586 Hours = 5,565 Hours

Step 4: Computation table [1] SH x SR 5,565 Hours x Rs.10 Rs. 55,650

E M Reddy

[2] AH x AR Rs. 71,823 Rs. 71,823

[3] AH x SR 6,861 Hours x Rs.10 Rs. 68,610

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AMA-Notes Step 5: Variances Calculation

Labour Rate Variance (3-2) = Rs.68,610 – Rs.71,823 = Rs.3,213 (Adverse)

E M Reddy

Labour Cost Variance (1-2) = Rs.55,650 – Rs.71,823 = Rs.16,173 (Adverse)

Labour Efficiency Variance (1-3) = Rs.55,650 – Rs.68,610 = Rs.12,960 (Adverse)

Page | 24

AMA-Notes 2. LINEAR PROGRAMMING 2.1. Learning Objectives

1) Maximization linear programming problem a) Graphical Method b) Simplex Method 2) Minimization linear programming problem a) Graphical Method b) Simplex Method 3) Infeasible Solution 4) Unbounded Solution 5) Multiple Optimal Solution 6) Primal Dual Issues 7) Interpretation of a dual Problem 8) Interpretation of a final simplex table 9) Shortcut Substitution 10) Formulation time 2.2. Introduction

1) Example: Products Contribution Rs. Raw Material Kgs per unit Contribution /Kg. Rank based Labour Hours per unit Contribution per hour Rank

X 4 1 Kg. 4 I 2 Hours 2 II

Y 6 2 Kg. 3 II 2 hours 3 I

2) When something limits our production it is called “Limiting Factor” which may be raw material resource availability or labour hour capacity etc., 3) When there exists a limiting factor it should be allocated to the most profitable product and the profitability is ranked using the contribution per limiting factor. 4) In the above example, there are two limiting factors (i) Raw Material – 100 Kgs (ii) Labour Hours – 100 Hours 5) Raw Material as a limiting factor selects Product X and labour hour Product Y. Thus there exists a conflict in ranking. In such a case the problem should be solved using LPP technique (Linear Programming Problem) technique. 6) This chapter will be applied when we have an objective to be achieved with multiple constraints. 7) The above situation can be formulated into a Linear Programming Problem as follows: Let X1 be number of units of Product ‘X’ and X2 be number of units of Product ‘Y’. Max Z = 4X1 + 6X2 Subject to X1 + 2X2 < 100

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AMA-Notes 2X1 + 2X2 < 100 Where X1 & X2 > 0 8) The first equation (Max Z = 4X1 + 6X2 ) is called “Objective Function” which can be of two types: a) Maximization – Maximize production, profit etc., b) Minimization – Minimize cost, time etc., 9) The objective function should be achieved subject to constraints which can be of 3 types: a) Not more than (<) b) At least (>) c) Exactly (=) 10) The items for which we should calculate values are called “Variables” which are represented as variables (Z, X1 , X2 etc.,) 11) The numbers prefixed to the variables are called “Coefficients”. For example, coefficient of X2 in objective function is ‘6’. 12) We have to find out the value of variables to achieve our object and this can be done by solving the LPP (Linear Programming Problems) under two approaches a) Graphical Approach b) Simplex Method Graphical approach can be used only for two variable problems and that to it can give only solution and not wealth of information which simplex can do. 2.3. Maximization Linear Programming Problem (LPP)

Question no 1: Maximize Z = 3𝐗 𝟏 + 4𝐗 𝟐 Subject to 2𝐗 𝟏 + 3𝐗 𝟐 < 16 (Raw Materials Kgs) Subject to 4𝐗 𝟏 + 2𝐗 𝟐 < 16 (Labour Hours) Subject to 𝐗 𝟏 >0, 𝐗 𝟐 >0 Solution: 2.3.1. Graphical Approach

Step 1: Identification of two points for each line (constraint functions) 2X1 + 3X2 = 16 Let X1 =0, X2 = Let X2 =0, X1 =

16 3 16 2

= 5.33 =8

4X1 + 2X2 = 16 Let X1 =0, X2 = Let X2 =0, X1 =

16 2 16 4

=8 =4

Step 2: Identifying feasible and extreme points

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AMA-Notes

Notes: 1) All the points on this straight line satisfies equality. Points above the straight line represents > to constraint and below the straight line < to constraint. 2) Since the both constraints are <, the feasible region should be below both the straight lines. However, it should not go below the origin because of non-negativity constraint (X1 >0, X2 >0) 3) All points on the feasible region satisfies all the constraints but there exists one point that gives maximum profit which is called as “Optimum Solution”. 4) Extreme point theorem states that optimum solution lies at the extreme points (corner points) of the feasible region. 5) One of the extreme is lying at the intersection of the two lines which can be found out by solving the two equations. Step 3: Optimum Solution Points (0,0) (0,5.33) (2,4) (4,0)

Calculation 3x0+4x0 3 x 0 + 4 x 5.33 3x2+4x4 3x4+4x0

Profit 0 21.33 22 12

Produce 2 units of X1 and 4 units of X2 to produce a maximum profit of 22. 2.3.2. Simplex Method

Step 1: Conversion of Inequalities into Equalities

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AMA-Notes Subject to 2X1 + 3X2 + S1 = 16 4X1 + 2X2 + S2 = 16 Objective function → Max Z = 3X1 + 4X2 + 0S1 + 0S2 ; where S1 & S2 are slack variables Notes: 1) The first step in any LPP (Linear Programming Problem) is to convert Inequalities into equalities. 2) The variables added in LHS (Left Hand Side) to make it equal to RHS (Right Hand Side) are called “Slack Variables”. 3) Slack Variable represents unused or idle resources. Here S1 represent unused raw material and S2 represents idle labour hours. 4) For example, say the production plan is (X1 , X2 ) = (2, 2). It consumes 10 kg [(2 kg x 2) + (3 kg x 2)] of raw materials and 12 hours [(4 Hours x 2) + (2 Hours x 2)] of labour time leaving 6 Kgs unused (S1) and 4 hours idle (S2 ). 5) Since unused or idle resources generates no profit the objective function co-efficient of slack variables is “0”. Step 2: First Simplex table Fixed Program Profit Quantity Ratio (FR) 0 16 S1 2/3 0 16 S2 Cj Zj Incoming Variable (I) = X2 Cj - Zj Outgoing Variable (O) = S1 NER (Net Evaluation Row)

𝐗𝟏

𝐗𝟐

𝐒𝟏

2 4 3 0 3

3 2 4 0 4

1 0 0 0 0

𝐒𝟐 Replacement Ratio (RR) 0 16/3 1 16/2=8 0 Outgoing 0 Variable 0

Incoming Variable Step 3: Second Simplex table Fixed Program Ratio (FR) 1/4 X2 S2

Profit Quantity

𝐗𝟏

𝐗𝟐

4 0

2/3 8/3 3 0 3

1 0 4 0 4

16/3 16/3 Cj Zj

Incoming Variable (I) = X1 Outgoing Variable (O) = S2

Cj - Zj NER (Net Evaluation Row)

𝐒𝟏 1/3 -2/3 0 0 0

𝐒𝟐 Replacement Ratio (RR) 0 8 1 2 0 Outgoing 0 Variable 0

Incoming Variable A B (Fixed Ratio X Key Row) A–B

E M Reddy

16 4 32/3 4/3 16/3 8/3

2 2 0

0 2/3 -2/3

1 0 1

Page | 28

AMA-Notes Step 4: Third Simplex table Fixed Ratio (FR)

Program Profit X2 X1

4 3

Quantity

𝐗𝟏

𝐗𝟐

4 2

0 1 3 3 0

1 0 4 4 0

Cj Zj Cj - Zj NER (Net Evaluation Row) A B (Fixed Ratio X Key Row) A–B

16/3 4/3 4

2/3 2/3 0

1 0 1

1/3 -1/6 1/2

𝐒𝟏

𝐒𝟐

1/2 -1/4 0 5/4 -5/4

-1/4 3/8 0 1/8 -1/8

Replacement Ratio (RR)

0 1/4 -1/4

Notes: 1) From the above simplex tables, we can make the following two observations: a. Basic Variables in any simplex table will form Unit Matrix. b. The NER (Net Evaluation Row) values of basic variables will always be zero ‘0’. 2) Final Solution: Produce 2 units of X1 and 4 units of X 2 giving a profit of Rs.22 [(Rs.3 X 2 Units) + (Rs.4 X 4 Units)] which was the answer we got in graphical approach also. 3) Like Graphical Approach, the Simplex Method also moves from one extreme point to another in search of Optimum solution. This can be understood as follows: Table Solution Remarks First Simplex Table S1 = 16 & S2 = 16 This table suggest that produce ‘0’ units of X1 & ‘0’ units of X2 and keep the entire raw material (S1 ) unused & labour time (S2 ) idle. This is the first extreme point (X1 , X2 ) = (0, 0). 16 16 Second Simplex Table X1 = 0 – as not in the program X 2 = 3 & S2 = 3 16 X2 = 3 = 5.33 S1 = 0 – as not in the program 16 S2 = 3 = 5.33 This means, produce ‘0’ units of X1 and 5.33 units of X2 consuming entire raw material (S1=0) and leaving 16/3 hours of labour time (S2 =16/3) as idle. This yet another extreme point (X1 , X2 ) = (0, 5.33). Third Simplex Table X 2 = 4 & X1 = 2 X1 = 2 X2 = 4 S1 = 0 – as not in the program S2 = 0 – as not in the program This means, produce ‘2’ units of X1 and ‘4’ units of X2 consuming entire raw material (S1=0) and the available labour time (S2 =0). This yet another

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AMA-Notes extreme point (X1 , X2) = (2, 4) as well as optimum solution. 4) Why least replacement ratio? a. In first table, we decided to produce X2 for improvement. b. Every X2 requires 3 Kgs and 2 Hours. With 16 Kgs available we can produce 16/3 units and with 16 hours available we can produce 8 units. c. If we decide to produce ‘8’ units we have labour hours (8 Units X 2 Hours = 16 House) but we do not have sufficient raw material (8 Units X 3 Kgs = 24 Kgs but have only 16 Kgs). d. Thus the least RR (16/3 Units) is the possible X2 output. e. When 16/3 units of X2 is produced i. Raw Material 1. Available – 16 Kgs 2. Used – 3 Kgs X 16/3 Units = 16 Kgs 3. Balance – ‘0’ Replaced Raw Material (S0 )fully hence became outgoing Variable. ii. Labour Hours 1. Available – 16 Hours 2. Used – 2 Hours X 16/3 Units = 32/3 Hours 3. Balance – 16/3 Hours Partially replaced hence continuous in the next table with balance 16/3 hours. 5) What is the meaning of NER (Net Evaluation Row)? a. NER in second simplex table is 1/3. This means if X1 as basic variable, for every X1 produced the profit increases by 1/3. b. The NER is influenced by 2 factors. i. Cj – It shows the profit increase due to introducing X1 which is 3 ii. Zj – It shows the sacrifice of profit due to introducing of X1 which is 8/3 c. Hence, the net profit increase is Cj − Zj which is 1/3. If this is positive improve else the solution is final. 6) Meaning of Zj ? a. To produce 1 unit of X1 we require 2 Kgs of Raw Material 4 Hours of Labour. b. Hours are available but the entire raw material is now consumed by X2 . Hence to produce X1 we should sacrifice some X2 . c. The second simplex table X1 column (key column) shows X2 = 2/3 and S2 = 8/3. This means to produce one unit of X1 we should sacrifice 2/3 units of X2 and 8/3 hours of idle time. d. The above sacrifice generates the following resources: X1  Sacrifice 2/3 X2 o Raw material released – 2/3 Units X 3 Kgs. = 2 Kgs o Labour hours released – 2/3 Units X 2 Hours = 4/3 Hours. These 4/3 hours release with 8/3 Hours idle time gives us requires 4 hours labour time.  Use 8/3 hours of idle time e. By sacrificing 2/3 units of X2 we lose Rs.4 X 2/3 Units = Rs.8/3 and by using idle time 8/3 Hours we lose Rs.0 X 8/3 = Rs.0. Hence the total lose is 8/3 + 0 = Rs.8/3 which is Zj . E M Reddy

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AMA-Notes 7) Concept of Shadow Cost or Opportunity Cost: a. In the final simplex table, NER value of S1 is -5/4. This means if S1 is introduced as basic variable, for every S1 introduced the profit drops by 5/4. b. Introducing S1 as basic variable means planning to keep a Kg. of raw material unused. Hence unused raw material Kg. or wasted raw material Kg. makes company lose 5/4 profit. This is the opportunity cost of raw material Kg. c. Same logic can be applied for labour hours (S2 = 1/8) 2.3.3. Steps in solving a maximization problem using Simplex Method

1) Convert inequalities in to equalities Convert of inequalities in to equalities by adding slack variables in the constraint equations. Slack variable represents idle or unused resources since idle resource do not generate any profit, the value of slack variable in the objective function is zero (0). 2) Constructs the initial simplex table The table should have the following columns. FR Program Profit Quantity 𝐗𝟏 𝐗𝟐 𝐒𝟏 𝐒𝟐 RR FR – Fixed Ratio =

Key Column Number Key Number Quantity Column

RR – Replacement Ratio = Key Column Number a. Write co-efficient of the constant functions in the first table against the respective variables. 1 0 0 1 b. Identify the variables forming the unit matrix [ ] or [ ] among them. These Variables 0 1 1 0 are the ones which should enter the program column as basic variables. c. Assume the value of all non-basic variables to be zero and find out the value if basic variables to be entered in quantity column. d. Calculate the values in net-evaluation row (NER). NER = Cj − Zj e. Cj is the co-efficient of the variable in the objective function and Zj is the product of numbers in profit column and respective variable columns. If all the numbers in NER or either negative (-) or zero, the solution is optimal else we have to go for improvement. 3) Step for improvement a. Identify the variable with highest positive number in NER. This is called as incoming variable (I). The column in which this variable is placed is called as “Key Column”. b. Calculate the replacement ratios for the existing basic variables. c. The variable having the least replacement ratio will be the outgoing variable (O). d. The number lying at the inter-section of key row and key column is referred to as key number. e. Construct the second simplex table where the incoming variable will enter the program column. f. The value of basic variables from quantity column till the replacement ratio column should be compared as follows: New basic Variable Continuing basic Variable Divide the existing values of the variable in Values are computed using A – B formula the first table by key number. The resulting where ‘A’ is the value of the variables in the values should be entered in new table. first table and ‘B’ is the product of fixed rate and key number.

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AMA-Notes g. Calculate values in NER for the new table and check for optimality. h. Repeat the above steps until the optimal solution is obtained. Note: Slack variables are used when there is < sign in the constraint functions. If the sign is > then surplus variables are to be used. When surplus variables are used then artificial variables should be included in the solution. Note: Steps for minimization problem are all most same as that of maximization. Wherever in ascertaining solution is optimal there should be no negative. 2.4. Minimization Linear Programming Problem (LPP)

Question no 2: A small township of 15,000 people requires, on the average, 300,000 gallons of water daily. The city is supplied water from a central water-works where the water is purified by such conventional methods as filteration and chlorination. In addition, two different chemical compounds: (i) softening chemical and (ii) health chemical are needed for softening the water and for health purposes. The waterworks plans to purchase two popular brands that contain these chemicals. One unit of Chemico Corporation's product gives 8 pounds of softening chemical and 3 pounds of health chemical. One unit of Indian Chemical's product contains 4 pounds and 9 pounds per unit, respectively, for the same purposes. To maintain the water at a minimum level of softness and to meet a minimum programme of health protection, experts have decided that 150 and 100 pounds of the two chemicals that make up each product must be added to water daily. At a cost of 8 and 10 per unit respectively for Chemico's and Indian Chemical's products, what is the optimal quantity of each product that should be used to meet the minimum level of softness and minimum health standard? Solution: Facts: Chemical Softening Chemical Health Chemical

Chemico Product 8 Pounds 3 Pounds

Indian Chemical Product 4 Pounds 9 Pounds

Minimum Requirement 150 Pounds 100 Pounds

Step 1: Formulation Let X1 be number units of Chemico product purchased and X2 be number units of Indian Chemical produce purchased. Minimize Z = 8X1 + 10X2 Subject to 8X1 + 4X2 > 150 (Softening Chemical requirement) 3X1 + 9X2 > 100 (Health Chemical requirement) Where X1 & X2 > 0

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AMA-Notes 2.4.1. Graphical Approach

Step 2: Solving Using Graphical Approach Step A: Identifying two points for each constraint equation

8X1 + 4X2 = 150 Let X1 =0, X2 = Let X2 =0, X1 =

150 4 150 8

= 37.5 = 18.75

3X1 + 9X2 = 100 Let X1 =0, X2 = Let X2 =0, X1 =

100 9 100 3

= 11.11 = 33.33

Step B: Identifying feasible and extreme points

Step C: Optimum Solution Points (0,37.5) (15.83,5.83) (33.33,0)

Computation 8 x 0 + 10 x 37.5 8 x 15.83 + 10 x 5.83 8 x 33.33 + 10 x 0

Cost 375 185 267

Purchase 15.83 units of Chemico Corporation’s product and 5.83 units of Indian Chemical 22 Product.

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AMA-Notes 2.4.2. Simplex Method

Step 3: Simplex Method Step A: Conversion of Inequalities into Equalities

Objective function → Min Z = 8X1 + 10X2 + 0S1 + 0S2 + MA1 + MA2 Subject to 8X1 + 4X2 - S1 + A1 = 150 3X1 + 9X2 - S2 + A2 = 100 Notes: 1) The variables S1 &S2 are called “Surplus Variables”. 2) Surplus variables represent resource on hand in excess of requirement. For example, if X1 =15 and X2 =15, the no. of pounds of softening chemical in hand will be 180 pounds [(8x15) + (4x15)] but we require only 180 pound and the excess 30 pounds is called surplus variable. Same way one can understand for S2 . 3) Since the cost of required resource and excess resource (150 pounds & 30 pounds) is already there in 8X1 & 10X2 , we do not incur any extra cost specifically for surplus variable. Hence its objective coefficient is “0”. 4) If we continue into the first table with surplus variable alone we will end up with negative quantity. To avoid this situation, we introduced artificial variable. 5) These artificial variables are imagined variables and hence will not disturb equality. Our final simplex solution should not recommend artificial variable. To prevent that we assign a very high cost to it (M=Infinity). Step B: First Simplex table

FR 4/9 -

Program Cost M A1 M A2

Incoming Variable (I) = X2 Outgoing Variable (O) = A2

Quantity 150 100 Cj Zj

𝐗𝟏 8 3 8 11M

Cj - Zj NER (Net Evaluation Row)

810 - M 11M 13M

𝐗𝟐 4 9 10 13M

𝐒𝟏 -1 0 0 -M

𝐒𝟐 0 -1 0 -M

𝐀𝟏 1 0 M M

𝐀𝟐 0 1 M M

M

0

0

RR 75/2 100/9 Outgoing Variable

Incoming Variable Step C: Second Simplex table

FR 1/20

Program Cost M A1 10 X2

E M Reddy

Quantity 950/9 100/9

𝐗𝟏 20/3 1/3

𝐗𝟐 0 1

𝐒𝟏 -1 0

𝐒𝟐 4/9 -1/9

𝐀𝟏 𝐀𝟐 1 -4/9 0 1/9

RR 95/6 100/3

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AMA-Notes 8

Cj Zj

Incoming Variable (I) = X1 Outgoing Variable (O) = A1

10 10

20M+10

0 -M

0 4M−10

3

M 10−4M

9

0

14−20M

Cj - Zj NER (Net Evaluation Row)

M M

M

9

10−4M

3

Outgoing Variable

0

13M−10

9

9

Incoming Variable A B (Fixed Ratio X Key Row) A–B

150 8 400/9 4/3 950/9 20/3

4 4 0

-1 0 -1

0 -4/9 4/9

1 0 1

0 4/9 -4/9

Step D: Third Simplex table

FR -

Program Cost 8 X1 10 X2

Quantity 95/6 35/6 Cj Zj

1 0 8 8

𝐗𝟏

Cj - Zj NER (Net Evaluation Row) A B (Fixed Ratio X Key Row) A–B X1 = X2 =

95 6 35 6

100/9 1/3 95/18 1/3 35/6 0

𝐗𝟐 0 1 10 10 0

0

1 0 1

𝐒𝟏 -3/20 1/20 0

𝐒𝟐 1/15 -2/15 0

𝐀𝟏 3/20 -1/20 M

𝐀𝟐 -1/15 2/15 M

−14

−12

14

12

20 14

15 12

20

20

15

0 -1/20 1/20

-1/9 1/45 -2/15

14

M – 20

0 1/20 -1/20

15

RR -

12

M – 15

1/9 -1/45 2/15

= 15.83 = 5.83

Question no 3: Maximize Z = 40𝐗 𝟏 + 35𝐗 𝟐 Subject to 2𝐗 𝟏 + 3𝐗 𝟐 < 60 Subject to 4𝐗 𝟏 + 3𝐗 𝟐 < 96 Subject to 𝐗 𝟏 >0, 𝐗 𝟐 >0 Solution: Question no 4: Minimize Z = 60𝐘𝟏 + 95𝐘𝟐 Subject to 2𝐘𝟏 + 4𝐘𝟐 > 40 Subject to 3𝐘𝟏 + 3𝐘𝟐 > 35 Subject to 𝐘𝟏 >0, 𝐘𝟐 >0

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AMA-Notes Solution: 2.5. Infeasible Solution

Question no 5: Minimize Z = 20𝐗 𝟏 + 30𝐗 𝟐 Subject to 2𝐗 𝟏 + 𝐗 𝟐 < 40 Subject to 4𝐗 𝟏 - 𝐗 𝟐 < 20 Subject to 𝐗 𝟏 >30 Subject to 𝐗 𝟏 & 𝐗 𝟐 >0 Solution: Step 1: Conversion of Inequalities into Equalities Objective function → Max Z = 20X1 + 30X2 + 0S1 + 0S2 + 0S3 - MA1 Subject to 2X1 + X2 + S1 = 40 4X1 - X2 + S2 = 20 X1 - S3 + A1 = 30 Note: In the maximization objective function the co-efficient of artificial variable should be -M as we are assuming infinite cost. Step 2: Final Simplex table Refer work book page no 267. In the final simplex table artificial variable appears in the program column as basic variable. Thus the problem does not have solution i.e. it is the problem with infeasible solution. Step 3: Identifying infeasibility using Graphical Approach Step A: Identification of two points for each constraint

2X1 + X2 = 40 Let X1 =0, X2 = 40 Let X2 =0, X1 =

40 2

= 20

4X1 - X2 = 20 Let X1 =0, X2 = -20 Let X2 =0, X1 =

20 4

=5

Step B: Drawing the straight lines and identifying feasible region

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AMA-Notes

Notes: 1) The feasible region towards the left of the graph satisfies the first two constraints but does not satisfy the third constraint and on the other hand the feasible region towards right satisfies the third constraint but not the first two. 2) Thus there exists there is no single point in the entire graph that satisfies all the three constraints. Hence, the problem does not have solution. 3) Infeasible solution arises when the constraints are conflicting. 4) The following can be observed while solving the above problem: a. In improvement there will be one new variable and two continuous variables. Hence every time we should do ‘A – B’ calculation two times. b. Outgoing variable is that variable having lease positive replacement ratio (see second simplex table). 2.6. Unbounded Solution

Question no 6: Maximize Z = 10𝐗 𝟏 + 20𝐗 𝟐 Subject to 2𝐗 𝟏 + 4𝐗 𝟐 > 16 Subject to 𝐗 𝟏 + 5𝐗 𝟐 < 15 Subject to 𝐗 𝟏 & 𝐗 𝟐 >0 Solution: Step 1: Conversion of inequalities into equalities

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AMA-Notes Objective function → Max Z = 10X1 + 20X2 + 0S1 + 0S2 - MA1 - MA2 Subject to 2X1 + 4X2 - S1 + A1 = 16 X1 + 5X2 - S2 + A2 = 15 Step 2: Final Simplex table Refer page no. 260 It could be seen that there is an improvement to do but outgoing variable couldn’t be identified due to all RR (Replacement Ratios) being negative. In this problem the problem is said to be having unbounded solution i.e. solution is (X1 ,X2 ) = (∞, ∞) Step 3: Understanding unboundness through Graphical Approach Step A: Identification of two points for each constraint

2X1 + 4X2 = 16 Let X1 =0, X2 = Let X2 =0, X1 =

16 4 16 2

=4 =8

X1 + 5X2 = 15 Let X1 =0, X2 =

15 5

=3

Let X2 =0, X1 = 15 Step B: Drawing the straight lines and identifying feasible region

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AMA-Notes Notes: 1) A feasible region in this graph extends to infinity (∞) and the problem is maximization. Hence, the optimum solution is (X1 ,X 2 ) = (∞, ∞) i.e. the solution is unbounded. 2) Maximization problems can have greater than or equal to (>) constraints but should at least have one less than or equal to (<) constraint to act as limiting factor or boundary else the solution will be unbounded. 3) Minimization problems can have less than or equal to (<) constraints but should at least have one greater than or equal to (>) constraint to prevent the solution from being nil i.e. (X1 ,X2 ) = (0, 0) 2.7. Multiple Optimal Solution

Question no 7: Maximize Z = 8𝐗 𝟏 + 16𝐗 𝟐 Subject to 𝐗 𝟏 + 𝐗 𝟐 < 200 Subject to 𝐗 𝟐 < 125 Subject to 3𝐗 𝟏 + 6𝐗 𝟐 < 900 Subject to 𝐗 𝟏 & 𝐗 𝟐 >0 Solution: Step 1: Conversion of inequalities into equalities Max Z = 8X1 + 16X2 + 0S1 + 0S2 + 0S3 Subject to X1 + X2 + S1 = 200 X2 + S2 = 125 3X1 + 6X2 + S3 = 900 Step 2: Final Simplex table Refer page no. 271 Notes: 1) In the final simplex table, one of the non-basic variable (S2 ) has ‘0’ value in NER. 2) This means when S2 made as incoming variable, for every S2 introduced the profit changes by ‘Rs.0’ i.e. it does not change. 3) Thus there exists another solution that gives the same profit. Hence the problem is having multiple optimal solution. 4) Profit for the current solution: S1 = 25 Units x 0 = Rs.0 X2 = 125 Units x 16 = Rs.2000 X1 = 50 Units x 8 = Rs.400 Total Profit = Rs.0 + Rs.2000 + Rs.400 = Rs.2400 5) Improvement in the profit by making S2 as incoming variable:

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AMA-Notes FR

Program S2 X2 X1

Profit 0 16 8

Quantity 25 100 100 Cj Zj Cj − Zj

𝐗𝟏 0 0 1 8 8 0

𝐗𝟐 0 1 0 16 16 0

𝐒𝟏 1 -1 2 0 0 0

𝐒𝟐 1 0 0 0 0 0

𝐒𝟑 -1/3 1/3 -1/3 0 8/3 -8/3

A B (Fixed Ratio X Key Row) A–B

Quantity 125 25 100

𝐗𝟏 0 0 0

𝐗𝟐 1 0 1

𝐒𝟏 0 1 -1

𝐒𝟐 1 1 0

𝐒𝟑

0 -1/3 1/3

𝐗𝟏 A B (Fixed Ratio X Key Row) A–B

Quantity 50 -50 100

𝐗𝟏 1 0 1

𝐗𝟐 0 0 0

𝐒𝟏 0 -2 2

𝐒𝟐 -2 -2 0

𝐒𝟑 1/3 2/3 -1/3

𝐗𝟐

RR

It could be seen that the above solution also gives a profit of Rs.2400 [(16 x 100) + (8 x 100)] 2.8. Degeneracy

*Question no 8: Using simplex method solve the following LPP: Minimize Z = 2𝐗 𝟏 +𝐗 𝟐 Subject to: 3𝐗 𝟏 + 𝐗 𝟐 = 3 Subject to: 4𝐗 𝟏 + 3𝐗 𝟐 > 6 Subject to: 𝐗 𝟏 + 2𝐗 𝟐 < 3 Subject to: 𝐗 𝟏 & 𝐗 𝟐 > 0 Solution: Step 1: Conversion of inequalities into equalities Min Z = 2X1 + X2 + 0S1 + 0S2 + MA1 + MA2 Subject to 3X1 + X2 + A1 = 3 4X1 + 3X2 - S1 + A2 = 6 X1 + 2X2 + S2 = 3 Step 2: First Simplex table FR 4/3 1/3

Program A1 A2 S2

E M Reddy

Cost M M 0

Quantity 3 6 3 Cj Zj

𝐗𝟏

3 4 1 2 7M

𝐗𝟐

1 3 2 1 4M

𝐒𝟏 0 -1 0 0 -M

𝐒𝟐 0 0 1 0 0

𝐀𝟏 1 0 0 M M

𝐀𝟐 0 1 0 M M

RR 1 3/2 3

Page | 40

AMA-Notes NER = CZ − Zj

2 – 7M

1 – 4M

M

0

0

0

𝐗𝟐 1/3 5/3 5/3 1

𝐒𝟏 0 -1 0 0 -M

𝐒𝟐 0 0 1 0 0

𝐀𝟏 1/3 -4/3 -1/3 M

𝐀𝟐 0 1 0 M M

M

0

Incoming Variable = X1 ; Outgoing Variable = A1 Step 3: Second Simplex table FR 1/5 1

Program X1 A2 S2

Cost 2 M 0

Quantity 1 2 2 Cj Zj

1 0 0 2 2

NER = CZ − Zj

0

𝐗𝟏

2+5M 3 1−5M

2−4M 3 7M−2

3

RR 3 6/5 6/5

0

3

Incoming Variable = X2 ; Outgoing Variable = A2 𝐀𝟐

Quantity 6 4 2

𝐗𝟏 4 4 0

𝐗𝟐 3 4/3 5/3

𝐒𝟏 -1 0 -1

𝐒𝟐 0 0 0

𝐀𝟏 0 4/3 -4/3

𝐒𝟐

Quantity 3 1 2

𝐗𝟏 1 1 0

𝐗𝟐 2 1/3 5/3

𝐒𝟏 0 0 0

𝐒𝟐 1 0 1

𝐀𝟏

𝐗𝟏 1 0 0 2 2 0

𝐗𝟐 0 1 0 1 1 0

𝐒𝟏 1/5 -3/5 1 0 -1/5 1/5

𝐒𝟐 0 0 1 0 0 0

𝐒𝟐 𝐀𝟏 0 1/3 0 -4/15 0 3/5

A B (Fixed Ratio X Key Row) A–B A B (Fixed Ratio X Key Row) A–B

0 1/3 -1/3

1 0 1 0 0 0

𝐀𝟐

𝐀𝟐

Step 4: Third Simplex table FR

Program X1 X2 S2

Cost 2 1 0

Quantity 3/5 6/5 0 Cj Zj NER = CZ − Zj

𝐀𝟏 3/5 -4/5 1 M 2/5 M – 2/5

𝐀𝟐 -1/5 3/5 -1 M 1/5 M – 1/5

RR

Incoming Variable = X2 ; Outgoing Variable = A2 𝐗𝟏 A B (Fixed Ratio X Key Row) A–B

Quantity 1 2/5 3/5

𝐗𝟏 1 0 1

𝐗𝟐 1/3 1/3 0

𝐒𝟏 0 -1/5 1/5

𝐒𝟐 A B (Fixed Ratio X Key Row) A–B

Quantity 2 2 0

𝐗𝟏 0 0 0

𝐗𝟐 5/3 5/3 0

𝐒𝟏 0 -1 1

E M Reddy

𝐒𝟐 1 0 1

𝐀𝟏 -1/3 -4/3 1

𝐀𝟐 0 1/5 -1/5 𝐀𝟐 0 1 -1

Page | 41

AMA-Notes Notes: 1) In this problem, A basic variable S2 show ‘0’ quantity. Instead of being a non-basic variable it sits as basic variable with ‘0’ quantity. 2) The above situation is called degeneracy and in this case even if improvement is possible it cannot be done because we will be having ‘0’ replacement ratio for degenerate variable. 3) Degeneracy occurs because of tie in Replacement Ratios in the previous simplex table i.e. X2 replaces A2 & S2 fully. While A2 is sent out, S2 continuous with ‘0’ quantity. 4) Suppose we send out S2 , in the next table A2 will continue with ‘0’ quantity. Can we call it infeasible solution? a. No, because really A2 is also non-basic variable. To call a solution as infeasible the artificial variable should appear in final simplex table with some quantity. 2.9. Interpretation of final simplex table

Question no 9: The simplex table for a maximization problem of linear programming is given here: 𝐂𝐣 (Profit) 5 0

𝐗 𝐣 (Program) 𝐗𝟐 𝐒𝟐 𝐂𝐣 𝐙𝐣 𝐂𝐣 − 𝐙𝐣

𝐗𝟏 1 1 4 5 -1

𝐗𝟐 1 0 5 5 0

𝐒𝟏 1 -1 0 5 -5

𝐒𝟐 0 1 0 0 0

Quantity (𝐛𝐣 ) 10 3

Answer the following questions, giving reasons in brief: (a) Is this solution optimal? (b) Are there more than one optimal solution? (c) Is this solution degenerate? (d) Is this solution feasible? (e) If 𝐒𝟏 is slack in machine A (in hours/week) and 𝐒𝟐 is slack in machine (in hours/week), which of these machines is being used to the full capacity when producing according to this solution? (f) A customer would like to have one unit of product 𝐗 𝟏 and is willing to pay in excess of the normal price in order to get it. How much should the price should be increased in order to ensure no reduction of profits? Solution: 2.10.

Primal and Dual

2.10.1. Conversion of Primal to Dual

1. Every linear programming problem has two sides to it namely (i) Primal (Original problem) and (ii) Dual (inverted problem). 2. The number of constraints in primal equal to number of variables in dual. 3. The RHS of primal constraints becomes the co-efficient of dual variables in objective function. 4. The rows in primal becomes in columns in dual and the columns in primal becomes in dual.

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AMA-Notes 5. The RHS of dual is the co-efficient of variables in the primal objective function. 6. If primal is maximization, then dual is minimization and vice versa. 7. If primal is having greater than or equal to constraint dual should be having less than equal to constraint and vice versa. 8. For writing a dual, the pre-condition is that all the primal constraints should be of the same type. 9. If the constraints are different types change the direction of the inequalities by multiplying by ‘-1’ on either sides. Question no 10: Write the dual of the following LPP: (a) Type – 1 Maximize Z = 40𝐗 𝟏 + 35𝐗 𝟐 Subject to 2𝐗 𝟏 + 3𝐗 𝟐 < 60 4𝐗 𝟏 + 3𝐗 𝟐 < 96 𝐗𝟏, 𝐗𝟐 > 0 (b) Type – 2 Minimize Z = 10𝐗 𝟏 + 20𝐗 𝟐 Subject to 3𝐗 𝟏 + 2𝐗 𝟐 > 18 𝐗 𝟏 + 3𝐗 𝟐 > 8 2𝐗 𝟏 - 𝐗 𝟐 < 8 𝐗𝟏, 𝐗𝟐 > 0 (C) Type – 3 Maximize Z = 8𝐗 𝟏 + 10𝐗 𝟐 + 5𝐗 𝟑 Subject to 𝐗 𝟏 - 𝐗 𝟑 < 4 2𝐗 𝟏 + 4𝐗 𝟐 < 12 𝐗𝟏 + 𝐗𝟐 + 𝐗𝟑 > 2 3𝐗 𝟏 + 2𝐗 𝟐 - 𝐗 𝟑 = 8 𝐗 𝟏 ,𝐗 𝟐 , 𝐗 𝟑 > 0 (d) Type – 4 Maximize Z = 3𝐗 𝟏 + 5𝐗 𝟐 + 7𝐗 𝟑 Subject to 𝐗 𝟏 + 𝐗 𝟐 + 3𝐗 𝟑 < 10 4𝐗 𝟏 - 𝐗 𝟐 + 2𝐗 𝟑 > 15 𝐗 𝟏 , 𝐗 𝟐 > 0 and 𝐗 𝟑 : unrestricted in sign Solution: Type – 1: Minimize Z’ = 60Y1 + 96Y2 Subject to 2Y1 + 4Y2 > 40 3Y1 + 3Y2 > 35 Y1 , Y2 > 0 Type – 2:

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AMA-Notes Step 1: Primal Revised

Minimize Z = 10X1 + 20X2 Subject to 3X1 + 2X2 > 18 X1 + 3X2 > 8 - 2X1 + X2 > -8 X1 , X 2 > 0 Step 2: Dual

Maximize Z’ = 18Y1 + 8Y2 - 8Y3 Subject to 3Y1 + Y2 - 2Y3 < 10 2Y1 + 3Y2 + Y3 < 20 Y1 ,Y2 , Y3 > 0 Type – 3: Step 1: Primal Revised

Maximize Z = 8X1 + 10X2 + 5X3 Subject to 1X1 + 0X2 - 1X3 < 4 2X1 + 4X2 + 0X3 < 12 1X1 + 1X2 + 1X3 > 2 3X1 + 2X2 - 1X3 < 8 3X1 + 2X2 - 1X3 > 8 X1 ,X2 , X3 > 0 Step 2: Primal again revised

Maximize Z = 8X1 + 10X2 + 5X3 Subject to 1X1 + 0X2 - 1X3 < 4 2X1 + 4X2 + 0X3 < 12 - 1X1 - 1X2 - 1X3 < -2 3X1 + 2X2 - 1X3 < 8 - 3X1 - 2X2 + 1X3 < -8 X1 ,X2 , X3 > 0 Step 3: Dual

Minimize Z’ = 4Y1 + 12Y2 - 2Y3 + 8Y4 - 8Y5 Subject to Y1 + 2Y2 - Y3 +3Y4 - 3Y5 > 8 4Y2 - Y3 + 2Y4 - 2Y5 > 10 - Y1 - Y3 - Y4 + Y5 > 5 Y1 , Y2 , Y3 , Y4 , Y5 > 0 Step 4: Dual Revised E M Reddy

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AMA-Notes Let Y6 = Y4 − Y5 Minimize Z’ = 4Y1 + 12Y2 - 2Y3 + 8Y6 Subject to Y1 + 2Y2 - Y3 +3Y6 > 8 4Y2 - Y3 + 2Y6 > 10 - Y1 - Y3 - Y6 > 5 Y1 , Y2 , Y3 , Y4 , Y5 > 0 and Y6 : Unrestricted sign Notes: 1) When we have equality in primal, first we should be splitting into two equations. For example, X1 = X2 can be written as X1 > X 2 and X1 < X2 . 2) In such case the dual will have more variables than the number of constraints in primal and variables can be reduced through substitution. 3) In the above problem, the variables Y4 and Y5 emerges from same constraint (equality constraint) due to splitting it into two. Hence we made a substitution Y6 = Y4 − Y5 . 4) Y1 ,Y2 ,Y3 ,Y4 , Y5 are original variables and hence should satisfy non-negativity but Y6 is a derived variable which can take any sign depending upon Y4 and Y5 values. Type – 4: Step 1: Primal Revised

Substitute X3 = X4 − X5 Maximize Z = 3X1 + 5X2 + 7X4 - 7X5 Subject to X1 + X2 + 3X4 - 3X5 < 10 4X1 - X2 + 2X4 - 2X5 > 15 X1 , X2 , X4 , X5 > 0 and X3 : unrestricted in sign Step 2: Primal again revised

Maximize Z = 3X1 + 5X2 + 7X4 - 7X5 Subject to X1 + X2 + 3X4 - 3X5 < 10 -4X1 + X2 - 2X4 + 2X5 < -15 X1 , X2 , X4 , X5 > 0 and X3 : unrestricted in sign Step 3: Dual

Minimize Z’ = 10Y1 - 15Y2 Subject to Y1 - 4Y2 > 3 Y1 + Y2 > 5 3Y1 - 2Y2 > 7 -3Y1 + 2Y2 > -7 X1 , X2 , X4 , X5 > 0 and X3 : unrestricted in sign

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AMA-Notes Reading the last two constraints together we can understand that 3Y1 - 2Y2 = 7 Notes: 1) When primal has equality then the dual should be having variable with unrestricted sign (Type – 3) and vice versa (Type – 4) Question no 11: Write the dual of the following LPPs: (i) Maximize Z = 3𝐗 𝟏 + 4𝐗 𝟐 Subject to 2𝐗 𝟏 + 3𝐗 𝟐 < 16 Subject to 4𝐗 𝟏 + 2𝐗 𝟐 < 16 Subject to 𝐗 𝟏 >0, 𝐗 𝟐 >0 (ii) Minimize Z = 8𝐗 𝟏 + 10𝐗 𝟐 Subject to 8𝐗 𝟏 + 4𝐗 𝟐 > 150 3𝐗 𝟏 + 9𝐗 𝟐 > 100 Where 𝐗 𝟏 & 𝐗 𝟐 > 0 Solution: (i) Minimize Z’ = 16Y + 16Y2 Subject to 2Y1 + 4Y2 > 3 Subject to 3Y1 + 2Y2 < 16 Subject to Y1 >0, Y2 >0 (ii) Maximize Z’ = 150Y1 + 100Y2 Subject to 8Y1 + 3Y2 < 8 Subject to 4Y1 + 9Y2 < 10 Subject to Y1 & Y2 > 0 2.10.2. Interpretation of dual problem and Comparison of simplex tables

Primal: Maximize Z = 40X1 + 35X2 Subject to 2X1 + 3X2 < 60 4X1 + 3X2 < 96 X1 , X 2 > 0 Dual: Minimize Z’ = 60Y1 + 96Y2 Subject to 2Y1 + 4Y2 > 40 3Y1 + 3Y2 > 35 Y1 , Y2 > 0 1) Meaning of Primal Problem: E M Reddy

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AMA-Notes a. Company has two products A & B, unit profit of Product A is Rs.40 and unit profit of product B is Rs.35. b. The company has to manufacture and sell X1 units of ‘A’ and X2 units of ‘B’ to get maximum profit. c. This should be achieved within material and labour constraints (60 Kgs and 96 hours) d. 1 unit of ‘A’ consumes 2 Kgs of raw materials and 4 hours of labour and 1 unit of ‘B’ consumes 3 Kgs of raw material and 3 hours of labour 2) Final Simplex table of Primal Problem – Relevant Portion FR Program Profit Quantity RR 𝐗𝟏 𝐗𝟐 𝐒𝟏 𝐒𝟐 35 8 0 1 2/3 -1/3 X2 40 18 1 0 -1/2 1/2 X1 NER 0 0 -10/3 -25/3 3) Meaning of dual problem: a. Suppose a person asks the company to sell all its raw materials and labour hours, what should be the minimum price that should be charged for every Kg of raw material and every hour of labour is what the dual tries to find out. b. The price should be so fixed that, if we give 2 Kgs of raw material and 4 hours of labour time, it should at least fetch us a profit of Rs.40 which the company would have earned had it used these sources to produce a unit of Product ‘A’. c. The same way we can understand that 3 Kgs of raw material and 3 hours of labour should give us Rs.35 profit. d. Y1 in dual represents the minimum price to be charged for a Kg of raw material and Y1 the minimum rate per hour of the labour time. 4) Final Simplex table of Dual Problem – Relevant Portion FR Program Cost Quantity RR 𝐘𝟏 𝐘𝟐 𝐒𝟏 𝐒𝟐 96 25/3 0 1 -1/2 1/3 Y2 60 10/3 1 0 1/2 -2/3 Y1 NER 0 0 18 8 5) Observations from the two simplex tables: a. Final Simplex table of Primal Final Simplex table of Dual Variables Quantity NER Variables Quantity NER 18 0 0 18 X1 S1 8 0 0 8 X2 S2 0 -10/3 10/3 0 S1 Y1 0 -25/3 25/3 0 S2 Y2 The variable X1 and X2 in primal the corresponding variables S1 and S2 in dual and S1 and S2 in primal will have corresponding Y1 and Y2 in dual. The quantity column values of primal will become NER values of dual and similarly the NER values of primal will be same as quantity value of dual. b. Both primal and dual will have the same objective function value. Primal: Max Z = 40X1 + 35X2 = 40 x 18 + 35 x 8 = 1000 E M Reddy

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AMA-Notes Dual:

Min Z’ = 60Y1 + 96Y2 10

25

= [60 x ] + [96 x ] 3 3 = 200 + 800 = 1000 6) The variables in primal represents quantities and their c- efficient represents values and in dual the variables represent the values and the co-efficient represents the quantity. 7) Thus when you read a final simplex table of dual we should understand the cost column to be quantity (96 Hours and 60 Kgs) and the quantity column to be price [Rs.25/3 and Rs.10/3] 8) In primal simplex table the NER value of S1 is -10/3 which means if we keep a Kg of raw material idle it pulls down the profit by Rs.10/3. In other words, a Kg of raw material is capable of giving Rs.10/3 profit which is the price we should charge for selling that Kg. (See Y1 quantity column in final simplex table of dual problem). Same logic for S1 also. 9) When we sell 60 Kgs of raw material and 96 hours of labour time we lose 18 units of X1 and 8 units of X2 production which is the NER value of S1 and S2 in dual. 10) Primal earns the profit by using the resources and dual earns through selling resources. 11) Primal objective function maximizes and the boundary is fixed by the constraint. On the other hand, dual constraints try to maximize but the limit is fixed through minimization objective function. Hence both reports the same profit. Question no 12: One unit of product A contributes Rs.7 and required 3 Kgs of raw material and 2 hours of labour. One unit of product B contributes Rs.5 and required one Kg of raw material and one hour of labour. Availability of the raw material at present is 48 Kgs and there are 40 hours of labour. (a) Formulate it as a linear programming problem. (b) Write it’s dual. (c) Solve the dual with simplex method and find the optimal product mix and shadow prices of the raw material and labour. Solution: Step 1: Formulating into Linear Programming Problem (Primal) Let X1 be no. of units of product ‘A’ and X2 be no. of units of product ‘B’. Maximize Z = 7X1 + 5X2 Subject to 3X1 + X2 < 48 2X1 + X2 < 40 Where X1 and X2 > 0 Step 2: Dual for the above primal Minimize Z’ = 48Y1 + 40Y2 Subject to 3Y1 + 2Y2 > 7 Y2 + Y2 > 5 Where Y1 and Y2 > 0

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AMA-Notes Step 3: Final Simplex table for Dual FR

Program Y2 S1

Cost 40 0

Quantity 5 3 Cj NER

𝐘𝟏 1 -1 48 8

𝐘𝟐 1 0 40 0

𝐒𝟏 0 1 0 0

𝐒𝟐 -1 -2 0 40

𝐀𝟏 0 1 M M

𝐀𝟐

RR

1 2 M M-40

Step 4: Answering the primal questions using the dual simplex table Final Simplex table of Dual Variables Quantity NER 0 8 Y1 5 0 Y2 3 0 S1 0 40 S2

Final Simplex table of Primal Variables Quantity NER 8 0 S1 0 -5 S2 0 -3 X1 40 0 X2

Produce ‘0’ units of X1 and ‘40’ units of X2 consuming the entire labour time available and leaving 8 Kgs of raw material unused. The Opportunity cost of the raw material is ‘0’ since it is remaining idle but for the labour hours it is Rs.5 (NER value of S2 in final simplex table of Primal). Question no 13: A company produces two products 𝐗 𝟏 and 𝐗 𝟐 with respective unit contributions of Rs.8 and Rs.6. Each product process through matching operations in two machine centers 𝐌𝟏 and 𝐌𝟐 whose capacities are limited to 60 and 48 hours respectively with corresponding slack variables 𝐒𝟏 and 𝐒𝟐 . Following table gives the value for in interaction under simplex method for maximization of contribution. Basic Variables 𝐗𝟏 𝐗𝟐 𝐒𝟏 𝐒𝟐 1 0 1/3 -1/6 𝐗𝟏 0 1 -1/6 1/3 𝐗𝟐 You are required to evaluate if this iteration represents the optimal solution. Find out the what will be the optimum contribution? Solution: Part 1: Checking for Optimality FR

Program X1 X2

Profit 8 6

Quantity

Cj Zj Cj − Zj

𝐗𝟏 1 0 8 8 0

𝐗 0 1 6 6 0

𝐒𝟏 1/3 -1/6 0 5/3 -5/3

𝐒𝟐 -1/6 1/3 0 2/3 -2/3

RR

The problem is maximization problem and all the numbers in the NER or either negative or ‘0’. Hence the solution is optimal.

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AMA-Notes Part 2: Optimum Contribution 1) The Simplex table gives us the profit per unit of X1 and X2 but does not give us the quantity. Hence, we cannot find out the profit using the production mix data. 2) However, we have NER values of S1 and S2 . S1 represents unused machine 1 time and S2 represents unused machine 2 time. 3) The opportunity cost of machine 1 time is 5/3 hours and machine 2 time is 2/3hours which means one hour of machine 1 time and machine 2 time is capable of giving Rs.5/3 and Rs.2/3 respectively. 5

2

Therefore, profit earned by using 60 hours and 48 hours is Rs.132 [(60x3) + (48x3)]. 2.11.

Formulation types

Question no 14: WELLTYPE manufacturing company produces three types of typewriters; manual type writer, electronic typewriters and deluxe electronic typewriters. All the three models are required to be machined first and then assembled. The time required for the various models are as follows: Type Machine Time (in hour) Assembly Time (in hour) Manual Typewriter 15 4 Electronic Typewriter 12 3 Deluxe Electronic Typewriter 14 5 The total available machine time and assembly time are 3,000 hours and 1,200 hours respectively. The data regarding the selling price and variable costs for the three types are: Manual Electronic Deluxe Electronic Selling Price (Rs.) 4,100 7,500 14,600 Labour, Material and other variable costs 2,500 4,500 9,000 The company sells al the three types on credit basis, but will collect the amount on the first next month. The labour, material and other variable expenses to be paid in cash. The company has taken a loan of Rs. 40,000 from a co-operative bank and this company will have repaid it to the bank on 1st April, 2002. The TNC bank from whom this company has borrowed Rs. 60,000 has expressed its approval to renew the loan. The Balance Sheet of this company as on 31.03.02 is as follows: Liabilities Rs. Assets Rs. Equity Share Capital 1,50,000 Land 90,000 Capital Reserve 15,000 Building 70,000 General Reserve 1,10,000 Plant & Machinery 1,00,000 Profit & Loss a/c 25,000 Furniture & Fixtures 15,000 Long term loan 1,00,000 Vehicle 30,000 Loan from TNC Bank 60,000 Inventory 5,000 Loan from Co-operative Bank 40,000 Receivables 50,000 Cash 1,40,000 5,00,000 5,00,000 The company will have to pay a sum of Rs. 10,000 towards the salary from top management executives and other fixed overheads for the month. Interest on long term loans is to be per every month at 24% per annum. Interest on loans from TNC and co-operative banks may be taken to be Rs. 1,200 for the month. Also this company has promised to deliver 2 manual typewriters and 8 deluxe electronic typewriters to one of its valued customers next month.

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AMA-Notes Company is subject to the availability of cash next month. This company will also to able to sell all their types of typewriter in the market. The senior manager of this company desires to know as to how many units of each typewriter must be manufactured in the factory next month so as to maximize profits of the company. Formulate this as a linear programming problem. The formulated problem need not be solved. Solution: Step 1: Defining Variables Let X1 be number of units of manual type writer, X2 be number of units of electronic type writer and X3 be number of units of deluxe electronic type writer. Step 2: Formulating into a linear programming problem Maximize Z = 1600X1 + 3000X2 + 5600X3 – 13,200 Subject to 15X1 + 12X2 + 14X3 < 3,000 (Machine time availability) Subject to 4X1 + 3X2 + 5X3 < 1200 (Assemble time availability) Subject to X1 > 2 Subject to X3 > 8 Subject to 2500X1 + 4500X2 + 9600X3 < 1,36,800 (Cash Availability constraint) (WN-2) Subject to X2 > 0 (non-negativity constraint) Working Note 1: Calculation of fixed cost per annum Particulars Salary Interest on TNC & Co-operative loan Interest on long term loan (1,00,000 x 24% x 1/12) Total Fixed Cost

Amount (Rs.) 10,000 1,200 2000 13,200

Working Note 2: Cash availability Particulars Cash Collection from debtors Total Less: Loan repaid Less: Fixed Cost (WN-1) Cash Available to meet variable production cost

Amount (Rs.) 1,40,000 50,000 1,90,00 (40,000) (13,200) 1,36,800

*Question no 15: Consider a company that must produce two products over a production period of three months of duration. The company can pay for materials and labour for two sources: The firm faces three decisions: (1) How many units should it produce of product 1? (2) How many units should it produce of product 2? (3) How much money should it borrow to support the production of the two products? In making these decisions, the firm wises to maximize the profit contribution subject to the E M Reddy

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AMA-Notes conditions stated below: (i) Since the company’s products are enjoying a seller’s market, it can sell as many units as it can produce. The company would therefore like to produce as many units as possible subject to production capacity and financial constraints. The capacity constraints, along with cost and price data, are given in Table-1. TABLE – 1 Capacity, Price and cost data Product Selling Price Cost of Requirement hours per unit in department Production A B C 1 14 10 0.5 0.3 0.2 2 11 8 0.3 0.4 0.1 Available hours per production period of three 500 400 200 months (ii) The available company funds during the production period will be Rs.3 lakhs. (iii) A bank will give loans up to Rs.2 lakhs per production period at an interest rate of 20% p.a. provided the company’s acid (quick) test ratio is at least 1 to 1 while the loan is outstanding. Take simplified acid-test ratio given by 𝐒𝐮𝐫𝐩𝐥𝐮𝐬 𝐜𝐚𝐬𝐡 𝐨𝐧 𝐡𝐚𝐧𝐝 𝐚𝐟𝐭𝐞𝐫 𝐩𝐫𝐨𝐝𝐮𝐜𝐭𝐢𝐨𝐧 + 𝐀𝐜𝐜𝐨𝐮𝐧𝐭𝐬 𝐫𝐞𝐜𝐞𝐢𝐯𝐚𝐛𝐥𝐞 𝐁𝐚𝐧𝐤 𝐁𝐨𝐫𝐫𝐨𝐰𝐢𝐧𝐠 + 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐚𝐜𝐜𝐫𝐮𝐞𝐝 𝐭𝐡𝐞𝐫𝐞𝐨𝐧 (iv) Also make sure that the needed funds are made available for meeting the production costs. Formulate the above as linear programming. Solution: Step 1: Defining Variables Let X1 be number of units of product 1, X2 be number of units of product 2 and X3 be the amount to be borrowed. Step 2: Formulating into a linear programming problem Maximize Z = 4X1 + 3X2 – 0.05X3 Subject to 0.5X1 + 0.3X2 < 500 (Department A Hours availability) Subject to 0.3X1 + 0.4X2 < 400 (Department B Hours availability) Subject to 0.2X1 + 0.1X2 < 200 (Department C Hours availability) Subject to X3 < 2,00,000 (Maximum loan amount) Subject to 10X1 + 8X2 < X3 + 3,00,000 (Fund available to meet production cost) X3 + 3,00,000 – (10X1 +8X2 )] + [14X1 + 11X2 ]

] Subject t [

X3 +0.05X3

> 1 (Acid-test ratio constraint)

Subject to X1 , X2 , X3 > 0 (non-negativity constraint) Notes: 1) Do not write the constraint X3 = Rs.2,00,000 because the condition is not to borrow more than Rs.2,00,000 and not exactly Rs.2,00,000. 2) The fund available for production expense is computed as X3 + Rs.3,00,000 and the interest is not reduced unlike the previous problem because the interest is not paid, it is only accrued.

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AMA-Notes 3) It is assumed that the entire sales are credit sales because quick ratio numerator has accounts receivables. 4) Generally, interest cost is fixed and does not vary with production but in this case the amount to be borrowed X3 is dependent on units to be produced X1 and X2 . Hence, interest cost is linked to production. **Question no 16: A refinery makes 3 grades of petrol (A, B, C) from 3 crude oils (D, E, F) crude can be used in any grade Grade Specifications Selling Price per liter A Not less than 50% of Crude D 8.0 Not more than 25% of Crude E B Not less than 50% of Crude D 6.5 Not more than 25% of Crude E C No Specifications 5.5 But the others satisfy the following specifications. There are capacity limitations on the amount of the three crude elements that can be used. Crude Capacity Price per liter D 500 9.5 E 500 5.5 F 300 6.5 It is required to produce the maximum profit. Solution: Step 1: Analyzing facts 1) A – Selling Price =Rs.8 a. D – Cost Rs.9.5 - X1 = -1.5 b. E – Cost Rs.5.5 - X2 = 2.5 c. F – Cost Rs.6.5 - X3 = 1.5 2) B – Selling Price =Rs.6.5 a. D – Cost Rs.9.5 - Y1 = -3 b. E – Cost Rs.5.5 - Y2 = 1 c. F – Cost Rs.6.5 - Y3 = 0 3) C – Selling Price =Rs.5.5 a. D – Cost Rs.9.5 - Z1 = -4 b. E – Cost Rs.5.5 - Z2 = 0 c. F – Cost Rs.6.5 - Z3 = -1 Step 2: Defining Variables Let X1 = Liters of crude oil D in Grade A petrol Let X2 = Liters of crude oil E in Grade A petrol Let X3 = Liters of crude oil F in Grade A petrol Let Y1 = Liters of crude oil D in Grade B petrol Let Y2 = Liters of crude oil E in Grade B petrol Let Y3 = Liters of crude oil F in Grade B petrol E M Reddy

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AMA-Notes Let Z1 = Liters of crude oil D in Grade C petrol Let Z2 = Liters of crude oil E in Grade C petrol Let Z3 = Liters of crude oil F in Grade C petrol Step 3: Formulation Maximization Z = -1.5X1 + 2.5X2 + 1.5X3 - 3Y1 + Y2 + 0Y3 - 4Z1 + 0Z2 - Z3 Subject to X1 + Y1 + Z1 < 500 (Crude D availability) Subject to X2 + Y2 + Z2 < 500 (Crude E availability) Subject to X3 + Y3 + Z3 < 300 (Crude F availability) Subject toX Subject toX Subject toY Subject toY

X1 1 +X2 +X3 X2 1 +X2 +X3 Y1 1 +Y2 +Y3 Y2 1 +Y2 +Y3

1

> 2 (Proportion of D in grade A) 1

< 4 (Crude E proportion in grade A) 1

> 4 (Crude D proportion in grade B) 1

< 2 (Crude D proportion in grade B)

Where X1 , X2 , X3 , Y1 , Y2 , Y3 , Z1 , Z2 , Z3 > 0 Question no 17: A leading CA is attempting to determine a ‘best’ investment portfolio and is considering six alternative investment proposals. The following table indicates point estimates for the price per shares, the annual dividend per share and a measure of risk associated with each investment. Shares under consideration Particulars A B C D E F Current price per share (Rs.) 80 100 160 120 150 200 Projected annual growth rate 0.08 0.07 0.10 0.12 0.09 0.15 Projected annual dividend per share 4.00 4.50 7.50 5.50 5.75 0.00 Projected risk in return 0.05 0.03 0.10 0.20 0.06 0.08 The total amount available for investment is Rs.25 lakhs and the following conditions are required to be satisfied: (i) The maximum rupee amount to be invested in alternative F is Rs.2,50,000 (ii) No more than Rs.5,00,000 should be invested in alternative A and B combined. (iii) Total weighted risk should not be greater than 0.10 where Total weighted risk =

𝐚𝐦𝐨𝐮𝐧𝐭 𝐢𝐧𝐯𝐞𝐬𝐭𝐞𝐝 𝐢𝐧 𝐚𝐥𝐭𝐞𝐫𝐧𝐚𝐭𝐢𝐞 𝐉 𝐱 𝐫𝐢𝐬𝐤 𝐨𝐟 𝐚𝐥𝐭𝐞𝐫𝐧𝐚𝐭𝐢𝐯𝐞 𝐉 𝐭𝐨𝐭𝐚𝐥 𝐚𝐦𝐨𝐮𝐧𝐭 𝐢𝐧𝐯𝐞𝐬𝐭𝐞𝐝 𝐢𝐧 𝐚𝐥𝐥 𝐭𝐡𝐞 𝐚𝐥𝐭𝐞𝐫𝐧𝐚𝐭𝐢𝐯𝐞𝐬

(iv) For the sake of diversity at least 100 shares of each stock should be purchased. (v) At least 10% of the total investment should be alternatives A and B. (vi) Dividends for the year should be at least Rs. 10,000. Rupee return per share of stock is defined as price per share one year hence less current price per share plus dividend per share. If the objective is to maximize total rupee return, formulate the lines at programming model for determining the optimal number of shares to be purchased in each of the shares under consideration. You may assume that the time horizon for investment is one year. The formulated LP problem is not required to be solved. Solution:

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AMA-Notes Step 1: Defining Variables Let

X1 = Number of Shares of A X2 = Number of Shares of B X3 = Number of Shares of C X4 = Number of Shares of D X5 = Number of Shares of E X6 = Number of Shares of F

Step 2: Calculation of return per share Particulars Dividend per share Capital gains (Price x growth rate) Total Return

A 4.00 6.40 10.40

B 4.50 7.00 11.50

C 7.50 16.00 23.50

D 5.50 14.40 19.90

E 5.75 13.50 19.25

F 0.00 30.00 30.00

Step 3: Formulation into LPP Maximize Z = 10.40X1 + 11.5X2 + 23.50X3 + 19.90X4 + 19.25X5 + 30X6 Subject to 80X1 + 100X2 + 160X3 + 120X4 + 150X5 + 200X6 < 25,00,000 (amount available for investment) 200X6 < 2,50,000 (maximum in F) 80X1 + 100X2 < 5,00,000 (maximum investment in A and B) X1 , X2 , X3 , X4 , X5 , X6 > 100 80X1 +100X2 80X1 +100X2 +160X3 +120X4 +150X5 +200X6

1

> 10 (Minimum proportion in A and B)

4X1 + 4.5X2 + 7.5X3 + 5.5X4 + 5.75X5 + 0X6 > 10,000 (Minimum dividend) (0.05 x 80X1) +(0.03 x 100X2) +(0.01 x 160X3) +(0.20 x 120X4) +(0.06 x 150X5) +(0.08 x 200X6) 80X1 +100X2 +160X3 +120X4 +150X5 +200X6

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AMA-Notes 3. ASSIGNMENT PROBLEMS 3.1. Introduction

1) Features: a) A type of linear programming problem b) Assigning jobs to men & women c) Can solve only minimization types d) The assignments pre-condition is one to one relationship 2) Types of Problems a) Minimization balanced assignment problems b) Maximization balanced assignment problems c) Minimization unbalanced assignment problems d) Maximization unbalanced assignment problems e) Degeneracy f) Prohibited routes g) Multiple optimal solution h) Travelling sales men problem (Concept of looping) 3) Types of LPP a) Linear Programing Problems i. Normal Linear Programming Problems ii. Transportation problems 1. Normal transportation problems 2. Assignment problems 3.2. Minimization balanced assignment problem – Hungarian Method

Question no 1: A machine tool company decides to make hour subassemblies through four persons. Each person is to be received only one subassembly. The cost of each assembly is determined by the bids by each person and shown in the table in hundreds of rupees. Assign the different subassemblies to contactors so as to minimize the total cost. Persons Subassembly 1 2 3 4 1 15 13 14 17 2 11 12 15 13 3 13 12 10 11 4 15 17 14 16 Solution: Step 1: Row operation Take the minimum number in the row and subtract if from others. Row Operation 15 13 14 17 2 0 1 4 11 12 15 13 0 1 4 2 13 12 10 11 3 2 0 1

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AMA-Notes 15

17

14

16

1

3

0

2

Step 2: Column Operation Take the minimum number in the column and subtract it from others. Column Operation 2 0 1 4 2 0 1 3 0 1 4 2 0 1 4 1 3 2 0 1 3 2 0 0 1 3 0 2 1 3 0 1 Step 3: Covering zeros with minimum number of lines 2 0 3 1

0 1 2 3

1 4 0 0

3 1 0 1

2 3 1 4

Step 4: Is number of lines equal to order of matrix? Number of lines = 4 Order of Matrix = 4 x 4 Yes, we can proceed to make assignment. Step 4: Assignment 2 ⓪ 3 1

⓪ 1 2 3

1 4 0 ⓪

3 1 ⓪ 1

i ii iv iii

Step 5: Final Solution Sub assembly 1 2 3 4 Total Cost

Person 2 1 4 5

Cost 13 11 11 14 49

Notes: 1) We can formulate the above assignment problem into a LPP as follows: Let X11 be first job given to 1st person, X12 first job given to 2nd person and so on... Minimize Z = 15X11 + 13X12 + 14X13 + 17X14 + 11X21 + 12X22 + 15X23 + 13X24 + 13X31 + 12X33 + 10X33 + 11X34 + 15X41 + 17X42 + 14X43 + 16X44 Subject to X11 + X12 + X13 + X14 = 1 (one job should be given to 1 person)

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AMA-Notes

2) 3)

4) 5)

X21 + X22 + X23 + X24 = 1 (one job should be given to 1 person) X31 + X32 + X33 + X34 = 1 (one job should be given to 1 person) X41 + X42 + X43 + X44 = 1 (one job should be given to 1 person) X11 + X21 + X31 + X41 = 1 (one job person should not be given more than 1 assignment) X12 + X22 + X32 + X42 = 1 (one job person should not be given more than 1 assignment) X13 + X23 + X33 + X43 = 1 (one job person should not be given more than 1 assignment) X14 + X24 + X34 + X44 = 1 (one job person should not be given more than 1 assignment) Xij = (0,1) The row operation is done to identify the efficient cell in each row. Efficient cells are those cells having zero value. Those cells represent zero regret. At the end of row operation, we ensure that each row has a zero but we cannot guarantee that each column will have a zero because sometimes the same person may be efficient in more than one job and another person not efficient in any job. For example, person 3 is good at job 3 and job 4 and person 4 not good at any job. To have zeros in each column we perform column operation. While allocating we always give preference to row or column having one zero because if we miss that zero we do not have any more efficient point there.

3.3. Maximization balanced assignment problem – Hungarian Method

Question no 2: A manager has 4 subordinates and 4 tasks. The subordinates differ in efficiency His estimate of the production each would do is given in the table. How the task should be allocated one to one man, so that total production is maximized. Subordinates Task I II III IV 1 8 26 17 11 2 13 28 4 26 3 38 19 18 15 4 19 26 24 10 Solution: Step 1: Conversion of maximization problem into Minimization (Regret matrix): 1 2 3 4

I 30 25 0 19

II 12 10 19 12

III 21 34 20 14

IV 27 12 23 28

Notes: 1) Assignment steps are devised to solve minimization. Hence, a maximization problem should be converted into minimization before applying assignment steps. 2) This can be done by taking the highest number in the matrix and reducing all the other numbers from it. Due to this we convert the matrix into regret matrix and by minimizing regret we can maximize production. E M Reddy

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AMA-Notes Step 2: Row Operation 1 2 3 4

I 30 25 0 19

II 12 10 19 12

III 21 34 20 14

IV 27 12 23 28

Row Operation 18 0 9 15 0 24 0 19 20 7 0 2

15 2 23 16

Column Operation 18 0 7 15 0 22 0 19 18 7 0 0

13 0 21 14

Step 3: Column Operation 1 2 3 4

I 18 15 0 7

II 10 0 19 0

III 9 24 20 2

IV 15 2 23 16

Step 4: Covering zeros with minimum number of lines 1 2 3 4

I 18 15 0 7

II 0 0 19 0

III 7 22 18 0

IV 13 0 21 14

Step 5: Is number of lines equal to order of matrix? Number of lines = 4 Order of Matrix = 4 x 4 Hence, we can proceed to make assignment. Step 6: Assignment I II III 1 18 ⓪ 7 2 15 22 ᴓ 3 19 18 ⓪ 4 7 ᴓ ⓪ Step 7: Final Solution Task Subordinates 1 II 2 IV 3 I 4 III

IV 13 ⓪ 21 14

i ii iii iv

Production 26 26 38 24

3.4. Minimization unbalanced assignment problem – Hungarian Method & Degeneracy

**Question no 3: A has one surplus truck in each city A, B, C, D & E and one deficit truck in each of the cities 1, 2,3,4,5, & 6. The distance between the cities in kilometers is shown in the matrix below. E M Reddy

Page | 59

AMA-Notes Cities 1 2 3 4 5 6 A 12 10 15 22 18 8 B 10 18 25 15 16 12 C 11 10 3 8 5 9 D 6 14 10 13 13 12 E 8 12 11 7 3 10 Find the assignment of truck from the cities in surplus to cities in deficit so that the total distance covered by vehicles in minimum? Solution: 1) The above problem is unbalanced because we have 5 rows and 6 columns. We should first make the matrix balanced by adding a dummy row. Always the value in the dummy row shall be ‘0’. 2) In this problem, dummy represents an imagined city and the distance between the imagined city and real city is ‘0’ kilometers. Step 1: Balanced matrix A B C D E F

1 12 10 11 6 8 0

2 10 18 10 14 12 0

3 15 25 3 10 11 0

4 22 15 8 13 7 0

5 18 16 5 13 3 0

6 8 12 9 12 10 0

4 14 5 5 7 4 0

5 10 6 2 7 0 0

6 0 2 6 6 7 0

Step 2: Row Operation A B C D E F

1 4 0 8 0 5 0

2 2 8 7 8 9 0

3 7 15 0 4 8 0

Note: Since every column has ‘0’ in it we need not do column operation because it results in the same matrix. Step 2: Covering zeros with minimum number of lines A B C D E F

1 4 0 8 0 5 0

E M Reddy

2 2 8 7 8 9 0

3 7 15 0 4 8 0

4 14 5 5 7 4 0

5 10 6 2 7 0 0

6 0 2 6 6 7 0

Page | 60

AMA-Notes Step 3: Is number of lines equal to order of matrix? Number of lines = 5 Order of Matrix = 6 x 6 Since, it is not equal the situation is called degeneracy. This matrix needs improvement before proceeding for assignment. Step 4: Improvement 1 Identify least uncovered number (2 in this problem) Elements Covered

Uncovred

Junctioned

NonJuncitoned

Add (+)

No Change

A B C D E F

1 6 0 10 0 7 2

2 2 6 7 6 9 0

3 7 13 0 2 8 0

4 14 3 5 5 4 0

5 10 4 2 5 0 0

Less (-)

6 0 0 6 4 7 0

Step 5: Covering zeros with minimum number of lines A B C D E F

1 6 0 10 0 7 2

2 2 6 7 6 9 0

3 7 13 0 2 8 0

4 14 3 5 5 4 0

5 10 4 2 5 0 0

6 0 0 6 4 7 0

Step 6: Is number of lines equal to order of matrix? Number of lines = 5 Order of Matrix = 6 x 6 Degeneracy continues. Hence, do further improvement. Step 7: Improvement 2 E M Reddy

Page | 61

AMA-Notes A B C D E F

1 6 0 12 0 9 4

2 0 4 7 4 9 0

3 5 11 0 0 8 0

4 12 1 5 3 4 0

5 8 2 2 3 0 0

6 0 0 8 4 9 2

Step 8: Covering zeros with minimum number of lines A B C D E F

1 6 0 12 0 9 4

2 0 4 7 4 9 0

3 5 11 0 0 8 0

4 12 1 5 3 4 0

5 8 2 2 3 0 0

6 0 0 8 4 9 2

Step 9: Is number of lines equal to order of matrix? Number of lines = 6 Order of Matrix = 6 x 6 Hence, proceed make assignment. Step 10: Assignment A B C D E F

1 6 ᴓ 12 ⓪ 9 4

2 ⓪ 4 7 4 9 ᴓ

3 5 11 ⓪ ᴓ 8 ᴓ

4 12 1 5 3 4 ⓪

5 8 2 2 3 ⓪ ᴓ

6 ᴓ ⓪ 8 4 9 2

Iv iii i ii v vi

Step 11: Final solution Cities Cities A 2 B 6 C 3 D 1 E 5 F 4 Total Kilometers

Kilometers 10 12 3 6 3 0 34

Notes: 1) There are 5 cities having surplus trucks and 6 cities requiring trucks. Naturally one city should be denied the truck. Which is that city? E M Reddy

Page | 62

AMA-Notes a. It is city 4 because it is assigned dummy. 2) It should be understood that dummy represents rejection (both assignment and transportation chapters). 3.5. Maximization unbalanced assignment problem – Hungarian Method

Question no 4: A management consulting firm has a backlog of 4 contracts. Work on these contracts must be started immediately. 3 project leaders are available for assignment to the contractors. Because of the varying work experience of the leaders, the profit to consulting firm will vary based on the assignment as shown below. The unassigned contract can be completed by subcontracting the work to an outside consultant. The profit on the subcontract is zero. Find out optimal assignment. Contract Project Leader 1 2 3 4 A 13 10 9 11 B 15 17 13 20 C 6 8 11 7 Solution: 1) The problem is maximization unbalanced. Hence, conversion and balancing are involved. 2) What should be done first? a. First Balance and then convert Step 1: Balancing 13 15 6 0

10 17 8 0

9 13 11 0

11 20 7 0

Step 2: Conversion 7 5 14 20

10 3 12 20

11 7 9 20

9 0 13 20

Step 3: Row Operation 0 5 5 0

3 3 3 0

4 7 0 0

2 0 4 0

Step 4: Covering zeros with minimum number of lines 0 5

3 3

E M Reddy

4 7

2 0

Page | 63

AMA-Notes 5 0

3 0

0 0

4 0

Step 5: Is number of lines equal to order of matrix? Number of lines = 4 Order of Matrix = 4 x 4 Hence, proceed to make assignment. Step 6: Assignment ⓪ 5 5 ᴓ

3 3 3 ⓪

4 7 ⓪ ᴓ

2 ⓪ 4 ᴓ

i ii iii iv

Step 7: Final Solution Project Leader A B C D Total Profit

Contract 1 4 3 2

Profit 13 20 11 0 44

There are 3 leaders and 4 contracts. Hence, one of the contract should be subcontracted and the assignment says contract 2 to be subcontracted because it is assigned to dummy leader. Question 5: WELLDONE company has taken the third floor of a multi-storyed building for rent with a view to locate one of their zonal offices. There are five main rooms in this floor to be assigned to five managers. Each room has its own advantages and disadvantages. Some have windows, some are closer to the washrooms or to the canteen or secretarial pool. The rooms are of all different sizes and shapes. Each of the five managers was asked to rank their room preferences amongst the rooms 301, 302, 303, 304 and 305. Their preferences were recorded in a table as indicated below: Manager 𝐌𝟏 𝐌𝟐 𝐌𝟑 𝐌𝟒 𝐌𝟓 302 302 303 302 301 303 304 301 305 302 304 305 304 304 304 * 301 305 303 * * * 302 * * Most of the managers did not list all the five rooms since they were not satisfied with some of these rooms and they have left off these from the list. Assuming that their preferences can be quantified by numbers, find out as to which manager should be assigned to which room so that their total preference ranking is a minimum. Solution: E M Reddy

Page | 64

AMA-Notes Step 1: Formulation 301 302 303 304 305

M1

1 2 3 -

M2 4 1 2 3

M3 2 5 1 3 4

M4

1 4 3 2

M5 1 2 3 -

The cells where no ranking is given like 301, M1 etc., are called prohibited cells. In those cells allocation should not be made. Hence, we assign a very high cost ‘M’ to those sells and if it is maximization assign “M”. 301 302 303 304 305

M1 M 1 2 3 M

M2 4 1 M 2 3

M3 2 5 1 3 4

M4 M 1 4 3 2

M5 1 2 M 3 M

M3 1 4 0 1 2

M4 M 0 3 1 0

M5 0 1 M 1 M

Step 2: Row Operation 301 302 303 304 305

M1 M 0 1 1 M

M2 3 0 M 0 1

Step 3: Covering zeros with minimum number of lines 301 302 303 304 305

M1 M 0 1 1 M

M2 3 0 M 0 1

M3 1 4 0 1 2

M4 M 0 3 1 0

M5 0 1 M 1 M

Step 4: Is number of lines equal to order of matrix? Number of lines = 5 Order of Matrix = 5 x 5 Hence, proceed to make assignment. Step 5: Assignment 301 302

M1 M ⓪

E M Reddy

M2 3 ᴓ

M3 1 4

M4 M ᴓ

M5 ⓪ 1

i v

Page | 65

AMA-Notes 303 304 305

1 1 M

M ⓪ 1

⓪ 1 2

3 1 ⓪

M 1 M

ii iii iv

Step 5: Final Solution Room Manager 301 M5 302 M1 303 M3 304 M2 305 M4 Note: If in spite of assigning ‘M’ to the prohibited cell, if allocation is made then the problem is said to be having infeasible solution. Question no 6: An organization producing four different products A, B, C, D having four operators P, Q, R, S who are capable of producing any of the four products work effectively 7 hours a day. The time in minutes required for each operator for producing each of the product given in the cells of the following matrix along with the profit in rupees per unit. Operator Product A B C D P 6 10 14 12 O 7 5 3 4 R 6 7 10 10 S 20 10 15 15 Profit (Rs. /unit) 3 2 4 1 Find out the assignment of operators to products which will maximize the profit. Solution: Part 1: Formulation into profit matrix P Q

A

B

C

420

420

420

6 420 7

R

420

S

420

P Q R S

6 20

x3 = 210 x3 = 180

10 420 5

x3 = 210

420

x3 = 63

420

A 210 180 210 63

E M Reddy

B 84 168 120 84

7 10

C 120 560 168 112

x2 = 84 x2 = 168

14 420 3

x2 = 120

420

x2 = 84

420

10 15

D x4 = 120 x4 = 560

420 12 420 4

x4 = 168

420

x4 = 112

420

10 15

x1 = 35 x1 = 105 x1 = 42 x1 = 28

D 35 105 42 28 Page | 66

AMA-Notes Part 2: Conversion into Minimization P Q R S

A 350 380 350 497

B 476 392 440 476

C 440 0 392 448

D 525 455 518 532

Part 3: Solution using assignment steps Step 1: Row Operation P Q R S

A 0 380 0 49

B 126 392 90 28

C 90 0 42 0

D 175 455 168 84

Step 2: Column Operation P Q R S

A 0 380 0 49

B 98 364 62 0

C 90 0 42 0

D 91 371 84 0

Step 3: Covering zeros with minimum number of lines P Q R S

A 0 380 0 49

B 98 364 62 0

C 90 0 42 0

D 91 371 84 0

Step 4: Is number of lines equal to order of matrix? Number of lines = 3 Order of Matrix = 4 x 4 There is degeneracy. Hence, proceed for improvement. Step 5: Improvement 1 P Q R S

A 0 422 0 91

B 56 364 20 0

C 48 0 0 0

D 49 371 42 0

Step 6: Covering zeros with minimum number of lines

E M Reddy

Page | 67

AMA-Notes P Q R S

A 0 422 0 91

B 56 364 20 0

C 48 0 0 0

D 49 371 42 0

Step 7: Is number of lines equal to order of matrix? Number of lines = 3 Order of Matrix = 4 x 4 Degeneracy continuous. Do further improvement. Step 8: Improvement 2 P Q R S

A 0 422 0 111

B 36 344 0 0

C 48 0 0 20

D 29 351 22 0

Step 9: Covering zeros with minimum number of lines P Q R S

A 0 422 0 111

B 36 344 0 0

C 48 0 0 20

D 29 351 22 0

Step 10: Is number of lines equal to order of matrix? Number of lines = 4 Order of Matrix = 4 x 4 Proceed to do assignment. Step 11: Assignment P Q R S

A ⓪ 422 ᴓ 111

B 36 344 ⓪ ᴓ

C 48 ⓪ ᴓ 20

Step 12: Final Solution Operator Product P A Q C R B S D Total Profit E M Reddy

D 29 351 22 ⓪

i ii iii iv

Profit (Rs.) 210 560 120 28 918 Page | 68

AMA-Notes 3.6. Multiple Optimal Solution

**Question no 7: An airline operates seven days a week has time table as shown below. Crews must have a minimum layover of 5 hours between flights. Obtain the pairing of flight that minimizes layover time away from home. For any give pairing the crew will be based at the city that results in smaller layover. For each pair also mention the town where the crew should be passed. Delhi Jaipur Jaipur Delhi Flight No. Departure Arrival Flight No. Departure Arrival 1 7.00 8.00 101 8.00 9.15 2 8.00 9.00 102 8.30 9.45 3 13.30 14.30 103 12.00 13.15 4 18.30 19.30 104 17.30 18.45 Solution: Part 1: Layover times when the crew is based in Delhi 1 2 3 4

101 24 23 17.30 12.30

102 24.30 23.30 18 13

103 28 27 21 16.30

104 9.30 8.30 27 22

Part 2: Layover times when the crew is based in Jaipur 1 2 3 4

101 21.45 22.45 28.15 9.15

102 21.15 22.15 27.45 8.45

103 17.45 18.45 24.15 5.15

104 12.15 13.15 18.45 23.45

Part 3: Mixed Matrix (whichever is best i.e. least) 1 2 3 4

101 21.45-J 22.45-J 17.30-D 9.15-J

102 21.15-J 22.15-J 18-D 8.45-J

103 17.45-J 18.45-J 21-D 5.15-J

104 9.30-D 8.30-D 18.45-J 22-D

Part 4: Converting the matrix into whole numbers Let 1 unit = ¼ hour. For example, 21.15 can be written as 85 [(21x4) +1] 1 2 3 4

101 87 91 70 37

E M Reddy

102 85 89 72 35

103 71 75 86 21

104 38 34 75 88

Page | 69

AMA-Notes Part 5: Solving the problem using the assignment steps Step 1: Row Operation 1 2 3 4

101 49 57 0 16

102 47 55 2 14

103 33 41 16 0

104 0 0 5 67

Step 2: Column Operation 1 2 3 4

101 49 57 0 16

102 45 53 0 12

103 33 41 16 0

104 0 0 5 67

Step 3: Covering zeros with minimum number of lines 1 2 3 4

101 49 57 0 16

102 45 53 0 12

103 33 41 16 0

104 0 0 5 67

Step 4: Is number of lines equal to order of matrix? Number of lines = 3 Order of Matrix = 4 x 4 Degeneracy exists. Hence, do improvement. Step 5: Improvement 1 1 2 3 4

101 16 24 0 16

102 12 20 0 12

103 0 8 16 0

104 0 0 38 100

Step 6: Covering zeros with minimum number of lines 1 2 3 4

101 16 24 0 16

102 12 20 0 12

103 0 8 16 0

104 0 0 38 100

Step 7: Is number of lines equal to order of matrix?

E M Reddy

Page | 70

AMA-Notes Number of lines = 3 Order of Matrix = 4 x 4 Degeneracy continuous. Do further improvement. Step 8: Improvement 2 1 2 3 4

101 4 12 0 4

102 0 8 0 0

103 0 8 28 0

104 0 0 50 100

Step 9: Covering zeros with minimum number of lines 1 2 3 4

101 4 12 0 4

102 0 8 0 0

103 0 8 28 0

104 0 0 50 100

Step 10: Is number of lines equal to order of matrix? Number of lines = 4 Order of Matrix = 4 x 4 There is no Degeneracy. Proceed for assignment Step 11: Assignment 1 2 3 4

101 4 12 ⓪ 4

102 ⓪ 8 ᴓ ᴓ

103 ᴓ 8 28 ⓪

104 ᴓ ⓪ 50 100

iii i ii iv

Step 12: Final Solution Flight No. Paired Flight No. 1 102 2 104 3 101 4 103 Total Layover time

Place Jaipur Delhi Delhi Jaipur

Layover Time 21.15 8.30 17.30 5.15 52.30

Step 13: Alternate assignment 1 2 3

101 4 12 ⓪

E M Reddy

102 ᴓ 8 0

103 ⓪ 8 28

104 ᴓ ⓪ 50

iii i ii Page | 71

AMA-Notes 4

4

⓪

100

ᴓ

iv

Step 14: Final Solution Flight No. Paired Flight No. 1 103 2 104 3 101 4 102 Total Layover time

Place Jaipur Delhi Delhi Jaipur

Layover Time 17.45 8.30 17.30 8.45 52.30

Notes: 1) In step 6, we had two rows with two ‘0’s (Row 1 & Row 3) and two columns with two ‘0’s (Column 3 & Column 4). As per the procedure since there is a tie we can draw either against the columns or against the rows. 2) We decided to draw against the columns and ultimately covered all the zeros with 3 lines. Had we chosen rows we would have covered using 4 lines. This is a small drawback in the procedure. 3) In the final assignment we had two ‘0’s to choose from i.e. cell (1,102) or cell (1,103). Either cell if we choose we will get the same minimum layover time. Thus the problem is having multiple solution. **Question no 8: A travelling salesman has to visit 5 cities. He wishes to start from a particular city, visit each city once and return to his starting point. The travelling cost for each city from a particular city is given below: F To City r A B C D E o A X 4 7 3 4 m B 4 X 6 3 4 C C 7 6 X 7 5 it D 3 3 7 X 7 y E 4 4 5 7 X What is the sequence of visit of the salesman, so that the cost is minimum? Solution: Part 1: Assigning ‘M’ to prohibited cells A B C D E

A M 4 7 3 4

B 4 M 6 3 4

C 7 6 M 7 5

D 3 3 7 M 7

E 4 4 5 7 M

Note: There is no travel possible from ‘A’ to ‘A’, ‘B’ to ‘B’, ‘C’ to ‘C’, ‘D’ to ‘D’ and ‘E’ to ‘E’. Hence, these cells are prohibited cells and a very high penalty imposed on it. Part 2: Solving the problem using assignment steps

E M Reddy

Page | 72

AMA-Notes Step 1: Row Operation A B C D E

A M 1 2 0 0

B 1 M 1 0 0

C 4 3 M 4 1

D 0 0 2 M 3

E 1 1 0 4 M

Step 2: Column Operation A B C D E

A M 1 2 0 0

B 1 M 1 0 0

C 3 2 M 3 0

D 0 0 2 M 3

E 1 1 0 4 M

Step 3: Covering zeros with minimum number of lines A B C D E

A M 1 2 0 0

B 1 M 1 0 0

C 3 2 M 3 0

D 0 0 2 M 3

E 1 1 0 4 M

Step 4: Is number of lines equal to order of matrix? Number of lines = 4 Order of Matrix = 5 x 5 Degeneracy exists. Hence, do improvement. Step 5: Improvement 1 A B C D E

A M 0 2 0 0

B 0 M 1 0 0

C 2 1 M 3 0

D 0 0 3 M 4

E 0 0 0 4 M

Step 6: Covering zeros with minimum number of lines A B C D E

A M 0 2 0 0

B 0 M 1 0 0

E M Reddy

C 2 1 M 3 0

D 0 0 3 M 4

E 0 0 0 4 M Page | 73

AMA-Notes Step 7: Is number of lines equal to order of matrix? Number of lines = 5 Order of Matrix = 5 x 5 There is no Degeneracy. Hence, proceed for assignment. Step 8: Assignment A B C D E

A M ᴓ 2 ⓪ ᴓ

B ⓪ M 1 ᴓ ᴓ

C 2 1 M 3 ⓪

D ᴓ ⓪ 3 M 4

E ᴓ ᴓ ⓪ 4 M

iv iii i v ii

Step 9: Final Solution as an assignment problem City City Assigned A B B D C E D A E C Total Cost

Cost 4 3 5 3 5 20

Step 10: Grouping Condition Loops: A→B→D→A and C→E→C Note: The assignment should form a loop. The loop would ensure the terminal point and the starting point as same. In the initial basic solution two loops were formed for a total cost of Rs.20 whereas the problem precondition is to form a single loop. Therefore, an improvement is to be sought. Step 11: Improved Solution Break the smaller loop of C→E→C i.e. do not assign against ‘0’ in row C (in 1st iteration). Instead second lowest value of ‘1’ shall be assigned that comes against column ‘B’. The overall cost is likely to exceed marginally. But the sequencing condition is complied. A B C D

A M ᴓ 2 ⓪

B ᴓ M ① ᴓ

E M Reddy

C 2 1 M 3

D ᴓ ⓪ 3 M

E ⓪ ᴓ ᴓ 4

iv v i iii Page | 74

AMA-Notes E

ᴓ

ᴓ

⓪ 4

M

ii

Step 12: Final Solution City City Assigned A E B D C B D A E C Total Cost

Cost 3 3 6 3 5 21

Sequence: A→E→C→B→D→A Question no 9: Suppose there exists a 4X4 matrix having ‘0’s in all the cells after row and column operation. How many solutions are possible? Solution: No. of Possible solutions = 4! = 4 x 3 x 2 x 1 = 24

E M Reddy

Page | 75

AMA-Notes 4. TRANSPORTATION 4.1. Introduction

1) Features: a) A type of linear programming problem b) It is all about matching demand and supply c) No need to have one to one relationship i.e. a factory can supply to multiple warehouses or a warehouse can take from multiple factories. d) Like assignment transportation steps also can solve only minimization types 2) Stages in solving a transportation problem: a) Obtaining Initial basic feasible solution (IBFS) i. Northwest corner method ii. Lease cost method iii. Vogel’s approximation method b) Testing for optimality – Moody’s optimality test 4.2. Minimization Balanced

Question no 1: Obtain the IBFS (Intima Basic Feasible Solution) for the following & also determine whether they satisfy the optimality test. W-1 W-2 W-3 Supply Factory 1 6 8 4 14 Factory 2 4 9 8 12 Factory 3 1 2 6 5 Demand 6 10 15 Solution: Stage 1: Obtaining Initial Basic Feasible Solution (IBFS) 4.2.1. Northwest Corner Method

W-1 Factory 1

W-2 6

W-3

6

8

4

9

Factory 2

4 2

Factory 3 1 Requirement 6/0

Availability 14/8/0

8 10

12/10/0

8

5 5/0 2 6 10/2/0 15/5/0 31

6 = supplied (Bold letters are supplied quantity)

Cost associated with the above solution: Allocated Cells F1 – W1 F1 – W2 F2 – W2

E M Reddy

Computation 6 Units X Rs.6 8 Units X Rs.8 2 Units X Rs.9

Cost (Rs.) 36 64 18

Page | 76

AMA-Notes F2 – W3 10 Units X Rs.8 F3 – W3 5 Units X Rs.6 Total transportation cost

80 30 228

4.2.2. Least Cost Method

W-1

W-2

W-3

8

4

Factory 1 6 Factory 2

1

4

Factory 3

10

9

5

Availability 14 14/8/0

8

1

12/11/10/0

5/0 6 15/1/0 31

1 2 Requirement 6/1/0 10/0

Cost associated with the least cost method solution: Allocated Cells Computation F1 – W3 14 Units X Rs.4 F2 – W1 1 Units X Rs.4 F2 – W2 10 Units X Rs.9 F2 – W3 1 Units X Rs.8 F3 – W1 5 Units X Rs.1 Total Transportation Cost

Cost (Rs.) 56 4 90 8 5 163

4.2.3. Vogel’s approximation method

W-1

W-2

W-3

6

8

4

Factory 1

14

Factory 2

6 4

Factory 3

1 Requirement 6/0 I 4 – 1= 3 II 6–4=4 III -

5

1

9

8

5 2 10/5 8–2=6 9–8=1 9–8=1

6 15/1 6–4=2 8 – 4= 4 8 – 4= 4

Availability I 14/0 6–4=2

II 6–4=2

III 8–4=4

12/6/5/0

8–4=4

8–4=4

9–8=1

5/0

2 – 1= 1

-

-

31

Cost associated with the Vogel’s solution: Allocated Cells Computation F1 – W3 14 Units X Rs.4 F2 – W1 6 Units X Rs.4 F2 – W2 5 Units X Rs.9 F2 – W3 1 Units X Rs.8 F3 – W2 5 Units X Rs.2 Total Transportation Cost

E M Reddy

Cost (Rs.) 56 24 45 8 10 143

Page | 77

AMA-Notes Notes: 1) North West corner method is the worst method because in selecting the cells ‘cost’ is not considered. 2) Between Least Cost and Vogel, the later is better because Least Cost Method allocates in absolute least cost cell while Vogel allocates in relative least cost cell. 3) For example, Least Cost Method made its first allocation in the lowest cost cell in the entire matrix which is F3 – W1 having Rs.1 cost. On the other hand, Vogel allocated in F3 – W12 having a cost of Rs.2 because the regret of missing that cell and moving to next least cell in that column (F1 – W2) is Rs.6 (Rs.8 – Rs.2) which is higher than the regret of Rs.3 for F3 – W1. Stage 2: Checking for Degeneracy Initial Basic Feasible Solution: 6

8 6

4

14

4 5

1 12

9

8 5

1 6

14

5

2 10

6 15

31

Number of allocated cells = 5 M + N – 1 = 3 + 3 – 1 = 5; where ‘M’ is number of rows and ‘N’ is number of columns. Since both are equal we can proceed for optimality test. Stage 3: Optimality test Step 1: Allocated cells Allocated Cells U1+V3= U2+V1= U2+V2= U2+V3= U3+V2=

Cost 4 4 9 8 2

Step 2: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = 4, U3 = -3, V1 = 0, V2 = 5, V3 = 4 Step 3: Unallocated Cells Unallocated Cells U1+V1= U1+V2= U3+V1= U3+V3= E M Reddy

𝐂𝐣 6 8 1 6

𝐙𝐣 0 5 -3 1

𝐂𝐣 − 𝐙𝐣 6 3 4 5 Page | 78

AMA-Notes Since all the numbers in Cj − Zj are positive the current solution is optimal. Notes: 1) The Number of variables in the optimality test will be ‘M+N’. In which we assume one variable to be ‘0’. Hence we need to find out the values for ‘M+N-1’ variables for which we required ‘M+N-1’ equations. Since allocated cells becomes equations in the optimality test, the number of allocated cells should necessarily be ‘M+N-1’. 2) How to understand Cj − Zj ? a. ‘Cj − Zj ’ value of the unallocated cell U1V1 is ‘6’. This means if this cell is made allocated for every allocation made the cost increases by Rs.6. b. The above can be understood as follows: (+) 1 6 4

(-) 13 14 8

(-) 5

1 6

4 5

9

5

2 10

8

(+) 2

12 5

6 15

31

Additional Cost = 6 – 4 + 8 – 4 = 6 which is Cj − Zj , New allocation cost (Cj ) = 6 Change in existing allocation (Zj ) = – 4 + 8 – 4 = 0 c. If there exists any negative number improvement is made because there exists scope for reduction of cost. 4.3. Minimization Balanced - Degeneracy

Question no 2: Find the optimal solution for the following problem. W-1 W-2 W-3 Supply Factory 1 50 30 220 1 Factory 2 30 45 170 3 Factory 3 250 200 50 4 Demand 4 2 2 Solution: Stage 1: Obtaining Initial Basic Feasible Solution (IBFS) using Vogel’s Method W-1 Factory 1 Factory 2

50 30

1 3

W-2

W-3

30

220

45

170

Factory 3 250 Requirement 4/1/0 E M Reddy

2 200 2/0

50 2/0

Availability I 1/0 20

II 20

3/0

15

15

2 4/2/0

150

50

8 Page | 79

AMA-Notes I II

20 20

15 15

120 -

Cost associated with the Vogel’s solution: Allocated Cells Computation F1 – W1 1 Units X Rs.50 F2 – W1 3 Units X Rs.30 F3 – W2 2 Units X Rs.200 F3 – W3 2 Units X Rs.50 Total Transportation Cost

Cost (Rs.) 50 90 400 100 640

Stage 2: Checking for Degeneracy Number of allocated cells = 4 M + N – 1 = 3 + 3 – 1 = 5; where ‘M’ is number of rows and ‘N’ is number of columns. We cannot proceed for optimality test because number of allocated cells are not equal to ‘M+N-1’. This is referred to as ‘Degeneracy’. The number of allocated cells should be made as ‘5’. This should be done by allocating an infinitely small quantity ‘e’ in the LEAST COST UNALLOCATED INDEPENDEDNT CELL. W-1 W-2 W-3 Availability Factory 1 1 e 1 50 30 220 Factory 2 3 3 30 45 170 Factory 3 2 2 4 250 200 50 Requirement 4 2 2 8 Stage 3: Optimality test Step 1: Allocated cells Allocated Cells U1+V1= U1+V2= U2+V1= U3+V2= U3+V3=

Cost 50 30 30 200 50

Step 2: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = -20, U3 = 170, V1 = 50, V2 = 30, V3 = -120 Step 3: Unallocated Cells Unallocated Cells E M Reddy

𝐂𝐣

𝐙𝐣

𝐂𝐣 − 𝐙𝐣 Page | 80

AMA-Notes U1+V3= U2+V2= U2+V3= U3+V1=

220 45 170 250

-120 10 -140 220

340 35 310 30

Since there is no negative number in Cj − Zj column, there is no scope for improvement and the current solution is optimal. 4.4. Maximization Unbalanced and Improvement through Looping

**Question no 3: Consider the following transportation profit table and determine the optimal solution. W-1 W-2 W-3 W-4 Supply Factory 1 40 25 22 33 100 Factory 2 44 35 30 30 30 Factory 3 38 38 28 30 70 Demand 40 20 60 30 Solution: Step 1: Balancing Factory 1 Factory 2 Factory 3 Demand

W-1 40 44 38 40

W-2 25 35 38 20

W-3 22 30 28 60

W-4 33 30 30 30

W-5 0 0 0 50

Supply 100 30 70 200

Step 2: Conversion into minimization and obtaining IBFS using Vogel W-1

W-2

W-3

4

19

22

11

44

9

14

14

44

40 16 60/20 2 6 6 6 6

14 30/0 3 3 3 3 -

44 50 0 0 0 0 0

Factory 1

W-4 20

Factory 2

W-5 30

50

30 0

Factory 3

10 6 Requirement 40/10/0 I 4 II 4 III 2 IV V -

20 6 20/0 3 13 -

Availability I II III 100/70 7 7 7

IV 11

V 22

30/0

9 -

-

-

-

70/50/40/0 0 0

8

2

28

200

Cost associated with the Vogel’s solution: Allocated Cells F1 – W3 F1 – W4 E M Reddy

Computation 20 Units X Rs.22 30 Units X Rs.11

Cost (Rs.) 440 330 Page | 81

AMA-Notes F1 – W5 F2 – W1 F3 – W1 F3 – W2 F3 – W3 Total Cost

50 Units X Rs.44 30 Units X Rs.0 10 Units X Rs.6 20 Units X Rs.6 40 Units X Rs.16

2200 0 60 120 640 3790

Step 2: Checking for degeneracy Initial Basic Feasible Solution: W-1 Factory 1 4 Factory 2 30 0 Factory 3 10 6 Requirement 40

W-2

W-3

W-4 20

19

22

W-5 30

11

50

Availability 100

44 30

9 6 20

14 20

16 60

14 40

14 30

44 44 50

70 200

Number of allocated cells = 7 M+N–1=3+5–1=7 Since there is no degeneracy we can proceed for optimality test. Step 3: Moody’s optimality test A: Allocated cells Allocated Cells U1+V3= U1+V4= U1+V5= U2+V1= U3+V1= U3+V2= U3+V3=

Cost 22 11 44 0 6 6 16

B: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = -12, U3 = -6, V1 = 12, V2 = 12, V3 = 22, V4 = 11, V5 = 44 C: Unallocated Cells Unallocated Cells U1+V1= U1+V2= U2+V2= U2+V3=

E M Reddy

𝐂𝐣 4 19 9 14

𝐙𝐣 12 12 0 10

𝐂𝐣 − 𝐙𝐣 -8 7 9 4

Page | 82

AMA-Notes U2+V4= U2+V5= U3+V4= U3+V5=

14 44 14 44

-1 32 5 38

15 8 9 6

The solution given by Vogel is not optimal and improvement is possible because one of the unallocated cell U1V1 had -8 column in Cj − Zj i.e. if we make that cell as allocated, for every allocation made the cost decreases by Rs.8. Step 4: Improvement through looping A: Looping Rules 1) 2) 3) 4) 5)

Start from most negative cell Use only Horizontal or Vertical Lines Terminal point of the lines used should be in allocated cells Start and complete by retiring into the same place of start. This is loop Assign ‘+’ & ‘-ve’ from the start alternatively. a. Choose from the quantities where ‘-ve’ were assigned. 6) Choose the lowest allocation for reshuffling B: Improvement through looping

Quantity allocated in ‘-ve’ cells is 10 & 20. Least of them i.e. 10 Units should be made as new allocation. Note: Suppose we allocate 11 units in the new cell U1V1, we will end up with a negative allocation (-1) in the cell U3V1. Hence, the maximum allocation possible is 10 units. This is similar selecting least Replacement Raito (RR) in simplex table. Improved Solution:

E M Reddy

Page | 83

AMA-Notes Cost associated with improved solution: Allocated Cells F1 – W1 F1 – W3 F1 – W4 F1 – W5 F2 – W1 F3 – W2 F3 – W3 Total Cost

Computation 10 Units X Rs.4 10 Units X Rs.22 30 Units X Rs.11 50 Units X Rs.44 30 Units X Rs.0 20 Units X Rs.6 50 Units X Rs.16

Cost (Rs.) 40 220 330 2200 0 120 800 3710

The regret has reduced from 3790 in Vogel solution to 3710 in improved solution i.e. it has decreased by Rs.80 because 10 units of new allocation results in cost reduction of 80 (10 Units x 8). Step 5: Moody’s optimality test A: Allocated cells Allocated Cells U1+V1= U1+V3= U1+V4= U1+V5= U2+V1= U3+V2= U3+V3=

Cost 4 22 11 44 0 6 16

B: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = -4, U3 = -6, V1 = 4, V2 = 12, V3 = 22, V4 = 11, V5 = 44 C: Unallocated Cells Unallocated Cells U1+V2= U2+V2= U2+V3= U2+V4= U2+V5= U3+V1= U3+V4= U3+V5=

𝐂𝐣 19 9 14 14 44 6 14 44

𝐙𝐣 12 8 18 7 40 -2 5 38

𝐂𝐣 − 𝐙𝐣 7 1 -4 7 4 8 9 6

The above solution is not optimal. Hence, do further improvement. Step 6: Improvement through looping

E M Reddy

Page | 84

AMA-Notes

Quantity allocated in ‘-ve’ cells is 10 & 30. Least of them i.e. 10 Units should be made as new allocation. Improved Solution: W-1 Factory 1 Factory 2

W-4

19

22

11

6 40

W-5 44

9

14

14

44

30

20 0

Requirement

W-3

20 4

Factory 3

W-2

50

10 6 20

20

16 60

50

Availability 100 30

14 30

44 50

70 200

Cost associated with improved solution: Allocated Cells F1 – W1 F1 – W4 F1 – W5 F2 – W1 F2 – W3 F3 – W2 F3 – W3 Total Cost

Computation 20 Units X Rs.4 30 Units X Rs.11 50 Units X Rs.44 20 Units X Rs.0 10 Units X Rs.14 20 Units X Rs.6 50 Units X Rs.16

Cost (Rs.) 80 330 2200 0 140 120 800 3670

The regret has reduced from 3710 in improved solution to 3671 in further improved solution i.e. it has decreased by Rs.40 because 10 units of new allocation results in cost reduction of 40 (10 Units x 4). Step 7: Moody’s optimality test A: Allocated cells Allocated Cells U1+V1= U1+V4= U1+V5= U2+V1= U2+V3= U3+V2= U3+V3=

E M Reddy

Cost 4 11 44 0 14 6 16

Page | 85

AMA-Notes B: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = -4, U3 = -2, V1 = 4, V2 = 8, V3 = 18, V4 = 11, V5 = 44 C: Unallocated Cells Unallocated Cells U1+V2= U1+V3= U2+V2= U2+V4= U2+V5= U3+V1= U3+V4= U3+V5=

𝐂𝐣 19 22 9 14 44 6 14 44

𝐙𝐣 8 18 4 7 40 2 9 42

𝐂𝐣 − 𝐙𝐣 11 4 5 7 4 8 5 2

The above solution is optimal. Step 8: Final Solution Allocated Cells F1 – W1 F1 – W4 F1 – W5 F2 – W1 F2 – W3 F3 – W2 F3 – W3 Total Profit

Computation 20 Units X Rs.40 30 Units X Rs.33 50 Units X Rs.0 20 Units X Rs.44 10 Units X Rs.30 20 Units X Rs.38 50 Units X Rs.28

Profit (Rs.) 800 990 0 880 300 760 1400 5130

Important Notes: 1) Suppose there is a tie in the negative cells quantities. For example, instead of 10 and 20 we have 10 and 10, then by making new allocation two existing old allocation will be replaced against degeneracy will arise. Resolve the degeneracy before proceeding for the optimality test for the improved solution. Thus degeneracy may occur in two stages: i. During IBFS (Initial Basic Feasible Solution) – Vogel’s Approximation ii. During Moody’s improvement 2) What happens if you are not able to form a loop during improvement? Answer: Such situation will never arise because the procedures ensure that all unallocated cells during optimality test are depended cells. That is reason why during degeneracy we make ‘e’ allocation in LEAST COST INDEPENDEDN UNALLOCATED CELL. So that no independent unallocated cell remains. 3) If one of the negative cell has ‘e’ quantity the reshuffling will change the allocations but will not change the cost, should we do the reshuffling? Answer: Yes, because the rearranged matrix will change UiVj values highlighting more possible improvements. E M Reddy

Page | 86

AMA-Notes 4) Can we make ‘e’ allocation in dummy cell? Answer: Yes 5) Will there be two ‘e’ allocations? Answer: Yes, it is possible. 4.5. Multiple Optimal Solution

Question no 4: Solve the following transportation problem. W-1 W-2 W-3 W-4 Supply Factory 1 5 3 6 2 19 Factory 2 4 7 9 1 37 Factory 3 3 4 7 5 34 Demand 16 18 31 25 Solution: Step 1: Obtaining IBFS using Vogel’s method Factory 1 Factory 2 Factory 3 Requirement I II III IV

W-1

W-2

5

3

4

12 4

3 16/4/0 1 1 2 2

W-3 18

7 4 18/0 1 1 1 -

6

W-4 1

Availability I II III IV 19/1/0 1 2 2 1

2

9

1 30

7 31/30/0 1 1 1 1

25 37/12/0

3 3

-

-

34/30/0

1 1

1

4

5 25/0 1 1

200

Cost associated with the Vogel’s solution: Allocated Cells F1 – W2 F1 – W3 F2 – W1 F2 – W4 F3 – W1 F3 – W3 Total Cost

Computation 18 Units X Rs.3 1 Units X Rs.6 12 Units X Rs.4 25 Units X Rs.1 4 Units X Rs.3 30 Units X Rs.7

Cost (Rs.) 54 6 48 25 12 210 355

Step 2: Checking for degeneracy Initial Basic Feasible Solution: W-1 W-2 W-3 Factory 1 18 5 3 6

E M Reddy

W-4 1

2

Availability 19

Page | 87

AMA-Notes Factory 2 Factory 3 Requirement

12

4

7

4

3 16

9

4 18

7 31

1 30

25

37 34

5 25

90

Number of allocated cells = 6 M+N–1=3+4–1=6 Since there is no degeneracy we can proceed for optimality test. Step 3: Moody’s optimality test A: Allocated cells Allocated Cells U1+V2= U1+V3= U2+V1= U2+V4= U3+V1= U3+V3=

Cost 3 6 4 1 3 7

B: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = 2, U3 = 1, V1 = 2, V2 = 3, V3 = 6, V4 = -1 C: Unallocated Cells Unallocated Cells U1+V1= U1+V4= U2+V2= U2+V3= U3+V2= U3+V4=

𝐂𝐣 5 2 7 9 4 5

𝐙𝐣 2 -1 5 8 4 0

𝐂𝐣 − 𝐙𝐣 3 3 2 1 0 5

The above solution is optimal because there are no negativity numbers to give improvement. But there exists another optimal solution i.e. if we make U3V2 allocated cell, for every allocation made the cost changes by Rs.0 i.e. it does not change. Hence the problem has multiple optimal solution. Step 4: Alternative Solution – Checking the multiple solution W-1 Factory 1

5

Factory 2

W-3 W-4 (+) 1 6 2

7

9

12 4

E M Reddy

W-2 (-) 18 3

Availability 19 25

37

1

Page | 88

AMA-Notes Factory 3 Requirement

3 16

4

4 18

+

(-) 30 7 31

34

5 25

90

Quantity allocated in ‘-ve’ cells is 18 & 30. Least of them i.e. 18 Units should be made as new allocation. Improved Matrix – Reshuffled Matrix: Factory 1 Factory 2

W-1

W-2

W-3

5

3

6

7

9

12

4

Factory 3 Requirement

4 3 16

18 4 18

W-4 19

2 1

12 7 31

Availability 19 25

37 34

5 25

90

Cost associated with the alternative solution: Allocated Cells F1 – W3 F2 – W1 F2 – W4 F3 – W1 F3 – W2 F3 – W3 Total Cost

Computation 19 Units X Rs.6 12 Units X Rs.4 25 Units X Rs.1 4 Units X Rs.3 18 Units X Rs.4 12 Units X Rs.7

Cost (Rs.) 104 48 25 12 72 84 355

It is proved that there exists another solution with the same 355 cost. Question no 5: The following table gives the unit transportation costs and the quantities demanded /supplied at different locations for a minimization problem: C1 C2 C3 C4 Total Units R1 100 120 200 110 20000 R2 160 80 140 120 38000 R3 180 140 60 100 16000 Total Units 10000 18000 22000 24000 You are required to find out which cell gets the 3rd allocation in the initial basic feasible solution under each of the following methods and to give the cell reference, cost per unit of that cell and the quantity allocated to that cell: (i) North west corner rule (ii) Vogel’s Approximation Method (iii) Least Cost Method Solution: North West corner method: C1 E M Reddy

C2

C3

C4

Supply Page | 89

AMA-Notes R1 R2 R3 Demand

100

10000

160

120 80

180 10000/0

10000 8000

200

110

140

120

140 60 18000/8000/0 22000

100 24000

20000/10000/0 38000/30000 16000 74000

In North West corner method is in the cell is R2C2 with a quantity of 8000 units at a cost Rs.80 per unit. Vogel’s Method: C1 R1

C2

C3

120

200

10000 100

R2 160

80

140

140 18000 40 40 40

38000

40 40 40

16000/0

40 -

120 16000

180 10000/0 60 60 -

Supply I II III 20000/10000 10 10 10

110 6000

R3 Demand I II III

C4

60 22000/6000/0 80 60 60

100 24000 10 10 10

-

74000

In Vogel the 3rd allocation is R2C3 and quantity allocated is 6000 units with a cost of Rs.140 per unit. Least Cost method: C1 R1 R2

100

10000

C2

C3

C4

120

200

110

140

120

18000

160

80

180 10000/0

140 18000/0

R3 Demand

16000 60 100 22000/6000 24000

Supply 20000/10000 38000/20000 16000/0 74000

In this method the 3rd allocation is made in R1C1 and quantity allocated 10000 units and the cost is Rs.100 per unit. Question no 6: The following matrix is a minimization problem for transportation cost. The unit transportation costs are given the right hand corners of the cells and ∆ij values are encircled. Destination Supply Factory D1 D2 D3 Units F1 3 4 4 500 F2 6 ② ⑧ 9 300 7 300 F3 5 200 ⓪ 4 ② 6 200 Demand 300 400 300 1000 Find the optimum solution (s) and the minimum cost? E M Reddy

Page | 90

AMA-Notes Solution: Factory F1 F2 F3 Demand

Destination D1 300 3 ⑧ 9 ⓪ 4 300

D2 100 300 ② 400

Supply Units 4 500 7 300 5 200 1000

D3 4 100 6 ② 6 200 300

Bold = Allocated quantity Circled numbers = Zj - Zj for that cell

Cost associated with the above solution: Allocated Cell F1 – D1 F1 – D2 F1 – D3 F2 – D2 F3 – D3 Total Cost

Computation 300 Units X Rs.3 100 Units X Rs.4 100 Units X Rs.4 300 Units X Rs.6 200 Units X Rs.5

Cost (Rs.) 900 400 400 1800 1000 3700

Notes: 1) ∆ij indicates the change in the cost that occurs when an unallocated cell in ith row and jth column is made allocated. It is nothing but Cj − Zj calculation. 2) Hence all the cells having the circled numbers are unallocated cells. 3) The solution is optimal because there exists no negative number to go for improvement. 4) The solution is multiple optimal even if cell U3V1 is made allocated the cost does not change because of its ‘0’ ∆ij value. Alternate solution or Improvement: Make U3V1 as allocated cell. Factory F1 F2 F3 Demand

Destination D1 300 (-) 3 ⑧ 9 ⓪ (+) 4 300

D2 100 300 ② 400

D3 4 100 6 ② 6 200 300

Supply Units (+) 4 500 7 300 (-) 5 200 1000

D3 4 400 6 ② 6 ⓪ 300

Supply Units 4 500 7 300 5 200 1000

Improved Solution: Factory F1 F2 F3 Demand

Destination D1 100 3 ⑧ 9 200 4 300

D2 100 300 ② 400

Cost associated with the above solution: E M Reddy

Page | 91

AMA-Notes Allocated Cell F1 – D1 F1 – D2 F1 – D3 F2 – D2 F3 – D1 Total Cost

Computation 100 Units X Rs.3 100 Units X Rs.4 100 Units X Rs.4 300 Units X Rs.6 200 Units X Rs.4

Cost (Rs.) 300 400 400 1800 800 3700

4.6. Formulation

Question no 7: Madhav ltd. has decided to launch an addition to its product range. The new product may be distributed through any combination of the two company warehouse W1 and W2. The available annual production capacities for the new product are: 100 Units at Plant P1 200 Units at Plant P2 300 Units at Plant P3 The three major concentrations of customer demand are at locations D1, D2 and D3 which are estimated to require each year: 90 Units at D1 80 Units at D2 90 Units at D3 The unit production costs amount to 3, 4 and 1 at P1, P2 and P3 respectively. The unit handling costs at the warehouse amount to 2 and 3 at W1 and W2 respectively. The unit transportation costs from plant to warehouse and unit delivery costs from warehouse to customer are as follows: W1 W2 D1 D2 D3 P1 6 6 W1 3 5 8 P2 5 5 W2 5 3 9 P3 13 4 Required: Determine an optimum production and distribution schedule. Solution: Step 1: Cost when routed through warehouse 1 Particulars P1 – W1 – D1 P1 – W1 – D2 P1 – W1 – D3 P2 – W1 – D1 P2 – W1 – D2 P2 – W1 – D3 P3 – W1 – D1 P3 – W1 – D2 P3 – W1 – D3

E M Reddy

Production Cost (Rs.) 3 3 3 4 4 4 1 1 1

Transport Cost (Rs.) 6 6 6 5 5 5 13 13 13

Handling Cost (Rs.) 2 2 2 2 2 2 2 2 2

Delivery Cost (Rs.) 3 5 8 3 5 8 3 5 8

Total Cost (Rs.) 14 16 19 14 16 19 19 21 24

Page | 92

AMA-Notes P1 P2 P3 Demand

D1 14 14 19 90

D2 16 16 21 80

D3 19 19 24 90

Supply 100 200 100

Step 2: Cost when routed through warehouse 2 Particulars P1 – W2 – D1 P1 – W2 – D2 P1 – W2 – D3 P2 – W2 – D1 P2 – W2 – D2 P2 – W2 – D3 P3 – W2 – D1 P3 – W2 – D2 P3 – W2 – D3 P1 P2 P3 Demand

D1 17 17 13 90

Production Cost (Rs.) 3 3 3 4 4 4 1 1 1 D2 15 15 11 80

D3 21 21 17 90

Transport Cost (Rs.) 6 6 6 5 5 5 4 4 4

Handling Cost (Rs.) 3 3 3 3 3 3 3 3 3

Delivery Cost (Rs.) 5 3 9 5 3 9 5 3 9

Total Cost (Rs.) 17 15 21 17 15 21 13 11 17

Supply 100 200 100

Step 3: Mixed Matrix (The Least should be selected) P1 P2 P3 Demand

D1 14 – W1 14 – W1 13 – W2 90

D2 16 – W2 15 – W2 11 – W2 80

D3 19 – W1 19 – W1 17 – W1 90

Supply 100 200 100

The above problem is minimization unbalanced. Balance it by adding by a dummy column with 140 units and assign ‘0’cost to the cells in the dummy column. Step 1: Obtaining IBFS using Vogel’s method D1

D2

14

16

19

0

14

15

19

0

13 90 1 -

11 80 4 1

17 90 2 1

P1

D3 80

D4 1

P2 P3 Demand I II

E M Reddy

30

1

Supply 100

I II III IV 14 16 2 1

140

200/60

14 15 -

-

100

11 11 1

4

30 0 140/0 0 0

400

Page | 93

AMA-Notes III IV

2 2

1 -

1 1

Cost associated with the Vogel’s solution: Allocated Cells F1 – W2 F1 – W3 F2 – W1 F2 – W4 F3 – W1 F3 – W3 Total Cost

Computation 18 Units X Rs.3 1 Units X Rs.6 12 Units X Rs.4 25 Units X Rs.1 4 Units X Rs.3 30 Units X Rs.7

Cost (Rs.) 54 6 48 25 12 210 355

Step 2: Checking for degeneracy Initial Basic Feasible Solution: W-1 Factory 1 5 Factory 2 12 4 Factory 3 4 3 Requirement 16

W-2

W-3 18

W-4

Availability 19

1

3

6

2

7

9

1

4 18

7 31

25 30

5 25

37 34 90

Number of allocated cells = 6 M+N–1=3+4–1=6 Since there is no degeneracy we can proceed for optimality test. Step 3: Moody’s optimality test A: Allocated cells Allocated Cells U1+V2= U1+V3= U2+V1= U2+V4= U3+V1= U3+V3=

Cost 3 6 4 1 3 7

B: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = 2, U3 = 1, V1 = 2, V2 = 3, V3 = 6, V4 = -1 C: Unallocated Cells

E M Reddy

Page | 94

AMA-Notes Unallocated Cells U1+V1= U1+V4= U2+V2= U2+V3= U3+V2= U3+V4=

𝐂𝐣 5 2 7 9 4 5

𝐙𝐣 2 -1 5 8 4 0

𝐂𝐣 − 𝐙𝐣 3 3 2 1 0 5

The above solution is optimal because there are no negativity numbers to give improvement. But there exists another optimal solution i.e. if we make U3V2 allocated cell, for every allocation made the cost changes by Rs.0 i.e. it does not change. Hence the problem has multiple optimal solution. **Question no 8: ABC manufacturing company wishes to develop a monthly production schedule for the next months. Depending upon the sales commitments, the company can either keep the production constant, allowing fluctuations in inventory or inventories can be maintained at a constant level, with fluctuating production. Fluctuating production necessities in working overtime, the cost of which is estimated to be double the normal production cost of Rs.12 per unit. Fluctuating inventories result in inventory carrying cost of Rs.2 per unit. If the company fails to fulfill its sales commitment, it incurs a shortage cost of Rs.4 per unit per month. The production capacities for the next three months are shows below. Production Capacity Month Regular Overtime Sales 1 50 30 60 2 50 0 120 3 60 50 400 Determine the optimal production schedule. Solution: Matrix: Month 1 Normal 1 Overtime 2 Normal 3 Normal 3 Overtime Requirement

1 12 24 16 20 32 60

2 14 26 12 16 28 120

3 16 28 14 12 23 40

Available 59 30 50 60 50

Notes: 1) The objective of this sum is to match production and sales at the minimum inventory cost. 2) There are 3 possibilities: i. Produce and sell in same month – Will incur only production cost of Rs.12 per unit. ii. Produce in previous month and sell in subsequent months – Will incur production cost & carrying cost Rs 2 per unit per month.

E M Reddy

Page | 95

AMA-Notes iii.

Sell in previous month and produce in subsequent months – Will incur production cost & shortage cost of Rs.4 per unit per month. 3) If production is done during overtime an additional time over time cost of Rs.12 per unit will be incurred. 4) The above is a minimization unbalanced transportation problem. Balance it by adding dummy column for 20 units with ‘0’ cost. Question no 9: As a result of an expansion in production capacity, the management of Minerva Manufacturing Ltd., has decided to take additional employees at each of its five plants in the south-west of India. The numbers required at each plant are: Plant 1 2 3 4 5 Employees required 45 74 50 82 63 All its employees currently come from three large towns in the area. Upon contracting the main employment agency in each town, Minerva finds that the numbers of suitable people available for employment are as follows: Agency (Town) A B C People available 120 100 154 Because of the rural situations of the five plant Minerva has agreed with the trade union concerned that daily return traveling expenses from each town will be paid by the company to employees. The rate is currently Rs.12 per mile, and the distance (in miles) between each plant and each town are as follows: Town 1 2 3 4 5 A 6 2 2 6 3 B 14 9 4 5 3 C 10 4 11 3 4 (a) How many people should Minerva aim to employ from each town in order to minimize the additional travelling expenses incurred? (b) What is the minimum value of these expenses in connection with the additional 314 employees? (c) In order to appear not to be unfair the potential employees from any one of the three towns, it has now been decided that the 60 people who are surplus to requirements should be spread equally between the three towns i.e. 20 from each. How much more than in A would the company have to pay out each day in travelling expenses in order to achieve the minimum cost? Solution: Step 1: Formulation Agency/Plant A B C Demand

1 72 168 120 45

2 24 108 48 74

3 24 48 132 50

4 72 60 36 82

5 36 36 48 63

Dummy 0 0 0 60

Supply 120 100 154 374

When the problem is absolved, obviously in the final solution allocations in the dummy will be there. For example, in Agency A, dummy allocated and in Agency C, dummy 40 allocated. This means rejects 20 employees from town A and 40 employees from B that means dummy allocation indicates rejection.

E M Reddy

Page | 96

AMA-Notes Step 2: Problem reformulated when surplus to requirement should be spread evenly between three cities Agency/Plant A B C Demand

1 72 168 120 45

2 24 108 48 74

3 24 48 132 50

4 72 60 36 82

5 36 36 48 63

Supply 100 80 134 314

Notes: 1) 374 persons applied and there are only 314 vacancies. Surely 60 applications need to be rejected which can be done in two ways. i. Rejections through dummy – The freedom to reject is given to Vogel and Moody and the only consideration is cost minimization. ii. Rejection by adjusting the supply – In the question does the reduction through a condition then rejection should be done by adjusting the demand or supply. Question 10: The brown chemical company produces a special oil-based material which is currently in short supply. Four of Brown’s customers have already placed orders which in total exceed the combined capacity of its two plans and the company needs to know how it should allocate its production capacity to maximize profits. The following distribution costs per unit have been determined. Customer C1 (Rs.) C2 (Rs.) C3 (Rs.) C4 (Rs.) Plant X 16 15 14 18 Plant Y 15 15 14 15 The variable unit production costs are Rs.10 per plant X and Rs.12 for plant Y. Since the four customers are in different industries, the pricing structure allows different prices to be charged to different customers. (The material undergoes slight variations for each customer at negligible costs). These prices are Rs.46 for C1, Rs.42 for C2, Rs.40 for C3 and Rs.44 for C4. The customer’s orders (in units) are: C1 C2 C3 C4 2000 5000 3500 2500 And the plant capacities at X and Y in the period concerned are 6000 and 3000 units respectively. Due to an industrial dispute the company can only supply customer C3 from plant Y. Required: (a) Use the transportation algorithm to determine the optimum solution. (b) If the industrial disputes were to be resolved so that customer C3 would be supplied from plant X, how would this affect your solution? Solution: Part 1: Profit Matrix (Selling Price – Variable Cost) X Y

C1 (Rs.) 46 – 26 = 20 46 – 27 = 19

C2 (Rs.) 42 – 25 = 17 42 – 27 = 15

C3 (Rs.) 40 – 24 = 16 40 – 26 = 14

C4 (Rs.) 44 – 28 = 16 44 – 27 = 17

Part 2: Formulating into transportation matrix when there is industrial dispute

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AMA-Notes Customer 3 should be supplier only from Plan Y. Hence the cell X, C3 is a prohibited cell. To prevent allocation in that cell, assign a high loss ‘-M’ too that cell. X Y Requirement

C1 20 19 2000

C2 17 15 5000

C3 -M 14 3500

C4 16 17 2500

Available 6000 3000

The problem is maximization unbalanced. First balance it by adding a dummy row having profit of ‘0’ in each cell and then the convert the problem into minimization then apply Vogel and moody for solution. Initial Basic Solution for the above problem:

Optimality test for final improved solution: A: Allocated cells Allocated Cells U1+V1= U1+V2= U2+V1= U2+V4= U3+V2= U3+V3=

Cost 0 3 1 3 20 20

B: Values Assume U1 value as ‘0’ and the remaining values will be as follows: U1 = 0, U2 = 1, U3 = 17, V1 = 0, V2 = 3, V3 = 3, V4 = 2 C: Unallocated Cells Unallocated Cells U1+V3= U1+V4= U2+V2= U2+V3= U3+V1= U3+V4=

𝐂𝐣 M 4 5 6 20 20

𝐙𝐣 3 2 4 4 17 19

𝐂𝐣 − 𝐙𝐣 M 2 1 2 3 1

Part 2: Formulation when industrial dispute resolved

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AMA-Notes C1 20 19 2000

X Y Requirement

C2 17 15 5000

C3 16 14 3500

C4 16 17 2500

Available 6000 3000

This part is similar to previous one except that in the cell X, C3 the regret is not M. But the regret is 4. We need not do from the beginning the solution, we can test for optimality in the final solution obtained in the previous part. For unallocated cell U1+V3, now the Cj − Zj = 4 – 3 = 1. Hence removing the dispute will not alter the solution. Question no 11: Management of Ranga ltd is very much worried about the continuing recession on the country. The company has 7 divisions (A to G). They have decided to close four divisions namely A, B, C and D transfer some of the employees to the remaining divisions. Personnel at the units to be closed has signified a willingness to move to any of the three remaining units and the company is willing to provide them with removal costs. The technology of production is different to some degree at each unit and retraining expenses will be incurred on transfer. Not all existing personnel can be absorbed by transfer and a number of redundancies will arise. Cost of redundancy is given as a general figure at each unit is to be closed. Number employed A-200, B-400, C-300, D-200. Retraining Cost A B C D Transfer to: Unit E 0.5 0.4 0.6 1.3 Unit F 0.6 0.4 0.6 0.3 Unit G 0.5 0.3 0.7 0.3 Removal Cost A B C D Transfer to: Unit E 2.5 3.6 3.4 3.7 Unit F 2.4 4.6 3.4 1.7 Unit G 2.5 2.7 3.3 2.7 Redundancy Payment 6 5 6 7 Additional personnel required at units remaining open: E-350, F-450, G-200. Use the transportation method to obtain an optimal solution to the problem of the cheapest mean to transfer personnel from the units to be closed to those which will be expanded. Solution: Availability A 200 B 400 C 300 D 200 Total 1100 Redundant People

A B

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E 3 4

Demand 350 450 200

E F G

Total 1000 1100 – 1000 = 100 F 3 5

G 3 3

Redundancy 6 5

Supply 200 400

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AMA-Notes C 4 4 4 6 D 5 2 3 7 Requirement 350 450 200 100

300 200 1100

The above is minimization balanced problem. Solve using Vogel and Moody.

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AMA-Notes 5. STANDARD COSTING or VARIANCE ANALYSIS: 5.1. Learning Objectives

1) Material Variance i. Single Raw Material ii. Mix of Raw Materials 2) Labour Variances i. With Idle time ii. Without Idle time 3) Variable Overhead Variances 4) Fixed Overhead Variances i. Without Calendar ii. With Calendar iii. With WIP (Work in progress) 5) ABC (Activity Based Costing) and Overhead Variances 6) Sales Variances i. Total Approach ii. Margin Approach iii. Reconciliation Problem 7) Reconciliation Problems i. Budgeted profit to actual profit (Absorption Costing System) ii. Budgeted profit to actual profit (Marginal Costing System) iii. Standard profit to actual profit (Absorption Costing System) iv. Standard profit to actual profit (Marginal Costing System) 8) Reconciliation with WIP 9) Reconciliation with opportunity cost 10) Reverse Working Problems 11) Planning and Operating Variance 12) Market size and market share variance 13) Miscellaneous Problems 5.2. Introduction

1) Standard Costing system provides information for control purpose. 2) Companies prepare budgets at the beginning of the period and had budgeted profit as the period’s target. At the end of the period, when actual profits are earned they are compared with budget and reasons analyzed. This is called variance analysis.

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AMA-Notes

Profit Variance Sales Variance

Cost Variance

Material Cost Variance

Labour Cost Variance

Variable Overhead Variance (VOH)

Overhead Cost Variance

Fixed Overhead Variance (FOH)

3) 4) If the variances increase the actual profit, then it is favorable else it is adverse. 5) In the first segment we will learn calculation of variances. In the next segment we will learn preparation of reconciliation statements (or) Operating Statements in various possible ways. The last segment we will discuss the following concepts: i. Partial Plan vs. Single Plan ii. Reverse working problems iii. Investigation of Variances 5.3. Understanding Standard Cost

Example: Budgeted output = 10000 Units Standard Cost per unit = Rs.10 Actual Output = 8000 Units Actual Cost = Rs.96000 1) The company plan to spend Rs.1,00,000 but actually spent only Rs. 96,000 thereby saving a cost of Rs. 4,000. Is this right? Answer: No, because we cannot compare a target cost for 10,000 units with the actual cost of 8,000 units. 2) We have to revise the target for actual output and then compare. 3) Three types of costs:

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AMA-Notes

Budgeted Cost

Standard Cost

Actual Cost

BO x SC/U

AO x SC/U

AO x AC/U

Cost Planned

Cost Allowed

Cost Incurred

10,000 Units x Rs.10 = Rs.1,00,000

8,000 Units x Rs.10 = Rs.80,000

8,000 Units x Rs.12 = Rs.96,000

4) Budgeted cost is for “budgeted cost for budget output” and Standard cost is “Budgeted cost for actual output”. Cost Variance is the difference between the Standard cost & actual cost and not budgeted cost & actual cost. 5.4. Cost Variances 5.4.1. Material Cost Variances – Single Raw Material Input

Step 1: Computation Table [1] SQ x SP

[2] AQ x AP

[3] AQ x SP

Where SQ = Standard Quantity for actual output (or) Quantity allowed Where SP = Standard Price Where AQ = Actual Quantity Where AP = Actual Price Step 2: Variance Calculation

Material Cost Variance (1-2)

Material Price Variance (3-2)

Material Usage Variance (1-3)

Question no 1: The following data is available for a product. Standard material cost per unit of output 2kgs at Rs.20 per kg. During a period, actual details are as under: Actual Output = 10,000 Units E M Reddy

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AMA-Notes Material Used = 22,000 Kgs Actual price is Rs.25 per kg. Find out material variances? Solution: Step 1: Computation table [1] SQ x SP 20000 x 20 4,00,000

[2] AQ x AP 22000 x 25 5,50,000

[3] AQ x SP 22000 x 20 4,40,000

Step 2: Variance Calculation

Material Cost Variance (1-2) = 4,00,000 – 5,50,000 = 1,50,000 (Adverse) Material Price Variance (3-2) = 4,40,000 – 5,50,000 = 1,10,00 (Adverse)

Material Usage Variance (1-3) = 4,00,000 – 4,40,000 = 40,000 (Adverse)

Working Note: Calculation of Standard quantity Input 2 Kgs 10000 x 2 Kgs = 20000 Kgs

Output 1 Unit 10000 Units

Notes: 1) For the output of 10,000 units the factory is allowed to consume 20,000 Kgs at a standard price of Rs.20 i.e. the cost allowed is Rs.4,00,000. 2) However, it actually consumes 22,000 Kgs at Rs.25 per Kg i.e. Rs.5,50,000. Thus there is an overspending of material cost of Rs.1,50,000. 3) The material cost may vary due to two reasons: i. Variation in Purchase Price – Price Variance ii. Variation in Quantity Consumed – Usage Variance 4) While calculating usage variance we multiply the excess usage of 2,000 Kgs with standard price of Rs.20 and not the actual price Rs.25? Answer: Because by taking the actual price we are considering the efficiency/inefficiency of purchase manager in evaluating the production manager performance. 5) However, while calculating price variance we multiply the price variance with actual quantity because the duty of the purchase manager is to purchase the entire quantity ordered at efficient price.

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AMA-Notes 6) Alternatively, the price variance can be calculated for the standard quantity and the balance reported as “Joint Variance”.

Material Cost Variance (1-2) = 4,00,000 – 5,50,000 = 1,50,000 (Adverse) Material Price Variance = (Rs.20 – Rs.25) x 20,000 = Rs.1,00,000 (Adverse)

Material Usage Variance = (20,000 – 22,000) x Rs.20 = Rs.40,000 (Adverse)

Material Joint Variance = Rs.5 x 2000 = Rs.10,000 (Adverse)

5.4.2. Material Cost Variances – Mix of Raw Materials

Step 1: Computation Table [1] SQ x SP

[2] AQ x AP

[3] AQ x SP

[4] RAQ x SP

Where SQ = Standard Quantity for actual output (or) Quantity allowed Where SP = Standard Price Where AQ = Actual Quantity Where AP = Actual Price Where RAQ = Revised Actual Quantity i.e. actual quantity in standard mix Step 2: Variance Calculation

Material Cost Variance (1-2)

Material Price Variance (3-2)

Material Usage Variance (1-3)

Material Mix Variance (4-3)

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Material Yield Variance (1-4)

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AMA-Notes Question no 2: The standard set for a chemical mixture of a firm is as under: Material Standard Mix% Standard Price per kg (Rs.) A 40 20 B 60 30 The standard loss in production is 10%. During a period, the actual consumption and price paid for a good output of 189 Kg are as under: Material Quantity in Kg. Actual Price per kg (Rs.) A 90 18 B 110 34 Calculate material variances. Solution: Step 1: Computation table

A B Total

[1] SQ x SP 84 x 20 126 x 30 5460

[2] AQ x AP 90 x 18 110 x 34 5360

[3] AQ x SP 90 x 20 110 x 30 5100

[4] RAQ x SP 80 x 20 120 x 30 5200

Step 2: Variance Calculations Material Cost Variance (1-2) = 5460 – 5360 = 100 (Favourable) Material Price Variance (3-2) = 5100 – 5360 = 260 (Adverse)

Material Usage Variance (1-3) = 5460 – 5100 = 360 (Favourable) Material Mix Variance (4-3) = 5200 – 5100 = 100 (Favourable)

Material Yield Variance (1-4) = 5460 – 5200 = 260 (Favourable)

Working Note 1: Computation of SQ Input 100 189 x 100 / 90 = 210

Output 90 189

Working Note 2: Computation of RAQ Actual Quantity = 110 + 90 = 200 Kgs A = 200 x 40% = 80 Kgs B = 200 x 60% = 120 Kgs E M Reddy

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AMA-Notes Notes: 1) Material Mix Variance: i. Material Mix Variance is “Column 4 – Column 3” ii. The difference between column 3 and column 4 is not price (both are SPs), is not quantity (both are AQs) but it is mix. Column 4 in standard mix and column 3 is actual mix. Hence, the difference is mix variance. iii. In this problem we increased Raw Material A proportion which is a cheaper Raw Material and decreased Raw Material B proportion which is an expensive Raw Material there by having a favorable mix variance of 100. 2) Material Yield Variance: i. Material Yield Variance is “Column1 – Column 4”. ii. Difference between column 1 and column 4 is not price (both are SPs), is not mix (both are standard mix) but is the quantity. iii. Particulars Standard (Kgs) Actual (Kgs) A. Input 210 200 B. Loss 21 11 C. Output (A – B) 189 189 D. % Loss (B/A x 100) 10% 5.5% E. % Yield (100 – D) 90% 94.5% This extra yield is called of 4.5% is called variance. iv. A ‘favorable’ yield varicose indicates ‘abnormal gain’ while an ‘adverse’ variance yield variance indicates ‘abnormal loss’. 3) Material Usage Variance: i. Material Usage Variance is ‘Column 1 – Column 3’ ii. The difference between column 1 and column is not the price (both are SPs) but it is mixed quantity. Column is standard quantity in standard mix and column is actual quantity in actual mix. iii. If we look at mix angle alone it is mix variance and quantity angle alone it is yield variance, both it is usage variance. Question no 3: SC Limited manufactures a special floor tile which measures ½ m x ¼ m x 0.01m. The tiles are manufactured in a process, which requires the following standard mix: Material Quantity (Kgs) Price (Rs.) Amount (Rs.) A 40 1.5 60 B 30 1.2 36 C 10 1.4 14 D 20 0.5 10 120 Each mix should produce 100 square meters of floor tiles of 0.01m thickness. During April, the actual output was 46,400 tiles from an input of: Material Quantity (Kgs) Price (Rs.) Amount (Rs.) A 2,200 1.6 3,520 B 2,000 1.1 2,200 C 500 1.5 750 E M Reddy

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AMA-Notes D

1,400

0.5

700 7,170

Calculate material variances. Solution: Step 1: Computation table

A B C D Total

[1] SQ x SP 2,320 x 1.5 1,740 x 1.2 580 x 1.4 1,160 x 0.5 6,960

[2] AQ x AP 2,200 x 1.6 2,000 x 1.1 500 x 1.5 1,400 x 0.5 7,170

[3] AQ x SP 2,200 x 1.5 2,000 x 1.2 500 x 1.4 1,400 x 0.5 7,100

[4] RAQ x SP 2,440 x 1.5 1,830 x 1.2 610 x 1.4 1,220 x 0.5 7,320

Step 2: Variance Calculations

Material Cost Variance (1-2) = 6960 – 7170 = 210 (Adverse) Material Usage Variance (1-3) = 6960 – 7100 = 140 (Adverse)

Material Price Variance (3-2) = 7100 – 7170 = 70 (Adverse) Material Mix Variance (4-3) = 7320 – 7100 = 220 (Favourable)

Material Yield Variance (1-4) = 6960 – 7320 = 360 (Adverse)

Working Note 1: Calculation of Standard Quantity Area of one tile = Length x Breadth = 0.5m x 0.25m = 0.125 sq. mts. So 100 sq. mts. = 100/0.125 = 800 tiles. 1 standard mix should produce 800 tiles. Input 1 Standard Mix 58 Standard Mix A B C D

58 x 40 58 x 30 58 x 10 58 x 20

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Output 800 tiles 46,400 tiles 2,320 1,740 580 1,160

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AMA-Notes Working Note 2: Computation of RAQ Actual Quantity = 2,200 + 2,000 + 510 + 1,400 = 6100 A = 6,100 x 40% = 2,440 Kgs B = 6,100 x 30% = 1,830 Kgs C = 6,100 x 10% = 610 Kgs D = 6,100 x 20% = 1,220 Kgs 5.4.3. Labour Variances – without mix

Step 1: Computation Table [1] SH x SR

[2] AH x AR

[3] AH x SR

Where SH = Standard Hours for actual output (or) Hours allowed Where SR = Standard Rate Where AH = Actual Hours Where AR = Actual Rate Step 2: Variance Calculation

Labour Cost Variance (1-2)

Labour Rate Variance (3-2)

Labour Efficiency Variance (1-3)

5.4.4. Labour Variances – with mix

Step 1: Computation Table [1] SH x SR

[2] AH x AR

[3] AH x SR

[4] RAH x SR

Where SH = Standard Hours for actual output (or) Hours allowed Where SR = Standard Rate Where AH = Actual Hours Where AR = Actual Rate Where RAH = Revised Actual Hours i.e. actual hours in standard mix

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AMA-Notes Step 2: Variance Calculation

Labour Cost Variance (1-2)

Labour Rate Variance (3-2)

Labour Efficiency Variance (1-3)

Labour Mix Variance/ Labour Gang Variance (4-3)

Labour Productivity Variance (1-4)

Question no 4: The data obtained from a manufacturing concern are: Particulars Men Women Number in standard gang 20 10 Standard rate per hour 9 8 Number in actual gang 16 14 Actual rate per hour (Rs.) 10 7 In a 48 hour-week, the gang as actually composed, produced 1200 standard hours. Compute labour variances. Solution: Step 1: Computation table

Men Women Total

[1] SH x SR 800 x 9 400 x 9 10,400

[2] AH x AR 768 x 10 672 x 7 12,384

[3] AH x SR 768 x 9 672 x 8 12,288

[4] RAH x SR 960 x 9 480 x 8 12,480

Step 2: Variance Calculation Labour Cost Variance (1-2) = 10400 – 12384 = 1984 (Adverse) Labour efficiency Variance (1-3) = 10400 – 12288 = 1888 (Adverse)

Labour Rate Variance (3-2) = 12288 – 12384 = 96 (Adverse) Labour Mix/Gang Variance (4-3) = 12480 – 12288 = 192 (Favourable)

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Labour Productivity Variance (1-4) = 10400 – 12480 = 2080 (Adverse)

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AMA-Notes Working Note 1: Calculation of standard hours Standard hours = 1200 hours Men = 1200 x 20/30 = 800 hours Women = 1200 x 10/30 = 400 hours Working Note 2: Calculation of actual hours Men Women

= 16 people x 48 hours = 768 hours = 14 people x 48 hours= 672 hours

Working Note 3: Calculation of Revised actual hours – Actual hours in standard mix Actual hours = 768 + 672 = 1440 hours Men = 1440 x 20/30 = 960 hours Women = 1440 x 10/30 = 480 hours 5.4.5. Labour Variance – Idle time

Question no 5: In a certain factory House paid for in a week 40 Standard rate per hour (Rs.) 8 Standard output of department per hour, taking into account the normal idle time (units) 20 Actual rate per hour (Rs.) 9 In a particular week, it was ascertained that 1000 units were produced despite 20% of the time paid for was lost owing to power failure. Calculate labour variances. Solution: Step 1: Computation table [1] SH x SR 50 x 8 = 400

[2] AH x AR 40 x 9 = 360

[3] AH x SR 40 x 8 = 320

Working Note 1: Calculation of standard hours Input 1 Hour 50 Hours

Output 20 Units 1000 Units

Step 2: Revised Labour efficiency variance [1] SH x SR 50 x 8 = 400

[2] AH x AR 40 x 9 = 360

[3] AH (W) x SR 32 x 8 = 256

Labour revised efficiency ratio (1 – 3) = 400 – 256 = 144 (Favorable)

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AMA-Notes Step 3: Variance Calculation

Labour Cost Variance (1-2) = 400 – 360 = 40 (Favourable) Labour Rate Variance (3-2) = 320 – 360 = 40 (Adverse)

Labour Efficiency Variance (1-3) = 400 – 320 = 80 (Favourable)

Labour idle time Variance = Idle time x Standard Rate = 8 Hours x 8 = 64 (Adverse)

Labour revised efficiency Variance (13) = 144 (favourable)

Notes: 1) 50 Hours job was completed in 40 hours and the workers have saved the company 10 Hours wages. Is this right? Answer: No, because 8 hours was idle time due to power cut and the workers have completed the job in 32 hours. The real time saving is 18 hours. This revised efficiency variance. 2) There are two types of actual hours: i. Actual hours paid – Considered for calculating rate variance ii. Actual hours worked – Actual Hours paid – idle time – used to calculated revised efficiency variance 5.4.6. Variable Overhead Variances

Step 1: Calculation of standard rate (SR) SR per unit SR per Hour

BVO/BO BVO/BH

Step 2: Computation table [1] SH x SR or AO x SR

[2] AVO

[3] AH x SR or SO x SR

Where SH = Standard Hours for actual output (or) Hours allowed Where SO = Standard Output for actual Hours Where AH = Actual Hours Where SR = Standard Rate Where AVO = Actual Variable overhead

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AMA-Notes When we multiply by hours use SR per hour and when we multiply by output use SR per unit. Step 3: Variance Calculation

Variable Overhead Cost Variance (1-2) Variable overhead expenditure Variance (3-2)

Variable overhead Efficiency Variance (1-3)

Question no 6: XYZ company has established the following standards for variable factory overhead. Standard hours per unit: 6 Variable overhead per hour: Rs.2/The actual data for the month are as follows: Actual variable overheads incurred Rs.2,00,000 Actual output (units) 20,000 Actual hours worked 1,12,000 Required to calculate variable overhead variances: a. Variable overhead cost variance. b. Variable overhead expenditure variance c. Variable overhead efficiency variance Solution: Step 1: Standard rates (SR) SR per hour = Rs.2 (Given) SR per unit = 6 Hours x Rs.2 = Rs.12 per hour Step 2: Computation table [1] SH x SR or AO x SR 1,20,000 Hours x Rs.2 (or) 20,000 Units x Rs.12 Rs.2,40,000

[2] AVO 1,12,000 x Rs.1.79 Rs.2,00,000

[3] AH x SR or SO x SR 1,12,000 Hours x Rs.2 or 18,667 Units x Rs.12 Rs.2,24,000

Working Note 1: Standard Hours for actual output Input 6 Hours 1,20,000 Hours

Output 1 Unit 20,000 Units

Working Note 2: Standard output for actual hours

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AMA-Notes Input 6 Hours 1,12,000 Hours

Output 1 Unit 18677 Units

Step 3: Variance Calculation

Variable overhead expenditure Variance (3-2) = 2,24,000 – 2,00,000 = 24,000 (Favourable)

Variable Overhead Cost Variance (1-2) = 2,40,000 – 2,00,000 = 40,000 (Favourable)

Variable overhead Efficiency Variance (1-3) = 2,40,000 – 2,24,000 = 16,000 (Favourable)

Notes: 1) In the entire chapter we assume the labour hours as the primary cost driver for overheads and the output as secondary cost driver. 2) In Other words, more the output more the labour hours and more the labour hours more the variable overheads. 3) For the 20,000 units output the cost allowed is Rs.2,40,000 but actually spent is only Rs.2,00,000. Thus there is a savings in variable overhead cost of Rs. 40,000. 4) The variable overhead may vary due to two reasons: i. Expenditure change – Plan to pay Rs.2 for hour but paid only Rs.1.79 per hour saving Rs.0.21 per 1,12,000 Hours which is equal to Rs. 24,000 (approximately) ii. Change in efficiency 5) Efficiency can be seen in two ways: i. In terms of hours – 1,20,00 Hours job has been done in 1,12,000 hours saving 8,000 Hours variable overhead (8,000 Hours x Rs.2 = Rs. 16,000) ii. In terms of output – In 1,12,000 Hours the company should have produced 18,677 units but produced 20,000 units therefore the 1,333 units are produced without any extra labour hours and variable overheads there by saving a cost of Rs. 16,000 (1,333 Units x Rs.12) 5.4.7. Fixed Overhead Variances – With Calendar

Step 1: Calculation of standard rate (SR) SR per unit SR per Hour

BFO/BO BFO/BH

Step 2: Computation table [1] SH x SR or AO x SR

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[2] AFO

[3] BFO [BO x SR or BH x SR]

[4] AH x SR or SO x SR

[5] PFO [BFO x AD/BD]

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AMA-Notes Where SH = Standard Hours for actual output (or) Hours allowed Where SO = Standard Output for actual Hours Where AH = Actual Hours Where SR = Standard Rate Where AFO = Actual Fixed overhead PFO = Possible fixed overheads Where AD = Actual Days Where BD = Budgeted days Step 3: Variance Calculation

Fixed Overhead Cost Variance (1-2)

Fixed overhead expenditure Variance (3-2)

Fixed overhead Capacity Variance (4-5)

Fixed overhead Volume Variance (1-3)

Fixed overhead Calendar Variance (5-3)

Fixed overhead efficiency Variance (1-4)

Question no 7: A manufacturing company operating a standard costing system has the following data in respect of July, 2006: Actual number of working days 22 Actual man-hours worked during the month 8,600 Units produced 850 Actual fixed overhead incurred Rs. 3,600 The following information is obtained from the company’s budget and standard cost data: Budgeted number of working days per month 20 Budgeted man-hours per month 8,000 Standard man-hours per unit 10 Standard fixed overhead rate per man hour Rs.0.50 Calculate fixed overhead variances. Solution: Step 1: Calculation of Standard rates Standard rate per hour = Rs.0.50 (given) Standard rate per unit = 10 Hours x Rs.0.50 = Rs.5 per hour Step 2: Computation table E M Reddy

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AMA-Notes [1] SH x SR or AO x SR 850 x 5 4,250

[2] AFO 3,600 3,600

[3] BFO [BO x SR or BH x SR] 8,000 x 0.5 4,000

[4] AH x SR or SO x SR 8,600 x 0.5 4,300

[5] PFO [BFO x AD/BD] 4,000 x 22/20 4,400

Step 3: Variance Calculation

Fixed Overhead Cost Variance (1-2) = 4250 – 3600 = 650 (Favourable)

Fixed overhead expenditure Variance (3-2) = 4000 – 3600 = 400 (Favourable)

Fixed overhead Capacity Variance (4-5) = 4300 – 4400 = 100 (Adverse)

Fixed overhead Volume Variance (1-3) = 4250 – 4000 = 250 (Favourable)

Fixed overhead Calendar Variance (5-3) = 4400 – 4000 = 400 (Favourable)

Fixed overhead efficiency Variance (1-4) = 4250 – 4300 = 50 (Adverse)

Notes: 1) Page no 168 (11 points) Question no 8: From the following figures extracted from the books of a company, compute appropriate variances: Particulars Budget Actual Output in units 12,000 13,000 Hours 6,000 6,600 Fixed Overhead Rs. 2,400 Rs. 2,500 Variable Overhead Rs. 12,000 Rs. 13,300 No. of days 50 54 Solution: Part 1: Variable overhead variances Step 1: Computation of Standard rates (SR) Standard Rate/Unit

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=

BVO BO

12,000

= 12,000 = Rs.1 per unit

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AMA-Notes Standard Rate/Hour =

BVO BO

=

12,000 6,000

= Rs.2 per hour

Step 2: Computation table [1] SH x SR or AO x SR 13,000 Units x Rs.1 Rs. 13,000

[2] AVO Rs. 13,300 Rs. 13,300

[3] AH x SR or SO x SR 6,600 Hours x Rs.2 Rs. 13,200

Step 3: Variance Calculation

Variable Overhead Cost Variance (1-2) = 13,300 – 13,000 = 300 (Adverse)

Variable overhead expenditure Variance (3-2) = 13,200 – 13,300 = 100 (Adverse)

Variable overhead Efficiency Variance (1-3) = 13,000 – 13,200 = 200 (Adverse)

Part 2: Fixed overhead variances Step 1: Computation of Standard rates (SR) =

BFO

Standard Rate/Hour =

BFO

Standard Rate/Unit

BO

BO

2,400

= 12,000 = Rs.0.2 per unit 2,400

= 6,000 = Rs.0.4 per hour

Step 2: Computation table [1] SH x SR or AO x SR 13,000 Units x Rs.0.2 Rs. 2,600

[2] AFO Rs. 2,500 Rs. 2,500

[3] BFO [BO x SR or BH x SR] Rs. 2,400 Rs. 2,400

[4] AH x SR or SO x SR 6,600 Hours x Rs.0.4 Rs. 2,640

[5] PFO [BFO x AD/BD] Rs. 2,400 x 54/50 Rs. 2,592

Step 3: Variance Calculation Fixed Overhead Cost Variance (1 – 2) = 2600 – 2500 = 100 (Favorable) Fixed Overhead Expenditure Variance (3 – 2) = 2400 – 2500 = 100 (Adverse) Fixed Overhead Volume Variance (1 – 3) = 2600 – 2400 = 200 (Favorable) Fixed Overhead Capacity Variance (4 – 5) = 2640 – 2592 = 48 (Favorable) Fixed Overhead Calendar Variance (5 – 3) = 2593 – 2400 = 192 (Favorable) Fixed Overhead Efficiency Variance (1 – 4) = 2600 – 2640 = 40 (Adverse)

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AMA-Notes 5.4.8. Fixed Overhead Variances – Without Calendar

Step 1: Calculation of standard rate (SR) SR per unit SR per Hour

BFO/BO BFO/BH

Step 2: Computation table [1] SH x SR or AO x SR

[2] AFO

[3] BFO [BO x SR or BH x SR]

[4] AH x SR or SO x SR

Where SH = Standard Hours for actual output (or) Hours allowed Where SO = Standard Output for actual Hours Where AH = Actual Hours Where SR = Standard Rate Where AFO = Actual Fixed overhead Step 3: Variance Calculation

Fixed Overhead Cost Variance (1-2)

Fixed overhead expenditure Variance (3-2)

Fixed overhead Volume Variance (1-3)

Fixed overhead Capacity Variance (4-3)

Fixed overhead efficiency Variance (1-4)

Question no 9: Calculate fixed production overhead variances in as much as details as possible, in the following situation: Particulars Budget Actual Fixed Overhead (Rs.) 2,46,000 2,59,000 Direct labour (hours) 1,23,000 1,41,000 Output (units) 6,15,000 (see below) The company operates a process costing system. At the beginning of the period 42,000 half completed units were in stock. During the period 6,80,000 units were completed and 50,000 half completed units remained in stock at the end of the period.

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AMA-Notes Solution: Step 1: Commutation of actual output using Statement of Equivalent units Output Item Opening WIP Introduced and completed Closing WIP Total

Equivalent Units % Units 50% 21,000 100% 6,38,000 50% 25,000 6,84,000

Units 42,000 6,38,000 50,000

Step 2: Computation of Standard Rates (SR) Standard Rate per unit =

BFO BO

Standard Rate per hour =

BFO BH

2,46,000

= 5,15,000 = Rs.0.40 per unit 2,46,000

= 1,23,000 = Rs.2 per hour

Step 3: Computation table [1] SH x SR or AO x SR 6,84,000 Units x Rs.0.4 Rs. 2,73,600

[2] AFO

[3] BFO [BO x SR or BH x SR] Rs. 2,46,000 Rs. 2,46,000

Rs. 2,59,000 Rs. 2,59,000

[4] AH x SR or SO x SR 1,41,000 Hours x Rs.2 Rs. 2,82,000

Step 4: Variance Calculation Fixed Overhead Cost Variance (1-2) = 2,73,600 – 2,59,000 = 14,600 (Favourable)

Fixed overhead expenditure Variance (3-2) = 2,46,000 – 2,59,000 = 13,000 (Adverse)

Fixed overhead Volume Variance (1-3) = 2,73,600 – 2,46,000 = 27,600 (Favourable)

Fixed overhead Capacity Variance (4-3) = 2,82,000 – 2,46,000 = 36,000 (Favourable)

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Fixed overhead efficiency Variance (1-4) = 2,73,600 – 2,82,000 = 8,400 (Adverse)

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AMA-Notes 5.4.9. Cost Variances Reconciliation

**Question 10: ABC ltd uses flexible budgets and standard costing for its single product PCM 30 produced at its factory at Solan. The following details relate to a particular month’s actual and also provide brief details of ‘Standards’ established. Standard quantity required for producing 1 unit of PCM 30 3 Kgs Standard cost of Raw Materials Rs. 4.40 per kg Cost of actual materials purchased and used in the relevant month Rs. 3,36,000 Actual price paid for the raw material in the relevant month Rs.4.20 per Kg Standard labour time required to produce 1 unit of PCM 30 30 minutes Standard wage rate Rs.5 per hour Actual wage rate Rs.5.40 per hour Sufficient direct labour time equivalent for producing 28,000 units was utilized but the actual production in the relevant month was only 25,000 units. The company has a normal operating capacity of 15,000 hours per month and flexible overhead budgets are: Hours of operation 12,500 14,000 15,000 Variable production overhead Rs. 1,50,000 Rs. 1,68,000 Rs. 1,80,000 Fixed production overhead Rs. 2,70,000 Rs. 2,70,000 Rs. 2,70,000 Actual fixed overheads incurred did not deviate from the budgeted amount. However, the variable overheads incurred amounted to Rs. 1,60,000 in the concerned month. 1. You are required to calculate the appropriate variances material, labour and overhead. 2. Show the variances in a statement suitable for presentation to management, reconciling the standard cost with the actual cost of production. Solution: Part 1: Analyzing volume (Output) and hours Particulars Output (units) Hours

Budgeted 30,000 (WN-1) 15,000

Standard 28,000 12,500 (WN-2)

Actual 25,000 14,000 (WN-3)

Working Note 1: Calculation of budgeted output Input 30 Minutes 15,000 Hours

Output 1 Unit 15,000 x 2 = 30,000 Units

Working Note 2: Calculation of Standard hours Input 30 Minutes 25,000 x 30 = 12,500 Hours

Output 1 Unit 25,000 Units

Working Note 3: Calculation of Actual Hours Input 30 Minutes

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Output 1 Unit

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AMA-Notes 28,000 x 30 = 14,000 Hours

28,000 Units

Part 1: Material Variances Step 1: Computation table [1] SQ x SP 75,000 Kg x Rs.4.4 Rs. 3,30,000

[2] AQ x AP 80,000 Kg x Rs.4.2 Rs. 3,36,000

[3] AQ x SP 80,000 Kg x Rs.4.4 Rs. 3,52,000

Step 2: Variance Calculation

Material Cost Variance (1-2) = 3,30,000 – 3,36,000 = 6,000 (Adverse) Material Price Variance (3-2) = 3,52,000 – 3,36,000 = 16,000 (Favourable)

Material Usage Variance (1-3) = 3,30,000 – 3,52,000 = 22,000 (Adverse)

Working Note: Calculation of Standard quantity for actual output (SQ) Input 3 Kgs 25,000 x 3 Kgs = 75,000 Kgs

Output 1 Unit 25,000 Units

Part 2: Labour Cost Variances Step 1: Computation Table [1] SH x SR 12,500 x Rs.5 Rs. 62,500

[2] AH x AR 14,000 x Rs.5.4 Rs. 75,600

[3] AH x SR 14,000 x Rs.5 Rs. 70,000

Step 2: Variance Calculation

Labour Rate Variance (3-2) = 70,000 75,600 = 5,600 (Adverse)

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Labour Cost Variance (1-2) = 62,500 – 75,600 = 13,100 (Adverse)

Labour Efficiency Variance (1-3) = 62,500 – 70,000 = 7,500 (Adverse)

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AMA-Notes Part 3: Variable Overhead Variances Step 1: Computation of Standard rates (SR) =

BVO

Standard Rate/Hour =

BVO

Standard Rate/Unit

BO

BO

=

1,80,000

=

1,80,000

= Rs.6 per unit

30,000

= Rs.12 per hour

15,000

Step 2: Computation table [1] SH x SR or AO x SR 12,500 Hours x Rs.12 or 25,000 Units x Rs.6 Rs. 1,50,000

[2] AVO Rs. 1,60,000

[3] AH x SR or SO x SR 28,000 Hours x Rs.6 or 14,000 Units x Rs.12 Rs. 1,68,200

Rs. 1,60,000

Step 3: Variance Calculation

Variable Overhead Cost Variance (1-2) = 1,50,000 – 1,60,000 = 10,000 (Adverse)

Variable overhead expenditure Variance (3-2) = 1,68,000 – 1,60,000 = 8,000 (Favourable)

Variable overhead Efficiency Variance (1-3) = 1,50,000 – 1,68,000 = 18,000 (Adverse)

Part 4: Fixed Overhead Variances Step 1: Computation of Standard Rates (SR) Standard Rate per unit =

BFO BO

Standard Rate per hour =

=

BFO BH

2,70,000

=

30,000

= Rs.9 per unit

2,70,000 15,000

= Rs.18 per hour

Step 2: Computation table [1] SH x SR or AO x SR 12,500 Hours x Rs.18 or 25,000 Units x Rs.9 Rs. 2,25,000

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[2] AFO Rs. 2,70,000

[3] BFO [BO x SR or BH x SR] Rs. 2,70,000

Rs. 2,70,000

Rs. 2,70,000

[4] AH x SR or SO x SR 14,000 Hours x Rs.18 or 28,000 Units x Rs.9 Rs. 2,52,000

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AMA-Notes Step 3: Variance Calculation Fixed Overhead Cost Variance (1-2) = 2,25,000 – 2,70,000 = 45,000 (Adverse)

Fixed overhead Volume Variance (1-3) = 2,25,000 – 2,70,000 = 45,000 (Adverse)

Fixed overhead expenditure Variance (3-2) = 2,70,000 – 2,70,000 = 0

Fixed overhead Capacity Variance (4-3) = 2,52,000 – 2,70,000 = 18,000 (Adverse)

Fixed overhead efficiency Variance (1-4) = 2,25,000 – 2,52,000 = 27,000 (Adverse)

Part 5: Computation of Standard Cost and Actual Cost Step 1: Standard Cost per unit Particulars Direct Materials Direct Labour Variable Overhead Fixed Overhead Total

Computation 3 Kg x Rs.4.4 ½ Hour x 5

Amount per Unit (Rs.) 13.20 2.50 6 9 30.70

Step 2: Computation of Standard Cost (Standard Cost for actual output) Actual Output = 25,000 Units Standard Cost per unit = Rs.30.70 Standard Cost = 25,000 Units x Rs.30.70 = Rs. 7,67,500 Alternatively, standard cost is the total of column 1 in all the variances table. Particulars Amount (Rs.) Direct Materials 3,30,000 Direct Labour 62,500 Variable Overhead 1,50,000 Fixed Overhead 2,25,000 Total 7,67,500 Step 3: Computation of actual cost Actual cost is column 2 total in all variances tables. Particulars Amount (Rs.) Direct Materials 3,36,000 Direct Labour 75,600

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AMA-Notes Variable Overhead Fixed Overhead Total

1,60,000 2,70,000 8,41,600

Notes: 1) There are 3 types of costs: i. Budgeted Cost – 30,000 Units x Rs.30.70 = Rs. 9,21,000 ii. Standard Cost – 25,000 Units x Rs.30.70 = Rs. 7,67,500 iii. Actual Cost – Rs.8,41,600 2) We should not compare the target cost for 30,000 units (Budgeted Cost) i.e. Rs.9,21,000 with actual cost spent for 25,000 units i.e. Rs.8,41,600. The right way is to compare the revised target of Rs.7,67,500 (Standard Cost) with actual cost. Part 6: Reconciliation Statement between standard cost and actual cost Particulars Standard Cost Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Fixed overhead capacity variance Fixed overhead efficiency variance Total Actual Cost

Favorable (Rs.) Adverse (Rs.) 16,000 8,000 24,000 24,000

22,000 5,600 7,500 18,000 18,000 27,000 98,100

Amount (Rs.) 7,67,500

74,100 (Adverse) 8,41,600

5.5. Marginal Costing vs. Absorption Costing

1) Profit = Sales – Expired Cost 2) Cost can be classified into two types: i. Product Cost – Are those costs considered for stock valuation i. Cost of goods sold - Expires ii. Stock - Unexpired ii. Period Cost – Are those cost not considered for stock valuation – Expires fully

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AMA-Notes

Cost

Non-Manufacturing (Administration and selling)

Manuafacturing

Material

Labour

Overheads

Always period cost

`

Always Product Cost

Variable

Product cost under absorption costing system

Fixed

Period cost under marginal costing system

3) 4) Thus Marginal Costing system values stock at Variable Manufacturing Cost (VMC) and Absorption costing system values stock at Full Manufacturing Cost (FMC). 5) Hence, in absorption costing we should unitize fixed manufacturing overheads which is done at standard rate (also called pre-determined rate or budgeted rate). BFO

6) Standard rate = BO where the budgeted output is normal capacity and in the absence of information 100% capacity can be considered as normal. 7) Fixed Manufacturing Overheads are charged to the Cost of Production at standard rate for actual output produced. This is called absorbed overheads. 8) At the end of year what is actually spent and what is absorbed may be different. This difference is called under/over absorption which needs to be adjusted while calculating absorption costing profit. 9) If the question silent is regarding the actual fixed cost assumed to be same as budgeted fixed cost. 10) Income statement under Absorption Costing: A Sales XXX B Cost of Goods Sold: Opening Stock of Finished Goods (FMC) XXX Add: Cost of Production XXX Less: Closing stock of Finished Goods (FMC) (XXX) (XXX) C Gross Profit (A – B) XXX D Administration and Selling Expenses (XXX) E Under absorption (XXX) F Over absorption XXX G Profit XXX

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AMA-Notes 11) Income statement under Marginal Costing: A Sales B Variable Cost of Goods Sold: Opening Stock of Finished Goods (VMC) Add: Variable Cost of Production Less: Closing stock of Finished Goods (VMC) C Gross Contribution (A – B) D Variable Administration and Selling Expenses E Contribution (C – D) F Fixed Manufacturing/Administration/Selling Expenses G Profit (E – F)

XXX XXX XXX (XXX) (XXX) XXX (XXX) XXX XXX XXX

Question no 10: From the following data compute the profit under (a) Marginal Costing, and (b) Absorption costing and reconcile the difference in profit. Particulars Rs. Per unit Selling Price 8 Variable Cost 4 Fixed Cost 2 Normal volume of production is 26,000 units per quarter. Both opening and closing stocks consisting of both finished goods and equivalent units of work-inprogress are as follows: Particulars Q1 Q2 Q3 Q4 Total Opening Stock 6,000 2,000 Production 26,000 30,000 24,000 30,000 1,10,000 Sales 26,000 24,000 28,000 32,000 1,10,000 Closing Stock 6,000 2,000 Solution: Part 1: Calculation of profit under marginal costing system A B

C D E F G

Particulars Sales Variable Cost of Goods Sold: Opening Stock of Finished Goods (VMC) Add: Variable Cost of Production Less: Closing stock of Finished Goods (VMC) Variable cost of Goods Sold Gross Contribution (A – B) Variable Administration and Selling Expenses Contribution (C – D) Fixed Manufacturing/Administration/Selling Expenses Profit (E – F)

Q1 (Rs.) 2,08,000

Q2 (Rs.) 1,92,000

Q3 (Rs.) 2,24,000

Q4 (Rs.) 2,56,000

0 1,04,000 0 1,04,000 1,04,000 0 1,04,000 52,000

0 1,20,000 (24,000) 96,000 96,000 0 96,000 52,000

24,000 96,000 (8,000) 1,12,000 1,12,000 0 1,12,000 52,000

8,000 1,20,000 0 1,28,000 1,28,000 0 1,28,000 52,000

52,000

44,000

60,000

76,000

Part 2: Calculation of Profit under absorption costing system Particulars

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Q1 (Rs.)

Q2 (Rs.)

Q3 (Rs.)

Q4 (Rs.)

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AMA-Notes A B

Sales Cost of Goods Sold: Opening Stock of Finished Goods (FMC) Add: Cost of Production Less: Closing stock of Finished Goods (FMC) Cost of Goods Sold C Gross Profit (A – B) D Administration and Selling Expenses E (Under)/Over Absorption F Profit

2,08,000

1,92,000

2,24,000

2,56,000

0 1,56,000 0 1,56,000 52,000 0 0 52,000

0 1,80,000 (36,000) 1,44,000 48,000 0 8000 56,000

36,000 1,44,000 (12,000) 1,68,000 56,000 0 (4000) 54,000

12,000 1,80,000 0 1,92,000 64,000 0 8000 72,000

Working Note 1: Calculation of under/over absorption of fixed overheads A B C

Particulars Actual Fixed Overhead Absorbed Overhead (Actual Output X Standard Rate) (Under)/Over Absorption (B – A)

Q1 (Rs.) 52,000 52,000 (26,000 x 2) 0

Q2 (Rs.) 52,000 60,000 (30,000 x 2) 8000

Q3 (Rs.) 52,000 48,000 (24,000 x 2) (4000)

Q4 (Rs.) 52,000 60,000 (30,000 x 2) 8000

Part 3: Reconciling Marginal Costing and Absorption Costing profit A B C D E F

Particulars Opening Stock (Quantity) Closing Stock (Quantity) Net Stock (B – A) Fixed Cost in net stock (C x Rs.2) Marginal Costing profit Absorption Costing Profit (D + E)

Q1 52,000 52,000

Q2 6,000 6,000 12,000 44,000 56,000

Q3 6,000 2,000 (4,000) (8,000) 60,000 54,000

Q4 2,000 (2,000) (4,000) 76,000 72,000

Notes: 1) Is the difference between the profits under the two systems due to under/over absorption? Answer: No, because it is already adjusted while calculating absorption costing profit. 2) Then why the profit is difference? Answer: It is due to the stock valuation. Marginal costing values stock at variable manufacturing cost and absorption costing at full manufacturing cost. The difference is the fixed inside the net stock (Closing Stock – Opening Stock). i. Net Stock ‘0’ – No change in Stock Position – Both system shows same profit ii. Net Closing Stock – Stock Increases – Absorption costing system shows more profit iii. Net Opening Stock – Stock Decreases – Marginal Costing system shows more profit. 5.6. Sales Variances

Part 1: Total Approach Step 1: Computation table [1] BQ x BP E M Reddy

[2] AQ x AP

[3] AQ x BP Page | 127

AMA-Notes Where BQ = Budgeted Quantity planned to be sold Where AQ = Actual quantity sold Where BP = Budgeted Selling Price Where AP = Actual Selling Price Step 2: Variance Computation

Total Sales Variance (1-2)

Selling Price Variance (3-2)

Sales Volume Variance (1-3)

Part 2: Sales Variance Margin Approach Step 1: Calculation of Margins

Absorption Costing

Marginal Costing

BM = BP – SC AM = AP – SC

BM = BP – SVC AM = AP – SVC

Where SVC = Standard Variable Cost Where SC = Standard Cost Where BP = Budgeted Selling Price Where AP = Actual Selling Price Where BM = Budgeted Margin Where AM = Actual Margin Note: In absorption costing margin should be under stood as profit per unit and in marginal margin should be understood as contribution per unit. Step 2: Computation table [1] BQ x BM

[2] AQ x AM

[3] AQ x BM

Where BQ = Budgeted Quantity planned to be sold Where AQ = Actual quantity sold

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AMA-Notes Where BM = Budgeted Margin Where AM = Actual Margin Step 3: Variance Computation

Total Sales Variance (1-2)

Selling Price Variance (3-2) Example: Budgeted Output Budged Selling price Actual Output Actual Selling Price Standard Cost per unit Standard Cost per unit Standard Cost per unit Standard Cost per unit

Sales Volume Profit Variance (1-3)

= 10,000 Units = Rs.15 per unit = 8,000 Units = Rs.14 per unit = Material: Rs.4 = Labour: Rs.3 = Variable overhead: Rs.2 = Fixed Overhead: Rs.2

Solution: Part 1: Total Sales Approach Step 1: Computation table [1] BQ x BP 10,000 x 15 1,50,000

[2] AQ x AP 8,000 x 14 1,12,000

[3] AQ x BP 8,000 x 15 1,20,000

Step 2: Computation of Variance

Selling Price Variance (3-2) = 1,20,000 – 1,12,000 = 8,000 (Adverse)

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Total Sales Variance (1-2) = 1,50,000 – 1,12,000 = 38,000 (Adverse)

Sales Volume Variance (1-3) = 1,50,000 – 1,20,000 = 30,000 (Adverse)

Page | 129

AMA-Notes Notes: 1) The company targeted to have a sale of Rs.1,50,000 but actually sold only goods worth Rs.1,12,000. Due to sales drop there is an adverse of variance of Rs. 38,000. 2) The sales changes due to two reasons: i. Due to change in selling price – Plant to Sell at Rs.15 but sold only at Rs.14 resulting in adverse price variance of Rs.1 per unit for 8,000 units. ii. Due to change in sales volume – Targeted to sell 10,000 units but sold only 8,000 units. Hence there is a volume drop of 2,000 units at Rs.15 resulting 30,000 adverse volume variance. Part 2: Margin Approach – Absorption Costing System Step 1: Calculation of Margins BM = BP – SC = Rs.15 – (Rs.4 + Rs.3 + Rs.2 + Rs.2) = Rs.15 – Rs.10 = Rs.5 AM = AP – SC = Rs.14 – (Rs.4 + Rs.3 + Rs.2 + Rs.2) = Rs.14 – Rs.10 = Rs.4 Step 2: Computation table [1] BQ x BM 10,000 x 5 50,000

[2] AQ x AM 8,000 x 4 32,000

[3] AQ x BM 8,000 x 5 40,000

Step 3: Variance Computation

Selling Price Variance (3-2) = 40,000 – 32,000 = 8,000 (Adverse)

Total Sales Variance (1-2) = 50,000 – 32,000 = 18,000 (Adverse)

Sales Volume Profit Variance (1-3) = 50,000 – 40,000 = 10,000 (Adverse)

Part 3: Margin Approach – Marginal Costing System Step 1: Calculation of Margins BM = BP – SVC = Rs.15 – (Rs.4 + Rs.3 + Rs.2) = Rs.15 – Rs.8 = Rs.7 AM = AP – SVC = Rs.14 – (Rs.4 + Rs.3 + Rs.2) = Rs.14 – Rs.8 = Rs.6 Step 2: Computation table [1] BQ x BM 10,000 x 7 70,000

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[2] AQ x AM 8,000 x 6 48,000

[3] AQ x BM 8,000 x 7 56,000

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AMA-Notes Step 3: Variance Computation

Selling Price Variance (3-2) = 56,000 – 48,000 = 8,000 (Adverse)

Total Sales Variance (1-2) = 70,000 – 48,000 = 22,000 (Adverse)

Sales Volume Profit Variance (1-3) = 70,000 – 56,000 = 14,000 (Adverse)

Notes: 1) In all the three approaches the selling price variance will be same because the difference in margins is also the difference in price because in budgeted and actual margin the cost is standard. 2) Understanding sales volume variance in all the three approaches: Total Approach

Absorption Costing

Marginal Costing

2000 Units decrease x Rs.15 = Rs. 30,000 (Adverse)

2000 Units decrease x (Rs.15 – Rs.10) = Rs. 10,000 (Adverse)

2000 Units decrease x (Rs.15 – Rs.8) = Rs. 14,000 (Adverse)

a. When volume drops by 2,000 units the sales drop by Rs. 30,000. This is sales volume variance under total sales approach. b. We want to know the impact of volume drop on profit and not on sales. c. When we don’t produce and sell 2,000 units we not only lose Rs.15 selling price but also save Rs.10 cost. Thus the loss in profit per unit is Rs.5 and for 2,000 units is Rs. 10,000. This is sales volume profit variance in absorption costing system. d. When volume drops only variable cost could be saved and hence the cost saved per unit is not Rs.10 but only Rs.8. Hence the profit drop due to volume drop is 2,000 Units x Rs.7 = Rs. 14,000 adverse marginal costing volume variance. 3) Correction made by absorption costing system: a. Since marginal costing does not absorb fixed overheads it has only one variance which is fixed overhead expenditure variance. b. In absorption costing system we also have fixed overhead volume variance. [1] [3] AO x SR BFO (BO x SR) 8,000 Units x Rs.2 10,000 Units x Rs.2 Rs. 16,000 Rs. 20,000 Fixed Overhead Volume Variance = 1 – 3 = 16,000 – 20,000 = Rs. 4,000 (Adverse) c. The volume has dropped by 2,000 Units. Had it been a variable cost we could have saved Rs. 4,000. Because of the cost being fixed this saving didn’t happen but while calculating sales

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AMA-Notes volume profit variance we wrongly considered this saving to happen which is now reversed through fixed overhead volume varices Rs. 4,000 adverse. 4) Cost Volume Variance: a. There are 3 types of costs: Budgeted Cost Standard Cost Actual Cost BO x SC per unit AO x SC per unit AO x AC per unit 10,000 Units x Rs.10 8,000 Units x Rs. 10 Assumed as Rs. 90,000 Rs. 1,00,000 Rs. 80,000 Rs. 90,000 Cost Volume Variance = Rs. 20,000 Cost Variance = Rs. 10,000 b. This cost volume variance is netted off against sales volume variance and reported as sales volume profit variance in the reconciliation statement. Sales Volume Variance (Total Approach) = Rs. 30,000 (Adverse) Less: Cost Volume Variance = Rs. 20,000 (Favorable) Sales Volume Profit Variance = Rs. 10,000 (Adverse) 5.7. Types of Reconciliation Problems

1) 2) 3) 4) 5)

Standard Reconciliation Reconciliation with WIP and Finished Goods Opportunity Cost Method of Reconciliation Reconciliation with Planning Variance and Operating Variance Balance Score Card Method of Reconciliation

5.7.1. Standard Reconciliation Statement

Question no 11: The budgeted production of a company is 20,000 units per month. The standard cost sheet is as under: Direct Material 1.5 Kgs @ Rs.6 per Kg Direct Labour 6 Hours @ Rs.5 per hour Variable Overhead 6 Hours @ Rs.4 per hour Fixed Overhead Rs.3 per unit Selling Price Rs. 72 per unit The following are the actual details for a month: Actual Sales 18,750 Units Actual Production 18,750 Units Direct Material 29,860 Kgs @ Rs.5.25 per Kg Direct Labour 1,18,125 Hours @ Rs.6 per hour Fixed Overhead Rs. 40,000 Variable Overhead Rs. 5,25,000 Required: (i) Calculate all variances (ii) Prepare reconciliation statement from budgeted profit as well as from standard profit. Solution: Part 1: Material Cost Variances E M Reddy

Page | 132

AMA-Notes Step 1: Computation table [1] SQ x SP 28,125 Kg x Rs.6 Rs. 1,68,750

[2] AQ x AP 29,860 Kg x Rs.5.25 Rs. 1,56,765

[3] AQ x SP 29,860 Kg x Rs.6 Rs. 1,79,160

Step 2: Variance Calculation

Material Cost Variance (1-2) = 1,68,750 – 1,56,765 = 11,985 (Favourable) Material Price Variance (3-2) = 1,79,160 – 1,56,765 = 22,395 (Favourable)

Material Usage Variance (1-3) = 1,68,750 – 1,79,160 = 10,410 (Adverse)

Working Note: Calculation of Standard quantity for actual output (SQ) Input 1.5 Kgs 18,750 x 1.5 Kgs = 28,125 Kgs

Output 1 Unit 18,750 Units

Part 2: Labour Cost Variances Step 1: Computation Table [1] SH x SR 1,12,500 x Rs.5 Rs. 5,62,500

[2] AH x AR 1,18,125 x Rs.6 Rs. 7,08,750

[3] AH x SR 1,18,125 x Rs.5 Rs. 5,90,625

Step 2: Variance Calculation

Labour Rate Variance (3-2) = 5,90,625 – 7,08,750 = 1,18,125 (Adverse)

Labour Cost Variance (1-2) = 5,62,500 – 7,08,750 = 1,46,250 (Adverse)

Labour Efficiency Variance (1-3) = 5,62,500 – 5,90,625 = 28,125 (Adverse)

Working Note: Calculation of Standard Hours for actual output (SQ) Input 6 Hours E M Reddy

Output 1 Unit Page | 133

AMA-Notes 18,750 x 6 Hours = 1,12,500 Hours

18,750 Units

Part 3: Variable Overhead Variances Step 1: Computation of Standard rates (SR) Standard Rate/Hour = Rs.4 per Hour (Given) Standard Rate/Unit

= Rs.4 x 6 Hours = Rs.24 per Unit

Step 2: Computation table [1] AO x SR 18,750 Units x Rs.24 Rs. 4,50,000

[2] AVO Rs. 5,25,000 Rs. 5,25,000

[3] AH x SR 1,18,125 Hours x Rs.4 Rs. 4,72,500

Step 3: Variance Calculation

Variable overhead expenditure Variance (3-2) = 4,72,500 – 5,25,000 = 52,500 (Adverse)

Variable Overhead Cost Variance (1-2) = 4,50,000 – 5,25,000 = 75,000 (Adverse)

Variable overhead Efficiency Variance (1-3) = 4,50,000 – 4,72,500 = 22,500 (Adverse)

Part 4: Fixed Overhead Variances Step 1: Computation of Standard Rates (SR) Standard Rate/Unit

= Rs.3 per Unit (Given)

Standard Rate/Hour = Rs.3/6 Hours = Rs.0.5 per hour Step 2: Computation table [1] AO x SR 18,750 Units x Rs.3

[2] AFO Rs. 40,000

Rs. 56,250

Rs. 40,000

[3] BFO [BO x SR] 20,000 Units x Rs.3 Rs. 60,000

[4] AH x SR 1,18,125 Hours x Rs.0.5 Rs. 59,062.5

Step 3: Variance Calculation

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AMA-Notes Fixed Overhead Cost Variance (1-2) = 56,250 – 40,000 = 16,250 (Favourable)

Fixed overhead expenditure Variance (3-2) = 60,000 – 40,000 = 20,000 (Favourable)

Fixed overhead Volume Variance (1-3) = 56,250 – 60,000 = 3,750 (Adverse)

Fixed overhead Capacity Variance (4-3) = 59,062.5 – 60,000 = 937.5 (Adverse)

Fixed overhead efficiency Variance (1-4) = 56,250 – 59,062.5 = 2,812.5 (Adverse)

Part 5: Sales Variances Step A: Total Approach Step 1: Computation table [1] BQ x BP 20,000 x 72 14,40,000

[2] AQ x AP 18,750 x 72 13,50,000

[3] AQ x BP 18,750 x 72 13,50,000

Step 2: Computation of Variance

Total Sales Variance (1-2) = 14,40,000 – 13,50,000 = 9,000 (Adverse)

Selling Price Variance (3-2) = 13,50,000 – 1,12,000 = 0

Sales Volume Variance (1-3) = 14,40,000 – 1,12,000 = 90,000 (Adverse)

Step B: Margin approach – Absorption Costing System Step 1: Calculation of Margins Standard Cost per unit: Material (1.5 Kg x Rs.6) Labour (6 Hours x Rs.5) Variable Overhead (6 Hours x Rs.4) Fixed Overhead Standard Cost per unit

= Rs.9 = Rs.30 = Rs.24 = Rs.3 = Rs.66

BM = BP – SC = Rs.72 – Rs.66 = Rs.6 AM = AP – SC = Rs.72 – Rs.66 = Rs.6 E M Reddy

Page | 135

AMA-Notes Step 2: Computation table [1] BQ x BM 20,000 x 6 1,20,000

[2] AQ x AM 18,750 x 6 1,12,500

[3] AQ x BM 18,750 x 6 1,12,500

Step 3: Variance Computation Total Sales Variance (1 – 2) = 1,20,000 – 1,12,500 = 7,500 (Adverse) Sales Price Variance (3 – 2) = 1,12,500 – 1,12,500 = 0 Sales Volume Profit Variance (1 – 3) = 1,20,000 – 1,12,500 = 7,500 (Adverse) Step C: Margin approach – Margin Costing System Step 1: Calculation of Margins Standard Variable Cost per unit: Material (1.5 Kg x Rs.6) Labour (6 Hours x Rs.5) Variable Overhead (6 Hours x Rs.4) Standard Cost per unit

= Rs.9 = Rs.30 = Rs.24 = Rs.63

BM = BP – SVC = Rs.72 – 63 = Rs.9 AM = AP – SVC = Rs.72 – 63 = Rs.9 Step 2: Computation table [1] BQ x BM 20,000 x 9 1,80,000

[2] AQ x AM 18,750 x 9 1,68,750

[3] AQ x BM 18,750 x 9 1,68,750

Step 3: Variance Computation

Total Sales Variance (1-2) = 1,80,000 – 1,68,750 = 11,250 (Adverse)

Selling Price Variance (3-2) = 1,68,750 – 1,68,750 = 0

Sales Volume Profit Variance (1-3) = 1,80,000 – 1,68,750 = 11,250 (Adverse)

Part 6: Budgeted profit and actual profit Step 1: Computation of Budgeted profit

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AMA-Notes Budgeted Units Budgeted Profit per unit Budgeted Profit

= 20,000 Units = Rs.6 = Rs. 1,20,000

Step 2: Computation of Actual profit Particulars Sales Less: Materials Less: Labour Less: Variable overhead Less: Fixed overhead Actual loss

Computation 18,750 Units x Rs.72 29,860 Kgs x Rs.5.25 1,18,125 Hours x Rs.6

Amount (Rs.) 13,50,000 1,56,765 7,08,750 5,25,000 40,000 80,515

Part 7: Reconciliation between budgeted profit and actual profit – Absorption Costing System Particulars Budgeted profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Fixed overhead capacity variance Fixed overhead efficiency variance Sales volume profit variance Total Actual Loss

Favorable (Rs.)

Adverse (Rs.)

22,395 20,000 42,395

10,410 1,18,125 28,125 52,500 22,500 937.5 2812.5 7,500 2,42,910

Amount (Rs.) 1,20,000

2,00,515 (Adverse) 80,515

Part 8: Reconciliation between budgeted profit and actual profit – Marginal Costing System Particulars Budgeted profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Sales volume profit variance Total Actual Loss

Favorable (Rs.)

Adverse (Rs.)

22,395 20,000 42,395

10,410 1,18,125 28,125 52,500 22,500 11,250 2,42,910

Amount (Rs.) 1,20,000

2,00,515 (Adverse) 80,515

Notes:

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AMA-Notes 1) Sales Volume profit variance Marginal Costing System = Sales Volume profit variance Absorption Costing System + Fixed Overhead Volume Variance = Rs.7500 (Adverse) + Rs. 3,750 (Adverse) = Rs. 11,250 (Adverse). Rs.6

2) Standard Net Profit Ratio = Rs.72 = 8.33% Rs.9

Standard P/V Ratio = Rs.72 = 12.5% Sales Volume Profit Variance – Absorption Costing System = Sales Volume Variance X Net Profit Ratio = Rs. 90,000 (Adverse) x 8.33% = Rs. 7,500 (Adverse) Sales Volume Profit Variance – Margin Costing System = Sales Volume Variance X P/V Ratio = Rs. 90,000 (Adverse) x 12.5% = Rs. 11,250 (Adverse) 5.8. Concept of Standard Profit

1) There are 3 types of Profits: a) Budgeted Profit – Budgeted profit for Budgeted output b) Standard Profit – Budgeted profit for Actual output (Everything is budgeted except for volume) (Flexible Budgeted profit) c) Actual Profit – Actually earned 2) All these 3 profits under Absorption Costing System:

Budgeted Profit

Standard Profit

Actual Profit

20,000 Units x Rs.6 = Rs.1,20,000 (Profit)

18,750 Units x Rs.6 = Rs.1,12,500 (Profit)

Rs.80,515 (Loss)

Sales Volume Profit Variance = Rs.7,500 (Adverse) 3) The three profits in Marginal Costing System:

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AMA-Notes

Budgeted Profit

Standard Profit

Actual Profit

Budgeted Contribution – Budgeted Fixed overheads

Standard Contribution – Budgeted Fixed overheads

Rs.80,515 (Loss)

20,000 Units x Rs.9 Rs.60,000 = Rs.1,20,00 (Profit)

18,750 Units x Rs.9 Rs.60,000 = Rs.1,08,750 (Profit)

Sales Volume Profit Variance = Rs.11,250 (Adverse) 4) Reconciliation between budgeted profit and actual profit – Absorption Costing System: Particulars Budgeted Profit Sales volume profit variance Standard Profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Fixed overhead capacity variance Fixed overhead efficiency variance Total Actual Loss

Favorable (Rs.)

Adverse (Rs.)

-

7,500

22,395 20,000 42,395

10,410 1,18,125 28,125 52,500 22,500 937.5 2812.5 2,35,410

Amount (Rs.) 1,20,000 7,500 (Adverse) 1,12,500

1,93,015 (Adverse) 80,515

5) Reconciliation between budgeted profit and actual profit – Marginal Costing System Particulars Budgeted profit Sales volume profit variance Standard Profit Material Price Variance Material Usage Variance Labour Rate Variance

E M Reddy

Favorable (Rs.)

Adverse (Rs.)

-

11,250

22,395 -

10,410 1,18,125

Amount (Rs.) 1,20,000 11,250 (Adverse) 1,08,750

Page | 139

AMA-Notes Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Total Actual Loss 6) An overview of the various numbers: Items Budget (20,000 Units) (Rs.) Materials 1,80,000 Labour 6,00,000 Variable Overhead 4,80,000 Fixed Overhead 60,000 Total Cost 13,20,000 Sales 14,40,000 Profit 1,20,000

20,000 42,395

Standard (18,750 Units) (Rs.) 1,68,750 5,62,500 4,50,000 56,250 12,37,500 13,50,000 1,12,500

28,125 52,500 22,500 2,31,660

1,89,265 (Adverse) 80,515

Actual (18,750 Units) (Rs.) 1,56,765 7,08,750 5,25,000 40,000 14,30,515 13,50,000 (80,515)

7) Cost Volume Variance = Rs. 13,20,000 – Rs. 12,37,500 = Rs. 82,500 (Favorable) Sales Volume Variance (Total Approach) = Rs.14,40,000 – Rs. 13,50,000 = Rs. 90,000 (Adverse) Sales Volume Profit Variance = Rs. 90,000 (Adverse) – Rs. 82,500 (Favorable) = Rs. 7,500 (Adverse) 8) By adjusting sales volume profit variance to budgeted profit we arrive at standard profit. The standard profit should be adjusted for cost variances and selling price variance to arrive at actual profit or loss. 5.9. Reconciliation with Work in Progress

Question no 12: The following particulars being a standard for a product set as under: Particulars Qty. or Hrs. per unit Rate in Rs. Amount per Unit Direct Material A 2 Kgs 3 6 B 1 Kg 4 4 Direct Wages 5 Hours 4 20 Variable Overheads 5 Hours 1 5 Fixed Overheads 5 Hours 2 10 Total 45 Standard Profit 5 Standard Selling Price 50 Budgeted output is 8,000 units per month. June 2008, the company produced and sold 6,000 Units. Other actual data are as follows: Particulars Rs. Sales Value 3,05,000 Material A 14,850 Kgs 43,065 Material A 7,260 Kgs 29,750 Direct Wages 32,000 Hours 1,27,500 Variable Overhead 30,000 Fixed Overhead 80,600

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AMA-Notes Closing working in progress was 600 units in respect of which material A and B were fully issued and labour and overhead were 50% complete. The direct labour hours worked was 31,800. Analyze the variances and present reconciliation statement in all possible ways. Solution: Analyzing question: 1) Cost Variances are related to production and sales variances are related to units sold. 2) When we mean units produced, it included both completed production and work in progress. 3) But units completed and WIP cannot be added. WIP has to be converted into equivalent units produced and then added to other completed units. Part 1: Calculation of equivalent completed units Particulars Completed Units Closing Work in progress Total

Material 6,000 600 6,600

Labour 6,000 300 6,300

Overhead 6,000 300 6,300

For calculating sales variance, the actual output is 6,000 Units, for Material Variance the actual output is 6,600 units and for labour and overhead variances the actual output is 6,300 Units. Part 2: Material Variances Step 1: Computation table

A B Total

[1] SQ x SP 13,200 x 3 6,600 x 4 66,000

[2] AQ x AP 43,065 29,750 72,815

[3] AQ x SP 14,850 x 3 7,260 x 4 73,590

[4] RAQ x SP 14,740 x 3 7,370 x 4 73,700

Step 2: Variance Calculations Material Cost Variance (1-2) = 66,000 – 72,815 = 6,815 (Adverse) Material Price Variance (3-2) = 73,590 – 72,815 = 775 (Favourable)

Material Usage Variance (1-3) = 66,000 – 73,590 = 7,590 (Adverse) Material Mix Variance (4-3) = 73,700 – 73,590 = 110 (Favourable)

E M Reddy

Material Yield Variance (1-4) = 66,000 – 73,700 = 7,700 (Adverse)

Page | 141

AMA-Notes Working Note 1: Computation of SQ (Standard Quantity of Raw Material for actual Output) Input 3 Kgs 6,600 Units x 3 Kgs = 19,800 Kgs

Output 1 Unit 6,600 Units

Material A = 19,800 Kgs x 2/3 = 13,200 Kgs Material B = 19,800 Kgs x 1/3 = 6,600 Kgs Working Note 2: Computation of RAQ Actual Quantity = 14,850 Kgs + 7,260 Kgs = 22,110 Kgs Material A = 22,110 Kgs x 2/3 = 14,740 Kgs Material B = 22,110 Kgs x 1/3 = 7,370 Kgs Part 3: Labour Variances Step 1: Computation table [1] SH x SR 31,500 x 4 1,26,000

[2] AH x AR 1,27,500 1,27,500

[3] AH x SR 32,000 x 4 1,28,000

Working Note 1: Calculation of SH (Standard Hours for actual Output) Input 5 Hours 6,300 Units x 5 Hours = 31,500 Hours

Output 1 Unit 6,300 Units

Step 2: Variance Calculation

Labour Cost Variance (1-2) = 1,26,000 – 1,27,500 = 1,500 (Adverse) Labour Rate Variance (3-2) = 1,28,000 – 1,27,500 = 500 (Favourable)

Labour Efficiency Variance (1-3) = 1,28,000 – 1,26,000 = 2,000 (Favourable)

Labour idle time Variance = Idle time x Standard Rate = 200 Hours x 4 = 800 (Adverse)

E M Reddy

Labour revised efficiency Variance = 1,200 (Adverse) (WN)

Page | 142

AMA-Notes Working Note: Revised Labour efficiency variance [1] SH x SR 31,500 x 4 1,26,000

[2] AH x AR 1,27,500 1,27,500

[3] AH (W) x SR 31,800 x 4 1,27,200

Labour revised efficiency ratio (1 – 3) = 1,26,000 – 1,27,200 = 1,200 (Adverse) Part 4: Variable Overhead Variances Step 1: Computation of Standard rates (SR) Standard Rate/Hour = Rs.1 per hour Standard Rate/Unit = 5 Hours x Rs.1 = Rs.5 per unit Step 2: Computation table [1] AO x SR 6,300 Units x Rs.5 Rs. 31,500

[2] AVO Rs. 30,000 Rs. 30,000

[3] AH (W) x SR 32,800 Hours x Rs.1 Rs. 31,800

Step 3: Variance Calculation

Variable overhead expenditure Variance (3-2) = 31,800 – 30,000 = 1,800 (Favourable)

Variable Overhead Cost Variance (1-2) = 31,500 – 30,000 = 1,500 (Favourable)

Variable overhead Efficiency Variance (1-3) = 31,500 – 31,800 = 300 (Adverse)

Part 5: Fixed Overhead Variances Step 1: Computation of Standard Rates (SR) Standard Rate/Hour = Rs.2 per hour Standard Rate/Unit = 5 Hours x Rs.2 = Rs.10 per unit Step 2: Computation table [1] AO x SR 6,300 Units x Rs.10 Rs. 63,000

[2] AFO Rs. 80,600 Rs. 80,600

[3] BFO [BO x SR] 8,000 Units x Rs.10 Rs. 80,000

[4] AH x SR 31,800 Hours x Rs.2 Rs. 63,600

Step 3: Variance Calculation

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AMA-Notes Fixed Overhead Cost Variance (1-2) = 63,000 – 80,600 = 17,600 (Adverse)

Fixed overhead Volume Variance (1-3) = 63,000 – 80,000 = 17,000 (Adverse)

Fixed overhead expenditure Variance (3-2) = 80,000 – 80,600 = 600 (Adverse)

Fixed overhead Capacity Variance (4-3) = 63,600 – 80,000 = 16,400 (Adverse)

Fixed overhead efficiency Variance (1-4) = 63,000 – 63,600 = 600 (Adverse)

Part 6: Sales Variances Step 1: Standard net profit ratio and P/V ratio Standard Net Profit Ratio = Standard PV Ratio =

Budgeted Profit per unit Budgeted Selling Price

Budgeted Contibution per unit Budgeted Selling Price

5

x 100 = 50 x 100 = 10%

x 100 =

5+10 50

x 100 = 30%

Step 2: Computation table – Total Approach [1] BQ x BP 8,000 x 50 4,00,000

[2] AQ x AP 3,05,000 3,05,000

[3] AQ x BP 6,000 x 50 3,00,000

Step 2: Computation of Variance

Selling Price Variance (3-2) = 3,00,000 – 3,05,000 = 5,000 (Favourable)

Total Sales Variance (1-2) = 4,00,000 – 3,05,000 = 95,000 (Adverse)

Sales Volume Variance (1-3) = 4,00,000 – 3,00,000 = 1,00,000 (Adverse)

Sales Volume profit variance – Absorption Costing = Sales Volume Variance X Standard Net Profit Ratio = Rs. 1,00,000 x 10% = Rs. 10,000 (Adverse) Sales Volume profit variance – Marginal Costing = Sales Volume Variance X Standard PV Ratio = Rs. 1,00,000 x 30% = Rs. 30,000 (Adverse)

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AMA-Notes Part 7: Closing Work in Progress Valuation Particulars

Computation

Material A Material A Labour Variable Overhead Fixed Overhead Total Cost

600 Equivalent Units x 2 Kgs x Rs.3 600 Equivalent Units x 1 Kg x Rs.4 300 Equivalent Units x 5 Hours x Rs.4 300 Equivalent Units x 5 Hours x Rs.1 300 Equivalent Units x 5 Hours x Rs.2

Absorption Costing (Rs.) 3,600 2,400 6,000 1,500

Marginal Costing (Rs.) 3,600 2,400 6,000 1,500

3,000 16,500

13,500

Part 8: Computation of Actual Profit Particulars Sales Less: Materials Less: Labour Less: Variable overhead Less: Fixed overhead Total Cost Less: Closing WIP Cost of Goods Sold Profit

Absorption Costing (Rs.) 3,05,000 72,815 1,27,500 30,000 80,600 3,10,915 16,500 2,94,415 10,585

Marginal Costing (Rs.) 3,05,000 72,815 1,27,500 30,000 80,600 3,10,915 13,500 2,97,415 7,585

Part 9: Reconciliation Statement – Absorption Costing System Particulars Budgeted profit (8,000 Units x Rs.5) Material Price Variance Material Mix Variance Material Yield Variance Labour Rate Variance Labour Idle Time Variance Labour Revised Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Fixed overhead capacity variance Fixed overhead efficiency variance Selling Price variance Selling Volume Profit Variance Total Actual Profit

Favorable (Rs.)

Adverse (Rs.)

775 110 500 1,800 5,000 8,185

7,700 800 1,200 300 600 16,400 600 10,000 37,600

Amount (Rs.) 40,000

29,415 (Adverse) 10,585

Part 10: Reconciliation between budgeted profit and actual profit – Marginal Costing System Particulars Budgeted profit (8,000 Units x Rs.5)

E M Reddy

Favorable (Rs.)

Adverse (Rs.)

Amount (Rs.) 40,000

Page | 145

AMA-Notes Material Price Variance Material Mix Variance Material Yield Variance Labour Rate Variance Labour Idle Time Variance Labour Revised Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Selling Price variance Selling Volume Profit Variance Total Actual Profit

775 110 500 1,800 5,000 8,185

7,700 800 1,200 300 600 30,000 40,600

32,415 (Adverse) 7,585

Notes: 1) When we have idle time for overhead variances AH means Actual Hours Worked because in working hours only production takes place and when production takes place only resources will be consumed. 2) Stock should be valued at Normal Cost (or) Standard Cost. Valuing the stocks at actual cost results in postponement of variance recognition to the next accounting period which is not desirable. 3) In previous problems, we have seen that Sales Volume Profit Variance – Marginal Costing = Sales Volume Profit Variance – Absorption Costing + Fixed Overhead Volume Variance. In this sum the equality is absent. Rs. 30,000 (Adverse) is not equal to ‘Rs. 10,000 (Adverse) + Rs. 17,000 (Adverse)’. 4) The difference is nothing but the difference between the profits under two systems which in turn is due to fixed cost inside net stock. 5) We targeted to produce and sell 8,000 units but produced and sold only 6,000 units. Due to 2,000 Units volume drop the profit lost is 2,000 Units x (Rs.50 – Rs.45) = Rs. 10,000 (Adverse) (Absorption Costing System). However, the real profit loss is 2,000 Units x (Rs.50 – Rs.35) = Rs. 30,000 (Adverse) (Marginal Costing System) because due to 2,000 Units volume drop Rs. 20,000 fixed cost (2,000 Units x Rs.10) could not be saved. 6) This mistake Absorption Costing System rectifies through Fixed Overhead Volume Variance. However, in this case the reversal didn’t happen for 2,000 Units drop but happened only for 1,700 Units (8,000 Units – 6,300 Units) drop. 7) The fixed cost for those 300 Units which is Rs. 3,000 (300 Units x Rs.10) is carried forward to next year. Hence, is not the cost of the current year and will not form part of variance. 5.10.

Opportunity Cost Method of Reconciliation

Question no 13: Blue Ltd manufactures a single product, the standards of which are as follows: Standard per unit (Rs.) (Rs.) Standard Selling Price 268 Less: Standard Cost Material (16 Kgs at Rs.4) 64 Labour (4 Hours at Rs.3) 12 *Overheads (4 Hours at Rs.24) 96 172 Standard Profit 96

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AMA-Notes Total overhead costs are allocated on the basis of budgeted direct labour hours. The following information relates to last month’s activities: Budgeted Actual Production and sales 600 Units 500 Units Direct Labour 2,400 Hours at Rs.3 2,300 Hours at Rs.3 Fixed Overheads Rs. 19,200 Rs. 20,000 Variable Overheads Rs. 38,400 Rs. 40,400 Materials 9,600 Kgs at Rs.4 per Kg 9,600 Kgs at Rs.4 per Kg The actual selling price was identical to the budgeted selling price and there was no opening or closing stocks during the period. You are required to calculate the variances and reconcile the budgeted and actual profit for each of the following methods: a) Traditional Method (Absorption Costing System) b) The opportunity cost method assuming materials are the limiting factor and materials are restricted to 9,600 Kgs for the period. c) The opportunity cost method assuming labour hours are the limiting factor and labour hours are restricted to 2,400 hours for the period. d) The opportunity cost method assuming there no scarce inputs. Solution: A. Traditional Method Reconciliation Part 1: Material Cost Variances Step 1: Computation table [1] SQ x SP 8,000 Kgs x Rs.4 Rs. 32,000

[2] AQ x AP 9,600 Kgs x Rs.4 Rs. 38,400

[3] AQ x SP 9,600 Kgs x Rs.4 Rs. 38,400

Step 2: Variance Calculation

Material Cost Variance (1-2) = 32,000 – 38,400 = 6,400 (Adverse) Material Usage Variance (1-3) = 32,000 – 38,400 = 6,400 (Adverse)

Material Price Variance (3-2) = 38,400 – 38,400 = 0

Working Note: Calculation of Standard quantity for actual output (SQ) Input 16 Kgs 500 Units x 16 Kgs = 8,000 Kgs E M Reddy

Output 1 Unit 500 Units Page | 147

AMA-Notes Part 2: Labour Cost Variances Step 1: Computation Table [1] SH x SR 2,000 x Rs.3 Rs. 6,000

[2] AH x AR 2,300 Hours x Rs.3 Rs. 6,900

[3] AH x SR 2,300 Hours x Rs.3 Rs. 6,900

Step 2: Variance Calculation

Labour Cost Variance (1-2) = 6,000 – 6,900 = 900 (Adverse) Labour Efficiency Variance (1-3 = 6,000 – 6,900 = 900 (Adverse)

Labour Rate Variance (3-2) = 6,900 – 6,900 =0

Working Note: Calculation of Standard Hours for actual output (SQ) Input 4 Hours 500 Units x 4 Hours = 2,000 Hours

Output 1 Unit 500 Units

Part 3: Variable Overhead Variances Step 1: Computation of Standard rates (SR) =

BVO

Standard Rate/Hours =

BVO

Standard Rate/Unit

BO

BH

=

38,400

=

38,400

600

2,400

= Rs.64 per unit. = Rs.16 per hour

Step 2: Computation table [1] AO x SR 500 Units x Rs.64 Rs. 32,000

[2] AVO Rs. 40,400 Rs. 40,400

[3] AH x SR 2,300 Hours x Rs.16 Rs. 36,800

Step 3: Variance Calculation

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AMA-Notes Variable Overhead Cost Variance (1-2) = 32,000 – 40,400 = 8,400 (Adverse)

Variable overhead expenditure Variance (3-2) = 36,800 – 40,400 = 3,600 (Adverse)

Variable overhead Efficiency Variance (1-3) = 32,000 – 36,800 = 4,800 (Adverse)

Part 4: Fixed Overhead Variances Step 1: Computation of Standard Rates (SR) =

BFO

Standard Rate/Hours =

BFO

Standard Rate/Unit

BO

BH

=

19,200

=

19,200

600

2,400

= Rs.32 per unit. = Rs.8 per hour

Step 2: Computation table [1] AO x SR 500 Units x Rs.32 Rs. 16,000

[2] AFO Rs. 20,000 Rs. 20,000

[3] BFO [BO x SR] Rs. 19,200 Rs. 19,200

[4] AH x SR 2,300 Hours x Rs.8 Rs. 18,400

Step 3: Variance Calculation Fixed Overhead Cost Variance (1-2) = 16,000 – 20,000 = 4,000 (Adverse)

Fixed overhead expenditure Variance (3-2) = 19,200 – 20,000 = 800 (Adverse)

Fixed overhead Volume Variance (1-3) = 16,000 – 19,200 = 3,200 (Adverse)

Fixed overhead Capacity Variance (4-3) = 18,400 – 19,200 = 800 (Adverse)

Fixed overhead efficiency Variance (1-4) = 16,000 – 18,400 = 2,400 (Adverse)

Part 5: Sales Variances – Total Approach Step 1: Computation table [1] BQ x BP 600 Units x Rs. 268 Rs. 1,60,800 E M Reddy

[2] AQ x AP 500 Units x Rs. 268 Rs. 1,34,000

[3] AQ x BP 500 Units x Rs. 268 Rs. 1,34,000 Page | 149

AMA-Notes Step 2: Computation of Variance

Total Sales Variance (1-2) = 1,60,800 – 1,34,000 = 26,800 (Adverse)

Selling Price Variance (3-2) = 1,34,000 – 1,34,000 = 0

Sales Volume Variance (1-3) = 1,60,800 – 1,34,000 = 26,800 (Adverse)

Step 3: Calculation of Standard PV Ratio and Net Profit Ratio Standard Net Profit Ratio = Standard PV Ratio =

Standard Profit per unit Budgeted Selling Price

Standard Contibution per unit Budgeted Selling Price

96

x 100 = 268 x 100 = 35.83%

x 100 =

(268−64−12−64) or (96+32) 268

128

x 100 =268x100=47.76%

Step 4: Sales Volume Profit Variance Sales Volume profit variance – Absorption Costing = Sales Volume Variance X Standard Net Profit Ratio = Rs. 26,800 x 35.83% = Rs. 9,600 (Adverse) Sales Volume profit variance – Marginal Costing = Sales Volume Variance X Standard PV Ratio = Rs. 26,800 x 47.76% = Rs. 12,800 (Adverse) Part 6: Reconciliation Statement Step 1: Budgeted profit Budgeted Output Budgeted Profit per unit Budgeted Profit

= 600 Units = Rs.96 = 600 Units x Rs.96 = Rs. 57,600

Step 2: Computation Actual profit Particulars Sales Less: Materials Less: Labour Less: Variable overhead Less: Fixed overhead Actual Profit

Amount (Rs.) 1,34,000 38,400 6,900 40,400 20,000 28,300

Step 3: Reconciliation between budgeted profit and actual profit – Traditional Method (Absorption Costing) Particulars Budgeted profit Material Price Variance E M Reddy

Favorable (Rs.)

Adverse (Rs.)

-

-

Amount (Rs.) 57,600

Page | 150

AMA-Notes Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Fixed overhead capacity variance Fixed overhead efficiency variance Sales Price Variance Sales volume profit variance Total Actual Profit

-

6,400 900 3,600 4,800 800 800 2,400 9,600 29,300

29,300 (Adverse) 28,300

B. Reconciliation Using Opportunity Cost Method – When Raw Material is Limiting Factor Step 1: Contribution per Kg of Raw Material Contribution per unit Kgs of Raw Material Required

= Rs.128 =16 Kgs Rs.128

Contribution per unit of Raw Material = 16 Kgs = Rs.8 per Kg Cost per Kg of Raw Material Wasted = Purchase Cost + Opportunity Cost = Rs.4 + Rs. 8 = Rs.12 Step 2: Material Usage Variance Material Usage Variance

= [SQ x SP] – [AQ x SP] = [500 Units x 16 Kgs x Rs.12] – [9,600 Kgs x Rs.12] = Rs. 96,000 – Rs.1,15,200 = Rs. 19,200 (Adverse)

Step 3: Reconciliation Statement Particulars Budgeted profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Total Actual Profit

Favorable (Rs.)

Adverse (Rs.)

-

19,200 900 3,600 4,800 800 29,300

Amount (Rs.) 57,600

29,300 (Adverse) 28,300

Notes: 1) When Raw Material is a limiting factor a Kg of Raw Material wastes not only results in loss of Rs.4 purchase price, it also results in loss of profit at Rs.8 per kg wasted. 2) Why Raw Material Usage affects the profit? E M Reddy

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AMA-Notes Answer: Since it is a limiting factor, when we waste a Kg we cannot purchase one more Kg and do the production. A Kg wasted results in production drop, sales drop and consequently profit drop. 3) The company targeted to produce and sell 600 Units but produced and sold only 500 Units. Prima facie we may think that the sales volume drop is due to inability of sales department to create demand thus loosing Rs. 12,800 (100 Units x Rs.8) 4) However, in this case the volume drop is not due to inability to sell but due to inability to produce and account of adverse usage of scarce Raw Material. 5) Company should have used 8,000 Kgs for the output but used 9,600 Kgs leading to 1,600 Kgs over usage. This has two impacts: i. Wastage of Purchase Price – 1,600 Kgs x Rs.4 = Rs. 6,400 (Adverse) ii.

Loss of Volume –

1,600 Kgs 16 Kgs

= 100 Units x Rs. 128 = Rs. 12,800 (Adverse)

Total = Rs. 6,400 (Adverse) + Rs. 12,800 (Adverse) = Rs. 19,200 (Adverse) This means, the production manager not only should take responsibility for the usage of Rs. 6,400 but also should take responsibility for the sales volume profit variance of Rs. 12,800 C. Reconciliation Using Opportunity Cost Method – When Labour Hours is Limiting Factor Step 1: Contribution per hour Contribution per unit Number of Hours per unit

= Rs.128 = 4 Hours

Contribution per hour Cost of wasted labour hour

= 4 Hours = Rs.32 = Wage Rate + Opportunity Cost = Rs.3 + Rs.32 = Rs.35

Rs.128

Step 2: Labour Efficiency Variance Labour Efficiency Variance

= [SH x SR] – [AH x SR] = [2,000 Hours x Rs.35] – [2,300 Hours x Rs.35] = Rs. 70,000 – Rs. 80,500 = Rs. 10,500 (Adverse)

Step 3: Labour Idle Capacity Variance The factory plan to work 2,400 Hours but actuary worked for 2,300 hours thus underutilizing a capacity of 100 Hours. For these 100 Hours there is no wage cost but there exists opportunity cost which is Rs. 3,200 (100 Hours x Rs.32). Alternatively, 100 Hours loss is equal to 25 Units ( lost the profit lost is Rs. 3,200 (25 Units x Rs.128).

100 Hours 4 Hours

) loss. When 25 units are

An overview:

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AMA-Notes Labour Variance = 13,700 (Adverse)

Labour Efficiency Variance = 900 (Adverse)

Sales Volume Profit Variance = 12,800 (Adverse) (100 Units x Rs.128)

Due to Inefficiency

Due to Under Utilisation

300 Hours x Rs.75 = 9,600 (Adverse)

25 units x Rs.128 = 3,200 (Adverse)

Conclusion: The efficiency variance of 10,500 (Adverse) is the responsibility of the worker and supervisor and the underutilization of capacity variance of 3,200 (Adverse) is the responsibility of the person who is responsible for the underutilization. For example, if the 100 Hours are lost due to a major machine break down, then maintenance department is responsible. If it is due to strike, HR and Management is responsible and so on…. Step 4: Reconciliation Statement Particulars Budgeted profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Capacity Variance Labour Efficiency Variance Variable overhead expenditure variance Variable overhead efficiency variance Fixed overhead expenditure variance Total Actual Profit

Favorable (Rs.)

Adverse (Rs.)

-

19,200 3200 10,500 3,600 4,800 800 29,300

Amount (Rs.) 57,600

29,300 (Adverse) 28,300

D. Reconciliation using Opportunity Cost Method when there is no scarce input In this case prepare reconciliation statement under Marginal Costing System.

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AMA-Notes 5.11.

Planning Variance vs. Operating Variance

Example: Budgeted Output Actual Output Original Budget Standard Quantity per unit Standard Price Revised Budget Standard quantity per unit (due to change in produce design) Standard price (due to general price level changes) Actual Actual Quantity Actual price paid

10,000 Units 8,000 Units 10 Kgs Rs.4 per Kg 12 Kg Rs.3.5 per Kg 85,000 Kgs Rs.3.75 per Kg

Solution: Part 1: Material Planning Variances Step 1: Computation table [1] SQ x SP 10,000 Units x 10 Kgs x Rs.4 Rs. 4,00,000

[2] AQ x AP 10,000 Units x 12 Kgs x Rs.3.5 Rs. 4,20,000

[3] AQ x SP 10,000 Units x 12 Kgs x Rs.4 Rs. 4,80,000

Step 2: Variance Calculation

Material Cost Variance (1-2) = 4,00,000 – 4,20,000 = 20,000 (Adverse) Material Price Variance (3-2) = 4,80,000 – 4,20,000 = 60,000 (Favourable)

Material Usage Variance (1-3) = 400,000 – 4,80,000 = 80,000 (Adverse)

Part 2: Material Operating Variances Step 1: Computation table [1] SQ x SP 8,000 Units x 12 Kgs x Rs.3.5 Rs. 3,36,000

[2] AQ x AP 85,000 Kgs x Rs.3.75 Rs. 3,18,750

[3] AQ x SP 85,000 Kgs x Rs.3.5 Rs. 2,97,500

Step 2: Variance Calculation

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AMA-Notes Material Cost Variance (1-2) = 3,36,000 – 3,18,750 = 17,250 (Adverse) Material Price Variance (3-2) = 2,97,500 – 3,18,750 = 21,250 (Adverse)

Material Usage Variance (1-3) = 3,36,000 – 2,97,500 = 38,500 (Favourable)

Notes: 1) When the budget is implemented sometimes there may be a change in environment and the budget needs to be revised for proper performance evaluation. 2) We have three sets of data: a. Budget Planning Variance b. Revised Budget Operating Variance c. Actuals 3) Planning variance are generally being uncontrolled and no person can be made responsible for that variance. Operating Variance are controllable and reflects the efficiency or inefficiency in performance. People should be made accountable only for operating variances. 4) In the above example, if you don’t analyses variance into planning and operating it may lead to wrong performance evaluations. 5) For example, the original budget asked Purchase Manger to purchase at Rs.4 per Kg and he actually purchase at Rs.3.75 per Kg. It seems he is efficient but in reality at the time of purchase there was a general price level decrease where everybody was purchasing at Rds.3.5 per Kg. In this background the Purchase Manager is really inefficient. This problem can be overcome by analyzing the variance into planning and operating variance. 6) Planning Variance compares two budgets Original and Revised. The word standard should be understood as Original Budget and actual as Revised Budget. 7) While calculating operating variance understand standard as revised budget and actual as actuals. Question no 14: Tungach Ltd makes and sells a single product. Demand for the product exceeds the expected production capacity of Tungach ltd. The holding of stocks of the finished product is avoided if possible because the physical nature of the produce is such that it deteriorates quickly and stocks may become unsaleable. A standard marginal cost system is in operation. Feedback reporting takes planning and operational variances into consideration. The Mgt accountant has given the following operating statement for period 9: Tungach Ltd. Operating Statement – Period 9 (Rs.) (Rs.) Original budgeted contribution 36,000 Revision Variances: Material usage 9,600 (Adverse) Material Price 3,600 (Favorable)

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AMA-Notes Wage rate 1,600 (Favorable) 4,400 (Adverse) Revised budgeted contribution 31,600 Sales volume variance: Causal factor Extra Capacity 4,740 (Favorable) Productivity drop 987.5 (Adverse) Idle time 592.5 (Adverse) Stock increase 2,370 (Adverse) 790 (Favorable) Revised Standard contribution for sales achieved 32, 390 Other Variances Material usage 900 (Favorable) Material Price 3,120 (Adverse) Labour Efficiency 1,075 (Adverse) Labour Idle time variance 645 (Adverse) Labour rate variance 2,760 (Adverse) 6,700 (Adverse) Actual Contribution 25,690 Other data are available are as follows: (i) The original standard contribution per product unit as determined at period 1 was: Particulars Rs. Rs. Selling Price 30 Less: Direct Material 1.5 Kilos at Rs.8 12 Direct Labour 2 hours at Rs.4.50 9 21 Contribution 9 (a) A permanent change in the product specification was implemented from period 7 onwards. It was estimated that this change would require 20% additional material per product unit. The current efficient price of the material has settled at Rs.7.50 per kilo. (b) Actual direct material used during period 9 was 7,800 Kilos of Rs.7.90 per Kilo. Any residual value is due to operational problems. (c)The original standard wage rate overestimated the degree of trade union pressure during negotiations and was 20 Paisa higher than the rate subsequently agreed. Tungach Ltd made a short-term operational decision to pay the workforce at Rs.4.60 per hour during period 7 to 9 in an attempt to minimize the drop in efficiency likely because of the produce specification change. The management succeeded in extending the production capacity during the period 9 and the total labour hours paid was 9,200 Hours which is included 150 Hours of Idle time. (ii) Budgeted production and sales quantity (period 9) 4,000 Units Actual Sales quantity (period 9) 4,100 Units Actual production quantity (period 9) 4,400 Units (iii) Stock of finished goods are valued at the current efficient standard cost. Required: (a) Prepare detailed figures showing how the material and labour variances in the operating statement have been calculated. (b) Prepare detailed figures showing how the sales volume variance has been calculated for each casual factor shown in the operating statement. Solution: E M Reddy

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AMA-Notes A. Part 1: Material Planning Variances Step 1: Computation table [1] SQ x SP 4,000 Units x 2 Hours x Rs.4.5 Rs. 48,000

[2] AQ x AP 4,000 Units x 2 Hours x Rs.4.6 Rs. 54,000

[3] AQ x SP 4,000 Units x 2 Hours x Rs.4.5 Rs. 57,600

Step 2: Variance Calculation

Total Material Planning Variance (12) = 48,000 – 54,000 = 6,000 (Adverse) Planning Material Price Variance (3-2) = 57,600 – 54,000 = 3,600 (Favourable)

Planning Material Usage Variance (1-3) = 48,000 – 57,600 = 9,600 (Adverse)

Part 2: Material Operating Variances Step 1: Computation table [1] SQ x SP 7,920 Kgs x Rs.7.5 Rs. 59,400

[2] AQ x AP 7,800 Kgs x Rs.7.9 Rs. 61,620

[3] AQ x SP 7,800 Kgs x Rs.7.5 Rs. 58,500

Step 2: Variance Calculation

Material Cost Variance (1-2) = 59,400 – 61,620 = 2,220 (Adverse) Material Price Variance (3-2) = 58,500 – 61,620 = 3,120 (Adverse)

Material Usage Variance (1-3) = 59,400 – 58,500 = 900 (Favourable)

Working Note: Calculation of Standard quantity for actual output (SQ) Input 1.8 Kgs 4,400 Units x 1.8 Kgs = 7,920 Kgs

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Output 1 Unit 4,400 Units

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AMA-Notes Part 3: Labour Planning Variances Step 1: Computation table [1] SH x SR 4,000 Units x 2 Hours x Rs.4.5 Rs. 36,000

[2] AH x AR 4,000 Units x 2 Hours x Rs.4.3 Rs. 34,400

[3] AH x SR 4,000 Units x 2 Hours x Rs.4.5 Rs. 36,000

Step 2: Variance Calculation

Labour Planning Variance (1-2) = 36,000 – 34,400 = 1,600 (Favourable) Labour Planning Rate Variance (3-2) = 36,000 – 34,400 = 1,600 (Favourable)

Labour Planning Efficiency Variance (1-3) = 36,000 – 36,000 = 0

Part 4: Labour Operating Variances Step 1: Computation table [1] SH x SR 8,800 Hours x Rs.4.3 Rs. 37,840

[2] AH x AR 9,200 Hours x Rs.4.6 Rs. 42,320

[3] AH x SR 9,200 Hours x Rs.4.3 Rs. 39,560

Step 2: Variance Calculation

Labour Cost Variance (1-2) = 37,840 – 42,320 = 4,480 (Adverse) Labour Rate Variance (3-2) = 39,560 – 42,320 = 2,760 (Adverse)

Labour Efficiency Variance (1-3) = 37,480 – 39,560 = 1,720 (Adverse)

Labour Idle time variance = Idle time x SR = 150 Hours x Rs.4.3 = 645 (Adverse) Labour Revised Efficiency Variance: [1] SH x SR 8,800 Hours x Rs.4.3 Rs. 37,840

E M Reddy

[3] AH (W) x SR 9,050 Hours x Rs.4.3 Rs. 38,915

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AMA-Notes Labour Revised efficiency variance (1-3) = 37,840 – 38,915 = 1,075 (Adverse) Working Note: Calculation of Standard Hours for actual output (SH) Input 2 Hours 4,400 Units x 2 Hours = 8,800 Hours

Output 1 Unit 4,400 Units

B. Part 1: Sales Volume Profit Variance – Margin Approach Step 1: Standard Cost per unit Particulars Computation Materials 1.8 Kgs x Rs.7.5 Labour 2 Hours x Rs.4.3 Standard Cost

Amount (Rs.) 13.50 8.6 22.1

Step 2: Calculation of Margins BM = BP – SC = Rs. 30 – Rs.22.1 = Rs.7.9 AM = AP – SC = Rs. 30 – Rs.22.1 = Rs.7.9 AP = BP, because there is no selling price variance in the sum. Step 3: Computation table [1] [2] BQ x BM AQ x AM 4,000 Units x Rs.7.9 4,100 Units x Rs.7.9 Rs. 31,600 Rs. 32,390

[3] AQ x BM 4,100 Units x Rs.7.9 Rs. 32,390

Step 4: Variance Calculation

Total Sales Variance (1-2) = 31,600 – 32,390 = 790 (Favourable) Sales Volume Variance (1-3) = 31,600 – 32,390 = 790 (Favourable)

Sales Price Variance (3-2) = 32,390 – 32,390 = 0 Part 2: Causal factors of sales volume variance Step 1: Extra Capacity Budgeted Hours

E M Reddy

4,000 Units x 2 Hours = 8,000 Hours

Page | 159

AMA-Notes Actual Hours Extra Capacity Extra Output Capacity Variance

9,200 Hours 9,200 Hours – 8,000 Hours = 1,200 Hours 1,200 Hours/2 Hours = 600 Units 600 Units x Rs.7.9 = Rs. 4,740 (Favorable)

Step 2: Productivity drop Standard Hours Actual Hours Worked Extra hours due to inefficiency Volume Drop Productivity Variance

4,400 Units x 2 Hours = 8,800 Hours 9,200 Hours – 150 Hours = 9,050 Hours 9,050 Hours – 8,800 Hours = 250 Hours 250 Hours/2 = 125 Units 125 Units x Rs.7.9 = Rs.987.5 (Adverse)

Step 3: Idle time variance Hours List Production Lost Idle time variance

150 Hours 150 Hours/2 Hours = 75 Units 75 Units x Rs.7.9 = 595.5 (Adverse)

Step 4: Stock Increase Production Sales Stock Variance

4,400 Units 4,100 Units 300 Units x Rs.7.9 = Rs. 2,370 (Adverse)

Notes: 1) There is a volume increase of 100 Units and since a unit can give Rs.7.9 profit the sales volume variance is Rs.790 (Favourable) (100 Units x Rs.7.9) 2) Understanding the reason for 4,000 Units sales increasing to 4,100 Units: Particulars Units Budgeted Output 4,000 Add: Extra Capacity 600 Less: Idle time (75) Less: Productivity Drop (125) Actual Production 4,400 Less: Increase in stock 300 Actual Sales 4,100 3) When volume drops by 1 Unit, we do not produce and sell 1 unit. Due to not selling 1 unit we lose Rs.30 selling price and by not producing 1 Unit we saved production cost of Rs.22.1, thereby loosing net Rs.7.9. 4) However, in case of stock increase of 300 Units we did not sell those units and hence lost selling price of Rs.30 but we cannot save Rs.22.1 because the units are produced. Then how we consider the Rs.22.1 to be saved in our calculation? Answer: The cost is incurred but deferred to the next year through closing stock. Hence it is considered as savings. 5) The sales department has managed to create an extra demand of 100 units, hence should be rewarded for their performance. E M Reddy

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AMA-Notes 6) Production department has produced 400 units extra out of which 300 units does not have demand. It reflects poor co-ordination between sales and production department. These inventories would involve extra holding cost. 7) Moreover, the production increase was achieved by creating extra capacity for which additional wage cost are involved and it is not due to efficiency, the volume has increased. Hence, no credit should be given to the production manager for the volume increase. Question no 15: Country Preserves produce Jams, marmalade and preserves. All products are produced in a similar fashion; the fruits are low temperature cooks in a vacuum process and then blended with glucose syrup with added citric acid and protein to help setting. Margins are tight and the firm operates a system of standard costing for each batch of jam. The standard cost data for a batch of raspberry jam are: Fruit extract 400 Kg At Rs.0.16 Per Kg Glucose Syrup 700 Kg At Rs.0.10 Per Kg Pectin 99 Kg At Rs.0.332 Per Kg Citric Acid 1 Kg At Rs.2.00 Per Kg Labour 18 Hours At Rs.36.25 Per Hour Standard processing loss 3%. The summer of 2002 proved disastrous for the raspberry crop with a late frost and cool, cloudy conditions at the ripening period, resulting in a low national yield. As a consequence, normal prices in the trade were Rs.0.19 per kg for fruit extract although good buying could achieve some savings. The impact of exchange rates on imports of sugar has caused the price of syrup to increase by 20%. The actual results for the batch were: Fruit extract 428 Kg At Rs.0.18 Per Kg Glucose Syrup 742 Kg At Rs.0.12 Per Kg Pectin 125 Kg At Rs.0.328 Per Kg Citric Acid 1 Kg At Rs.0.95 Per Kg Labour 20 Hours At Rs.30 Per Hour Actual output was 1,164 Kgs of raspberry jam. You are required to: (a) Calculate the ingredients planning variances that are deemed uncontrollable; (b) Calculate the ingredients operating variances that are deemed controllable; (c) Comment on the advantages and disadvantages of variance analysis using planning and operating variance. (d) Calculate the mixture and yield variances. (e) Calculate the total variances for the batch. Solution: Part 1: Material Planning Variances Step 1: Computation table Particulars Fruit extract Glucose Syrup E M Reddy

[1] SQ x SP 400 Kgs x Rs.0.16 700 Kgs x Rs.0.10

[2] AQ x AP 400 Kgs x Rs.0.19 700 Kgs x Rs.0.12

[3] AQ x SP 400 Kgs x Rs.0.16 700 Kgs x Rs.0.10 Page | 161

AMA-Notes Pectin Citric Acid Total

99 Kgs x Rs.0.332 1 Kg x Rs.2 Rs. 168.87

99 Kgs x Rs.0.332 1 Kg x Rs.2 Rs. 194.87

99 Kgs x Rs.0.332 1 Kg x Rs.2 Rs. 168.87

Step 2: Variance Calculation

Material Planning Variance (1-2) = 168.87 – 194.87 = 26 (Adverse) Planning Material Price Variance (3-2) = 168.87 – 194.87 = 26 (Adverse)

Planning Material Usage Variance (1-3) = 168.87 – 168.87 = 0

Planning Material Price for Fruit extract Planning Material Price for Glucose Syrup

= 400 Kgs x Rs.0.03 = Rs.12 (Adverse) = 700 Kgs x Rs.0.02 = Rs. 14 (Adverse)

Part 2: Material Operating Variances Step 1: Computation table Particulars Fruit extract Glucose Syrup Pectin

[1] SQ x SP 400 Kgs x Rs.0.19 700 Kgs x Rs.0.12 99 Kgs x Rs.0.332

[2] AQ x AP 428 Kgs x Rs.0.18 742 Kgs x Rs.0.12 128 Kgs x Rs.0.328

[3] AQ x SP 428 Kgs x Rs.0.19 742 Kgs x Rs.0.12 128 Kgs x Rs.0.332

Citric Acid Total

1 Kg x Rs.2 Rs. 194.87

1 Kg x Rs.0.95 Rs. 208.03

1 Kg x Rs.2 Rs. 213.86

[3] RAQ x SP 432 Kgs x Rs.0.19 756 Kgs x Rs.0.12 106.92 Kgs x Rs.0.332 1.08 Kg x Rs.2 Rs. 210.46

Step 2: Variance Calculation Material Cost Variance (1-2) = 194.87 – 208.03 = 13.16 (Adverse) Material Price Variance (3-2) = 213.86 – 208.03 = 5.83 (Favourable)

Material Usage Variance (1-3) = 194.87 – 213.86 = 18.99 (Adverse) Material Mix Variance (4-3) = 210.46 – 213.86 = 3.40 (Adverse)

E M Reddy

Material Yield Variance (1-4) = 194.87 – 210.46 = 15.59 (Adverse)

Page | 162

AMA-Notes Working Note 1: Calculation of SQ (Standard quantity for actual output) Input 100 Kgs 1,164/97 x 100 = 1,200 Kgs

Output 97 Kgs 1,164 Kgs

Fruit extract = 400 Kgs, Glucose Syrup = 700 Kgs, Pectin = 99 Kgs, Citric Acid = 1 Kg Working Note 2: RAQ (Actual Quantity in Standard Mix) Actual Quantity = 428 + 742 + 125 +1 = 1,296 Kgs (in 400:700:99:1) 1296

Fruit Extract = 1,200 x 400 = 432 Kgs 1296

Glucose Syrup = 1,200 x 700 = 756 Kgs 1296

Pectin

=

Citric Acid

= 1,200 x 1 = 1.08 Kgs

1,200 1296

x 99 = 106.92 Kgs

Part 3: Labour Variances Step 1: Computation table Step 1: Computation table [1] SH x SR 18 Hours x Rs.36.25 Rs. 652.5

[2] AH x AR 20 Hours x Rs.30 Rs. 600

[3] AH x SR 20 Hours x Rs.36.25 Rs. 725

Step 2: Variance Calculation

Labour Cost Variance (1-2) = 652.5 – 600 = 52.5 (Favourable) Labour Rate Variance (3-2) = 725 – 600 = 125 (Favourable) 5.12.

Labour Efficiency Variance (1-3) = 652.5 – 725 = 1,720 (Adverse)

Planning vs. Operating Variance – Market Size and Market Share Variance

**Question no 16: Super computers manufacture and sell three related PC models. The budgeted and actual data for 2008 is as follows: Budgeted for 2008 Selling Price per Variable cost per Contribution Sales Volume in unit Rs. unit Rs. margin per unit units Rs. Rs.

E M Reddy

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AMA-Notes PC 24,000 Portable PC 16,000 Super PC 1,00,000 Actual for 2008 Selling Price per unit Rs.

14,000 10,000 60,000

10,000 6,000 40,000

7,000 1,000 2,000

Variable cost per unit Rs.

Contribution Sales Volume in margin per unit units Rs. Rs. PC 22,000 10,000 12,000 8,250 Portable PC 13,000 8,000 5,000 1,650 Super PC 70,000 50,000 20,000 1,100 Super Computers derived its total unit sales budget for 2008 from the internal management estimate of a 20% market share and an industry sales forecast by computer manufacturers association of 50,000 units. At the end of the year the association reported actual industry sales of 68,750 Units. Required to compute: 1. Market Share Variance 2. Market Size Variance 3. Sales Quantity Variance Solution: Part 1: Calculation of Sales Quantity Variance Particulars PC Portable PC Super PC Total

[1] BQ x BM 7,000 Units x Rs. 10,000 1,000 Units x Rs. 6,000 2,000 Units x Rs. 40,000 Rs. 15,60,00,000

[4] RAQ x BM 7,700 Units x Rs. 10,000 1,100 Units x Rs. 6,000 2,200 Units x Rs. 40,000 Rs. 17,16,00,000

Sales Quantity Variance (1 – 4) = Rs. 15,60,00,000 – Rs. 17,16,00,000 = Rs. 1,56,00,000 (Favorable) Working Note: Calculation of RAQ (Actual Quantity in standard mix) Actual Quantity = 8,250 + 1,650 + 1,100 = 11,000 Units (7:1:2) PC = 7,700 Units Portable PC = 1,100 Units Super PC = 2,200 Units Alternatively, the sales quantity variance can be calculated as follows: Weighted Contribution (or) Average Contribution: Particulars Computation PC Rs. 10,000 x 70% Portable PC Rs. 6,000 x 10% Super PC Rs. 40,000 x 20% Average Weighted Margin

E M Reddy

Budgeted Margin (Rs.) 7,000 600 8,000 15,600

Page | 164

AMA-Notes Budgeted Quantity = 10,000 Units Actual Quantity = 11,000 Units Increase in Quantity = 1,000 Units Sales Quantity Variance = 1,000 Units x Rs. 15,600 = Rs. 1,56,00,000 (Favorable) Part 2: Market Size Variance Budgeted Quantity Revised Budgeted Quantity Increase in Quantity Market Size Variance

50,000 Units x 20% = 10,000 Units 68,750 Units x 20% = 13,750 Units 13,750 Units – 10,000 Units = 3,750 Units 3,750 Units x Rs. 15,600 = Rs. 5,85,00,000 (Favourable)

Alternatively, Market Size variance can be calculated as follows: Market Size Variance = (Budgeted Market Size – Actual Market Size) x Budgeted Market Share X Average Contribution per unit = (50,000 Units – 68,750 Units) x 20% x Rs. 15,600 = Rs, 5,85,00,000 (Favourable) Part 3: Market Share Variance Revised Budgeted Quantity Actual Quantity Decrease in Quantity Market Share Variance

13,750 Units 11,000 Units 13,750 Units – 11,000 Units = 2,750 Units 2,750 Units x Rs. 15,600 = Rs. 4,29,00,000 (Adverse)

Alternatively, Market Share variance can be calculated as follows: Market Share Variance = (Budgeted Market Share – Actual Market Share) x Actual Market Size X Average Contribution per unit = (20% – 16%) x 68,750 Units x Rs. 15,600 = Rs, 4,29,00,000 (Favourable) Working Note: Actual Market Share 11,000 Units

Actual Market Share = 68,750 Units x 100 = 16% Summary: Sales Quantity Variance = Rs. 1,56,00,000 (Favourable) Change in Market Size

Change in Market Size

Market size Variance = Rs. 5,85,00,000 (Favourable)

Market Share Variance = Rs. 4,29,00,000 (Adverse)

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AMA-Notes Notes: 1) The company targeted to sell 10,000 Units but actually sold 11,000 Units. Can we conclude that the sales department has done an efficient job? Answer: No, the sales quantity increase may happen due to reasons i. The overall market base has increased hence the quantity increased – It is Market Size Variance and Uncontrollable – Should not be considered for performance evaluation i.e. it is a planning variance ii. The company penetrated more into the market increasing its market share thereby increasing its sales quantity – Increasing Market Share is indicative of Sales department operational performance. It is operating Variance and hence controllable. 2) In this problem, due to increase in market size the sales should have increased by 3,750 Units had they retained their targeted market share of 20% 3) However, since they could achieve only 16% penetration it could increase the quantity only by 1,000 Units thereby unable to sell possible 2,750 Units. 5.13.

Balance Score Card Method of Reconciliation

Question no 17: ABC ltd manufactures three types of products namely P1, P2 and P3. The production process requires a single input raw material, a single type of direct labour and a single energy input. Overheads are shared by all the three products. Budgeted details of the three products are shown below. Particulars P1 P2 P3 Labour Hours 0.20 0.25 0.40 Material Kg per unit 1.0 1.1 1.3 Kilo watt Hours 0.5 0.6 0.8 Budgeted sales in units 10,000 6,000 2,000 Forecasted price 15 20 40 The committed fixed overheads are expected to cost Rs. 80,000 per period and the unit cost for the input resources are as follows: Labour Rs.20 per hour Material Rs.4 per Kg Energy Rs.6 per kilo watt hour The actual financial results for ABC ltd for the concerned budgeted period are show below: Sales Rs. 3,85,000 Labour Rs. 1,09,452 Material Rs. 96,448 Energy Rs. 61,671 Total Cost Rs. 2,67,571 Contribution Rs. 1,17,429 Committed fixed cost Rs. 84,000 Profit Rs. 33,429 Additional information regarding inputs and outputs during the concerned period are provided to you below: Outputs Inputs Product Quantity Price Cost Quantity Price P1 12,000 16 Labour 5,212 Hours 21 E M Reddy

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AMA-Notes P2 5,500 22 Materials 21,920 Kg 4.4 P3 1,800 40 Energy 10,633 KWH 5.8 With the help of the above information you are required to calculate the standard margin (contribution) and subsequently compute the following variances in order to reconcile budgeted profits with the actual profits. A. Sales-Activity Variance b. Price-Recovery Variance c. Productivity Variance Solution: Part 1: Calculation of Material variances [1] SQ x SP 20,390 Kg x Rs.4 Rs. 81,560

[2] AQ x AP 21,920 Kg x Rs.4.4 Rs. 96,448

[3] AQ x SP 21,920 Kg x Rs.4 Rs. 87,680

Working note: SQ for AO P1 1 Kg x 12,000 Units P2 1.1 Kg x 5,500 Units P3 1.3 Kg x 1,800 Units Total

12,000 Kgs 6,050 Kgs 2,340 Kgs 20,390 Kgs

Material Variances: Material Price Variance (3 – 2) = Rs. 8,768 (Adverse) – Price Recovery Material Usage Variance (1 – 3) = Rs. 6,120 (Adverse) - Productivity Part 2: Calculation of Labour variances [1] SH x SR 4,495 Hours x Rs20 Rs. 89,900

[2] AH x AR 5,212 Hours x Rs.21 Rs. 1,09,452

[3] AH x SR 5,212 Hours x Rs.20 Rs. 1,02,240

Working note: SH for AO P1 0.2 Hours x 12,000 Units P2 0.25 Hours x 5,500 Units P3 0.4 Hours x 1,800 Units Total

2,400 Hours 1,375 Hours 720 Hours 4,495 Hours

Labour Variances: Labour rate variance (3 – 2) = 5,212 (Adverse) – Price recovery Labour efficiency variance (1 – 3) = 14,340 (Adverse) – Productivity

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AMA-Notes Part 3: Energy cost variance (Variable Overhead Variance) [1] SKWH x SR 10,740 KWH x Rs.6 Rs. 64,440

[2] AKWH x AR 10,633 KWH x Rs.5.8 Rs. 61,671

[3] AKWH x SR 10,633 KWH x Rs.6 Rs. 63,798

Working note: SKWH for AO P1 0.5 KWH x 12,000 Units P2 0.6 KWH x 5,500 Units P3 0.8 KWH x 1,800 Units Total

6,000 KWH 3,300 KWH 1,440 KWH 10,740 KWH

Energy Variances: Energy expenditure variance (3 – 2) = 2,127 (Favourable) – Price Recovery Energy efficiency variance (1 – 3) = 642 (Favourable) – Productivity Part 4: Fixed overhead variance – Committed cost Expenditure variance = BFO – AFO = 80,000 – 84,000 = 4,000 (Adverse) – Price Recovery Part 5: Sales Variances under Total Approach Products P1 P2 P3 Total

[1] BQ x BP 10,000 x 15 6,000 x 20 2,000 x 40 3,50,000

[2] AQ x AP 12,000 x 16 5,500 x 22 1,800 x 40 3,85,000

[3] AQ x BP 12,000 x 15 5,500 x 20 1,800 x 40 3,62,000

[4] RAQ x BP 10,723 x 15 6,433 x 20 2,144 x 40 3,75,265

Sales Variances: Selling Price Variance (3 – 2) = 23,000 (Favourable) – Price recovery Sales volume Variance (1 – 3) = 12,000 (Favourable) – Growth component Sales Mix Variance (4 – 3) = 13,265 (Adverse) – Growth Component Sales Quantity Variance (1 – 4) = 25,265 (Favourable) – Growth Component Working Note: Computation of RAQ (Actual Quantity in Standard Mix) Actual Quantity = 12,000 + 5,500 + 1,800 = 19,300 Units P1 = 19,300 Units x 10/18 = 10,723 Units P2 = 19,300 Units x 6/18 = 6,433 Units P3 = 19,300 Units x 2/18 = 2,144 Units Part 6: Material Cost volume variance [1] BQ x SP E M Reddy

[2] SQ x SP Page | 168

AMA-Notes 19,200 Kgs x Rs.4 Rs. 76,800

20,390 Kgs x Rs.4 Rs. 81,560

Working note: SQ for BO P1 1 Kg x 10,000 Units P2 1.1 Kg x 6,000 Units P3 1.3 Kg x 2,000 Units Total

10,000 Kg 6,600 Kg 2,600 Kg 19,200 Kg

Material cost variance due to growth in volume = 4,760 (Adverse) – Growth Component Part 7: Labour cost volume variance [1] BH x SR 4,300 Hours x 20 86,000

[2] SH x SR 4,495 Hours x 20 89,900

Working note: SH for BO P1 0.2 Hours x 10,000 Units P2 0.25 Hours x 6,000 Units P3 0.4 Hours x 2,000 Units Total

2,000 Hours 1,500 Hours 800 Hours 4,300 Hours

Labour cost variance due to growth in volume = 3,900 (Adverse) – Growth Component Part 8: Energy cost volume variance (Variable Overhead Variances) [1] SKWH x SR 10,200 x 6 61,200

[2] SKWH x SR 10,740 x 6 64,440

Working note: SKWH for AO P1 0.5 KWH x 10,000 Units P2 0.6 KWH x 6,000 Units P3 0.8 KWH x 2,000 Units Total

5,000 KWH 3,600 KWH 1,600 KWH 10,200 KWH

Energy cost variance due to growth in volume = 3,240 (Adverse) – Growth Component Part 9: Computation of Budgeted Profit Particulars Budgeted Sales Less: Budgeted Material Cost

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Amount (Rs.) 3,50,000 76,800

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AMA-Notes Budgeted Labour Cost Budgeted Energy Cost Budgeted Committed Cost Budgeted Profit

86,000 61,200 80,000 46,000

Part 10: Reconciliation Statement Items Sales Materials Labour Energy Committed Profit

Budget 3,50,000 76,800 86,000 61,200 80,000 46,000

Growth 12,000 (F) 4,760 (A) 3,900 (A) 3,240 (A) 100 (F)

Price Recovery 23,000 (F) 8,768 (A) 5,212 (A) 2,127 (F) 4,000 (A) 7,147 (F)

Productivity 6,120 (A) 14,340 (A) 642 (F) 19,818 (A)

Actual 3,85,000 96,448 1,09,452 61,671 84,000 33,429

Notes - Balance Score card approach of presenting Reconciliation Statement: 1) A company’s profit can increase or decrease due to following 3 factors: i. Increase in volume results in increase in profits. – This is called “Growth Component”. ii. Increase in Volume alone cannot assure increase in profits. The output prices should be properly recovering the input prices. – This is called “Price Recovery Component”. iii. Increase in volume and efficient recovery of prices need not assure increased profit. It also depends on how the resources are utilized with minimum wastage. – This is called “Productivity Component”. 2) In our Reconciliation Statement we classified all the variances into one of the three categories. i. Growth Component a) Sales Volume Variance b) Material Cost Volume Variance c) Labour Cost Volume Variance d) Variable Overhead Volume variance ii. Price Recovery Component a) Selling Price Variance b) Material Price Variance c) Labour Rate Variance d) Variable Overhead Expenditure Variance e) Fixed Overhead Expenditure Variance iii. Productivity Component a) Material Usage Variance b) Labour Efficiency Variance c) Variable Overhead Efficiency Variance 3) Items Growth Price Recovery Productivity Sales Yes Yes No Material Yes Yes Yes Labour Yes Yes Yes Variable Overhead Yes Yes Yes Fixed Overhead Yes -

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AMA-Notes 5.14.

Miscellaneous Concepts – Standard Costing Ratios

1) There are 3 Standard Costing Ratios:

Volume Ratio (1/3) Capacity Ratio (4/3)

Efficiency Ratio (1/4)

Note: Columns has to be taken from the Fixed Overhead Computation table 2) It is further expanded as follows: SH x SR

SH

AH x SR

AH

i.

Volume Ratio = BH x SR = BH

ii.

Capacity Ratio = BH x SR = BH

iii.

Efficiency Ratio =

SH x SR

AH x SR

=

SH

AH

Question no 18: The budgeted production for July in the finishing department of a pottery manufacturer is 4,500 cups, 4,000 saucers and 6,250 plates. In one standard hour a direct operative is expected to be able to finish either, 30 cups, or 40 saucers, or 25 plates. During period July, 400 direct labour hours were worked and actual production was 4,260 cups, 6,400 Saucers and 3,950 plates. Required: Using the above information calculate for July: (i) Productivity/Efficiency Ratio (ii) Production Volume/Activity Ratio (iii) Capacity utilization Ratio Solution: Step 1: Calculation of Budgeted Hours Particulars Cups Saucers Plates Total Hours

Computation 4,500 Cups / 30 Cups 4,000 Saucers / 40 Saucers 6,250 Plates / 25 Plates

Hours 150 Hours 100 Hours 250 Hours 500 Hours

Step 2: Calculation of Standard Hours Particulars Cups Saucers Plates Total Hours

Computation 4,260 Cups / 30 Cups 6,400 Saucers / 40 Saucers 3,950 Plates / 25 Plates

Hours 142 Hours 160 Hours 158 Hours 460 Hours

Step 3: Actual Hour (Given) = 400 Hours

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AMA-Notes Step 4: Calculation of Production Ratios/Standard Costing Ratios

Volume Ratio (SH/ BH) = 460/500 = 92%

Capacity Ratio (AH/ BH) = 400/500 = 80%

Efficiency Ratio (SH/ AH) = 460/400 = 115%

Notes: 1) The Company Plan to work 500 Hours but actually worked only for 400 Hours producing 460 Hours of Output. 2) In other words, it utilized only 80% of its capacity at 115% efficiency to achieve 92% if the targeted volume. 3) Volume Ratio = Capacity Ration X Efficiency Ratio 4) Volume Ratio also called “Activity Ratio”, Efficiency Ratio also called “Productivity Ratio” and Capacity Raito also called “Capacity Utilization Ratio”. **Question no 19: Following a strategy of production differentiation, West Wood Corporation makes a high-end kitchen range good, KE8. Westwood presents the following data for the years 2008 and 2009. 2008 2009 Units of KE8 produced and sold 40,000 42,000 Selling price Rs. 1,000 Rs. 1,100 Direct Materials (Sq. feet) 1,20,000 1,23,000 Direct materials costs per square feet Rs.100 Rs.110 Manufacturing capacity of KE8 50,000 units 50,000 units Total conversation costs Rs. 100,00,000 Rs. 110,00,000 Conversion costs per unit of capacity Rs.200 Rs.220 Selling and customer-service capacity 300 Customers 290 Customers Total selling and customer-service costs Rs.72,00,000 Rs.72,50,000 Cost per customer of selling and customer – Service Capacity Rs. 24,000 Rs. 25,000 Westwood produces no defective units, but it reduces direct materials usage per unit of KE8 in 2009. Conversion costs in each year depend upon production capacity defined in terms of KE8 units that can be produced. Selling and customer – service costs depend upon the number of customers that the selling and service functions are designed to support. Westwood has 230 customers in 2008 and 250 customers in 2009. Required: 1. Describe briefly key elements that you would include in Westwood's balanced score card. 2. Calculate the growth, price-recovery, and productivity components that explain the change in operating Income from 2008 to 2009.

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AMA-Notes Solution: Part 1: Calculation of Budgeted Profit (2008) and Actual Profit (2009) Items Sales Less: Material Cost Conversion Cost (Labour + Overheads) Selling and Customer Service Cost Profit

Budget (Rs. in ‘000) 40,000

Actual (Rs. in ‘000) 46,200

12,000 10,000 7,200 10,800

13,530 11,000 7,250 14,420

Increase in Profit = Rs. 36,20,000 Part 2: Change in operating income due to growth component Step 1: Sales Volume Variance [1] BQ x BP 40,000 Units x Rs. 1,000 Rs. 4,00,00,000

[3] AQ x BP 42,000 Units x Rs. 1,000 Rs. 4,20,00,000

Sales Volume Variance (1 – 3) = 20,00,000 (Favourable) Step 2: Material Cost Volume Variance [1] BQ x BP 40,000 Units x 3 Sq. feet x Rs.100 Rs. 1,20,00,000

[2] SQ x BP 42,000 Units x 3 Sq. feet x Rs.100 Rs. 1,26,00,000

Material Cost change due to growth in volume = 6,00,000 (Adverse) Note: The change in operating income due to change in volume or growth in business is Rs. 20,00,000 (Favourable) – Rs. 6,00,000 (Adverse) = Rs. 14,00,000 (Favourable). This is nothing but Sales Volume Variance under margin approach (Marginal Costing System) Part 3: Change in operating income due to price recovery component Step 1: Selling Price Variance [2] AQ x AP 42,000 Units Rs. 1,100 Rs. 4,62,00,000

[3] AQ x BP 42,000 Units Rs. 1,000 Rs. 4,20,00,000

Selling Price Variance (3 – 2) = 42,00,000 (Favourable) Step 2: Material Price Variance

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AMA-Notes [2] AQ x AP 1,23,000 Sq. feet x Rs.110 Rs. 1,35,30,000

[3] AQ x SP 1,23,000 Sq. feet x Rs.100 Rs. 1,23,00,000

Material Price Variance (3 – 2) = Rs. 12,30,000 (Adverse) Step 3: Conversion cost expenditure variance [2] AFOH Rs. 1,10,00,000

[3] BFOH Rs. 1,00,00,000

Fixed Overhead Expenditure Variance (3 – 2) = 10,00,000 (Adverse) Step 4: Selling and customer service capacity variance [2] Actual Capacity x AP 290 Customer Capacity x Rs. 25,000 Rs. 72,50,000

[3] Actual Capacity x SP 290 Customer Capacity x Rs. 24,000 Rs. 69,60,000

Customer service Capacity variance (3 – 2) = 2,90,000 (Adverse) Part 4: Change in operating income due to productivity Step 1: Material Usage Variance [1] SQ x SP 42,000 Units x 3 Sq. feet x Rs.100 Rs. 1,26,00,000

[3] AQ x SP 1,23,000 Kgs x Rs.100 Rs. 1,23,00,000

Material Usage Variance (1 – 3) = Rs. 3,00,000 (Favourable) Step 2: Selling and customer service capacity variance [1] Budgeted Capacity x SP 300 Customer Capacity x Rs. 24,000 Rs. 72,00,000

[3] Actual Capacity x SP 290 Customer Capacity x Rs. 24,000 Rs. 69,60,000

Customer service Capacity variance (1 – 3) = 2,40,000 (Favourable) Part 5: Reconciliation Statement Rs. in ‘000 Items Sales Materials

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Budget 40,000 (12,000)

Growth 2,000 (F) 600 (A)

Price Recovery 4,200 (F) 1,230 (A)

Productivity 300 (F)

Actual 46,200 (13530)

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AMA-Notes Conversion Cost Customer Support Cost Profit

(10,000) (7,200) 10,800

1,400 (F)

1,000 (A) 290 (A) 1,680 (F)

240 (F) 540 (F)

(11,000) (7250) 14,420

Notes: 1) Variable costs are Volume driven costs and fixed costs are Capacity driven costs. 2) We can compare two years fixed cost only if they are designed to support the same capacity. 3) Conversion cost incurred in 2008 and 2009, both are to support the same 50,000 Units capacity. Thus the Rs. 10,00,000 extra fixed cost is purely due to expenditure and classified under price recovery component. 4) The 2008 customer service cost Rs. 72,00,000 is incurred to support 300 customer capacity. However, the 2009 cost can support only 290 customer capacity. Hence we cannot compare 2008 and 2009 cost and say expenditure variance is Rs. 50,000 (Adverse) because they are supporting different capacities. 5) The increase in fixed cost of Rs. 50,000 should be analyzed as follows: i. Change due to Capacity – (300 – 290) x Rs. 24,000 = Rs. 2,40,000 (Favourable) – By downsizing excess capacity the management is saving a fixed cost of Rs. 2,40,000 which is due to they are efficient decision making. Hence it is productivity component. ii. Change due to Expenditure – (Rs. 69,60,000 – Rs.72,50,000) = Rs. 2,90,00 (Adverse) – Had they negotiated the expenditure at the same price level of 2008 they should have incurred only Rs. 6,60,000 but they incurred actually Rs. 72,50,000. This extra cost is price recovery component. 5.15.

Partial Plan vs. Single Plan

Partial Plan “WIP & Finished Goods” Stock is valued at “Standard Cost” and “Raw Material” Stock at “Actual Cost” WIP account is debited with Actual Cost All Variances arises from WIP account Both Material Price & Usage Variance are calculated at the time of consumption For Price & Usage variance AQ means Actual Quantity Consumed Variances are calculated at the end of the period Question no 20: Material purchased 10,000 pieces at Rs.1.10 Material consumed 9,500 pieces at Rs.1.10 Actual wages paid 2,475 hours at Rs.3.50 Actual factory expenses incurred Budgeted factory overheads Units produced and sold The standard rates and prices are as under:

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Single Plan All the “three stocks” are valued at “Standard Cost” WIP account is debited with Standard Cost Variances arises from their respective accounts Material price variance calculated at the time of purchase and Usage variance at the time of consumption For Price Variance AQ means Actual Quantity purchased and for usage AQ means Actual Quantity consumed Variance are calculated on real time basis as and when they arise Rs. 11,000 Rs. 10,450 Rs. 8,662.50 Rs. 17,000 Rs. 16,500 900 units @ Rs.60 per unit.

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AMA-Notes Direct Materials Rs.1.00 per piece Standard input 10 pieces per unit Direct Labour rate Rs.3.00 per hour Standard labour requirement 2.5 hours per unit Overheads Rs.6.00 per labour hour Prepare ledger accounts under partial and single plan. Solution: Part 1: Calculation of Cost Variances Step 1: Material Cost Variance [1] SQ x SP 9,000 Pcs x Rs.1 9,000

[2] AQ x AP 9,500 Pcs x Rs.1.1 10,450

[3] AQ x SP 9,500 Pcs x Rs.1 9,500

Material Variances: Material Price Variance (3 – 2) = 950 (Adverse) Material usage variance (1 – 3) = 500 (Adverse) Step 2: Labour cost variances [1] SH x SR 900 x 2.5 Hours x 3 6,750

[2] AH x AR 2,475 Hours x 3.5 8,662.5

[3] AH x SR 2,475 Hours x 3 7,425

Labour Variances: Labour rate variance (3 – 2) = 1,237.5 (Adverse) Labour efficiency variance (1 – 3) = 675 (Adverse) Step 3: Fixed Overhead Variance [1] SH x SR or AO x SR 900 Units x 15 13,500

[2] AFOH 17,000 17,000

[3] BFOH 16,500 16,500

[4] AH x SRs or SO x SR 2,475 x 6 14,850

Fixed Overhead Variances: Fixed Overhead expenditure variance (3 – 2) = 500 (Adverse) Fixed Overhead volume variance (1 – 3) = 3,000 (Adverse) Fixed Overhead capacity variance (4 – 3) = 1,650 (Adverse) Fixed Overhead efficiency variance (1 – 4) = 1,350 (Adverse)

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AMA-Notes Part 2: Ledger accounts under partial plan Raw Material Control Account To Cash 11,000 By WIP By Bal C/d Total 11,000 Total

10,450 550 11,000

WIP Control Account To Raw Material Control a/c To Wages Control a/c To Production OH Control a/c

10,450 8,662.5 17,000

Total

36,112.5

Finished Goods Control Account To WIP 29,250 By Cost of Sales Total 29,250 Total

By MPV a/c By MUV a/c By LRV a/c By LEV a/c By FOEXV a/c By FOVVOLV a/c BY FG a/c Total

29,250 29,250

Wages Control Account To Cash 8,662.5 By WIP Total 8,662.5 Total

8,662.5 8,662.5

POH Control Account To Cash 17,000 By WIP Total 17,000 Total

17,000 17,000

Cost of Sales Account To FG 29,250 By Costing P&L Total 29,250 Total Costing P&L Account To Cost of sales a/c 29,250 By Sales To MPV a/c 950 To MUV a/c 500 To LRV a/c 1,237.5 To LEV a/c 675 To FOEXV a/c 500 To FOVOLV a/c 3,000 To Profit 17,887.5 Total 54,000 Total

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950 500 1,237.5 675 500 3,000 29,250 36,112.5

29,250 29,250 54,000

54,000

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AMA-Notes Notes: 1) In Partial Plan the material price variance is calculated only for consumed units. The units in stock will be valued at actual cost and the price variance inside it will be recognized in the next period when the stock is consumed. Raw Material – 10,000 Pcs purchased at Rs.1.1 i. 9,500 Pcs Consumed – Rs.0.10 price variance for the 9,500 Pcs i.e. Rs.950 (Adverse) is recognized in this year. ii. 500 Pcs in Stock – Valued at Rs.1.10 i.e. actual cost. 500 Pcs x Rs.1.10 = Rs.550. The Price variance of 50 (Adverse) taken to next year. 2) The WIP has been debited with actual cost but WIP & Finished Goods should be valued at standard cost. Hence, the actual cost WIP account should be brought to standard cost by debiting and crediting variances. i. Favourable Variances – Credit the Variance Account and Debit the WIP Account ii. Adverse Variances – Debit the Variance Account and Credit the WIP Account 3) Since the WIP account is brought to standard cost, what goes out of that account to finished goods will also be standard cost and what remains as closing WIP will also be at standard cost. 4) Standard Cost per unit: Material (10 Pcs x Rs.1) = Rs.10 Labour (2.5 Hours x Rs.3) = Rs.7.5 Fixed Overhead (2.5 Hours x Rs.6) = Rs.15 Total Cost = Rs.325 Standard Cost of FG produced = 900 Units x Rs.32.5 = Rs. 29,250 5) In the costing P&L account, we credit actual sales but debit standard cost of sales. Hence, we need to bring the standard cost of sales to actual cost of sales. This can be done by glossing all the variance accounts and transferring into Costing P&L account. Part 3: Preparation of Ledger accounts under single plan A. Calculation of Material Price Variances: [2] AQ (Purchased) x AP 10,000 Pcs x Rs.1.1 11,000

[3] AQ (Purchased) x SP 10,000 Pcs x Rs.1 10,000

Material Price Variance (3 – 2) = 1,000 (Adverse) B. Ledger Accounts Raw Material Control Account To Cash 11,000 By MPV By MUV By WIP By Bal c/d Total 11,000 Total

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1,000 500 9,000 500 11,000

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AMA-Notes WIP Control Account To Raw Material Control a/c To Wages control a/c To Production OH control a/c Total

9,000 6,750 13,500 29,250

Finished Goods Control Account To WIP 29,250 By Cost of Sales Total 29,250 Total Wages Control Account To Cash 8,662.5 By WIP By LRV By LEV Total 8,662.5 Total

BY FG a/c

29,250

Total

29,250

29,250 29,250

6,750 1,237.5 675 8,662.5

POH Control Account To Cash 17,000 By WIP By FOEXP By FOVOLV Total 17,000 Total

13,500 500 3,000 17,000

Cost of Sales Account To FG 29,250 By Costing P&L Total 29,250 Total Costing P&L Account To Cost of sales a/c 29,250 By Sales To MPV a/c 1,000 To MUV a/c 500 To LRV a/c 1,237.5 To LEV a/c 675 To FOEXV a/c 500 To FOVOLV a/c 3,000 To Profit 17,837.5 Total 54,000 Total

29,250 29,250 54,000

54,000

Notes: 1) In Single Plan Material Price Variance is recognized as soon as the purchase is over. Hence, the Rs.0.10 excess payment for entire pieces is booked as variance in this year itself. 2) The Raw Material Stock of 500 Pieces is valued at Standard Price of Rs.1 i.e. Rs.500 (500 Pieces x Rs.1). 3) The Variances are booked on Real time basis. For example, for a job order of 900 Units the bill of materials allows 9,000 Pcs (900 Units x 10 Pcs). In the first instance the stores department issues only 9,000 Pcs. Any additional requisition will be issued by booking the cost to usage variance and not the WIP account.

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AMA-Notes 4) Profit under Single Plan is Rs. 17,837.5 and in Partial Plan it is Rs. 17,887.5. The difference in profit is nothing but the price variance inside the Raw material stock. Question no 21: ST company manufactures ceramic vases. It uses its standard costing system when developing its flexible budget amounts. In April 2007, 4,000 finished units were produced. The following information is related to its two direct manufacturing cost categories: Direct Materials and direct manufacturing labour. Direct Materials used were 8,000 Kilos. The standard direct material input allowed for one output unit is 2 Kilos at Rs.15 per kilo. ST purchased 10,000 Kg of materials at Rs.16.50 per kg at a total cost of Rs. 16,500. Actual direct manufacturing labour hours were 6,500 hours at a total cost of Rs. 1,32,600. Standard manufacturing labour time allowed is 1.5 hours per output unit and the standard direct manufacturing labour cost is Rs.20 per hour. Required: 1. Calculate the direct materials price variance and efficiency variance and the direct manufacturing labour price variance and efficiency variance. Base the direct materials price variance on a flexible budget for actual quantity purchased but base the direct materials efficiency variance on a flexible budget for actual quantity used 2. Prepare journal entries for a standard costing system that isolated variances at the earliest time possible. Solution: Part 1: Calculation of Material Variances Step 1: Material Price Variances Material Price Variance

= [AQ Purchased x SP] – [AQ Purchased x AP] = [10,000 Kgs x Rs.15] – [10,000 Kgs x Rs.16.5] = Rs. 1,50,000 – Rs. 1,65,000 = Rs. 15,000 (Adverse)

Step 2: Material Usage Variance Material Usage Variance

= [SQ x SP] – [AQ Consumed x SP] = [8,000 Kgs x Rs.15] – [8,000 Kgs x Rs.15] = Rs. 1,20,000 – Rs. 1,20,000 =0

Working Note: Calculation of Standard quantity for actual output (SQ) Input 2 Kgs 4,000 Units x 2 Kgs = 8,000 Kgs

Output 1 Unit 4,000 Units

Part 2: Labour Variances Step 1: Computation table E M Reddy

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AMA-Notes [1] SH x SR 6,000 Hours x Rs.20 Rs. 1,20,000

[2] AH x AR Rs. 1,32,600 Rs. 1,32,600

[3] AH x SR 6,500 Hours x Rs.20 Rs. 1,30,000

Step 2: Variance Calculation Labour Rate Variance (3 – 2) = Rs.1,30,000 – Rs.1,32,600 = Rs. 2,600 (Adverse) Labour Efficiency Variance (1 – 3) = Rs. 1,20,000 – Rs. 1,30,000 = Rs. 10,000 (Adverse)

Working Note: Calculation of Standard Hours for actual output (SH) Input 1.5 Hours 4,000 Units x 1.5 Hours = 6,000 Hours

Output 1 Unit 4,000 Units

Part 3: Ledger Accounts Raw Material Control Account To Cash 1,65,000 By MPV 15,000 By WIP 1,20,000 By Bal c/d 30,000 Total 1,65,000 Total 1,65,000 Closing Raw Material = [10,000 Kgs – 8,000 Kgs] x Rs.15 = Rs. 30,000 Wages Control Account To Cash 1,32,6000 By WIP By LRV By LEV Total 1,32,600 Total WIP Control Account To Raw Material Control a/c To Wages control a/c Total

1,20,000 2,600 10,000 1,32,600 1,20,000 1,20,000 2,40,000

BY FG a/c

2,40,000

Total

2,40,000

Amount transferred to FG = 4,000 Units x Rs.60 = Rs.2,40,000 Working Note: Standard Cost per unit Items Material Labour Total

Computation 2 Kgs x Rs.15 1.5 Hours x Rs.20

Amount (Rs.) 30 30 60

Question no 22: X ltd. produces and sells a single product. Standard cost card per unit of the product is as follows:

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AMA-Notes Particulars Rs. Direct Material: A 10 Kgs @ Rs.5 per Kg 50.00 : B 5 Kgs @ Rs.6 per Kg 30.00 Direct wages 5 Hours @ Rs.5 per hour 25.00 Variable production overheads 5 hours @ 12 per hour 60.00 Fixed production overheads 25.00 Total Standard Cost 190.00 Standard gross profit 35.00 Standard selling price 225.00 The fixed production overhead has been absorbed on the expected annual output of 25,200 units produced evenly throughout the year. During the month of December, 2009, the following were for the actual production of 2,000 unit: Particulars Rs. Sales 2,000 Units @ Rs.225 4,50,000 Direct Material: A 18,900 Kg 99,225 : B 10,750 Kg 61,275 Direct wages 10,500 hours (actually worked 10,300 hours) 50,400 Variable production overheads 1,15,000 Fixed production overheads 56,600 Total 3,82,500 Gross profit 67,500 The material price variance is extracted at the time of receipt materials. Material purchases were A: 20,000 Kgs @ Rs. 5.25 per kg; B 11,500 Kgs @ Rs. 5.70 per kg. Required: (i) Calculate all variances. (ii) Prepare an operating statement showing Standard gross profit, Variances Actual gross profit. (iii) Explain the reason for the difference in actual gross profit in the question and calculated in (ii) above. Solution: Notes: 1) Material usage variance is related to consumption. So for its calculation AQ means Actual Quantity consumed always. 2) Regarding price variance, the variance can be recognized as soon as the materials are purchased (Single plan) or only at the time of consumption (Partial plan). 3) In case of single plan, AQ for price variance calculation means AQ purchased. The raw material stock is valued at standard material cost. 4) In case of partial plan, for price variance computation AQ means AQ consumed and raw material stock is valued at actual cost. A. Part 1: Material Variances Step 1: Material Usage Variances Raw Materials E M Reddy

[1]

[3]

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AMA-Notes A B Total

SQ x SP 20,000 Kgs x Rs.5 10,000 Kgs x Rs.6 Rs. 1,60,000

AQ Consumed x SP 18,900 Kgs x Rs.5 10,750 Kgs x Rs.6 Rs. 1,59,000

RAQ x SP 19,766.66 Kgs x Rs.5 9883.33 Kgs x Rs.6 Rs. 1,58,133

Working note 1: Calculation of SQ (Standard quantity for actual output) Input 15 Kgs 2,000 Units x 15 Kgs = 30,000 Kgs

Output 1 Unit 2,000 Units

A = 30,000 Kgs x 10/15 = 20,000 Kgs B = 30,000 Kgs x 5/15 =10,000 Kgs Working note no 2: Calculation of RAQ (Actual Quantity in standard mix) Actual Quantity = 18,900 Kgs + 10,750 Kgs = 29,650 Kgs A = 29,650 Kgs x 10/15 = 19,766.66 Kgs B = 29,650 Kgs x 5/15 =9,883.33 Kgs Material Variances: Material Usage Variance (1 – 3) = Rs.1,60,000 – Rs.1,59,000 = Rs.1,000 (Favourable)

Material Yield Variance (1 – 4) = Rs.1,60,000 – Rs.1,58,133 = Rs.1867 (Favourable)

Material Mix Variance (4 – 3) = Rs.1,58,133 – Rs.1,59,000 = Rs.867 (Adverse)

Step 2: Material Price Variance Raw Materials A B Total

[2] AQ Purchased x AP 20,000 Kgs x Rs.5.25 11,500 Kgs x Rs.5.7 Rs. 1,70,550

[3] AQ Purchased x SP 20,000 Kgs x Rs.5 11,500 Kgs x Rs.6 Rs. 1,69,000

Material Price Variance (3 – 2) = Rs. 1,69,000 – Rs. 1,70,550 = Rs. 1,550 (Adverse) Part 2: Labour Variances Step 1: Computation table [1]

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[2]

[3]

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AMA-Notes SH x SR 10,000 Hours x Rs.5 Rs. 50,000

AH x AR 10,500 Hours x Rs.4.8 Rs. 50,400

AH x SR 10,500 Hours x Rs.5 Rs. 52,500

Working Note: Calculation of SH (Standard Hours for Actual Output) Input 5 Hours 2,000 Units x 5 Hours = 10,000 Hours

Output 1 Unit 2,000 Units

Step 2: Variance Calculation Labour Cost Variance (1 – 2) = Rs. 50,000 – Rs. 50,400 = Rs.400 (Adverse)

Labour Rate Variance (3 – 2) = Rs. 52,500 – Rs. 50,400 = Rs.2,100 (Favourable)

Labour Efficiency Variance (1 – 3) = Rs. 50,000 – Rs. 52,500 = Rs 2,500 (Adverse)

Step 3: Idle time Variance and Revised Labour efficiency variance Idle time Variance = Idle time x Standard Rate = 200 Hours x Rs.5 = Rs.1000 (Adverse) Revised efficiency variance = Rs. 2,500 (Adverse) – Rs. 1,000 (Adverse) = Rs. 1,500 (Adverse) Part 3: Variable Overhead variances Step 1: Standard Rates Standard Rate/Hour = Rs.12 (Given) Standard Rate/Unit = 5 Hours x Rs.12 = Rs.60 Step 2: Computation table [1] AO x SR 2,000 Units x Rs.60 Rs. 1,20,000

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[2] AVO Rs. 1,15,000 Rs. 1,15,000

[3] AH x SR 10,300 Hours x Rs.12 Rs. 1,23,600

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AMA-Notes Step 3: Variance Calculation

Variable Overhead Cost Variance (1-2) = Rs.1,20,000 – Rs.1,15,000 = Rs.5,000 (Favourable) Variable overhead expenditure Variance (3-2) = Rs.1,23,600 – Rs.1,15,000 = Rs.8,600 (Favourable)

Variable overhead Efficiency Variance (13) = Rs.1,20,000 – Rs.1,23,600 = Rs.3,600 (Adverse)

Part 3: Variable Overhead variances Step 1: Standard Rates Standard Rate/Unit = Rs.25 (Given) Rs.25

Standard Rate/Hour = 5 Hours = Rs.5 Step 2: Computation table [1] AO x SR 2,000 Units x Rs.25 Rs. 50,000

[2] AFO Rs. 56,600 Rs. 56,600

[3] BFO 2,100 Units x Rs.25 Rs. 52,500

[4] AH x SR 10,300 Hours x Rs.5 Rs. 51,500

Note: Budgeted output per annum = 25,000 Units Budgeted output per month =

25,000 Units 12 Months

= 2,100 Units

Step 3: Variance Calculation

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AMA-Notes Fixed Overhead Cost Variance (1-2) = Rs.50,000 – Rs.56,600 = Rs.6,600 (Adverse) Fixed overhead expenditure Variance (3-2) = Rs.52,500 – Rs.56,600 = Rs.4,100 (Adverse)

Fixed overhead Volume Variance (1-3) = Rs.50,000 – Rs.52,500 = Rs.2,500 (Adverse)

Fixed overhead Capacity Variance (4-3) = Rs.51,500 – Rs.52,500 = Rs.1,000 (Adverse)

Fixed overhead efficiency Variance (14) = Rs.51,500 – Rs.50,000 = Rs.1,500 (Adverse)

Part 5: Sales Variances – Margin Approach Step 1: Calculation of Margins BM = BP – SC = Rs.225 – Rs.190 = Rs.35 AM = AP – SC = Rs.225 – Rs.190 = Rs.35 Step 2: Computation table [1] BQ x BM 2,100 Units x Rs.35 Rs. 73,500

[2] AQ x AM 2,000 Units x Rs.35 Rs. 70,000

[3] AQ x BM 2,000 Units x Rs.35 Rs. 70,000

Step 3: Variance Computation

Total Sales Variance (1-2) = Rs.73,500 – Rs.70,000 = Rs.3,500 (Adverse)

Selling Price Variance (3-2) = Rs.70,000 – Rs.70,000 = 0

Sales Volume Profit Variance (1-3) = Rs.73,500 – Rs.70,000 = Rs.3,500 (Adverse)

B. Reconciliation Statement – Absorption Costing System

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AMA-Notes Particulars Budgeted profit Sales volume profit variance Standard Profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Idle Time Variance Labour Revised Efficiency Variance Variable Overhead Expenditure Variance Variable Overhead Efficiency Variance Fixed Overhead Expenditure Variance Fixed Overhead Capacity Variance Fixed Overhead Efficiency Variance Total Actual Profit

Favorable (Rs.)

Adverse (Rs.)

1,000 2,100 8,600 11,700

3,500 1,550 1,000 1,500 3,600 4,100 1,000 1,500 14,250

Amount (Rs.) 73,500 (3,500) 70,000

2,550 (Adverse) 67,450

C. Step 1: Actual profit Absorption costing system (Single Plan followed) Sales Material Labour Variable Overhead Fixed Overhead Total Less: Value of Closing Raw Material Profit

Rs. 4,50,000 Rs. 1,70,550 Rs. 50,400 Rs. 1,15,000 Rs. 56,600 Rs. 3,92,550 Rs. 10,000

Rs. 3,82,550 67,450

Valuation of Raw Material Stock using Single Plan: Material A: [20,000 Kgs – 18,900 Kgs] x Rs.5 = 1,100 Kgs x Rs.5 = Rs. 5,500 Material B: [11,000 Kgs – 10,250 Kgs] x Rs.6 = 750 Kgs x Rs.6 = Rs. 4,500 Total Value of Raw Material Stock = Rs. 5,500 + Rs. 4,500 = Rs. 10,000 Step 2: Understanding the difference in profit 1) In the question, the actual profit was calculated using Partial Plan. This can be proved as follows: Sales Material Labour Variable Overhead Fixed Overhead Total Less: Value of Closing Raw Material Profit

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Rs. 4,50,000 Rs. 1,70,550 Rs. 50,400 Rs. 1,15,000 Rs. 56,600 Rs. 3,92,550 Rs. 10,050

Rs. 3,82,500 67,500

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AMA-Notes Valuation of Raw Material Stock using Single Plan: Material A: [20,000 Kgs – 18,900 Kgs] x Rs.5.25 = 1,100 Kgs x Rs.5.25 = Rs. 5,775 Material B: [11,000 Kgs – 10,250 Kgs] x Rs.5.70 = 750 Kgs x Rs.5.70 = Rs. 4,275 Total Value of Raw Material Stock = Rs. 5,775 + Rs. 4,275 = Rs. 10,050 2) We value under Single Plan the stock at Rs. 10,000 but the question has valued under Partial Plan at Rs. 10,050. This difference is the reason for the difference between two profits. 3) To be more elaborate the Rs.50 difference is nothing but the variance inside Raw Material Stock which can be proved as follows: Material A: 1,100 Kgs x [Rs.5 – Rs.5.25] = 1,100 Kgs x Rs.0.25 = Rs.275 (Adverse) Material B: 750 Kgs x [Rs.6 – Rs.5.70] = 750 Kgs x Rs.0.30 = Rs.225 (Favourable) Net Amount = Rs. 275 (Adverse) + Rs.225 (Favourable) = Rs.50 (Adverse) **Question no 23: From the following intonation show how profit had gone up in detail: Particulars 2007 2008 Materials 1,00,000 1,32,000 Labour 60,000 66,000 Variable Overhead 12,000 14,000 Fixed Overhead 20,000 24,000 Total Cost 1,92,000 2,36,000 Profit 8,000 17,000 Sales 2,00,000 2,53,000 During the year 2008, selling price and material price have each gone up by 10% and labour by 10%, when compared to 2007. Solution: Part 1: Sales Variance – Total Approach Step 1: Computation table [1] BQ x BP Rs. 2,00,000

[2] AQ x AP Rs. 2,53,000

[3] AQ x BP Rs. 2,30,000

Working Note: Calculation of “AQ x BP” AP

AP = BP x 110% → BP = 110% AP

AQ x BP = AQ x 110% =

AQ x AP 110%

=

Rs.2,53,000 110%

= Rs. 2,30,000

Step 2: Variance Calculation Total Sales Variance (1 – 2) = Rs. 2,00,000 – Rs. 2,53,000 = Rs. 53,000 (Favourable) Selling Price Variance (3 – 2) = Rs. 2,30,000 – Rs. 2,53,000 = Rs. 23,000 (Favourable) Sales Volume Variance (1 – 3) = Rs. 2,00,000 – Rs. 2,30,000 = Rs. 30,000 (Favourable)

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AMA-Notes Notes: 1) Actual Price = Budgeted Price x 110% (Given in the question) Budgeted Price = Actual Price / 110%. Therefore, AQ x BP = [AQ x AP]/110%. 2) Budgeted Sales [BQ x BP] is Rs. 2,00,000 and Standard Sales [Budgeted Sales for Actual Output – AQ x Rs.30,000

BP] is Rs. 2,30,000. Hence, we can conclude that the volume has increased by Rs.2,00,000 x 100 = 15% Step 3: Sales Volume Profit Variance Standard Net Profit Ratio = Standard P/V Ratio =

Budgeted Profit Budgeted Sales

Budgeted Contribution Budgeted Sales

Rs.8,000

= Rs.2,00,000 x 100 = 4% Rs.28,000

= Rs.2,00,000 x 100 = 14%

Sales Volume Profit Variance – Absorption Costing System = Sales Volume Variance X Net Profit Ratio = Rs. 30,000 (F) x 4% = Rs. 1,200 (F) Sales Volume Profit Variance – Marginal Costing System = Sales Volume Variance X PV Ratio = Rs. 30,000 (F) x 14% = Rs. 4,200 (F) Part 2: Material Cost Variances Step 1: Computation table [1] SQ x SP Rs. 1,00,000 x 115% Rs. 1,15,000

[2] AQ x AP Rs. 1,32,000 Rs. 1,32,000

[3] AQ x SP Rs. 1,20,000 Rs. 1,20,000

Working Note: Calculation of “AQ x SP” AP

AP = SP x 110% → SP = 110% AP

AQ x SP = AQ x 110% =

AQ x AP 110%

=

Rs.1,32,000 110%

= Rs. 1,20,000

Step 2: Variance Calculation Material Cost Variance (1 – 2) = Rs. 1,15,000 – Rs. 1,32,000 = Rs. 17,000 (Adverse) Material Price Variance (3 – 2) = Rs. 1,20,000 – Rs. 1,32,000 = Rs. 12,000 (Adverse) Material Usage Variance (1 – 3) = Rs. 1,15,000 – Rs. 1,20,000 = Rs. 5,000 (Adverse) Part 3: Labour Variances Step 1: Computation table [1] SH x SR Rs. 60,000 x 115%

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[2] AH x AR Rs. 66,000

[3] AH x SR Rs. 1,20,000

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AMA-Notes Rs. 69,000

Rs. 66,000

Rs. 60,000

Working Note: Calculation of “AH x SR” AR

AR = SR x 110% → SR = 110% AR

AH x SR = AH x 110% =

AH x AR 110%

=

Rs.66,000 110%

= Rs. 60,000

Step 2: Variance Calculation Labour Cost Variance (1 – 2) = Rs. 69,000 – Rs. 66,000 = Rs. 3,000 (Favourable) Labour Rate Variance (3 – 2) = Rs. 60,000 – Rs. 66,000 = Rs. 6,000 (Adverse) Labour Efficiency Variance (1 – 3) = Rs. 69,000 – Rs. 60,000 = Rs. 9,000 (Favourable) Part 4: Variable overhead Variances [1] SH x SR or AO x SR Rs. 12,000 x 115% Rs. 13,800

[2] AVO Rs. 14,000 Rs. 14,000

Variable Overhead Cost Variance (1 – 2) = Rs. 13,800 – Rs. 14,000 = Rs. 200 (Adverse) Part 5: Fixed Overhead Variance Step 1: Computation table [1] [2] [3] SH x SR or AO x SR AFO BFO Rs. 20,000 x 115% Rs. 24,000 Rs. 23,000 Rs. 24,000

Rs. 20,000 Rs. 20,000

Step 2: Variance Calculation Fixed Overhead Cost Variance (1 – 2) = Rs. 23,000 – Rs. 24,000 = Rs. 1,000 (Adverse) Fixed Overhead Expenditure Variance (3 – 2) = Rs. 20,000 – Rs. 24,000 = Rs. 4,000 (Adverse) Fixed Overhead Volume Variance (1 – 3) = Rs. 23,000 – Rs. 20,000 = Rs. 3,000 (Favourable) Part 6: Reconciliation Statement – Absorption Costing System Particulars Budgeted profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable Overhead Cost Variance Fixed Overhead Expenditure Variance

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Favorable (Rs.)

Adverse (Rs.)

9,000 -

1,200 5,000 6,000 200 4,000

Amount (Rs.) 8,000

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AMA-Notes Fixed Overhead Volume Variance Selling Price Variance Sales Volume Profit Variance Total Actual Profit

3,000 23,000 1,200 36,200

27,200

9,000 (Favourable) 17,000

Part 7: Reconciliation Statement – Marginal Costing System Particulars Budgeted profit Material Price Variance Material Usage Variance Labour Rate Variance Labour Efficiency Variance Variable Overhead Cost Variance Fixed Overhead Expenditure Variance Fixed Overhead Volume Variance Selling Price Variance Sales Volume Profit Variance Total Actual Profit 5.16.

Favorable (Rs.)

Adverse (Rs.)

9,000 23,000 4,200 36,200

1,200 5,000 6,000 200 4,000 27,200

Amount (Rs.) 8,000

9,000 (Favourable) 17,000

Reverse Working Problems

Question no 24: A company manufactures a food product, data for which for one week have been analyzed as follows: Standard Cost Data (Rs.) Direct Materials: 10 Kgs at Rs.1.50 15 Direct Wages: 5 Hours at Rs.4.00 20 Production Overhead: 5Hours at Rs.5.00 25 Total 60 Profit Margin is 20% of sales price. Budgeted sales are Rs. 30,000 per week. Actual Data (Rs.) Sales 29,880 Direct Materials 6,435 Direct Wages 8,162 Analysis of variances: Adverse (Rs.) Favourable (Rs.) Direct Materials Price 585 Direct Materials Usage 375 Direct Labour Rate 318 Direct Labour Efficiency 180 Production Expenditure 200 Overhead Volume 375 It can be assumed that the production and sales achieved resulted in no changes of stock. You are required, from the data given, to calculate: a. The actual output; E M Reddy

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AMA-Notes b. The actual profit; c. The actual price per unit of material; d. The actual rate per labour hour; e. The amount of production overhead incurred; f. The amount of production overhead absorbed; g. The production overhead efficiency variance; h. The selling price variance; i. The sales volume profit variance Solution: Part 1: Material Variances [1] SQ x SP 4,150 Kgs x Rs.1.5 Rs. 6,225

[2] AQ x AP 3,900 Kgs x Rs.1.65 Rs. 6,435

[3] AQ x SP 3,900 Kgs x Rs.1.5 Rs. 5,850

Working Note 1: Actual Quantity of Raw Materials Material Price Variance (3 – 2) = (AQ x Rs.1.5) – Rs. 6,435 AQ x Rs.1.5 AQ x Rs.1.5 AQ

= – Rs.585 = Rs. 6,435 – Rs.585 = Rs. 5,850 = Rs. 5,850/Rs.1.5 = 3,900 Kgs

Working Note 2: Calculation of Standard Quantity Material Usage Variance (1 – 3) = (SQ x Rs.1.5) – Rs. 5,850 AQ x Rs.1.5 AQ x Rs.1.5 AQ

= Rs.375 = Rs. 5,850 + Rs.375 = Rs. 6,225 = Rs. 6,225/Rs.1.5 = 4,150 Kgs

Working note 3: Actual Output SQ means Standard Quantity for actual output. Input Output 10 Kgs 1 Unit 415 Units x 10 Kgs = 4,150 Kgs 415 Units Part 2: Labour Variances [1] SH x SR 2,075 Hours x Rs.4 Rs. 8,300

[2] AH x AR 2,120 Hours x Rs.3.85 Rs. 8,162

[3] AH x SR 2,120 Hours x Rs.4 Rs. 60,000

Working Note 1: Calculation of AH

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AMA-Notes Labour Rate Variance (3 – 2) = (AH x Rs.4) – Rs. 8,162 AQ x Rs.4 AQ x Rs.4 AQ

= Rs.318 = Rs. 8,162 + Rs.318 = Rs. 8,480 = Rs. 8,480/Rs.4 = 2,120 Hours

Working note 2: Calculation of SH (Standard Hours for Actual Output) Input 5 Hours 415 Units x 5 Hours = 2,075 Hours

Output 1 Unit 415 Units

Part 3: Fixed Overheads [1] AO x SR 415 Units x 5 Hours x Rs.5 Rs. 10,375

[2] AFO Rs. 9,800 Rs. 9,800

[3] BFO (BO x SR) 400 Units x 5 Hours x Rs.5 Rs. 10,000

[4] AH x SR 2,120 Hours x Rs.5 Rs. 10,600

Working Note 1: Calculation of BFO Fixed Overhead Volume Variance (1 – 3) = Rs. 10,375 – BFO= Rs. 375 BFO = Rs. 10,375 – Rs.375 BFO = Rs. 10,000 Working Note 2: Calculation of AFO Fixed Overhead Expenditure Variance (3 – 2) = Rs. 10,000 – AFO= Rs. 200 AFO = Rs. 1,000 – Rs.200 AFO = Rs. 9,800 Working Note 3: Break Up of Volume Variance Fixed Overhead Volume Variance (1 – 3) = Rs. 10,375 – Rs. 10,000 = Rs. 375 (Favourable) Fixed Overhead Capacity Variance (4 – 3) = Rs. 10,600 – Rs. 10,000 = Rs. 600 (Favourable) Fixed Overhead Capacity Variance (1 – 4) = Rs. 10,375 – Rs. 10,600 = Rs. 225 (Adverse) Part 4: Sales Variances Step 1: Calculation of Margins Budgeted Sales

Rs.30,000

Budgeted Price = Budgeted Output = 400 Units = Rs.75 Actual Sales

Rs.29,880

Actual Price = Actual Output = 450 Units = Rs.72 BM = BP – SC = Rs.75 – Rs.60 = Rs.15 AM = AP – SC = Rs.72 – Rs.60 = Rs.12

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AMA-Notes

Step 2: Computation table [1] BQ x BM 400 Units x Rs.15 Rs. 6,000

[2] AQ x AM 450 Units x Rs.12 Rs. 4,980

[3] AQ x BM 450 Units x Rs.15 Rs. 6,225

Step 3: Variance Computation Total Sales Variance (1 – 2) = Rs. 6,000 – Rs. 4,980 = Rs. 1,020 (Adverse) Selling Price Variance (3 – 2) = Rs. 6,225 – Rs. 4,980 = Rs. 1,245 (Adverse) Sales Volume Variance (1 – 3) = Rs. 6,000 – Rs. 6,225 = Rs.225 (Favourable) Part 5: Actual Profit Items Sales Less: Material Labour Production Overhead Actual Profit

Amount (Rs.) 29,880 (6435) (8162) (9800) 5,483

Part 6: Final Solution Particulars Actual Output Actual Profit Actual Price per Unit of Material Actual Rate per Labour Hour Amount of Production Overhead Incurred Amount of Production Overhead Absorbed Production Overhead Efficiency Variance Selling Price Variance Sales Volume Profit Variance

Answer 415 Units Rs. 5,483 1.65 per Kg 3.85 per Hour Rs. 9,800 Rs. 10,375 Rs. 225 (Adverse) Rs. 1,245 (Adverse) Rs. 225 (Favourable)

Question no 25: A company produces a product, which has a standard variable production cost of Rs.8 per unit made up as follows: Direct Materials Rs.4.6 (2 Kg x Rs.2.3) Direct Labour Rs.2.1 (0.7 Hours x Rs.3 per Hour) Variable Overheads Rs.1.3 Fixed manufacturing costs are treated as period cost. The following information is available for the period just ended: Particulars Rs. Variable manufacturing cost of sales (at standard cost) 2,63,520 Opening stock of finished goods (at standard cost) 1,20,800 Closing stock of finished goods (at standard cost) 1,46,080 E M Reddy

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AMA-Notes Direct Material price variance Raw Material used in manufacture (at actual cost) Direct labour rate variance Direct labour efficiency variance Required for the period ended: 1. Number of units produced 2. Raw Material usage variance 3. Total actual direct labour 4. Actual cost per Kg of raw material

2,571 (Adverse) 1,70,310 4,760 (Adverse) 3,240 (Favourable)

Solution: Step 1: Calculation of Number of Units Produced Particulars Sales Add: Closing Stock Less: Opening Stock Units Produced

Computation 2,63,520/8 1,46,080/8 1,20,800/8

Units 32,940 18,260 15,100 36,100

Step 2: Material Variances [1] SQ x SP 72,200 Kgs x Rs.2.3 Rs. 1,66,060

[2] AQ x AP 72,930 Kgs x Rs.2.34 Rs. 1,70,310

[3] AQ x SP 72,930 Kgs x Rs.2.3 Rs. 1,67,739

Material Usage Variance (1 – 3) = Rs. 1,66,060 – Rs. 1,67,739 = Rs. 1,679 Adverse) Working Note 1: Actual Quantity of Raw Materials Material Price Variance (3 – 2) = (AQ x Rs.2.3) – Rs. 1,70,310= – Rs. 2,571 AQ x Rs.2.3 = Rs. 1,70,310 – Rs. 2,571 AQ x Rs.2.3 = Rs. 1,67,739 AQ = Rs. 1,67,739/Rs.2.3 = 72,930 Kgs Working Note 2: Calculation of SQ (Standard Quantity for Actual Output) Input 2 Kgs 36,100 Units x 2 Kgs = 72,200 Kgs

Output 1 Unit 36,100 Units

Step 3: Labour Variances [1] SH x SR 25,2705 Hours x Rs.3 Rs. 75,810

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[2] AH x AR 24,190 Hours x Rs.3.20 Rs. 77,330

[3] AH x SR 24,190 Hours x Rs.3 Rs. 72,570

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AMA-Notes

Working note 1: Calculation of SH (Standard Hours for Actual Output) Input 0.7 Hours 36,100 Units x 0.7 Hours = 25,270 Hours

Output 1 Unit 36,100 Units

Working Note 2: Calculation of AH Labour Efficiency Variance (1 – 3) = Rs. 75,810 – (AH x Rs.3) = Rs. 3,240 AQ x Rs.3 = Rs. 75,810 – Rs. 3,240 AQ x Rs.3 = Rs. 72,570 AQ = Rs. 72,570/Rs.3 = 24,190 Hours Working Note 3: Calculation of Actual Labour Cost Labour Rate Variance = (AH x SR) – (AH x AR) - Rs. 4,760 = Rs. 72,570 – (AH x AR) AH x AR = Rs. 72,570 + Rs. 4,760 AH x AR = Rs. 77,330 Step 4: Final Solution Number of units produced Raw Material usage variance Total actual direct labour Actual cost per Kg of raw material 5.17.

= 36,100 Units = Rs. 1,670 (Adverse) = Rs. 77,330 = Rs.2.34

Investigation of Variances

Question no 26: A company using a detailed system of standard costing finds that the cost of investigation of variances is Rs. 20,000. If after investigation an out of control situation is discovered, the cost of correction is Rs. 30,000. If no Investigation is made, the present value of extra cost involved is Rs. 1,50,000. The probability of the process being in control involved is 0.82 and the probability of the process being out of control is 0.18. You are required to advise: i. Whether investigation of the variances should be undertaking or not; and ii. The probability at which it is desirable not to institute investigation into variances. Solution:

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AMA-Notes

Conclusion: The expected cost when investigation is ordered is Rs. 25,400 but the expected without the investigation is Rs. 27,000. Hence, it is desirable to investigate. Calculation of Indifference probability: Let probability of system in control be ‘P’ and system out of control be ‘1 – P’. The indifference probability is the one where both the decisions has the same expected cost. [20,000 x P] + [50,000 x (1 – P)] = 1,50,000 (1 – P) 20,000P + 50,0000 – 50,000P = 1,50,000 – 1,50,000 P 20,000P + 1,50,0000P – 50,000P = 1,50,000 – 50,000 1,20,000P = 1,00,000 P = 1,00,000/1,20,000 P = 0.83 1 – P = 1 – 0.83 = 0.17 Conclusion: If the company believes that there is 17% chance of the system being out of control then it is indifferent between Investigation or No investigation. If the probability exceeds 17%, it will order for investigation else it will not. Notes: 1) When variances are reported the company has to make a decision whether or not to order investigation. 2) The advantage of investigation is that it may discover frauds and help the company to prevent the variances from recurring but there is a cost involved in investigation. 3) 3 factors affect the investigation decisions: E M Reddy

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AMA-Notes i. The Materiality of the Variances ii. Cost involved in investigation and correction iii. Probability of system being out of control 4) Decision should be made based on expected cost.

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AMA-Notes 6. RELEVANT COSTING 6.1. Learning Objectives

1) 2) 3) 4) 5) 6)

Relevant Cost of Materials Relevant Cost of Labour Relevant Cost of Overheads Comprehensive Problems Limiting Factor and Relevant Costing Relevant Costing under uncertainty

6.2. Relevant Cost of Materials

1) In Stock i. Regularly Used – Relevant Cost (RC) = Purchase Price (or) Replacement Cost ii. Not Regularly Used a) Has Disposal Value – Relevant Cost (RC) = Realizable Value b) Has Alternative Use – Relevant Cost (RC) = The Cost of Material Substituted c) Has Both – Relevant Cost (RC) = Higher of the Two 2) Not in Stock – Relevant Cost (RC) = Purchase Price Question no 1: X ltd. has been approached by a customer who would like a special job to be done for him and is willing to pay Rs.22,000 for it. The job would require the following materials. Material Total Units Units already Book value of units Realizable Replacement Required in stock in stock Rs. /Unit value Rs./Unit Cost Rs./Unit A 1,000 0 6 B 1,000 600 2 2.5 5 C 1,000 700 3 2.5 4 D 200 200 4 6 9 a) Material B is used regularly by X ltd. And if stocks were required for this job they would need to be replaced to meet other production demand. b) Material C and D are in stock as the result of previous excess purchase and they have a restricted use. No other use could be found for material C but material D could be used in another job as substitute for 300 units of material E, which currently cost Rs.5 per unit (of which the company has no units in stock at the moment). What are the relevant costs of material, in deciding whether or not to accept the contract? Assume all other expenses on this contract to be specially incurred beside the relevant cost of material are Rs.550. Solution: Part 1: Relevant Material Cost for this Job Step 1: Material A Material A is not in stock and hence need to be specifically purchased for this job. Therefore, relevant cost is its “Purchase Price”. Relevant Cost = 1,000 Units x Rs.6 = Rs.6,000 E M Reddy

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AMA-Notes Step 2: Material B Material B is partly in stock and partly needs to be purchased. For the units to be purchased, the relevant cost is “Purchase Price” and since the units in stock are regularly used, they need to be replaced if used for this job, the relevant cost is “Replace Cost (or) Purchase Price”. 1,000 Units In Stock = 600 Units – Relevant Cost = 600 Units x Rs.5 = Rs.3,000 Not in Stock

= 400 Units – Relevant Cost = 400 Units x Rs.5 = Rs.3,000

Total Relevant Cost = Rs.5,000 Step 3: Material C Material C also is partly in stock and partly to be purchased. For the units to be purchased, the relevant cost is “Purchase Price”. The units in stock could be sold for Rs.2.5 if it is not used hence the relevant cost of using it is “Realizable Value lost”. 1,000 Units In Stock = 700 Units – Relevant Cost = 700 Units x Rs.2.5 = Rs.1,750 Not in Stock

= 300 Units – Relevant Cost = 300 Units x Rs.4 = Rs.1,200

Total Relevant Cost = Rs.2,950 Step 4: Material D Material D is in stock and not regularly used. If it is not used for this contract the company has two options. i. ii.

Can be disposed off for a realizable value of Rs. 1,200 (200 Units x Rs.6) Cab be used in place of 300 Units of E. Thereby saving a cost of Rs.1,500 (300 Units x Rs.5)

Obviously, the company will select best of the two. Hence, relevant cost is higher of the two Rs.1,500. Part 2: Statement of Benefit and Cost Particulars A. Benefit (Job Price) B. Cost Material A Material B Material C Material D Other Cost C. Net Benefit (A – B)

Amount (Rs.) 22,000 6,000 5,000 2,950 1,500 550 6,000

Since, net benefit is positive the job should be accepted. Notes: The book value of units in stock is irrelevant because it is Historical or Sunk Cost.

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AMA-Notes 6.3. Relevant Cost of Labour

1) Skilled Labour – Paid on Time guaranteed basis i. Currently Idle – Relevant Cost (RC) = Nil ii. Busy a) Cannot be substituted – Relevant Cost = Contribution lost from abandoned job b) Can be substituted – Relevant Cost = Wages paid to the substitute worker 2) Unskilled Labour – Appointed on Hire & Fire Basis, hence Relevant Cost is Wages paid Question no 2: Ram Ltd is evaluating the feasibility of a contract requiring supply of 1,000 units of component ZED. The labour specification for this contract is as follows: Type of Labour Hours/Unit Rate/Hour Remarks Skilled labour 4 5 # Difficult to recruit. # Paid on time-guarantee basis. Unskilled labour

6

3

# To be specifically hired for this contract

Ascertain the relevant cost of labour for this contract. Solution: 1) Skilled Labour: a) Skilled worker are paid on time-guarantee basis. Hence, the wages paid to them is irrelevant because it is committed cost. b) Since, no other detail is given we assume that at present they are idle and the Relevant Cost is “Nil”. 2) Unskilled Labour: a) They are specifically hired for this contact. Hence, their entire wages is relevant. b) Relevant Cost (RC) = 1,000 Units x 6 Hours x Rs.3 = Rs.18,000. Question no 3: A ltd is at present carrying out a research project, which requires spending of Rs.40,000 towards skilled labour. They are paid on time guaranteed basis. Had they not been employed in this project, they could have been in some other productive job fetching revenue of Rs.1,50,000 to the company. For this job, the company has to incur a prime cost of Rs.1,00,000. Ascertain the relevant labour cost for this research project. Solution: 1) The time guaranteed wages of Rs.40,000 is irrelevant because it is committed. 2) If the research project is done, then A ltd. could have used this employee for other productive job. By doing this project, we lose contribution from other job which is opportunity cost. Revenue = Rs.1,50,000 Less: Cost = Rs.60,000 Contribution Loss = Rs.90,000 3) The Relevant wage cost is contribution loss which is Rs.90,000 Note: 1) While calculating contribution loss (or) profit loss, we ignored the wages of Rs.40,000 because whether or not the other job is done it will still be incurred. 2) In study material answer is presented as follows:

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AMA-Notes Labour Cost

= Wages + Opportunity Cost = Rs.40,000 + Rs.50,000 = Rs.90,000

Question no 4: XYZ ltd received an order to produce 10,000 units of a component named super-x. It requires 5 hours of skilled labour. The company already has in its roll an employee possessing the necessary skills, who is currently paid Rs.5 per hour on time guaranteed basis. At present he is busy with an urgent job, which would be affected on undertaking this order. To get this job continued the company has to hire a temporary employee who will paid at Rs.4 per hour. Ascertain the relevant labour cost for producing the component of super-X. Solution: 1) The Rs.5 per hour, time guaranteed wages is irrelevant because it is committed. 2) The skilled worker is busy with another job. If he is used for this job, the company has to hire a substitute worker to continue the other job. The Relevant cost is “Wages paid to substitute worker”. 3) Relevant Cost = 10,000 Units x 5 Hours x Rs.4 = Rs.2,00,000. Question no 5: A ltd is in construction business, which also carries out painting and maintenance work during severe winter not being conducive for construction activities. At present the company is evaluating the viability of a proposal to build a housing complex, for which it has to employ contract basis a team of highly skilled craftsmen. The compensation for this team works out of Rs.3,00,000. Though a period of 9 months is sufficient for completion of the contract, due to spells of bad weather it is estimated to be over in over in a year’s time. During winter, this team could be used for painting and maintenance work already undertaken by the company, which otherwise would require to be subcontracted to outsiders. For this, the company has received quotations from two jobbing builders, one for Rs.50,000 and another for Rs.40,000. This painting and maintenance work, which if done by the company requires spending on material Rs.10,000. Ascertain the relevant labour cost for building the housing complex. Solution: 1) Since the craftsmen or specifically hired for this contract, their wages of Rs.3,00,000 is relevant. 2) Due to the craftsmen, the company can save a net cost of Rs.30,000 (Rs.40,000 – Rs.10,000) on its maintenance work i.e. Subcontracting charges saved – Rs.40,000 (Lowest Quotation) and material cost incurred – Rs.10,000. 3) Relevant Labour Cost = Rs.3,00,000 – Rs.30,000 = Rs.2,70,000 6.4. Relevant Cost of Overheads

1) Variable Overheads – Always Relevant 2) Fixed Overheads i. General Fixed Cost - Irrelevant ii. Specific Fixed Cost – Relevant Question no 6: ABC ltd receives an offer for producing 1,000 units of components used in manufacture of aircraft. For manufacturing each and every unit 4 machine hours are required. The company absorbs overheads on the basis of machine hours. Currently, the machine hour rate is Rs.20 per hour, of which Rs.7 us variable and Rs.13 is fixed. If the contract is accepted, the

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AMA-Notes company will additionally incur a fixed overhead of Rs.3,200. Ascertain the relevant overhead cost for this contract. Solution: 1) Variable overheads are relevant because they are incremental cost. Relevant Variable overheads = 1,000 Units x 4 Hours x Rs.7 = Rs.28,000 2) The absorbed fixed overheads will be incurred whether or not the units are produced. It is nonincremental, hence irrelevant. 3) Additional fixed cost of Rs.3,200 is specific for this contract. Hence, it is relevant. 4) The relevant overhead cost for this contract is Rs.31,200 (Rs.28,000 + Rs.3,200) 6.5. Comprehensive Problems

Question no 7: A research project, which to date has cost the company Rs.1,50,000 is under review. It is anticipated that should the project be allowed to proceed, it will be completed in approximately one year when the results would be sold to a government agency for Rs.3,00,000. Shown below are the additional expenses, which the managing director estimated will be necessary to complete the work. Material – Rs.60,000. This material, which has just been received, is extremely toxic and if not used on the project would have to be disposed of by special means, at a cost of Rs.5,000. Labour – Rs.40,000. The men are highly skilled and very difficult to recruit. They were transferred to the project from a production department and, at a recent board meeting, the works director claimed that if the men were returned to him he could earn the company each year Rs.1,50,000 extra sales. The accountant calculated that the prime cost of those sales would be Rs.1,00,000 and the overhead absorbed (all fixed) would amount to Rs.20,000. Research staff – Rs.60,000. A decision has already been taken that this will be the last major piece of research undertaken, and consequently when work on the project ceases the staff involved will be made redundant. Redundancy and severance pay have been estimated at Rs.25,000. Share of general building service – Rs.35,000. The managing director is not very sure what is included in this expenses. He knows, however, that the accounts staff charges similar amount every year to each department. Required: Assuming the estimates are accurate, advice the managing director whether the project should be allowed to proceed. You must carefully and clearly explain the reasons for your treatment of each expense item. Solution: 1) The cost spent to date on this project of Rs.1,50,000 is irrelevant because it is Sunk cost. 2) The government agency’s fee of Rs.3,00,000 is the relevant benefit of continuing the project. 3) The material price of Rs.60,000 is irrelevant because it is historical (the material is just received and hence is in stock). 4) If the material is not used for this project, the company should dispose it off by spending Rs.5,000. The usage avoids this spending. Hence, Rs.5,000 is relevant benefit. E M Reddy

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AMA-Notes 5) The relevant labour cost is Rs.90,000 (Refer Question no 3) 6) The Research staff wages of Rs.60,000 is a relevant cost because it will be paid if the project is continued and avoided if the project is abandoned. 7) The redundancy cost of Rs.25,000 is irrelevant because if the project is abandoned it will be paid today and if continued will be paid a year later. 8) Share of general building service of Rs.35,000 is irrelevant because it is an apportion expense. 9) Fixed overheads of Rs.20,000 is irrelevant because it is not incremental. Statement of Cost-Benefit analysis: A. B. C.

Particulars Benefits Agency fees Savings in material disposal cost Cost Labour Research Staff Wages Net Benefit (A – B)

Amount (Rs.)

Amount (Rs.)

3,00,000 5,000

3,05,000

90,000 60,000

1,50,000 1,55,00

Recommended to continue the research project since the net benefit is positive. Question no 8: A company has been making a machine to order for a customer but the customer has since gone into liquidation and there is no prospect that any money will be obtained from the winding up of the company. Costs incurred to date in manufacturing the machine are Rs.50,000 and the progress payments of Rs.15,000 had been received from the customer prior to the liquidation. The sale department has found another company willing to buy the machine for Rs.34,000 once it has been completed. To complete the work, the following costs would be incurred. 1. Materials: These have been bought at a cost of Rs.6,000. They have no other use and if the machine is not finished they would be sold for scrap of Rs.2,000. 2. Further labour cost would be Rs.8,000. Labour is in short supply and if the machine is not finished, the work force would be switched to another job which would earn Rs.30,000 in revenue and incur direct cost of Rs.12,000. 3. The absorbed fixed overheads is Rs.8,000. 4. Consultancy fees of Rs.4,000. If the work is not completed the consultants contract would be cancelled at a cost of Rs.1,500. 5. General overheads of Rs.8,000 would be added to the cost of additional work. Required: Asses whether new customer order should be accepted. Solution: Cost-benefit analysis of accepting the new order: A. B.

Particulars Benefits Sales value of new order Cost Material

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Amount (Rs.)

Amount (Rs.)

34,000

34,000

2,000

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AMA-Notes

C.

Labour (30,000 – 4,000) Consultancy fee (4,000 – 1,500) Net Benefit (A – B)

26,000 2,500

30,500 3,500

1)

Continue the work by accepting new order since the net benefit is positive. Note: Reasons should be written as above. **Question no 9: Vishwakarma is a builder. His business will have spare capacity over the coming six months and he has been investigating two projects. Project A: Vishwakarma is tendering for a Scholl extension contract. Normally he prices a contract by adding 100% to direct costs, to cover overheads and profit. He calculates direct costs as the actual cost of materials valued on first-in-firs-out basis, plus the estimated wages of direct labour. But for this contract he has prepared more detailed information. Four types of material will be needed: Material Quantity (units): Price per unit: (in Rs.) Needed for Already Purchase price of Current Current contract in stock units in stock purchase price resale price Z 1,100 100 7.00 10.00 8.00 Y 150 200 40.00 44.00 38.00 X 600 300 35.00 33.00 25.00 W 200 400 20.00 21.00 10.00 Z and Y are in regular use. Neither X nor W is currently used; X has no foreseeable use in the business, but W could be used on other jobs in place of material currently costing Rs.16 per unit. The contract will last for six months and requires two craftsmen, whose basic annual wage cost is Rs.16,000 each. To complete the contract in time it will also be necessary to pay them a bound of Rs.700 each. Without the contract they would be retained at their normal pay rate, doing work, which will otherwise be done by temporary workers, engaged for the contract period at a total cost of Rs.11,800. Three casual labourers would also be employed specifically for the contract at a cost of Rs.4,000 each. The contract will require two types of equipment: general – purpose equipment already owned by Vishwakarma, which will be retained at the end of the contract, and specialized equipment to be purchased second-hand, which will be sold at the end of the contract. The general-purpose equipment cost Rs.21,000 two years ago is being depreciated on a straight line basis over a seven year life (with assumed zero scrap value). Equivalent new equipment can be purchased currently for Rs.49,000. Second-hand prices for comparable general-purpose equipment, and those for the relevant specialized equipment, are shown below: General – Purpose equipment Specialized equipment Purchase Price Resale Price Purchase Price Resale Price (Rs.) (Rs.) (Rs.) (Rs.) Current 20,000 17,200 9,000 7,400 After 6 months: If used for 6 months: 15,000 12,600 7,000 5,800 If not used 19,000 16,400 8,000 6,500 The contract will require the use of a yard on which Vishwakarma has a four-year lease at a fixed rental of Rs.2,000 per year. If Vishwakarma does not get the contract the yard will probably remain empty. The contact will also incur administrative expenses estimated at Rs.5,000. E M Reddy

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AMA-Notes Project B: If Vishwakarma does not get the contract he will buy a building plot for Rs.20,000 and build a house. Building cost will depend on weather conditions: Weather Condition A B C Probability 0.4 0.4 0.2 Building costs (excluding land) (000s) Rs.60 Rs.80 Rs.95 Similarly the price obtained for the house will depend on market conditions: Weather Condition D E Probability 0.7 0.3 Sale Price (net of selling expenses) Rs.1,00,000 Rs.1,20,000 Vishwakarma does not have the resources to undertake both projects. The costs of his supervision time can be ignored. Requirements: (a) Ignoring the possibility of undertaking Project B, calculate: i. The price at which Vishwakarma would tender for the school extension contract if the used his normal pricing method, and ii. The tender price at which you consider Vishwakarma would neither gain nor lose by taking the contract. (b) Explain, with supporting calculations, how the availability of Project B should affect Vishwakarma’s tender for the school extension contract. Solution: a. Part 1: Tender price when Vishwakarma uses normal pricing method Tender Price = Direct Cost + 100% Mark Up Particulars A. Materials Z Y X W Total Material Cost B. Wages Crafts men wages Crafts men bonus Casual labour wages Wage Total C. Direct Cost D. Margin E. Tender Price

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Computation

Amount (Rs.)

[100 Units x Rs.7] + [1,000 Units x Rs.10] 150 Units x Rs.40 [300 Units x Rs.35] + [300 Units x Rs.33] 200 Units x Rs.20

10,700 6,000 20,400 4,000 41,100

2 men x Rs.16,000 x 6/12 2 men x Rs.700 3 men x Rs.4,000

16,000 1,400 12,000 29,400 70,500 70,500 1,41,000

A+B C x 100% = Rs.70,500 x 100% C+D

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AMA-Notes Part 2: Calculation of Relevant Cost for doing this school extension contract Step 1: Relevant cost of Materials Particulars Computation Z [100 Units x Rs.10] + [1,000 Units x Rs.10] Y 150 Units x Rs.44 X [300 Units x Rs.25] + [300 Units x Rs.33] W 200 Units x Rs.16 Total Relevant Cost

Amount (Rs.) 11,000 6,600 17,400 3,200 38,200

Step 2: Relevant cost of wages Particulars Crafts Men Wages Crafts Men Bonus Casual labour wages Total Relevant Cost

Computation Temporary workers wages 2 Men x Rs.700 3 Men x Rs.4,000

Amount (Rs.) 11,800 1,400 12,000 25,200

Step 3: Relevant cost of Special Purpose equipment A Specialized equipment are specifically purchased for the contract and will be disposed off after the contract gets completed. Hence, the relevant cost is current purchase price – Resale price after 6 months = Rs.9,000 – Rs.5,800 = Rs.3,200. Step 4: General Purpose Equipment 1) General purpose equipment is already with the company and the company will continue to have it even after the contract completion. 2) The cost at which it was purchased 2 years ago i.e. Rs.21,000 is irrelevant because it is historical or sunk. 3) If the general purpose equipment is sold today we can realize Rs.17,200 but if it is used for 6 months and then sold it will realize only Rs.12,600. Thus there is a loss in value of Rs.17,200 – Rs.12,600 = Rs.4,600. i. Loss in value due to efflux of time – Rs.17,200 – Rs.16,400 = Rs.800 – Irrelevant because it will happen whether or not the contract is accepted. ii. Loss in value due to usage – Rs.16,400 – Rs.12,600 = Rs.3,800 – Relevant because it happens due to usage in this contract. Step 5: Other relevant costs 1) The fixed rental for the yard of Rs.2,000 is irrelevant because it is a committed cost 2) If the yard is not used for the school contract it will remain empty and idle resource has got no relevant cost. 3) Administration expense of Rs.5,000 is relevant because it is incremental. Step 6: Minimum tender price where Vishwakarma will neither gain nor lose Particulars Materials Wages Special Purpose Equipment

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Amount (Rs.) 38,200 25,200 3,200

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AMA-Notes General Purpose Equipment 3,800 Administrative Expenses 5,000 Total Relevant cost 75,400 If tender price is fixed as Rs.75,400 then Vishwakarma could recover all the relevant costs and make no gain or no loss from the contract. b. Tender Price for the school extension contract if House building contract is available Step 1: Expected profit from house building contract Particulars Computation Expected Sales [0.7 x Rs.1,00,000] + [0.3 x Rs.1,20,000] Less: Cost of land Given Expected building cost [0.4 x Rs.60,000] + [0.4 x Rs.80,000] + [0.2 x Rs.95,000] Expected profit from building contract

Amount (Rs.) 1,06,000 (20,000) (75,000) 11,000

Step 2: Revised tender price for the school extension contract Particulars Relevant cost in part 2 Add: Profit lost from building contract (Opportunity cost) Revised tender price

Amount (Rs.) 75,400 11,000 86,400

6.6. Limiting Factor and Relevant Costing

***Question no 10: Following a fire at the factor of Elgar ltd, the management team met to review the proposed operations for the next quarter. The fire has destroyed all the finished goods stock, some of the raw materials and about half of the machined in the forming shop. At the meeting of the management team the following additional information was provided. i.

ii. iii.

Only 27,000 machine hours of forming capacity will be available in the forthcoming quarter. Although previously it was thought that sales demand would be the only binding limitation on production it has now become apparent that for the forthcoming quarter the forming capacity is also limiting factor. It will take about three months to reinstate the forming shop to its previous operational capacity. Hence the restriction on forming capacity is for the next quarter only. Some details of the product range manufactured by Elgar are provided in the following table: Product A B C D E Sales price (Rs.) 50 60 40 50 80 Units of special material required for production: W or X 2 2 2 1 3 Y - 6 Z 1 2 1 1 Other direct materials cost (Rs.) 6 12 6 5 13 Other variable production costs (Rs.) 8 4 8 4 4 Fixed production costs (based on standard costs) (Rs.) 6 3 6 3 3 Forming hours required 5 6 2 10 6

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AMA-Notes iv.

The forecasts of demand, in units, for the forthcoming quarter are: Product Product Product Product Product A B C D E Units demanded 2,000 2,000 4,000 3,000 4,000

v.

Due to purchasing error there is an excess of material ‘W’ in stock. This has a book value of Rs.6 per unit, which is also its current replacement cost. This could be sold to realize Rs.4 per unit after sales and transportation costs. Material ‘X’ could be used instead of material ‘W’; material ‘X; is not in stock and has a current replacement cost of Rs.5 per unit. vi. Material ‘Y; was in stock at a book value of Rs.2 per unit, which is its normal cost if ordered 3 months in advance, but the stocks of this material were entirely destroyed by the fire. In order to obtain the material quickly a price of Rs.3 per unit will have to be paid for the first 3,000 units obtained in the quarter and any additional units required will cost Rs.6 per unit. These special prices will apply only to this quarter’s purchases. vii. The fire destroyed some of the stock of material ‘Z’. The remaining stock of 2,000 units have a book value of Rs.7 per unit. The replacement price for ‘Z’ is currently Rs.8 per unit. viii. As a result of the fire it is estimated that the fixed production costs will be Rs.42,000 for the next quarter and the administration and office overheads will amount to Rs.11,500. ix. The demand figures shown in note (iv) include a regular order from a single customer for 3,000 units of C, and 3,000 units of E. The order is usually placed quarterly and the customer always specifies that the order be fulfilled in total or not at all. Required: (a) Ignoring the information contained in note (ix) for the section of the question, determine the optimum production plan for the forthcoming quarter and the resulting profit. (b) Prepare the statement, which clearly shows the management of the company the financial consequences of both acceptance and rejection of the order mentioned in note (ix). Solution: Part 1: Step 1: Calculation of contribution per unit and contribution per hour Items Selling Price (Rs.) Less: Variable Cost Material ‘W’ (Rs.) Material ‘Y’ (Rs.) Material ‘Z’ (Rs.) Other direct material cost Other variable cost Contribution per unit Hours per unit Contribution per hour Rank

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A B 50 60

C D 40 50

E 80

E1 80

8 8 6 8 20 5 4 3

8 8 6 8 10 2 5 2

12 18 13 4 33 6 5.5 1

12 36 13 4 15 6 2,5 6

8 16 12 4 20 6 3.33 4

4 8 5 4 29 10 2.9 5

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AMA-Notes Notes: 1) Material ‘W’ is in stock and irregularly used. Its book value is irrelevant because it is historical and current replacement cost is also irrelevant because it will not be replaced. 2) If Material ‘W’ is used for production we lose a realizable value of Rs.4 per unit which is its relevant cost. 3) Instead of ‘W’ if we use ‘X’ which is not in stock we should spend Rs.5 per unit to purchase it. Hence, its relevant cost is Rs.5. 4) Between ‘W’ and ‘X’, ‘W’ is cheaper and should be used. 5) Units of ‘Y’ required to produce 4,000 units of E = 4,000 x 6 Units = 24,000 Units i. First 3,000 units of ‘Y’ purchased at Rs.3 per unit – This can produce 500 units of E. ii. Balance 21,000 units ‘Y’ of purchased at Rs.6 per unit – This can produce 3,500 units of E which we called as E1. 6) ‘Z’ is partly in stock and partly to be purchased. The book value of units in stock is irrelevant because it is historical. Since the units in stock are regularly used, the relevant cost is its replacement cost of Rs.8. For the units to be purchased also the relevant cost is Rs.8. Step 2: Allocation of limiting factor Product E C A B

Units 500 4,000 2,000 1,000

Hours/Unit 6 2 5 6

Hours 3,000 8,000 10,000 6,000

∑ 𝐇𝐨𝐮𝐫𝐬 3,000 11,000 21,000 27,000

Contribution/hour (Rs.) 5.5 5 4 3.3 Total Contribution

Contribution (Rs.) 16,500 40,000 40,000 20,000 1,16,500

Part 2: Step 1: Allocation of limiting factor – Specific order rejected Product E C A B

Units 500 1,000 2,000 2,000

Hours/Unit 6 2 5 6

Hours 3,000 2,000 10,000 12,000

∑ 𝐇𝐨𝐮𝐫𝐬 3,000 5,000 15,000 27,000

Contribution/hour (Rs.) 5.5 5 4 3.3 Total Contribution

Contribution (Rs.) 16,500 10,000 40,000 40,000 1,06,500

Step 2: Allocation of limiting factor – Specific order accepted Product E E1 C A

Units 500 2,500 4,000 200

Hours/Unit 6 6 2 5

Hours 3,000 15,000 8,000 1,000

∑ 𝐇𝐨𝐮𝐫𝐬 3,000 18,000 26,000 27,000

Contribution/hour (Rs.) 5.5 2.5 5 4 Total Contribution

Contribution (Rs.) 16,500 37,500 10,000 4,000 98,000

It is recommended to reject the specific order because the contribution is highest on rejection.

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AMA-Notes

6.7. Joint product and Relevant Costing

1) When from a process more than one product emerges, the process is called joint process and the products are called joint products. 2) The stage at which the product separate is called “Separation Point” or “Split off Point”. 3) All costs spent before split off point are called “Joint Costs” and cost spent after it are called “Further processing cost”. 4) Joint cost should be apportioned to the joint products for the purpose of stock valuation because value of stock is share of joint cost plus further processing cost. 5) However, for decision making purpose the point costs are irrelevant which can be seen in the following two types of decisions: i. Further Process or not: The company may sell the joint product at split off point or after further processing it. It depends on cost and benefit. a) Benefit – Incremental Sales from improved product b) Cost – Further processing cost In this decision joint costs are irrelevant because they will anyhow be incurred whether are not we further process i.e. they are non-incremental. ii. Continuance or Discontinuance of a product: For example, the product ‘B’ has a share of joint cost of Rs.8 per unit and further processing cost of Rs.15 per unit and selling price of Rs.20 per unit. It gives a loss of Rs.3 (Rs.20 – Rs.23) per unit. Can we discontinue it? Answer: No, A independent joint product cannot be discontinued because if we produce ‘Á’, ‘B; will automatically get produced and joint cost cannot be avoided just because we don’t sell E M Reddy

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AMA-Notes ‘B’ i.e. Rs.8 is irrelevant. By selling ‘B’ we get Rs.20 and incur Rs.15 further processing cost giving a Rs.5 contribution towards the joint cost recovery. Hence, once again joint cost irrelevant for decision making. Question no 11: A company incurs joint production cost of Rs.3,00,000 for production of two products A & B. This joint cost comprises of Rs.2,40,000 as fixed cost and Rs.5 per unit as variable cost. Other details are as follows: Products Units Produced Units Sold FPC per unit Selling Price A 10,000 10,000 8 40 B 2,000 2,000 10 35 A new customer approaches the company with an offer to purchase 600 units of product ‘B’ at Rs.25 per unit. This sale will not affect the market price to the other customers. Should the specific offer be accepted? What should be done to make the order acceptable? Solution: Step 1: Profit or loss from the specific offer The joint produce ratio is A: B = 5:1 To produce 600 units of B, we should also produce 3,000 units of A. Thus the input processed in joint process is 3,600 units. Particulars Sales Joint Cost Further processing cost Profit/(Loss)

Computation 600 Units x Rs.25 3,600 Units x Rs.5 600 Units x Rs.10

Amount (Rs.) 15,000 (18,000) (6000) (9000)

Step 2: Minimum selling price for 3,000 units of A Particulars Computation Further processing cost of A 3,000 Units x Rs.8 Loss from specific offer Required sales

Amount (Rs.) 24,000 9,000 33,000

Rs.33,000

Minimum selling price = 3,000 Units = Rs.11 per Unit Conclusion: The specific order of 600 units of B can be accepted only when we can sell 3,000 units of A at least at a selling price of Rs.11 per unit. Check: Particulars Sales of ‘A’ Sales of ‘B’ Joint cost Further processing cost of ‘A’ Further processing cost of ‘B’

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Computation 3,000 Units x Rs.11 600 Units x Rs.25 3,600 Units x Rs.5 3,000 Units x Rs.8 600 Units x Rs.10

Amount (Rs.) 33,000 15,000 (18,000) (24,000) (6,000)

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AMA-Notes Profit/(Loss)

0

Independently ‘B’ alone cannot be accepted. Question no 12: HTM ltd using 12,00,000 units of material M produces jointly 2,00,000 units of H and 4,00,000 units of T. The cost and sales details are as under: Direct material M @ Rs.5 per unit Rs.60,00,000 Other variable cost Rs.42,00,000 Total fixed cost Rs.18,00,000 Selling price of H per unit Rs.25 Selling price of T per unit Rs.20 The company receives an additional order for 40,000 units of T at the rate of Rs.15 per unit. If this order is accepted, the existing price of T will not be affected. However the present price of H should be reduced evenly on the entire sale of H to market the additional units to be produced. Find the minimum average selling price to be charged on H to sustain the increased sales. Solution: Step 1: Profit or loss from accepting the specific offer The joint produce ratio is T: H = 2:1 To produce 40,000 units of T, we should also produce 20,000 units of H by processing 1,20,000 units of ‘M’. Joint Variable cost = Rs.60,00,000 + Rs.42,00,000 = Rs.1,02,00,000 Input processed = 12,00,000 Units Joint Variable cost per unit

=

Rs.1,02,00,000 12,00,000 Units

= Rs.8.5 per unit

Particulars Computation Sales 40,000 Units x Rs.15 Joint cost of processing 1,20,000 Units x Rs.8.5 Profit/(Loss)

Amount (Rs.) 6,00,000 (10,20,000) (4,20,000)

This specific order independently cannot be accepted. Step 2: Minimum selling price of H Particulars Computation Existing Sales 2,00,000 Units x Rs.25 Loss to be recovered Required sales Units sold 2,00,000 Units + 20,000 Units

Amount (Rs.) 50,00,000 4,20,000 54,20,000 2,20,000 Units

Rs.54,20,000

Minimum selling price = 2,20,000 Units = Rs.24.64 per Unit Conclusion: For the new order to be accepted we should be able to sell 2,20,000 units of ‘H’ at a minimum selling price of Rs.24.64.

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AMA-Notes Question no 13: A company manufactures three joint products A, B and C. C has no NRV unless it undergoes further processing. The cost details of C are as follows: Particulars Rs. per unit Up to point of separation Marginal Cost 30 Fixed Cost 20 After point of separation Marginal Cost 15 Fixed Cost 5 C can be sold at Rs.37 per unit and not more than that.  Would you recommend production of C?  Would your recommendation be different if A, B and C are not joint products? Solution: Step 1: Viability of ‘C’ if it is a joint product The joint variable cost of Rs.30 is irrelevant because even if we decide to discontinue ‘C’ the production of ‘A’ and ‘B’ automatically results in production of ‘C’ and this Rs.30 cannot be avoided. By further processing and selling ‘C’ we get a selling price of Rs.37 and spend variable cost of Rs.15 which gives Rs.22 contribution towards joint cost. Hence, should be continued. Step 2: Viability of ‘C’ it is not a joint product Selling price = Rs.37 Variable Cost = Rs.45 Conurbation = Rs.8 Since contribution is negative ‘Ç’ should be discontinued. 6.8. Relevant Costing under Uncertainty

Question no 14: W ltd is to produce new products in short-term venture which will utilize some obsolete materials and expected spare capacity. The new product will be advertised in Quarter I with production and sales taking place in Quarter II. No further production or sales are anticipated. Sales volume are uncertain but will, to some extent, be a function of sales price. The possible sales volumes and the advertising costs associated with each potential sales price are follows: Sales price Rs.20 per unit Sales price Rs.25 per unit Sales price Rs.40 per unit Sales volume Probability Sales volume Probability Sales volume Probability (units 000’s) (units 000’s) (units 000’s) 4 0.1 2 0.1 0 0.2 6 0.4 5 0.2 3 0.5 8 0.5 6 0.2 10 0.2 8 0.5 15 0.1 Advertising Cost Rs.20,000 Advertising Cost Rs.50,000 Advertising Cost Rs.1,00,000 The resources used in the production of each unit of the product is: Production Grade I – 2 Hours Grade II – 1 Hours Materials X – 1 Units E M Reddy

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AMA-Notes Y – 2 Units The normal cost per hour of labour is: Grade I – Rs.2 Grade II – Rs.3 However, before considering the effect of the current venture there is expected to be 4,000 hours of idle time for each grade of labour in quarter II. Idle time is paid at the normal rates. Material X is in stock at a book value of Rs.8 per unit is widely used within the firm and any usage for the purpose of this venture will require replacing. Replacement cost in Rs.9 per unit. Material Y is obsolete stock. There are 16,000 units in stock at a book value of Rs.3.50 per unit any stock not used will have to be disposed of a cost, to W ltd. of Rs.2 per unit. Further quantities of Y can be purchased for Rs.4 per unit. Overhead recovery rates are: Variable overhead Rs.2 per direct labour hour worked. Fixed overhead Rs.3 per direct labour hour worked. Total fixed overheads not alter as a result of the current venture. Feedback from advertising will enable the exact demand to be determined at the end of quarter I and production in quarter II will be set to equal that demand. However it is necessary to decide now on the sales price in order that it can be incorporated into the advertising campaign. Required: (a) Calculate the expected money value of the venture at each sales price and on the basis of this advice W ltd of its best course of action. (b) Briefly explain why the management of W ltd. might rationally reject the sales price leading to the highest expected money value and prefer one of the other sales prices. Solution: Part A: Step 1: Calculation of total cost at all output levels Units

Quant ity of X 2,000 2,000 3,000 3,000 4,000 4,000 5,000 5,000 6,000 6,000 8,000 8,000 10,000 10,000 15,000 15,000

Rs.(X) 18,000 27,000 36,000 45,000 54,000 72,000 90,000 1,35,000

Quant ity of Y 4,000 6,000 8,000 10,000 12,000 16,000 20,000 30,000

Rs.(Y) (8,000) (12,000) (16,000) (20,000) (24,000) (32,000) (16,000) 24,000

Grade I Hours 4,000 6,000 8,000 10,000 12,000 16,000 20,000 30,000

Grade I (Rs.) 4,000 8,000 12,000 16,000 24,000 32,000 52,000

Grade II Hours 2,000 3,000 4,000 5,000 6,000 8,000 10,000 15,000

Grade II (Rs.) 3,000 6,000 12,000 18,000 33,000

Variab le OH (Rs.) 12,000 18,000 24,000 30,000 36,000 48,000 60,000 90,000

Total 22,000 37,000 52,000 70,000 88,000 1,24,000 1,84,000 3,34,000

Notes: 1) Material ‘X’ is in stock and regularly used. Hence the relevant cost is its replacement cost of Rs.9 per unit. The book value of per unit is irrelevant because it is historical cost. 2) 16,000 units of Material ‘Y’ is in stock due to excess purchase. If not used will be disposed off by spending Rs.2 per unit. Hence, usage saves disposal cost which is a relevant benefit.

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AMA-Notes 3) Any usage in excess of 16,000 units need to be purchased by spending Rs.4 per unit which is the relevant cost for the excess consumption. For example: 30,000 Units a. In stock – 16,000 Units – Relevant benefit = 16,000 Units x Rs.2 = Rs.32,000 b. To be purchased – 14,000 Units – Relevant Cost = 14,000 Units x Rs. 4 = Rs.56,000 Net Relevant cost = Rs,24,000 4) 4,000 hours of idle time of G – I and G – II available and relevant cost for using idle time is ‘Nil’. Any excess hours above 4,000 will have a relevant cost of Rs.2 and Rs.3 for G – I and G – II respectively. 5) Variable cost per unit is Rs.6 (3 Hours x Rs.2). 6) Fixed costs are irrelevant because they do not alter due to the current venture. Step 2: Profit when selling price is Rs.20 Units Probability Computation (Sales – Variable Cost – Advertising Cost) 4,000 0.1 80,000 – 52,000 – 20,000 6,000 0.4 1,20,000 – 88,000 – 20,000 8,000 0.5 1,60,000 – 1,24,000 – 20,000 Total Profit/(Total Loss)

Profit (Rs.) 8,000 12,000 16,000

Expected Profit (Rs.) 800 4,800 8,000 13,600

Step 3: Profit when selling price is Rs.25 Units Probability Computation (Sales – Variable Cost – Advertising Cost) 2,000 0.1 50,000 – 22,000 – 50,000 5,000 0.2 1,25,000 – 70,000 – 50,000 6,000 0.2 1,50,000 – 88,000 – 50,000 8,000 0.5 2,00,000 – 1,24,000 – 50,000 Total Profit/(Total Loss)

Profit (Rs.) (22,000) 5,000 12,000 26,000

Expected Profit (Rs.) (2,200) 1,000 2,400 13,000 14,200

Step 4: Profit when selling price is Rs.40 Units

Probability Computation (Sales – Variable Cost – Advertising Cost) 0 0.2 0 – 0 – 1,00,000 3,000 0.5 1,20,000 – 37,000 – 1,00,000 10,000 0.2 4,00,000 – 1,84,000 – 1,00,000 15,000 0.1 6,00,000 – 3,34,000 – 1,00,000 Total Profit/(Total Loss)

Profit (Rs.) (1,00,000) (17,000) 1,16,000 1,66,000

Expected Profit (Rs.) (20,000) (8,500) 23,200 16,600 11,300

The highest expected money value comes in Option – 2. Hence it should be selected i.e. price the new product at Rs.25. Part B: Why management may reject Rs.25 selling price? 1) A selling price of Rs.20 guarantees no loss. Even when the demand is lowest it gives a profit of Rs.8,000. 2) Selling price of Rs.40 promises a profit as high as Rs.1,66,000 and hence may be preferred by management. E M Reddy

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AMA-Notes 3) However selling price of Rs.25 neither guarantees no loss nor promises high profit. Hence, can be rationally rejected by management. Conclusion: Is expected money value decision wrong i.e. is the mean unreliable for decision making? Answer: Mean (Average) is superior to all tactical methods. The selling price of Rs.25 has only 10% chance of having loss. Due to this on should not go for selling price of Rs.20. If it is made, then the business men is unwilling to take risk. Selling price of Rs.40 has 70% chance of loss. In that option it is undue risk. Business is all about taking calculated risk which happens by making decisions based on expected values. Question no 15: Ram ltd has spare capacity in two of its manufacturing departments – Department 4 and Department 5. A five-day week of 40 hours is worked but there is only enough internal work for three days per week so that two days per week (16 hours) could be available in each department. In recent months Ram ltd has sold this time to another manufacturer but there is some concern about the profitability of this work. The accountant has prepared a table giving the hourly operating costs in each department. The summarized figures are as follows: Particulars Department 4 (Rs.) Department 5 (Rs.) Power Costs 40 60 Labour Costs 40 20 Overhead Costs 40 40 Total 120 120 The labour force is paid on time basis and there is no change in the weekly wage bill whether or not the plant is working at full capacity. The overhead figures are taken from the firm’s current capacity. The overheads figures are taken the firm’s current overhead absorption rates. These rates are designed to absorb all budgeted overhead (fixed and variable) when the departments are operating at 90% full capacity (assume a 50 week year). The budgeted fixed overhead attributed to department 4 is Rs.36,000 p.a. and that for department 5 is Rs.50,400 p.a. As a short term expedient the company has been selling processing time to another manufacturer who has been paying Rs.70 per hour for time in either department. This customer is very willing to continue this arrangement and to purchase any spare time available but Ram ltd is considering the introduction of a new product on a minor scale to absorb the spare capacity. Each unit of the new product would require 45 minutes in department 4 and 20 minutes in department 5. The variable cost of the required input material is Rs.10 per unit. It is considered that:  With a selling price of Rs.100 the demand would be 1,500 units p.a.;  With a selling price of Rs.110 the demand would be 1,000 units p.a.; and  With a selling price of Rs.120 the demand would be 500 units p.a.; You are required to calculate the best weekly programme for the slack time in the two manufacturing departments and to determine the best price to charge for the new product. Solution: Step 1: Calculation of Variable Overheads per Hour Particulars Department 4 Department 5 A. Full Capacity (100%) (40 Hours x 50 Weeks) 2,000 Hours 2,000 Hours

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AMA-Notes B. Normal Capacity (90% x 2,000 Hours) C. Budgeted Fixed Overheads D. Fixed overheads per hour (C/B) E. Overheads per hour F. Variable overheads per hour

1,800 Hours Rs.36,000 Rs.20 Rs.40 Rs.20

1,800 Hours Rs.54,000 Rs.28 Rs.40 Rs.12

Step 2: Relevant cost per hour for operating each department Particulars Power Cost per Hour Variable overheads per hour Total

Department 4 Rs.40 Rs.20 Rs.60

Department 5 Rs.60 Rs.12 Rs.72

Notes: 1) Labour cost per hour is irrelevant because it is paid on time guaranteed basis and hence committed. 2) Selling idle department 4 hour for Rs.70 is viable because we can earn Rs.10 contribution per hour by selling the idle time. 3) However to run department 5 for one hour cost Rs.72 but the realization is only Rs.70 per hour. Hence it is better to keep it idle rather than selling it. Step 3: Variable cost per unit of new product Particulars Direct Materials cost per unit Department 4 relevant cost per unit Department 4 opportunity cost per unit Department 5 relevant cost per unit Total Cost per unit

Computation Given Rs.60 x 45 Minutes/60 Minutes Rs.10 x 45 Minutes/60 Minutes Rs.72 x 20 Minutes/60 Minutes

Amount (Rs.) 10 45 7.5 24 86.5

Step 4: Contribution per unit of new product Particulars Selling Price per unit Variable cost per unit Contribution per unit

Option – 1 (Rs.) 100 (86.5) 13.5

Option – 2 (Rs.) 110 (86.5) 23.5

Option – 3 (Rs.) 120 (86.5) 33.5

Step 5: Determination of Volume 16 Hours x 50 Weeks

Possible Production using department 4 idle time = 45 Minutes (or) 0.75 Hours = 1,067 Units 16 Hours x 50 Weeks

Possible Production using department 5 idle time = 20 Minutes (or) 0.33 Hours = 2,400 Units To conclude, we can maximum produce only 1,067 units of the new product. Particulars Selling Price Demand

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Option – 1 Option – 2 Option – 3 Rs.100 Rs.110 Rs.120 1,500 Units 1,000 Units 500 Units

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AMA-Notes Production 1,067 Units 1,067 Units 1,067 Units Possible Volume 1,067 Units 1,000 Units 500 Units Step 6: Contribution of each option Particulars Possible Volume Contribution per unit Total Contribution

Option – 1 1,067 Units Rs.13.5 Rs.14,405

Option – 2 1,000 Units Rs.23.5 Rs.23,500

Option – 3 500 Units Rs.33.5 Rs,16,750

The company should fix a selling price of Rs.110 and sell 1,000 Units since this option gives highest incremental contribution. Step 7: Plan to use spare capacity and the resulting incremental profit Department 4:- 800 Hours - New Product – 1,000 Units x 0.75 Hours = 750 Hours - Sell – 50 Hours Department 5:- 800 Hours - New Product – 1,000 Units x 0.333 Hours = 333 Hours - Keep idle – 467 Hours Due to the above decision the incremental profit to the company is Rs.23,500 due to using the spare capacity for new product and Rs.934 (467 Hours x Rs.2) by avoiding Rs.2 loss on account of sale of the idle capacity. Therefore, incremental profit is Rs.24,434 (Rs.23,500 + Rs.934).

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AMA-Notes 7. MARGINAL COSTING 7.1. Learning Objectives

1) Basics in Marginal Costing a) Income statement b) PV Raito c) Break-even point (Value and Units) d) Margin of Safety (Value and Units) e) Profit 2) Issues in the concept of Break-even point a) Multiple Break-even points (Step fixed cost) b) Break-even point and semi variable cost c) Marginal costing break-even point vs. Absorption costing break-even point d) Break-even point with specific fixed cost 3) Indifference point a) Basic problem b) Indifference point as a state of demand c) Indifference point and Break-even point d) Indifference point with specific fixed cost e) Indifference point expressed as a limiting factor 4) Differential Costing (marginal cost, Marginal Revenue analysis) 5) Limiting factor problems a) Basic limiting factor allocation b) Limiting factor in a make or buy situation c) Limiting factor allocation with specific fixed cost d) Multiple limiting factor allocation having consistent ranks 6) Concept of shutdown point 7) Miscellaneous problems 7.2. Basics in Marginal Costing

Example: Selling price per unit = Rs.10 Variable cost per unit = Rs.6 Fixed Cost = Rs.10,000 Sales = 6,000 Units Prepare or Calculate: 1) Income Statement 2) PV Ratio 3) Break-even point or Break-even sales (Units/Value) 4) Margin of Safety (Units & Value) 5) Profit Solution:

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AMA-Notes 7.2.1. Income Statement

Step 1: Income Statement Particulars Sales Less: Variable Cost Contribution Less: Fixed Cost Profit

Computation Amount (Rs.) 6,000 Units x Rs.10 60,000 6,000 Units x Rs.6 (30,000) 24,000 Given (10,000) 14,000

Notes: 1) The above income statement is very helpful in assessing the impact of volume on cost and profit. 2) Hence, the chapter is also referred as Cost Volume Profit analysis (CVP analysis). 7.2.2. PV Ratio

Step 2: PV Ratio PV Ratio =

Contribution per unit

PV Ratio =

Contribution

Selling Price

Sales

Rs.4

= Rs.10 = 40%

Rs.24,000

= Rs.60,000 = 40%

Notes: 1) A PV ratio of 40% means, when the sales is Rs.100 contribution is Rs.40. 2) It also means when the sales changes by Rs.100, the profit and contribution changes by Rs.40. 3) Change in Profit = Change in Contribution because fixed cost does not change. 7.2.3. Breakeven Point

Step 3: Break-even Point 1) Break-even point is the sales level at which the profit is ‘0’. 2) At that sales level sales = Total cost & contribution = fixed cost. 3) This break-even point or sales can be expressed in two ways: Fixed Cost

a. In units = Contribution per unit =

Rs.10,000 Rs.4

= 2,500 Units

b. In Value i. Break-even point in units x Selling price per unit – 2,500 Units x Rs.10 = Rs.25,000 ii.

Fixed Cost PV Ratio

=

Rs.10,000 40%

= Rs.25,000

7.2.4. Margin of Safety

Step 4: Margin of Safety 1) Margin of Safety is the sales above break-even sales. E M Reddy

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AMA-Notes 2) It is the sales that can drop before the company starts incurring losses. 3) It is profit generating sales. 4) This Margin of Safety also can be expressed in units or value: a. In Units i. Actual Sales – Break-even Point = 6,000 Units – 2,500 Units = 3,500 Units ii.

Profit Contribution per Unit

=

Rs.14,000 Rs.4

= 3,500 Units

b. In Value i. Actual Sales – Break-even Sales = Rs.60,000 – Rs.25,000 = Rs.35,000 ii. Margin of Safety x Selling Price = 3,500 Units x Rs.10 = Rs.35,000 iii.

Profit PV Ratio

=

Rs.14,000 40%

= Rs.35,000

Notes: 1) Contribution is linked to sales, fixed cost to break-even sales and profit to Margin of Safety. 2) When we produce and sell 1 unit, we incur variable cost and also receive selling price. What stays in hand is Contribution. 3) Contribution contributes: a. Towards Fixed Cost Recovery – Up to Breakeven Sales b. Towards Profit – For Margin of Safety Sales 7.2.5. Profit

Step 5: Profit 1) 2) 3) 4)

Profit = Sales – Cost = Rs.60,000 – Rs.46,000 = Rs.14,000 Profit = Contribution – Fixed Cost = Rs.24,000 – Rs.10,000 = Rs.24,000 Profit = Margin of Safety in Units x Contribution per unit = 3,500 Units x Rs.4 = Rs.14,000 Profit = Margin of Safety in value x PV Ratio = Rs.35,000 x 40% = Rs.14,000

Conclusion: For the all above formulas to be true the volume should not affect selling price, variable cost per unit or the total fixed cost. In other words we assume in linearity in relationship. If the linearity assumption does not hold good what happens is the subject matter of discussion. 7.3. Issues in the concept of Break-even point 7.3.1. Multiple break-even points (Step fixed cost)

1) Whenever the fixed cost and variable cost/unit are varying at different levels, then the usage of formula will not be rewarding. 2) Use the spirit of basic knowledge of marginal costing in solving the Break-even Point. 3) At Break-even Point, Sales = Cost (or) Profit = 0 Question no 1: A firm sells its produce at Rs.25 per unit. Its cost behavior for various production ranges is: Units of production Cumulative fixed cost Variable cost per unit 0 – 16,000 2,50,000 16.00 16,001 – 60,000 3,50,000 17.00 60,001 and above 5,00,000 20.00 E M Reddy

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AMA-Notes Identify the break-even point(s) in units. Solution: Step 1: Calculation of Break-even in range I Items Selling Price Less: Variable Cost Contribution Fixed Cost Break-even Point (Rs.2,50,000/Rs.9)

Particulars Rs.25 (Rs.16) Rs.9 Rs.2,50,000 27,778 Units

We cannot call 27,778 units as Break-even point because Range I exist only up to 16,000 Units, beyond which the cost pattern itself changes. We can conclude that there is no break-even in Range I i.e. Range I generates only loss. Step 2: Unrecovered fixed cost in Range I Contribution (16,000 Units x Rs.9) Less: Fixed Cost Unrecovered fixed cost

= Rs.1,44,00 = Rs.2,50,000 = Rs.1,06,000

Step 3: Calculation of Break-even in range II Items Selling Price Less: Variable Cost Contribution Incremental fixed cost for Range II (Rs.3,50,000 – Rs.2,50,000) Unrecovered fixed cost of Range I Fixed cost recoverable in Range II Units required to recover fixed cost (Rs.2,06,000/Rs.8) Break-even point (25,750 Units + 16,000 Units) Check: Particulars Computation Contribution [16,000 Units x Rs.9] + [25,750 Units x Rs.8] Less: Fixed Cost Given Profit

Particulars Rs.25 (Rs.17) Rs.8 Rs.1,00,000 Rs.1,06,000 Rs.2,06,000 25,750 Units 41,750 Units Amount (Rs.) 3,50,000 3,50,000 0

Company breaths air of profit only on reaching 41,750 units in Range II. Range II extends up to 60,000 units. From 41,750 units to 60,000 units the contribution generated results in profit. Step 4: Profit generated by Range II Profit generating units (60,000 Units – 41,750 Units) = 18,250 Units Contribution per unit = Rs.8 Profit (18,250 Units x Rs.8) = Rs.1,46,000

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AMA-Notes Step 5: Calculation of Break-even in Range III Items Selling Price Less: Variable Cost Contribution Incremental fixed cost for Range III (Rs.5,00,000 – Rs.3,50,000) Recovery through profit from Range II Fixed cost recoverable in Range III Units required to recover fixed cost (Rs.4,000/Rs.5) Break-even point (60,000 Units + 800 Units)

Particulars Rs.25 (Rs.20) Rs.5 Rs.1,50,000 Rs.1,46,000 Rs.4,000 800 Units 60,800 Units

Check: Particulars Computation Contribution [16,000 Units x Rs.9] + [44,000 Units x Rs.8] + [800 Units x Rs.5] Less: Fixed Cost Given Profit

Amount (Rs.) 5,00,000 5,00,000 0

Step 6: Analysis of profitability and sales range Sales Range 0 – 41,749 Units 41,750 Units 41,751 – 60,000 Units 60,001 – 60,799 Units 60,800 Units Above 60,800 units

Profitability Loss Zero (BEP1) Profit Loss Zero (BEP2) Profit

Notes: 1) When we have step fixed cost i.e. fixed cost increases at output different output ranges, we may have multiple breakeven points. 2) In such situation break-even should be analyzed range by range. 3) Generally higher volumes results in higher profit only when linearity is satisfied. In case of step fixed cost this linearity is absent. Hence, more volume need not give higher profits. For example, at 60,000 units the profit is Rs.1,46,000 but at 60,801 units the profit is only Rs.5. Question no 2: SCV is a leading cable TV service provide with its operations spread over different cities. It has recently been approached by the city of Chennai to operate its cable television operations. Chennai city officials have become tired to reporting on the cable television company they have operated for the past five years. SCV makes the following assumptions in its planning after negotiations with key parties. A basic set of 10 cable television stations will be offered at Rs.20 per month per subscriber. These 10 stations include a sports channel, a news channel and other general audience channels. Chennai would retain ownership of the physical facilities and would maintain them in working condition. Under a leasing agreement, SVC will pay Chennai the following charges:

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AMA-Notes 

Fixed commitment charges: Rs.50,000 per month if number of subscribers is 10,000 or less and Rs.75,000 per month, if the number of subscribers is more than 10,000.  Variable revenue share: 10% of the monthly revenues from the first 10,000 subscribers and 5% from additional subscribers. SCV will receive the ten channels in its basic service from interlink cable. Interlink acts as a intermediary between cable television stations and companies such as SCV, which sell to individual subscribers. Interlink charges a monthly-fixed fees of Rs.20,000 plus monthly charge of Rs.8 per subscriber for the first 20,000 subscribers and Rs.6 per subsequent subscriber. SCV estimates its own operating costs to include both a fixed and variable component. The fixed component if Rs.55,000 per month up to 20,000 subscribers. It is expected to increase by Rs.15,000 per month, if number of subscribers exceeds 20,000 subscribers. Variable cost per subscriber is Rs.2 per month. Required: a) How does the contribution margin per subscriber behave over the 0 to 30,000 – subscriber range? b) Calculate the break-even number of subscribers per month for SCV. c) What is the operating income per month to SCV with (a) 10,000 (b) 20,000 (c) 30,000 subscribers? Comment on the results. Solution: Step 1: Analysis of facts 1) SCV collects a revenue of Rs.20 from each subscriber. 2) It incurs the following costs: i. Payment to Chennai Corporation ii. Payment to Interlink iii. Own Operating Cost 3) Payment to Chennai Corporation: i. Variable Cost a) Up to 10,000 Subscribers – 10% x Rs.20 = Rs.2 b) Beyond 10,000 Subscribers – 5% x Rs.20 = Rs.1 ii. Fixed Cost a) Up to 10,000 Subscribers – Rs.50,000 b) Beyond 10,000 Subscribers – Rs.75,000 4) Payment to Interlink i. Variable Cost a) Up to 20,000 Subscribers – Rs.8 per Subscriber b) Beyond 20,000 Subscribers – Rs.6 per Subscriber ii. Fixed Cost – Rs.20,000 5) Own operating Cost i. Variable Cost – Rs.2 per subscriber ii. Fixed Cost a) Up to 20,000 subscribers – Rs.55,000 b) Beyond 20,000 subscribers – Rs.70,000

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AMA-Notes Step 2: Behavior of costs at different Ranges Particulars Selling Price Less: Variable Cost Own Variable Cost Paid to Interlink Chennai Corporation Contribution Less: Fixed Cost Own Variable Cost Paid to Interlink Chennai Corporation Fixed Cost

0 – 10,000 (Rs.) 10,001 – 20,000 (Rs.) 20,001 – 30,000 (Rs.) 20 20 20 (2) (8) (2) 8

(2) (8) (1) 9

(2) (6) (1) 11

55,000 20,000 50,000 1,25,000

55,000 20,000 50,000 1,50,000

70,000 20,000 75,000 1,65,000

Step 3: Summary of the above analysis Range 0 -10,000 10,001 – 20,000 20,001 – 30,000

Fixed Cost (Rs.) 1,25,000 1,50,000 1,65,000

Contribution/Subscriber (Rs.) 8 9 11

Step 4: Break-even point in Range I Fixed Cost Contribution/Subscriber

= Rs.1,25,000 = Rs.8

Break-even point

=

Rs.1,25,000 Rs.8

= 15,625 Subscribers

We cannot call 15,625 subscribers as break-even point because Range I exists only up to 10,000 subcribers beyond which the cost pattern changes. We can conclude that there is no break-even point in Range I and Range I ends up with unrecovered fixed cost. Step 5: Unrecovered fixed cost in Range I Contribution (10,000 Subscribers x Rs.8) Less: Fixed Cost Unrecovered fixed cost

= Rs.80,000 = Rs.1,25,000 = Rs.45,000

Step 6: Break-even point in Range II Contribution per subscriber Incremental fixed cost (Rs.1,50,000 – Rs.1,25,000) Unrecovered fixed cost brought forward from Range I Recoverable fixed cost in Range II (Rs.25,000 + Rs.45,000) Subscribers required to recover (Rs.70,000/Rs.9) Break-even point (10,000 + 7,778)

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= Rs.9 = Rs.25,000 = Rs.45,000 = Rs.70,000 = 7,778 Subscribers = 17,778 Subscribers

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AMA-Notes Range II extends up to 20,000 subscribers. The Margin of Safety in Range II is 2,222 subscribers (20,000 – 17,778). Profit at the end of Range II = 2,222 Subscribers x Rs.9 = Rs.19,998 or Rs.20,000. Thus Range II ends with profit of Rs.20,000. Step 7: Break-even point in Range III Contribution per subscriber Incremental fixed cost in Range III (Rs.1,65,000 – Rs.1,50,000) Profit brought forward from Range II

= Rs.11 = Rs.15,000 = Rs.20,000

Range III need not break-even because its entire incremental fixed cost is recovered from Range II profit. The Range III starts with a profit of Rs.5,000. Step 8: Calculation of profit to SCV at the end of each Range Subscribers 10,000 20,000 30,000

Profit/(Loss) (Rs.) (45,000) 20,000 5,000 + [10,000 x 2] = 1,50,000

7.3.2. Break-even point with semi-variable cost

**Question no 3: Kalyan University conducts a special course on computer application during summer. For this purpose, it invites applications from graduates. An entrance test is given to the candidates and based on the same, a final selection of a hundred candidates is made. The entrance test consists of four objective type of examination and is spread over four days, one examination per day. Each candidate is charged a fee of Rs.50 for raking up the entrance test. The following data was gathering for the past two years. Statement of net Revenue from the Entrance test for the course on “Computer Application” Particulars Year 1 (Rs.) Year 2 (Rs.) Gross Revenue (Fees collected) 1,00,000 1,50,000 Costs Valuation 40,000 60,000 Question booklets 20,000 30,000 Hall rent at Rs.2,000 per day 8,000 8,000 Honorarium to chief 6,000 6,000 Administrator Supervision charges 4,000 6,000 1 supervisor for every 100 candidates at Rs.50 per day General Administration expenses 6,000 6,000 Total Cost 84,000 1,16,000 Net Revenue 16,000 34,000 Required to compute: a) The budgeted net revenue, if 4,000 candidates take up the entrance test Year 3. b) The break-even number of candidates. c) The number of candidates to be enrolled if the net income desired is Rs.20,000

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AMA-Notes Solution: Step 1: Analysis of the cost behavior pattern Particulars No.of students Revenue (Rs.) Cost: Valuation Questions Booklet Supervision Hall Rent Honorarium Administration expenses

Year 1

Year 2

Incremental (Rs.) 2,000 3,000 1,000 1,00,000 1,50,000 50,000

Analysis

40,000 20,000 4,000

60,000 30,000 6,000

20,000 10,000 2,000

8,000 6,000 6,000

8,000 6,000 6,000

-

Variable @ Rs.20 Variable @ Rs.10 Variable for every 100 students @ Rs.2 per student Fixed Fixed Fixed

Variable @ Rs.50

Step 2: Calculation of contribution per student Particulars Fees collected Less: Valuation Less: Questions Booklet Less: Supervision cost Total Cost Contribution

Within 100 students (Rs.) 50 (20) (10) 30 20

For every 100 students (Rs.) 50 (20) (10) (2) 32 18

Step 3: Profit calculation when 4,000 students write the exam Particulars Computation Contribution 4,000 Students x Rs.18 Less: Fixed Cost Profit Alternatively, Particulars Gross Revenue Less: Costs Valuation Question Booklet Supervision Hall Rent Honorarium General Administration charges Net Revenue

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Amount (Rs.) 72,000 (20,000) 52,000

Computation 4,000 Students x Rs.50

Amount (Rs.) 2,00,000

4,000 Students x Rs.20 (80,000) 4,000 Students x Rs.10 (40,000) 40 Supervisors x Rs.200 (8,000) (8,000) (6,000) (6,00) 52,000

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AMA-Notes Step 4: Calculation of Break-even point Contribution per student for every 100 students Fixed Cost

= Rs.18 = Rs.20,000

Break-even point Additional fixed to recover [200 – (11 x 2)] Contribution per student within every 100 students

= Rs.18 = 1,111 Students = Rs.178 = Rs.20

Additional students to recover additional fixed cost Break-even students (1,111 Students + 9 Students)

= Rs.20 = 9 Students = 1,120 Students

Rs.20,000

Rs.178

Check: Particulars Fees Less: Variable Cost Less: Supervision cost Less: Fixed Cost Profit/(Loss)

Computation 1,120 Students x Rs.50 1,120 Students x Rs.20 12 Supervisors x Rs.12

Amount (Rs.) 56,000 33,600 2,400 20,000 0

Step 5: Number of students to make a profit of Rs.20,000 Contribution per student for every 100 students Fixed Cost Profit Contribution required (Rs.20,000 + Rs.20,000)

= Rs.18 = Rs.20,000 = Rs.20,000 = Rs.40,000

Number of students Additional fixed to recover [200 – (22 x 2)] Contribution per student within every 100 students

= Rs.18 = 2,222 Students = Rs.156 = Rs.20

Additional students to recover additional fixed cost Break-even students (2,222 Students + 8 Students)

= Rs.20 = 8 Students = 2,230 Students

Rs.40,000

Rs.156

7.3.3. Marginal Costing (vs.) Absorption Costing Break-even point

Question no 4: A company uses absorption costing system based on standard costs. The total variable manufacturing cost is Rs.6 per unit. The standard production rate is 10 units per machine hour. Total budgeted and actual fixed production overhead costs are Rs.8,40,000. Fixed production overhead is allocated at Rs.14 per machine hour. Assume this same standard for the last year and current year. Selling price is Rs.10 per unit. Variable selling overheads is Rs.2 per unit and fixed selling costs are Rs.2,40,000. Beginning inventory was 30,000 units and ending inventory was 40,000 units. 1. Compute BEP under absorption costing system. 2. Compute BEP under marginal costing system. 3. Calculate profit under absorption costing system for the BEP sale under marginal costing system with the stock level as given below.

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AMA-Notes Solution: Facts: Selling Price Variable manufacturing cost Budgeted and Actual fixed manufacturing cost Variable selling cost Fixed selling cost Opening stock Closing Stock Standard rate per hour Standard Rate per unit

Rs.10 Rs.6 Rs.8,40,000 Rs.2 Rs.2,40,000 30,000 Units 40,000 Units Rs.14 Rs.14 = Rs.1.4 10 Units

Step 1: Break-even point under absorption costing system: Total Fixed Cost Fixed manufacturing cost in net stock c/f to next year Net fixed cost recoverable this year through unit sold Contribution per unit Break-even point

Rs.10,80,000 10,000 Units x Rs.1.4 = Rs.14,000 Rs.10,66,000 Rs.10 – Rs.6 – Rs.2 = Rs.2 Rs.10,66,000/Rs.2 = 5,33,000 Units

Step 2: Profit when sales is 5,33,000 Units Particulars Sales Cost of Goods Sold Gross Profit Less: Variable Selling Expenses Less: Fixed Selling Expenses Less: Under Absorption Profit/(Loss)

Computation 5,33,000 Units x Rs.10 5,33,000 Units x Rs.7.4

Amount (Rs.) 53,30,000 (39,44,200) 13,85,800 5,33,000 Units x Rs.2 (10,66,000) Given (2,40,000) 5,43,000 Units x Rs.1.4 – Rs.8,40,000 (79,800) 0

Working Notes: 1) Calculation of cost of goods sold: Full Manufacturing cost per units (Rs.6 + Rs.1.4) = Rs.7.4 Value of opening Stock of finished goods (30,000 Units x Rs.7.4) = Rs.2,22,000 Cost of production (5,43,000 Units x Rs.7.4) = Rs.40,18,200 Value of closing Stock of finished goods (40,000 Units x Rs.7.4) = (Rs.2,96,000) Cost of goods sold (5,33,000 Units x Rs.7.4) = Rs.39,44,200 Rs.7.4 is common, when we take it out the cost of goods sold is Rs.7.4 (30,000 + 5,43,000 – 40,000). 2) Units produced = Units Sold + Closing Stock – Opening Stock = 5,33,000 Units + 40,000 Units – 30,000 Units = 5,43,000 Units

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AMA-Notes Step 3: Profit under marginal costing system when 5,33,000 units are sold Particulars Sales Variable Cost of Goods Sold Gross Contribution Less: Variable Selling Expenses Contribution Less: Fixed Cost Profit/(Loss)

Computation 5,33,000 Units x Rs.10 5,33,000 Units x Rs.6

Amount (Rs.) 53,30,000 (31,98,000) 21,32,000 5,33,000 Units x Rs.2 (10,66,000) 10,66,000 Rs.8,40,000 + Rs.2,40,000 (10,80,000) (14,000)

Step 4: BEP under marginal costing system Total Fixed Cost Rs.10,80,000 Contribution per unit Rs.10 – Rs.6 – Rs.2 = Rs.2 Break-even point Rs.10,80,000/Rs.2 = 5,40,000 Units Step 5: Profit under absorption costing system when sales is 5,40,000 units Particulars Sales Cost of Goods Sold Gross Profit Less: Variable Selling Expenses Less: Fixed Selling Expenses Less: Under Absorption Profit/(Loss)

Computation 5,40,000 Units x Rs.10 5,40,000 Units x Rs.7.4

Amount (Rs.) 54,00,000 (39,96,000) 14,04,000 5,40,000 Units x Rs.2 (10,80,000) Given (2,40,000) 5,50,000 Units x Rs.1.4 – Rs.8,40,000 (70,000) 14,000

Notes: 1) It is known that at a given sales level, marginal costing income statement and absorption costing statement reports different profits when there exists stock. 2) This means when there is stock, the sales level at which the marginal costing reports ‘0’ profit will not be the sales level at which the absorption costing has ‘0’ profit. Thus break-even point is different for marginal and absorption costing systems. 3) In absorption costing system the sales need not recover the entire current year’s fixed cost when there is net closing stock because that portion of fixed cost inside net closing stock escapes to next year. In this problem, out of Rs.10,80,000 fixed cost Rs.14,000 goes to next year. What needs to be recovered only is Rs.10,66,000. 4) Similarly, when there is net opening stock the sales should recover not only the current year fixed stock but also a portion if fixed cost from previous year. 5) Thus when stock are given absorption costing break-even point is calculated as follows: a. Net Closing Stock – Break-even point =

Total Fixed Cost – Fixed Cost in net Closing Stock

b. Net Opening Stock – Break-even point =

Contribution per unit Total Fixed Cost+ Fixed Cost in net Opening Stock Contribution per unit

6) We can observe that at absorption costing break-even point i.e. 5,33,000 units, the absorption costing profit is ‘0’ and the marginal costing loss is Rs.14,000. Similarly, at marginal costing break-even point of 5,40,000 units, the marginal costing profit is ‘0’ and absorption costing profit is Rs.14,000. To conclude, E M Reddy

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AMA-Notes absorption costing system profit is Rs.14,000 is always higher than marginal costing system profit because of fixed inside net stock (10,000 Units x Rs.1.4). **Question no 5: The following is the production and sales given for six periods: In ‘000 P1 P2 P3 P4 P5 P6 Sales 150 120 180 150 140 160 Production 150 150 150 150 170 140 Other details are: Selling Price Rs.10 Variable manufacturing cost Rs.6 Fixed manufacturing cost (Budget and Actual) Rs.3,00,000 Non-manufacturing overhead Rs.1,00,000 Budgeted activity level for the period 1,50,000 Units Calculate BEP under Absorption costing and Marginal costing system for all the periods. Solution: Facts: Selling Price = Rs.10 Variable Manufacturing Cost = Rs.6 Fixed Manufacturing Overheads = Rs.3,00,000 Fixed non-manufacturing overheads = Rs.1,00,000 Units produced – Years 1 – 4 = 1,50,000 Units Year 5 = 1,70,000 Units Year 6 = 1,40,000 Units Denominator level unit/Normal Capacity = 1,50,000 Units Break-even Point under absorption costing system: FMOH

TFC−[ UD xUP] TFC−Absorbed FMOH Break-even Point = FMOH or SP−VC−Absorption Rate SP−VC− UD

Period Computation Break-even Point P1 – P4 [4,00,000−3,00,000x1,50,000] 50,000 Units 1,50,000

P5

10−6−2 3,00,000 [4,00,000− x1,70,000] 1,50,000

30,000 Units

10−6−2

P6

3,00,000 x1,40,000] 1,50,000

[4,00,000−

60,000 Units

10−6−2

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AMA-Notes Break-even point formula: FMOH

TFC−[ UD xUP] TFC−Absorbed FMOH Break-even Point = FMOH or SP−VC−Absorption Rate; where SP−VC− UD

TFC = Total Fixed Cost (FMOH + FNMOH) FMOH = Fixed Manufacturing Capacity UD = Normal Capacity/Denominator Level Units VC = Variable cost per unit (VMC + VNMC) Notes: 1) Derivation of the Formula: a. Calculation of Total Cost: FMOH

Manufacturing cost of goods sold – [VMC + ] x US UD Add: Variable non-manufacturing cost – [US x VNMC per unit] Add: Fixed Non-manufacturing cost FMOH

Add: FMOH – [UP x UD xUP] (Actual Overheads – Absorbed Overheads) b. The total cost formula can be further simplified as follows: FMOH

Total Cost = Units Sold x [VC + UD ] + FNMC + FMOH c. It can be further simplified as follows: FMOH

FMOH UD

xUP]

FMOH

Total Cost = US x [VC + UD ] + TFC - UD xUP d. The units sold can be called as break-even point only when sales = Total Cost US x SP = US x [VC + US x SP – US x [VC + US [SP – VC – US =

FMOH

FMOH

UD FMOH

UD FMOH

UD

] + TFC -

] = TFC -

FMOH

FMOH

UD

UD

] = TFC -

UD

xUP

xUP

x UP

FMOH xUP] UD FMOH SP−VC− UD

TFC−[

“US” is called Break-even point. 2) For decision making purpose always use marginal costing break-even point. 3) When manager’s financial rewards are linked to division’s profits calculated using absorption costing system, they would like to know the sales demand to break-even and work towards achieving that demand. 4) However, if the company is lenient on stock policy, the absorption costing may be counter-productive. For example, if the manager feels the demand will be only 50,000 units compared to the budgeted 1,50,000 units, he may still break-even by producing more (1,50,000 Units). What happens is by increasing production the stock is increased and by increasing stock fixed cost recondition is postponed and low sales can even break-even which is for good for the company. 5) To conclude, both for decision making and performance evaluation it is better to use marginal costing system.

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AMA-Notes 7.3.4. Break-even point with two products

Question no 6: Ezee ltd. makes two products E and Z. All units produced are sold. There is no inventory buildup. Production facilities may be used interchangeably for both the products. Sales units are the limiting factor. The following information is given: Price Level Proposed Increase E Z Total Total Contribution p.u. 25 20 Fixed Cost 46,000 47,500 Sales Units 3,000 2,000 5,000 4,000 For increase in quantities above 4,000 units for each product, there will be an increase in variable selling costs (for the increased portion only) thereby reducing the contribution per unit to the following figures: Units Contribution per unit of E Contribution per unit of Z 4,001 – 5,000 20 15 5,001 – 6,000 15 10 Above 6,000 No Sales Possible i. For the present level, find the break-even point with the present product. ii. What is the minimum number of incremental units to be sold to recover the additional fixed cost of Rs.47,500 to be incurred? (Present product mix need not be maintained) iii. If you are allowed to choose the best product mix for the incremental level (while taking the present mix given in the first table above for the present level) what would be the individual product quantities and the corresponding total contributions, the total average contribution per unit and the total profits for the complete production? Solution: Part 1: Break-even point for present situation When we have multiple products with a given sales mix, Fixed Cost

BEP = Weighted Contribution per unit 3

2

Weighted Contribution per unit = [5 x25] + [ 5 x20] = Rs.23 BEP =

Rs.46,000 Rs.23

= 2,000 Units

Product ‘E’ = 2,000 Units x 3/5 = 1,200 Units Product ‘Z’ = 2,000 Units x 3/5 = 800 Units Check: Contribution from product ‘E’ (1,200 Units x Rs.25) Contribution from product ‘Z’ (800 Units x Rs.20) Total Contribution Less: Fixed Cost Profit/(Loss)

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= Rs.30,000 = Rs.16,000 = Rs.46,000 = (Rs.46,000) =0

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AMA-Notes Part 2: Calculation of units to be sold to recover incremental fixed cost Increment Fixed Cost to be recovered Contribution through additional units of product ‘E’ (1,000 Units x Rs.25) Fixed cost to be recovered through product ‘Z’ Contribution per unit of Product ‘Z’ Additional units to be sold of product ‘Z’

Rs.22,500 Rs.20

= Rs.47,500 = (Rs.25,000) = Rs.22,500 = Rs.20 = 1,125 Units

Alternatively, Increment Fixed Cost to be recovered Contribution through additional units of product ‘E’ (1,000 Units x Rs.25) Contribution through incremental units of product ‘E’ (1,000 Units x Rs.20) Fixed cost to be recovered through product ‘Z’ Contribution per unit of Product ‘Z’ Additional units to be sold of product ‘Z’

Rs.2,500 Rs.20

= Rs.47,500 = (Rs.25,000) = (Rs.20,000) = Rs.2,500 = Rs.20 = 1,125 Units

In both the cases, we recover Rs.47,500 fixed cost. Part 3: Production plan for the new plant 4,000 Units - Product ‘E’ (3,000 Units – 4,000 Units) = 1,000 Units x Rs.25 = Rs.25,000 - Product ‘E’ (4,000 Units – 5,000 Units) = 1,000 Units x Rs.20 = Rs.20,000 - Product ‘Z’ (2,000 Units – 4,000 Units) = 2,000 Units x Rs.20 = Rs.40,000 Contribution = Rs.25,000 + Rs.20,000 + Rs.40,000 = Rs.85,000 Fixed Cost = Rs.47,500 Profit = Contribution – Fixed Cost = Rs.85,000 – Rs.47,500 = Rs.37,500 Rs.85,000

Average contribution per unit = 4,000 Units = Rs.21.25 per unit 7.4. Indifference Point 7.4.1. Introduction to Indifference point

1) Concept of indifference point will arise when we have two options: a. Option 1 – Low fixed cost and high variable cost per unit b. Option 2 – Low variable cost per unit and high fixed cost 2) When the volume is high it is better to go for low variable cost option and at low volume low fixed cost option. 3) At some volume, both options will give same profit or have same cost which is called indifference point. 4) This indifference point volume can be expressed in two ways: a. In Units i. ii.

Difference in Fixed Cost Difference in Variable Cost per Unit Difference in Fixed Cost Difference in Contribution per Unit

b. In Volume i. E M Reddy

Difference in Fixed Cost Difference in Variable Cost Ratio

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AMA-Notes ii.

Difference in Fixed Cost Difference in PV Ratio

Question no 7: Company Variable cost per unit Fixed Cost P 9 60,000 Q 5 50,000 At what sale range is P more profitable than Q and vice versa? Assume that both the products have the same selling price. Solution: Step 1: Indifference point Difference in Fixed Cost

Indifference point = Difference in Variable Cost per Unit =

90,000−60,000 9−5

=

30,000 4

= 7,500 Units

Check: The cost of both companies at 7,500 units volume is as follows: Particulars P Q Variable Cost 7,500 Units x Rs.9 = Rs.67,500 7,500 Units x Rs.5 = Rs.37,500 Fixed Cost Rs.60,000 Rs.90,000 Total Cost Rs.127,500 Rs.127,500 At 7,500 units total cost is same for P & Q and since selling price is also same, they should have the same profit. Step 2: Conclusion Range Less than 7,500 Units At 7,500 Units More than 7,500 Units

Company P P or Q Q

Reason Low fixed cost Indifference Point Low Variable Cost

Question no 8: Two business AB ltd. and CD ltd. sells the same type of product in the same type of market. Their budget profit and loss accounts for the year ending 2008 are as follows: AB ltd. CD ltd. Rs. Rs. Rs. Rs. Sales 1,50,000 1,50,000 Less: Variable Costs 1,20,000 1,00,000 Less: Fixed Costs 15,000 35,000 1,35,000 1,35,000 Net profit budgeted 15,000 15,000 You are required to: a) Calculate the break-even point of each business b) Calculate the sales volume at which each of the business will earn Rs.5,000 profit; and c) State which business is likely to earn greater profits in conditions of: i. Heavy demand for the product; ii. Low demand for the product.

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AMA-Notes Solution: Step 1: Calculation of Break-even point Particulars Sales Less: Variable Cost Contribution PV Ratio (Contribution/Sales) Fixed Cost Break-even sales (Fixed Cost/PV Ratio)

AB ltd. Rs.1,50,000 (Rs.1,20,000) Rs.30,000 20% Rs.15,000 Rs.75,000

CD ltd. Rs.1,50,000 (Rs.1,00,000) Rs.50,000 33.33% Rs.35,000 Rs.1,05,000

Step 2: Sales to earn profit of Rs.5,000 Particulars Profit Add: Fixed Cost Contribution PV Ratio Sales (Contribution/PV Ratio)

AB ltd. Rs.5,000 Rs.15,000 Rs.20,000 20% Rs.1,00,000

CD ltd. Rs.5,000 Rs.35,000 Rs.40,000 33.33% Rs.1,20,00

Step 3: Calculation of indifference point Indifference point =

Difference in Fixed Cost Difference in PV Ratio

=

35,000−15,000 33.33%−20%

20,000

= 13.33% = Rs.1,50,000

Analysis of the company over the different sales range: Sales Range Less than Rs.1,50,000 At Rs.1,50,000 Greater than Rs.1,50,000

Company AB ltd. AB ltd. or CD ltd. CD ltd.

Reason Low fixed cost (or) Low Break-even Sales Indifference Point Low Variable Cost Ratio (or) High PV Ratio

7.4.2. Indifference point as a state of demand

Question no 9: The current average weekly trading results of the Hotel Saravana Bhavan are shown below. (Rs.) (Rs.) Turnover 2,800 Operating Costs: Materials 1,540 Power 280 Staff 340 Building Occupancy costs 460 2,620 Profit 180 The average selling price of each meals is Rs.4; materials and power may be regarded as a variable cost varying with the number of meals provided. Staff costs are semi-variable with a fixed cost of Rs.200 per week; the building occupancy costs are all fixed. Required: Calculate the number of meals required to be sold in order to earn a profit of Rs.300 per week.

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AMA-Notes The owners of the restaurant are considering expanding their business and using under-utilized space diversifying into either (1) take-away foods, or (2) high quality meals. The sales estimates for both proposals are rather uncertain and it is recognized that actual sales volume could be up to 20% either higher or lower than that estimated. The estimated sales and costs of each proposal are: Take-Away Foods High Quality Meals Sales Volume, per week 720 200 Meals (Rs.) Meals (Rs.) Average selling price, per meal 1.60 6.00 Variable costs, per meal 0.85 4.66 Incremental fixed costs, per week 610.00 282.00 If either of the above proposals were implemented it has been estimated that the existing restaurant’s operations would be affected as follows: i. As a result of bulk purchasing, material costs incurred would be reduced by 10 paisa per meal. This saving would apply to all meals produced in the existing restaurant. ii. Because more people would be aware of the existence of the restaurant it is estimated that turnover would increase. If the take-away apply to all meals produced in the existing restaurant’s sales would increase by one meal, alternatively if the high quality meals section were open then for every five such meals sold the existing restaurant’s sales would increase by one meal. iii. A specific effect of implementing the take away food proposal would be a change in the terms of the staff in the existing restaurant, the result of which would be that the staff wage of Rs.340 per week would have to be regarded as fixed cost. Required: Calculate, for each of the proposed methods of diversification: i. The additional profit, which would be earned by the owners of the restaurant if the, estimated sales were achieved. ii. The sales volume at which the owners of the restaurant would earn no additional profits from the proposed diversification. Solution: Part 1: Number of meals to be sold to earn a profit of Rs.300 Particulars Sales (Rs.280/Rs.4 = 700 Units) Less: Variable Cost Material (Rs.1,540/700 Meals) Power (Rs.280/700 Meals) Staff (Rs.140/700 Meals) Total Variable Cost Contribution Less: Fixed Cost Building Fixed Staff Cost Total Fixed Cost Profit

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Per Unit (Rs.) Existing (Rs.) Proposed (Rs.) 4 2,800 2.2 0.4 0.2 2.8 1.2

1,540 280 140 1,960 840

960

460 200 660 180

660 300

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AMA-Notes Target Contribution = Rs.960 Contribution per meals= Rs.1.2 Target meals = Rs.960/Rs1.2 = 800 Meals Alternatively, Additional profit Incremental Meals Target Units

= Rs.300 – Rs.180 = Rs.120 = Rs.120/Rs.1.2 = 100 Meals = 700 Meals + 100 Meals = 800 Meals

Part 2: Diversification Step 1: Additional profit the hotel can earn when diversification is made After Diversification Before Diversification Take Away Existing Take Away Selling Price 4 4 1.6 Material 2.2 2.1 0.85 Given Power 0.4 0.4 Staff 0.2 Total Variable Cost 2.8 2.5 0.85 Contribution 1.2 1.5 0.75 Numbers (Meals) 700 772 720 Contribution 840 1158 540 1698 Fixed Cost: Building 460 460 610 Given Staff 200 200 + 140 Total Fixed Cost 660 800 610 1410 Profit 180 288

High Quality Existing High Quality 4 6 2.1 4.66 Given 0.4 0.2 2.7 4.66 1.3 1.34 740 200 962 268 1230 460 200 660 942 288

282 Given 282

If the estimated diversification sales is achieved then both the options gives us Rs.108 additional profit (Rs.288 – Rs.180). Step 2: Number of take away meals to be sold to earn no additional profit from diversification Particulars Quantity Contribution per unit Total Contribution Fixed Cost Profit Existing 700 + 1/10 of X 1.5 1.5 (700 + 1/10X) 800 Take Away X 0.75 0.75X 610 1,410 180 1.5 (700 + 1/10X) + 0.75X – 1,410 = 180 1,050 + 0.15X + 0.75X – 1,410 – 180 = 0 0.9X = 540 → X = 600 Step 3: Number of High quality meals to be sold to earn no additional profit from diversification E M Reddy

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AMA-Notes Particulars Quantity Contribution per unit Total Contribution Fixed Cost Profit Existing 700 + 1/5 of Y 1.30 1.3 (700 + 1/5Y) 660 High Quality Y 1.34 1.34Y 282 942 180 1.3 (700 + 1/5Y) + 1.34Y – 942 = 180 910 + 0.26Y + 1.34Y = 180 + 942 1.6Y = 180 + 942 – 910 Y = 133 Units Conclusion: If the hotel is able to sell 600 take away meals or 133 high quality meals, it earns no additional profit through diversification i.e. it just breaks-even. Notes: 1) Interpretation of the two options viability: Particulars Estimate Maximum Minimum Break-even Take Away (Meals) 720 864 576 600 High Quality (Meals) 200 240 160 133 2) At normal state of demand both options are equally good as they give the same additional profit of Rs.108. 3) If we fear a fall in demand below normal it is better to select high quality meals because even if maximum 20% drop occurs still 160 meals could be sold which is above the break-even point of 133 meals i.e. this option surely gives additional profit even at lowest demand. 4) Since at normal demand both are good, at low demand high quality is good, at high demand take away should be better. 5) Here indifference point is not expressed in units but expressed as a state of demand. 7.4.3. Limiting Factor and Indifference Point

Question no 10: Modern packaging corporation specializes in the manufacture of plastic bottles through moulding operations. The firm has four moulding machines, each capable of producing of 100 bottles per hour. The firm estimates that the variable cost of producing a plastic bottler is 20 paisa. The bottles are sold for 50 paisa each. A local toy company that would like the firm to produce a moulded plastic toy for them has approached management. The toy company is willing to pay Rs.3 per unit for the toy. The variable cost to manufacture the toy will be Rs.2.40. In addition, modern packaging corporation would have to incur a cost of Rs.20,000 to construct the needed mould exclusively for this order. Because the toy uses more plastic and is of more intricate shape than bottle, a moulding machine can produce only 40 units per hour. The customer want 1,00,000 units. Assume that modern packaging corporation has the total capacity of 10,000 machine hours available during the period in which the toy company wants the delivery of toys. The firm’s fixed costs, excluding the costs to construct the toy mould, during the same period will be Rs.2,00,000. Required:

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AMA-Notes a) If the management predicts that the demand for its bottles will require the use of 7,500 machine hours (or) less during the period, should the special order be accepted? Give reasons. b) If the management predicts that the demand for its bottles will be higher than its ability to produce bottles, should the order be accepted? Why? c) The management has located a form that has just entered the moulded plastic business. This firm has considerable excess capacity and more efficient moulding machines and is willing to sub-contract the toy job (or) any portion of it, for Rs.2.80 per unit. It will construct its own toy mould. Determine modern pacing corporation’s minimum expected excess machine hour capacity needed to justify production any portion of the order itself rather that subcontracting it entirely. d) The management predicted that it would have 1600 hours of excess machine capacity available during the period. Consequently, it accepted the toy order and subcontracted 36,000 units to the other plastic company. In fact, demand for bottles turned out to be 9,00,000 units for the period. The firm was able to produce only 8,40,000 units because it has produced the toys. What was the cost of prediction error of failure to predict demand correctly? Solution: Step 1: Calculation of contribution per machine hour and ranking Particulars Selling Price Variable Cost Contribution Units/Hour Contribution/Hour Rank Fixed Cost

Bottle (Rs.) 0.50 (0.20) 0.30 100 30 1 2,00,000

Toy (Rs.) 3.00 (2.40) 0.60 40 24 2 20,000

Step 2: Can toy order be accepted if the bottle uses maximum 7,500 hours In this case we have unused machine capacity of 2,500 hours which is sufficient to produce the 1,00,000 toys (2,500 Hours x 40 Toys = 1,00,000 Toys). The toy order can be accepted if it is viable financially. Contribution from Toy order (2,500 Hours x 24 Less: Incremental fixed cost Incremental Profit

= Rs.60,000 or (1,00,000 Toys x 0.6) = Rs.20,000 = Rs.40,000

Instead of keeping 2,500 hours idle it is better to use it for Toy order and earn an additional profit of Rs.40,000. Step 3: Can toy order be accepted if the bottle demand requires more than 10,000 machine hours No, because we should not transfer the limiting factor from first rank product to second rank i.e. from Bottle to toys hours should not be accepted. Toy can be manufactured only when hours of left after manufacturing for bottle demand. E M Reddy

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AMA-Notes Step 4: Manufacture (vs.) Subcontract Particulars Selling Price Less: Variable Cost Contribution/unit Fixed Cost

Manufacture (Rs.) 3.00 (2.40) 0.60 20,000

Sub-Contract (Rs.) 3.00 (2.80) 0.20 -

Advantage of manufacturing is low variable cost and advantage of sub-contracting is no fixed cost. At high volumes manufacturing is better and at low volumes sub-contracting is better. Difference in fixed csot

Indifference point = Difference in varibale cost per unit = Indifference point in hours = 1) 2) 3) 4)

50,000 Toys 40 Toys/Hour

20,000−0 2.8−24

= 50,000 Toys

= 1,250 Hours

It is worth manufacturing toys only when we plan to manufacture more than 50,000 toys. To manufacture more than 50,000 toys we require at least 1,250 hours after meeting bottle demand. Thus the minimum excess capacity required to justify the toy manufacturing is 1,250 Hours. The implication of the above number can be understood as follows: a. Situation 1 – Bottle demand uses 9,000 Hours – Only 1,000 Hours left for toy manufacture. Since it is less than 1,250 hours do not manufacture toys and sub-contract fully leaving 1,000 hours idle. b. Situation 2 – Bottle demand uses 8,000 Hours – Since available hours 2,000 greater than the minimum 1,250 hours, manufacture 80,000 (2,000 Hours x 40 Toys) toys in this 2,000 hours and sub-contract balance 20,000 Toys.

Step 5: Cost of prediction error Step A: Based on the actual data as implemented by the management Particulars Units (Actual) (Toys) Contribution/Unit (Rs.) Total Contribution (Rs.) Fixed Cost (Rs.) Profit (Rs.)

Bottles 8,40,000 0.30 2,52,000 2,00,000 52,000

Toy Manufacture 64,000 (1,600 Hours x 40 Toys) 0.60 38,400 20,000 18,400

Toy Sub-Contract 36,000 0.20 7,200 7,200

Total Profit (Rs.) = 52,000 + 18,400 + 7,200 = 77,600 Step B: Should have been if the bottle demand is predicted correctly Particulars Units (Actual) (Toys) Contribution/Unit (Rs.) Total Contribution (Rs.) Fixed Cost (Rs.) Profit (Rs.)

E M Reddy

Bottles 9,00,000 0.30 2,70,000 2,00,000 70,000

Toy Manufacture - (Note 1) -

Toy Sub-Contract 1,20,000 0.20 20,000 20,0000

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AMA-Notes Total Profit (Rs.) = 70,000 + 20,000 = 90,000 Note 1: Surplus Hours = 10,000 Hours – [9,00,000 Bottles/100 Bottles per Hour) = 1,000 Hours which is less than 1,250 Hours. Therefore, do not manufacture. Cost of prediction error = Rs.90,000 – Rs.77,600 = Rs.12,400 Additional Notes: 1) It is generally believed that keeping capacity idle is bad but sometimes it may be good to keep the capacity idle rather than use it. Example: After bottle manufacture if hours available is less than 1,250 hours it is better to leave the hours unused and subcontract the toy order. 2) Let us consider two situations: i. Situation 1: Bottle requires 7,600 Hours ii. Situation 2: Bottle requires 9,000 Hours There is no sub-contracting option. How to deal with these two situations i.e. should toy order be accepted or rejected. 3) In situation 1, the toy order can be accepted only by transferring 100 hours from bottle to toy. i. Benefit → Profit from Toy order = Rs.40,000 ii. Cost → Contribution lost from Bottles = Rs.3,000 (100 Hours x Rs.30) In this situation we break the myth that all the hours should be given to first rank product i.e. we compromise on the limiting factor ranking to use full capacity. 4) In situation 2,the toy order can be accepted only by transferring 1,500 hours from bottle to toy. i. Benefit → Profit from Toy Order = Rs.40,000 ii. Cost → Contribution lost from Bottles = Rs.45,000 (1,500 Hours x Rs.30) Here, we should reject the toy order i.e. it is better to keep the capacity idle rather than compromising on limiting factor ranking. 5) There should be an indifference point between limiting factor compromise and idle capacity. It is as follows: Particulars Fixed Profit Variable profit Limiting Factor Rs.40,000 Idle Capacity Rs.30 Change in profit Rs.40,000 Rs.30 Rs.40,000

Indifference point = = 1,333 Hours Rs.30 Indifference point = 7,500 Hours + 1,333 Hours = 8,833 Hours Range Selection 7,500 Hours – 8,833 Hours Do bottle and toy by compromising on limiting factor 8,833 Hours Compromise on limiting factor or keep the capacity is idle i.e accept or reject toy order Greater than 8,833 Hours Reject Toy order and keep the capacity is idle

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AMA-Notes 7.4.4. Understanding how to analyze a semi-variable cost

Example 1: Units 1,000 2,000 3,000

Cost (Rs.) 15,000 20,000 25,000

1) The above cost is not fixed because it changes with volume. It is neither variable because it is not constant per unit. This is semi-variable cost. 2) Semi-variable cost should be analyzed into variable and fixed portion which is done as follows: Change in cost

Variable cost per unit = Change in units =

20,000−15,000 2,000−1,000

= Rs.5 per unit

Fixed cost = Total Cost – Variable Cost = Rs.15,000 – Rs.5,000 (1,000 Units x Rs.5) = Rs.10,000

Example 2: Units 1,000 2,000 3,000

Cost (Rs.) 15,000 19,000 25,000

1) The cost is semi-variable but the relationship between volume and cost is not perfectly correlated because the points do not fit into but are scattered. E M Reddy

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AMA-Notes 2) We have to analyze the semi-variable cost using regression method by finding out line of best fit which is done as follows: Y = mX + C ∑ Y = nC + m∑ X → Equation no.1 ∑ XY = C∑ X + m∑ X 2 → Equation no.2 When we solve the equations we will get m and C i.e. variable cost and fixed cost. X Y XY 𝐗𝟐 1,000 Units 15,000 1,50,00,000 10,00,000 2,000 Units 19,000 3,80,00,000 40,00,000 3,000 Units 25,000 7,50,00,000 90,00,000 16,000 Units 59,000 12,80,00,000 1,40,00,000 59,000 = 3C + 6,000m 12,80,00,000 = 6,000C + 1,40,00,000m When we solve the two equations we obtain m and C, m is variable cost and C is fixed cost. Question no 11: Super press ltd is considering launching a new monthly magazine at a selling price of Rs.1 per copy. Sales of the magazine are expected to be 5,00,000 copies for month, but it is possible that the actual sales could differ quite significantly from this estimate. Two different methods of producing the magazine are being considered and neither would involve any additional capital expenditure. The estimated production costs for each of the two methods of manufacture, together with the additional marketing and distribution costs of selling the new magazine, are summarized below: Method A Method B Variable Costs 55 paisa per copy 50 paisa per copy Specific Fixed Costs Rs.80,000 per month Rs.1,20,000 per month For semi-variable cost the following estimate have been obtained: 3,50,000 copies Rs.55,000 pm Rs.47,500 pm 4,50,000 copies Rs.65,000 pm Rs.52,500 pm 6,50,000 copies Rs.85,000 pm Rs.62,500 pm It may be assumed that the fixed cost content of the semi-variable cost will be remaining constant throughout the range of activity shown. The company currently sells a magazine covering related topics to those that will be included in the new publication and consequently it is anticipated that sales of this existing magazine will be adversely affected. It is estimated that for every ten copies sold of the new publication, sales of the existing will be reduced by one copy. Sales and cost data of the existing magazine are shown below: Sales 2,20,000 copies per month Selling Price 85 paisa per copy Variable Costs 35 paisa per copy Specific Fixed Costs Rs.80,000 per month Required: (a) Calculate, for each production method, the net increase in company profits which will result from the introduction of the new magazine, at each of the following levels of activity.  5,00,000 copies per month  4,00,00o copies per month

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AMA-Notes  6,00,000 copies per month (b) Calculate, for each production method, the amount by which sales volume of the new magazine could decline from the anticipated 5,00,000 copies per month, before the company makes no additional profit from the introduction of the new publication. (c) Briefly identify and conclusions which may be drawn from your calculations. (d) Calculate additional profit if the demand for the magazine is 7,00,000 copies. Solution: Step 1: Segregating semi-variable cost into variable and fixed portion Change in Cost

Variable cost per unit = Change in units 65,000−55,000

Method A = 4,50,000−3,50,000 = Rs.0.10 per copy 52,500−47,500

Method B = 4,50,000−3,50,000 = Rs.0.05 per copy Fixed Cost = Total Cost – Variable cost Method A = Rs.55,000 – (3,50,000 Copies x Rs.0.10) = Rs.20,000 Method B = Rs.47,500 – (3,50,000 Copies x Rs.0.05) = Rs.30,000 Step 2: Contribution lost Selling price (old magazine) = Rs.0.85 Variable cost (old magazine) = Rs.0.35 For every 10 new magazines sold, 1 old magazine sales lost i.e. for 10 new magazines contribution lost = Rs.0.50. Therefore, contribution loss per new magazine sold Rs0.05 (Rs.0.5/10 Copies) Step 3: Analyzing data for method ‘A’ and method ‘B’ Particulars Selling Price Less: Variable Direct Semi Variable Opportunity Cost Total Variable Cost Contribution Less: Fixed Cost Fixed Cost Semi-Variable Total Fixed Cost

Method A (Rs.) Method B (Rs.) 1.00 1.00 0.55 0.1 0.05 0.70 0.30 80,000 80,000 20,000 1,00,000

0.50 0.05 0.05 0.60 0.40 1,20,000 1,20,000 30,0000 1,50,000

Step 4: Calculation of profit at different sales level under both methods Method – A:

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AMA-Notes Levels Contribution @ 30 paisa (Rs.) Less: Fixed Cost Profit

5,00,000 Units 1,50,000 1,00,000 50,000

4,00,000 Units 1,20,000 1,00,000 20,000

6,00,000 Units 1,80,000 1,00,000 80,000

5,00,000 Units 2,00,000 1,50,000 50,000

4,00,000 Units 1,60,000 1,50,000 10,000

6,00,000 Units 2,40,000 1,50,000 90,000

Method – B: Levels Contribution @ 20 paisa (Rs.) Less: Fixed Cost Profit Step 5: Indifference point Difference in fixed cost

Indifference point = Differnce in contribution per unit = Sales Range Less than 5,00,000 copies 5,00,000 copies More than 5,00,000 copies

1,50,000−1,00,000

Method Selected Method A Method A or Method B Method B

0.4−0.3

=

50,000 0.1

= 5,00,000 Copies

Reason Low fixed cost Indifference point Low Variable cost

Step 6: Calculation of break-even sales and margin of safety for the new magazine Particulars Fixed Cost Contribution per unit BEP (Copies) Total Sales Margin of Safety

Method A 1,00,000 0.30 3,33,333 5,00,000 1,66,667

Method B 1,50,0000 0.40 3,75,000 5,00,000 1,25,000

If method A is adopted, from the anticipated 5,00,000 copies we can tolerate 1,66,667 copies drop. If method B is adopted, we can tolerate a drop of 1,25,000 copies drop. If the drop is beyond this level the incremental profit is ‘0’ and existing profit is eroded. Step 7: Analysis of the different sales range We have to make two decisions based on marketing team’s inputs. 1) Old magazine or new magazines 2) Method A or Method B First decision is based on break-even point and second decision based on indifference point. Sales Range Less than 3,33,333 copies 3,33,333 copies – 5,00,000 copies 5,00,000 Copies More than 5,00,000 Copies

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Decision Only old Magazine Old & New Magazine – Method A Produce new magazine using Method A or Method B along with old magazine Produce new magazine using Method B along with old magazine

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AMA-Notes Step 8: Incremental profit when new magazine demand is 7,00,000 copies Contribution (7,00,000 Copies x Rs.0.4) Less: Fixed Cost Incremental Profit

= Rs.2,80,000 = (Rs.1,50,000) = Rs.1,30,000

This calculation is wrong.

Alternatively, Contribution from new magazine (7,00,000 Copies x Rs.0.45) = Rs.3,15,000 Less: Contribution lost from old magazine (70,000 x Rs.0.35) = (Rs.35,000) Less: Incremental fixed cost = (Rs.1,50,000) Incremental profit = Rs.1,30,000 Specific fixed cost of old magazine Contribution per copy of old magazine

This calculation is wrong.

= Rs.80,000. = Rs.0.50 Rs.80,000

BEP (Old Magazine) = = 1,60,000 Units Rs.0.50 If old magazine demand is less than 1,60,000 copies it is better to close the old magazine because the contribution does not recover the specific fixed cost. Current sales of old magazine Less: Break-even sales Drop in sales allowed

= 2,20,000 Copies = 1,60,000 Copies = 60,000 Copies

Any drop beyond 60,000 copies the old magazine will be closed. The maximum new magazine that could be sold for old magazine to continue is 6,00,000 copies, beyond that old magazine would be discontinued. At 7,00,000 copies only new magazine using method B. Contribution from new magazine (7,00,000 copies x Rs.0.40) = Rs.3,15,000 Less: Contribution lost from old magazine (2,20,000 x Rs.0.5) = (Rs.1,10,000) Add: Savings in specific fixed cost = Rs.80,000 Less: Incremental fixed cost of new magazine = (Rs.1,50,000) Incremental Profit = Rs.1,35,000 Question no 12: XY ltd. makes two products X and Y, whose respective fixed costs are F1 and F2. You are given that the unit contribution of Y is one fifth less than the unit contribution of X, that the total of F1 and F2 is Rs.1,50,000, that the BEP of X is 1,800 units (for BEP of X F2 is not considered) and that 3,000 units is the indifference point between X and Y (i.e. X and Y make equal profits at 3,000 unit volume, considering their respective fixed costs). There is no inventory build up as whatever is produced is sold. You are required to find out the values F1 and F2 and units contribution of X and Y. Solution: Let Contribution per unit of ‘X’ be ‘C’. Therefore contribution per unit of ‘Y’ is ‘C – 1/5C = 4/5C’. Fixed Cost

Breakeven Point = Contribution per unit

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AMA-Notes Breakeven Point of ‘X’ = Indifference point

F1 C

= 1,8000 → F1 = 1800C Difference in Fixed Cost

= Difference in contributino per unit = 3,000 F1 −F2 1 c 5

= 3,000

600C = F1 − F2 600C = 1,800 C - F2 F2 = 1,200C F1 + F2 = 1,50,000 1,800 C + 1,200 C= 1,50,000 3,000C = 1,50,000 C=

1,50,000

4

3,000 4

5

5

= Rs.50

C = x 50 = Rs.40

F1 = 1,800C = 1,800 x Rs.50 = Rs.90,000 F2 = 1,200C = 1,200 x Rs.50 = Rs.60,000 Conclusion: Contribution per unit of ‘X’ Contribution per unit of ‘Y’ Fixed Cost of ‘X’ Fixed Cost of ‘Y’

= Rs.50 = Rs.40 = Rs.90,000 = Rs.60,000

7.5. Limiting Factor Problems 7.5.1. Basic Limiting factor allocation problems

Question no 12: As a part of its rural upliftment programme, the government has put under cultivation a farm of 96 hectares to grow tomatoes of four varieties: Royal Red, Golden Yellow, Juicy Crimson and Sunny Scarlet. Of the total, 68 hectares are suitable for all four varieties but the remaining 28 hectares are suitable for growing only Golden Yellow and Juicy Crimson. Labour is available for all kinds of farm and is no constraint. The market requirement is that all four varieties of tomatoes must be produced with a minimum of 1,000 boxes of any one variety. The farmers engaged have decided that the area devoted to any crop should be in terms of complete hectares and not in fractions of a hectare. The other limitation is that not more than 20,000 boxes of any one variety should be produced. The following data re relevant. Royal Golden Juicy Sunny Red Yellow Crimson Scarlet Annual Yield: Boxes per hectare 350 100 70 180 Costs: Rs. Rs. Rs. Rs. Direct Materials 476 216 196 312 Labour:

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AMA-Notes Growing per hectare Harvesting and packaging per box Transport per box Market price per box

896

608

371

528

5.20 15.38

5.20 15.87

4.00 18.38

9.60 22.27

Fixed Overheads per annum Rs. Growing 11,200 Harvesting 7,400 Transport 7,200 General Administration 10,200 Required: (a) Within the given constraints, the area to be cultivated with each variety of tomatoes if the largest total profit has to be earned. (b) The amount of such profit in rupees. Solution: Step 1: Calculation for contribution per hectare of each variety of each variety Particulars Selling Price Less: Variable Cost Direct Material Labour Harvesting Transport Total Variable cost (Rs.) Contribution per box (Rs.) Yield/Hectare (Boxes) Contribution per Hectare (Rs.) Rank – Versatile Rank – Specialized

Royal Red Golden Yellow Juicy Crimson Sunny Scarlet 15.38 15.87 18.38 22.27 1.36 2.56 3.60 5.20 12.72 2.66 350 931 I -

2.16 6.08 3.28 5.20 16.72 (-0.85) 100 -85 IV II

2.80 5.30 4.40 4.00 16.50 1.88 70 131.6 III I

1.73 2.93 5.20 9.60 19.46 2.81 180 505.80 II -

Step 2: Calculation of Minimum and Maximum hectares We should produce minimum 1,000 boxes of each variety and maximum 20,000 boxes of each variety. Particulars A) Yield/Hectare (Boxes) B) Minimum boxes to be produced C) Maximum boxes can be produced D) Allocation Category E) No.of hectares for minimum requirement (B/A) F) No.of hectares for maximum requirement (C/A)

Royal Red 350 1,000 20,000 Versatile 3

Golden Yellow 100 1,000 20,000 Specialized 10

Juicy Crimson 70 1,000 20,000 Specialized 15

Sunny Scarlet 180 1,000 20,000 Versatile 6

57

NA

NA

NA

Step 3: Allocation of 96 hectares

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AMA-Notes Production

Minimum Versatile Royal Red 3 Golden Yellow Juicy Crimson Sunny Scarlet 6 Total 9

Specialized 10 15 25

Balance Versatile 54 5 59

Total Specialized 3 3

57 10 18 11 96

Step 4: Calculation of the profit from the above mix Production Hectare Contribution/Hectare (Rs.) Royal Red 57 931 Golden Yellow 10 (85) Juicy Crimson 18 131.6 Sunny Scarlet 11 505.80 Total Contribution Total Contribution (Approximately) Less: Fixed Cost Profit

Contribution (Rs.) 53,067 (860) 2,368.80 5,563.80 60,149.60 60,150 (36,000) 24,150

Notes: 1) We cannot allocate fraction of hectares to any crop. Hence we round off and allocate. 2) Minimum Hectares is always rounded off to the higher number. For example, for juicy crimson 1,000/70 =14.28 hectares but rounded off to 15 hectares because rounding off to 14 hectares will not ensure minimum 1,000 boxes. 3) In case of maximum the rounding off should be understood as follows: Royal Red = 20,000/350 = 57.14 hectares. The company has two options i. Allocate 58 hectares to royal red and cultivate 57.14 hectares living balance 0.86 hectares idle → Advantage is maximum 1st rank is produced and disadvantage is idle capacity. ii. Allocate 57 hectares to royal red and cultivate one full hectare sunny scarlet → Advantage is no idle capacity and disadvantage is 0.14 hectares transferred from 1st rank to 2nd rank product. 4) By rounding off to 57 hectares: i. Benefit → Contribution from Sunny Scarlet = Rs.505.80 ii. Cost → Contribution lost from Royal Red – Rs.931 x 0.14 hectares = Rs.130.34 Hence, rounded off to 57 hectares 501.80

5) Indifference point = = 0.54 Hectares → 57 Hectares + 0.54 Hectares = 57.54 Hectares 931 If the fraction is above this round off to 58 hectares else round off to 57 hectares. 7.5.2. Limiting factor in Make or Buy Situation

1) Generally, it is believed that making is cheaper than buying because making involved only variable cost and buying includes share of fixed cost, supplier’s profit etc., in purchase price. 2) Make (or) buy decision can be classified into types:

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AMA-Notes i. ii.

A Long term investment decision → For making we require machine. Hence capital outlay occurs in year 0. Due to making operationally we saved cost each year which results inflow. If NPV is positive make by investing in machine else buy. A Short term limiting factor allocation → In this case we have facilities to make but limiting factor exists that prevents making the entire requirement. Here what should be made using limited source and what should be bought from outside is the decision to be made.

Question no 13: A company is preparing its production budget for the year ahead. Two of its processes are concerned with the manufacture of three components, which are used in several of the company’s products. Capacity (machine hours) in each of these two processes is limited to 2,000 hours. Production costs are as follows: Component X Component Y Component Z (Rs. Per unit) (Rs. Per unit) (Rs. Per unit) Direct Materials 15.00 18.50 4.50 Direct Labour 12.00 12.50 8.00 Variable Overhead 6.00 6.25 4.00 Fixed Overhead: Process M 6.00 6.00 4.50 Process N 10.50 10.50 3.50 Total Cost 49.50 53.75 24.50 Requirements for components X, Y and Z (in units) for the following year: X 300 Y 300 Z 450 Fixed overhead is absorbed on the basis of machine hours at the following rates: Process M Rs.3.00 per hour Process N Rs.3.50 per hour Components X and Z could be obtained from an outside supplier at following prices per unit. X Rs.44.00 Z Rs.23.00 Required: (a) Demonstrate the insufficient capacity is available to produce the requirements for components X, Y and Z in the year ahead, and calculate the extent of the shortfall. (b) Determine the requirements for bought in components in order to satisfy the demand for components at minimum cost. Solution: Step 1: Identifying limiting factor Particulars Requirement of Hours per unit M N X 6/3 = 2 Hours 10.5/3.5 = 3 Hours Y 6/3 = 2 Hours 10.5/3.5 = 3 Hours Z 4.5/3 = 1.5 Hours 3.5/3.5 = 1 Hour Total Hours Required

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Units Hours for Process. M N 300 300 x 2 = 600 300 x 3 =900 300 300 x 2 = 600 300 x 3 =900 450 450 x 1.5 = 675 300 x 1 =300 1,875 2,250

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AMA-Notes Available Hours Surplus/ (Short fall)

2,000 125

2,000 250

The entire requirement cannot be produced. From the above because we have insufficient process N hours. Hence, we should buy some requirements from outside. Product ‘Y’ should be necessarily manufactured because it does not have buying option. But ‘X’’ or ‘Z’ should be decided based on based on the relative extra cost. Step 2: Make (or) Buy Table Product X Y

Buy Cost 44 23

Variable Cost 33 16.5

Contribution 11 6.5

Prod. ‘N’ hours/unit 3 1

Contribution/ Rank Hour (N) 3.67 2 6.5 1

# Manufacture

# Manufacture to the extent possible and the remaining shall be bought out. Step 3: Allocation of limiting factor Components No.of Manufacturing Units hours/unit Y 300 3 Z 450 1 X 216 3 X 84 Buy (300 – 216)

Manufacturing hours 900 450 650 (Balance)

Cumulative Hours (Max 200) 900 450 2000

Question no 14: X ltd manufactures and sells a range of sports equipments. The marketing director would like to increase X ltd.’s share of the market, and is considering an advertising campaign in order to stimulate demand for the products. Two alternative sales budgets have been put forwarded for the year ahead. Product (‘000 Units) A B C D Budget 1 – without advertising 180 280 260 150 Budget 1 – with advertising 200 310 285 165 The advertising campaign would cost Rs.2,90,000. Selling prices and variable production costs are budgets as follows: [Rs. per unit] Products A B C D Selling Prices 9.95 11.95 22.95 19.95 Variable production costs: Direct Materials 4.20 5.50 12.70 10.40 Direct Labour 1.70 1.70 2.80 2.65 Variable Overhead 0.60 0.60 1.00 0.90 The variable overheads are absorbed on a machine hour basis at a rate of Rs.1.00 per hour. Fixed overheads total Rs.25,70,000. Production capacity is limited to 7,15,000 machine hours in the year ahead. Products A and C could be bought in ad X ltd would be prepared to do this to make up any shortfall of production requirements if necessary and justify. Products A and C could be bought-in for Rs.8.90 per unit and Rs.20.00 per unit respectively.

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AMA-Notes If the advertising campaign was shown to be successful, increased production requirements would then be met in the long run by investment in additional facilities. In the meantime, the company would like to assesse the potential of the advertising campaign in the year ahead, and if justified, determine the best way to obtain the required quantities of Product A and C. Required: On the basis of expectations for the year ahead, determine whether investment in the advertising campaign would be worthwhile and how production facilities would be best utilized. Solution: Step 1: Identification of limiting factor Product Machine Sales ‘000 (Units) Hours/Unit Without With Advertising Advertising A 0.60 180 200 B 0.60 280 310 C 1.00 260 285 D 0.90 150 165 Total Hours Required Available Hours

Hours ‘000 Without Advertising 108 (180 x 0.6) 168 (280 x 0.6) 260 (260 x 1.0) 135 (150 x 0.9) 671 715

With Advertising 120 (200 x 0.6) 186 (310 x 0.6) 285 (285 x 1.0) 148.5 (165 x 0.9) 739.5 715

The machine hours per unit is calculated with the help of variable overhead absorption rate of Rs.1 per hour. For example ‘A’ is charge 0.60 variable overhead per unit which means ‘A’ consumes 0.60 ( Rs.0.60 x 1 Hour) Step 2: Make (or) Buy Decision If the company decides to advertise to meet the increased demand it requires 7,35,000 machine hours but only 7,15,000 hours are available. Thus it is not possible to produce and sell the entire demand. A part of the demand has to be bought and sold. Product ‘B’ and ‘D’ does not have buying option. They should be compulsorily manufactured. Hence will not participate in make (or) buy ranking. Product

Buying Cost 8.9 20

A C

Variable Cost 6.5 16.5

Contribution 2.4 3.5

Manufacturing Hours 0.6 1

Contribution/ Rank Hour (N) 4 1 3.5 2

Manufacture ‘A’, Manufacture ‘C’ to the extent possible and balance requirement of ‘C’ should be bought from outside. Step 3: Allocation of Limiting factor (Machine Hours) Product B D A

Units 310 165 200

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Hours/Unit 0.6 0.9 0.6

Hours 186 148.5 120

∑ 𝐇𝐨𝐮𝐫𝐬 186 334.5 454.5 Page | 254

AMA-Notes C C

260.5 1 260.5 Buy 24.5 (385 – 260.5)

715

Step 4: Advertise or not Product Selling Price A 9.95 B 11.95 C 22.95 C (Buy) 22.95 D 19.95 Total Contribution Less: Fixed Cost Total Profit

Variable Cost 6.50 7.80 16.5 20.00 13.95

Contribution per Unit 3.45 4.15 6.45 2.95 6

Before ‘000s Units Contribution 180 621 280 1,162 260 1,677 150 900 4,360 2,570 1,790

After ‘000s Units Contribution 200 690 310 1,286.50 260.5 1,680.22 24.5 72.28 165 990 4,719 2,860 1,859

Alternatively, Incremental Contribution due to advertisement (4,719 – 4,360) Less: Specific Advertisement Cost Incremental profit due to advertising

= 359 = (290) = 69

Conclusion: Recommended to go for advertisement campaign and manage the shortfall in production requirement by purchasing product ‘C’ to the extent of 24,500 units. Notes: 1) Short term decisions should be purely short term, should not be extended to long periods. For example, a company’s plant capacity is 1,00,000 units and current demand is 80,0000 units with a selling price of Rs.50, variable cost of Rs.30. An offer comes for purchase of 20,000 units at a selling price of Rs.31. Should this offer be accepted? a) If it is a onetime offer? b) If it is an offer for next four years? Answer: a) Instead of having the capacity idle it is better to accept the offer and have contribution of Rs.20,000 (20,000 Units x Rs.1) towards the factory fixed cost but this decision should be purely short term (or) one time. b) If it is for four years, it become long term decision for which short term decision making concepts should not be applied. If we feel that for next four years, the demand is going to be only 80,000 units, the company should think off downsizing the plant and save fixed cost rather than use the idle capacity for a nominal Rs.1 contribution. 2) In the above problem, the decision to buy a portion of product ‘C’s requirement is purely short term. In long term the company should try to remove the limiting factor by investing in additional facilities. **Question no 15: A processing company EF is extremely busy. It has increased its output and sales from 12,900 kg in quarter 1 to 17,300 kg in quarter 2 but, though demand is still rising, it cannot increase its outputs more than another 5% from the existing labour force which is now at its maximum. Data in quarter 2 for its four products were: E M Reddy

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AMA-Notes P Q R S Output (kg) 4,560 6,960 3,480 2,300 Selling price (Rs. per kg) 16.20 11.64 9.92 13.68 Costs (Rs. Per kg) Direct Labour (at Rs6 per hour) 1.96 1.30 0.99 1.70 Direct Materials 6.52 4.90 4.10 5.42 Direct packaging 0.84 0.74 0.56 0.70 Fixed overhead (absorbed on basis of direct labour cost) 3.92 2.60 1.98 3.40 Total 13.24 9.54 7.63 11.22 The XY company has offered to supply 2,000 kg of any of the product at a delivered price of 90% of EF’s selling price. The company will then be able to produce extra another product in its place up to the plant’s total capacity. Required to state, with supporting calculations: Which product should be purchased and which other product should be produced in it place up to the plant’s total capacity so that the company reports the maximum profit? Assume XY’s quality and delivery are acceptable. Solution: Step 1: Identification of Limiting Factor Product No. of Kgs Hours per Kg P 4,560 1.96/6 = 0.3267 Q 6,960 1.30/6 = 0.2167 R 3,480 0.99/6 = 0.1650 S 2,300 1.706 = 0.2833 Total Hours Add: Overtime 5% (4,233 x 5%) Maximum Hours

Hours 1,489 1,508 574 651 4,223 212 4,435

Step 2: Contribution per limiting factor (or) Contribution per hour Product Selling Price P 16.2 Q 11.64 R 9.92 S 13.68

Variable Cost 9.32 6.94 5.65 7.82

Contribution per Unit 6.88 4.7 4.27 5.86

Hours Contribution per hour 0.3267 21.05(6.88/0.3267) 0.2167 21.69(4.7/0.2167) 0.1650 25.87(4.27/0.1650) 0.2833 20.68(5.86/0.2833)

Rank Significance III II I IV

Manufacture during the extra 5% capacity

Step 3: Calculation of capacity release if 2,000 Kgs are bought Product P Q R S

Hours Released 2,000 x 0.3267 = 653.4 Hours 2,000 x 0.2167 = 433.4 Hours 2,000 x 0.1650 = 330 Hours 2,000 x 0.2833 = 566.6 Hours

Remark Company will not buy all only one of them will be purchased from outside

Step 4: Make (or) Buy table

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AMA-Notes Product Supply price (90% of SP) (a) P 14.58 Q 10.47 R 8.93 S 12.31

Variable Cost (b) 9.32 6.94 5.65 7.82

Extra cost of Buy (c) = (a) – (b) 5.26 3.53 3.28 4.49

Extra cost per hour (d) 5.26/0.3267 = 16.10 3.53/0.2167 = 16.28 3.28/0.165 = 19.87 4.49/0.2833 = 15.84

Rank

Incremental Contribution (e) = (a) x (d) 6,384 4,156 5,683

Rank

2 3 4 1

Step 5: Selection of the product to be purchased from outside Product Hours Contribution per hour from R (a) (b) P 653.4 25.87 Q 433.4 25.87 S 566.6 25.87

Contribution per hour lost (c) 16.10 16.28 15.84

Incremental Contribution (d) = (b) – (c) 9.77 9.59 10.03

1 3 2

Step 6: Quantity allocation for Buy & Manufacturing Product

Total Quantity P 4,560 Q 6,960 Old 5% R (0.165) Released 8,721 S 2,300

Allocation Manufacture 2,560 6,960 574 Hours 212 Hours 653 Hours 8,721 2,300

Buy 2,000 1,439 Hours -

Step 7: Calculation of profit as per the new allocation and identifying increase in profit Product Present Units SP P 4,560 16.2

New VC Cn. Total Cn. Units SP VC 9.32 6.88 31,373 2,560 (mfg.) 16.2 9.32 2,000 (buy) 16.2 14.58 Q 6,960 11.64 6.94 4.70 32,712 6,960 11.64 6.94 R 3,480 9.92 5.65 4.27 14,860 8,721 9.92 5.65 S 2,300 13.68 7.82 5.86 13,478 2,300 13.68 7.82 Total Contribution 92,423 Total Contribution Less: Fixed Cost (WN – 1) 50,681 Less: Fixed Cost (WN – 1) Profit 41,742 Profit

Cn. 6.88 1.62 4.70 4.27 5.86

Total Cn. 17,613 3,240 32,712 37,238 13,478 1,04,281 50,681 53,600

Due to our recommendation the profit has increased by Rs.11,858 (Rs.53,600 – Rs.41,742). WN – 1: Fixed Cost = (3.92 x 4,560) + (2.6 x 6,960) + (1.98 x 3,480) + (3.4 x 2,300) = 50,681 Notes:

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AMA-Notes 1) From Step 4 it could be observed that it is cheaper to release a hour by purchasing product ‘S’ from outside because the extra buying cost is only Rs.15.84 per hour. 2) In step 5 also it could be seen that product ‘S’ gives highest contribution per hour of Rs.10.03 but still we decided to buy 2,000 Kgs of product ‘P’ because it may have few paisa extra cost per hour but it releases more hours enabling us to produce more product ‘R’. 7.5.3. Multiple Limiting factors in Make or Buy Situation

Question no 16: A construction company has accepted a contract to lay underground pipe work. The contract requires than 2500m of 10 inch pipe and 2000m 28 inch pipe be laid each week. The limiting factor is the availability of specialized equipment. The company owns 15 excavating machine (type A) and 13 lifting and joining machines (type B). The normal operating time is 40 hours a week but up to 50% overtime is acceptable to the employees. The time taken to handle each meter of pipe is: Size of Pipe Minutes per meter Machine A Machine B 10 Inches 6 12 18 Inches 18 12 The cost of operating the machines are: Machine A (Rs.) Machine B (Rs.) Fixed Costs, per week, each 450 160 Labour, per crew, per hour: Up to 40 hours per week 10 12 Over 40 hours per week 15 18 The cost of materials are supplies per meter are: 10 Inches Rs.10 18 Inches Rs.5 A subcontractor has offered to lay any quantity of the 10 inches’ pipe at Rs.18 per meter and of the 18 inches’ pipe atRs.12 per meter. You are required to calculate: (a) Calculate the most economical way of undertaking the contract; (b) State they weekly cost involved in your solution to (a) above. Solution: Step 1: Identification of limiting factor Pipe Size

Quantity required per week 2,500

10 Inches 18 2,000 Inches Total Hours Required Hours Available: No. of machines

E M Reddy

Minutes A

B

Hours A

B

15,000 (2,500 x 6)

30,000 (2,500 x 12)

250

500

36,000 (2,000 x 18)

24,000 (2,000 x 12)

600

1,000

850

1,500

15

13

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AMA-Notes No. of hours per week No. of machine hours available per week

40 600 It is a limiting factor

40 520 It is a limiting factor

Note: Overtime is not considered, will be considered later. It is not possible to lay on our own the entire requirement because limiting factor exists. Some portion has to be necessarily sub-contracted. The ranking will be given based on the make (or) buy table as below: Step 2: Own Work (vs.) Sub-contract Pipe Size Per unit VC SC Cn. Per Hour Material Labour Cn. Per limiting factor A B Total A B 10 Inches 10 1 2.4 3.4 13.4 18 4.6 46 (4.6/6 x 60) 23 (4.6/12 x 60) 18 Inches 5 3 2.4 5.4 10.4 12 1.6 5.34 (1.6/18 x 60) 8 (1.6/12 x 60)

Rank A B 1 1 2 2

Both Machine ‘A’ and Machine ‘B ranks the 10 inches’ pipe as the first rank product. Hence, there is a consistency in ranking. If there is a conflict in ranking between liming factors, then solve using linear programming technique. Step 3: Allocation of Normal Machine ‘A’ and Machine ‘B’ hours Product

Units Required

Allocation of Hours

2,500

Hours’ time requires A B 250 500

10 inches’ pipe 18 inches’ pipe

A (600) 250

B (520) 500

2,000

600

100 Units x 18/60 = 30 Hours

20 Hours 20 Hours x 60/12 = 100 Units 520(Max)

400

Units Mfg. 2,500 Units

Balance hours of A: 600 – 250 – 30 = 320 Hours Step 4: Viability of normal Machine ‘A’ and overtime Machine ‘B’ against sub-contracting Subcontract charges Own work: Material Direct Labour – A (Rs.10 x 18/60) Direct Labour – B (Rs.18 x 12/60) Own work with OT B

= Rs.12 = Rs.5 = Rs.3 = Rs.3.60 = Rs.11.60

It is better to lay on our own with overtime ‘B’ because it is Rs.0.40 cheaper than sub-contracting option. Step 5: Allocation of normal ‘A’ and OT ‘B’ hours – Units possible Machine Available Hours A 320

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Machine Hours per unit Units Possible 18/60 320 x 60/18 = 1,067

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AMA-Notes B 260 (Overtime 50% of 520) 12/60 Only 1,067 can be produced

260 x 60/12 = 1,300

At the end of this stage the entire normal machine ‘A’ hours are used. The next step is to check the viability of OT ‘A’ and OT ‘B’ against sub-contracting. Step 6: Viability of OT ‘A’ and OT ‘B’ Subcontract charges Own work: Material Direct Labour – A (Rs.15 x 18/60) Direct Labour – B (Rs.18 x 12/60) Own work with OT ‘A’ & ‘B’

= Rs.12 = Rs.5.00 = Rs.4.50 = Rs.3.60 = Rs.13.10

In this case it is better to contract rather than do on our own using OT ‘A’ and OT ‘B’. Alternatively, Advantage of own work (Normal ‘A’ & OT ‘B’) = Rs.0.4 (-) Over time ‘A’ premium [(Rs.15 – Rs.10) x 18/60] = (Rs.1.5) Extra Advantage = (Rs.1.10) Step 7: Allocation of products Product

Required Own Sub-contracting Normal of A & B OT of B & Normal of A 10 Inches pipe 2,500 2,500 18 Inches pipe 2,000 100 1,067 833 (Balance) Step 8: Weekly Cost statement Product 10 Inches Pipe – Normal 18 Inches Pipe – Normal 18 Inches Pipe – OT ‘B’ 18 Inches Pipe – Sub-contracting Total Variable Cost

Units 2,500 Units 100 Units 1,067 Units 833 Units

Variable Cost (Rs.) 13.4 10.4 11.6 12.0

Total Cost (Rs.) 33,500 1,040 12,377 9,996 56,913

Fixed Cost: Machine Nos. Fixed Cost(Rs.) A 15 450 B 13 160 Total Fixed Cost

Total Cost (Rs.) 6,750 2,080 8,830

Total Weekly Cost = Variable Cost + Fixed Cost = Rs.56,913 + Rs.8,830 = Rs.65,743

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AMA-Notes Question no 17: A car manufacturing company needs four components W, X , Y, Z. The manufacturing components may be procured from outside. The cost, purchase price for the component and other information are given below: W (Rs.) X (Rs.) Y (Rs.) Z (Rs.) Direct Material 60 70 75 60 Direct Wages 30 40 60 40 Direct Expenses @ Rs.20 per MH 40 30 40 40 Fixed Cost 20 20 15 25 150 160 190 165 Purchase price from market 250 160 200 135 Units required for the year 3,000 3,500 2,000 3,000 (i) There are constrains in machine time is manufacturing all components. Total machine hours available are only 12,000. (ii) Other alternative is to use machine time in a second shift which will attract 20% extra wages and other fixed overheads @ Rs.3,000 for 1,000 hours or part thereof. Give your suggestion about to course of action for maximization of profit. Solution: Step 1: Identification of Limiting factor Product Hours/Unit W 2 X 1.5 Y 2 Z 2 Total Requirement Hours Available

Units 3,000 3,500 2,000 3,000

Hours 6,000 5,250 4,000 6,000 21,250 12,000

If we compare the manufacturing cost & buying cost for product ‘Z’ is alone, buying is cheaper. Hence ‘Z’ should be compulsorily purchased and not manufactured. 6,000 Hours of ‘Z’ will not be counted for limiting factor. The hour requirement is only 15,250 Hours (21,250 – 6,000). Still it is a limiting factor. Step 2: Make (or) Buy Table Product Buying Cost (Rs.) W 150 X 160 Y 200

Variable Cost (Rs.) 130 140 175

Contribution (Rs.) 20 20 25

Machine Hours 2 1.5 2

Contribution per hour (Rs.) 10 13.33 12.5

Rank 3 1 2

Manufacture ‘X’ and ‘Y’. Manufacture ‘W’ to the extent possible and meet the remaining demand second shift (or) outside purchase. Step 3: Allocation of Machine Hours Product Units Hours/Unit Hours ∑ 𝐇𝐨𝐮𝐫𝐬 E M Reddy

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AMA-Notes X Y W

3,500 2,000 1,375

1.5 2 2

5,250 4,000 2,750

5,250 9,250 12,000

W (Second Shift /Purchase) = 1,625 units (3,000 Units – 1,375 Units) Step 4: Second shift (vs.) Buy Particulars Variable cost/Unit – Second shift Variable cost Additional fixed cost for 3,250 Hours (1,625 x 2) Total Manufacturing cost in second shift Buying cost

Computation Rs.60 + Rs.30 x 120% + Rs.40 1,625 Units x Rs.136 4 thousand’s Hours x Rs.3,000 1,625 Units x Rs.150

Amount (Rs.) 136 2,21,000 12,000 2,23,000 2,43,750

Recommended to go for second shift rather than buying. Additional improvement to the solution: We can manufacture 1,500 units in second shift and buy the balance 125 units from outside. Variable Manufacturing cost (1,500 Units x Rs.136) = Rs.2,04,000 Additional Fixed Cost (3 thousand’s hours x Rs.3,000)= Rs.9,000 Buying cost (125 Units x Rs.150) = Rs.18,750 Total Cost = Rs.2,31,750 This is better than manufacturing the entire 1,065 units in 2nd shift as it saves a cost of Rs.1,250 (Rs.2,23,000 – Rs.2,31,750). Alternatively, 1) Benefit → Savings in fixed cost by not producing 125 units = Rs.3,000 2) Cost → Additional variable cost due to buying 125 units = 125 Units x (Rs.150 – Rs.136) = Rs.1,750 Net Saving = Rs.3,000 – Rs.1,750 = Rs.1,250 Indifference point: Particulars Manufacture (Rs.) Buy (Rs.) Variable Cost 136 150 Fixed Cost 3,000 Difference in Fixed Cost

3,000−0

Indifference point = Difference in variable cost per unit = 150−136 = 214 Units (or) 428 Hours It will be worth to commit Rs.3,000 fixed cost only when we have work load of at least 428 hours (or) 214 units. Since, we had only 125 Units workflow (or) 250 hours work load we deiced to buy it. 7.5.4. Limiting factor with Specific Fixed Cost

Question no 18: Bloom ltd. makes 3 products A, B and C. The following information is available: E M Reddy

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AMA-Notes Particulars

Figures in Rs. /Units A B C Selling price (peak season) 550 630 690 Selling price (off season) 550 604 690 Material Cost 230 260 290 Labour (peak season) 110 120 150 Labour (off season) 100 99 149 Variable production overhead 100 120 130 Variable selling overhead (only for peak season) 10 20 15 Labour hours required for one unit of production 8 11 7 Material cost and variable production overheads are the same for the peak season and off season. Variable selling overheads are not incurred in the off season. Fixed costs amount to Rs.26,780 for each season of which Rs.2,000 is towards salary for special technician incurred only for product , and Rs.4,780 is the amount that will be incurred on after sales warranty and free maintenance of only product C to match competition. Labour force can be interchangeably used for all the product. During peak season there is labour shortage and the maximum labour hours available are 1,617 hours. During off season labour is freely available but demand is limited to 100 units of A, 115 units of B and 135 units of C with production facility being limited to 215 units of A, B and C put together. Required: (i) Advise the company about the best production mix during peak season for maximum profit. (ii) What will be the maximum profit for the off season? Solution: Step 1: Peak Season ranking of products Items Selling Price Less: Variable Cost Direct Materials Direct Labour Variable overhead – Production Variable overhead - Selling Total Variable Cost Contribution per unit Hours per unit Contribution per hour Rank

A (Rs.) B (Rs.) C (Rs.) 550 630 690 230 110 100 10 450 100 8 12.5 2

260 120 120 20 520 110 11 10 3

290 150 130 15 585 105 7 15 1

Step 2: Analysis of fixed cost Total Fixed Cost = Rs.26,780 Specific fixed cost of ‘B’ = Rs.2,000 Specific fixed cost of ‘C' = Rs.4,780 General fixed cost = Rs.20,000 Step 3: Allocation of 1,617 labour hours E M Reddy

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AMA-Notes 1) Allocating it to product ‘C’ Contribution (1,617 Hours x Rs.15) Less: Specific fixed cost Profit/ (Loss) 2) Allocating the hours to product ‘A’ Contribution (1,617 Hours x Rs.12.5) Less: Specific fixed cost Profit/ (Loss) 3) Allocating it to product ‘B’ Contribution (1,617 Hours x Rs.10) Less: Specific fixed cost Profit/ (Loss)

= Rs.24,255 = (Rs.24,780) = (Rs.525) = Rs.20,213 = (Rs.20,000) = Rs.213 = Rs.16,170 = (Rs.22,000) = (Rs.5,830)

It is recommended to allocated the 1,617 hours to product ‘A’ because it gives the highest profit. Notes: 1) Allocating the 1,617 hours to product ‘C’ (1st rank product) gives us the maximum contribution. 2) When contribution is maximized the profit also will be maximized. That is why we allocate limiting factor generally to high contribution products. 3) However, when there exists specific fixed cost, it is not necessary that high contribution gives high profit. In this problem product ‘C’ gives high contribution but due to it’s specific fixed cost it results in loss. 4) When we have specific fixed cost the limiting factor should be allocated to maximize profit and not contribution. Alternatively, the solution can be presented as follows: Items C A B

Unties Possible 1,617/7 = 231 Units 1,617/8 = 202 Units 1,617/11 = 142 Units

Required to Break-even 24,780/105 = 236 Units 20,000/100 = 200 Units 22,000/110 = 200 Units

Decision Do not produce Produce Do not produce

1,617 hours should be allocated to product ‘A’ because product ‘B’ and product ‘C’ does not break-even. Step 4: Off season ranking the products Items Selling Price Less: Variable Cost Direct Materials Direct Labour Variable overhead – Production Total Variable Cost Contribution per unit Rank Max demand (Units) Overall limit (Units)

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A (Rs.) B (Rs.) C (Rs.) 550 604 690 230 260 100 99 100 120 430 479 120 125 3 1 100 115 215 Units

290 149 130 569 121 2 135

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AMA-Notes Step 5: Profitability under different options Items Contribution per unit Option 1: Units Amount Option 2: Units Amount Option 3: Units Amount

A 120

B 125

C 121

-

115 100 215 14,375 12,100 26,475 26,780

(305)

100 115 215 12,000 14,375 26,375 22,000 22,000

4,375

80 9,600

1,155

-

Total

Fixed Cost Profit/(Loss)

135 215 16,335 25,935 24,780

Select option since the profit is highest. Question no 19: Question no 27 Solution: Step 1: Calculation of net contribution required to earn profit of Rs.1,800 Profit General Fixed Cost Net contribution required

= Rs.1,800 = Rs.4,000 = Rs.5,800

Step 2: Calculation of net contribution given by 50,000 leaflets of A & B Products Units Contribution/1000 Contribution (‘000s) A 50 60 3,000 B 50 150 7,500 Total Net Contribution

Specific Fixed Cost 2,400 4,000

Net Contribution 600 3,500 4,100

Step 3: Number of units ‘C’ required to earn a profit of Rs.1,800 Additional net contribution required Add: Specific Fixed Cost Contribution required from C Contribution/1000 leaflets of C

= Rs.5800 – Rs.4,100 = Rs.1,700 = Rs.9,500 = Rs.11,200 = Rs.320

No.of units of C

=

Rs.11,200 Rs.320

= 35,000 leaflets

We required to print 35,000 leaflets of C to earn a profit of Rs.1,800. Notes: 1) When we have specific fixed cost we should understand that there exists two levels of contribution.

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AMA-Notes i. ii.

Gross Contribution → Contributes towards (a) Specific Fixed Cost (b) General Fixed Cost and then (c) Profit Net Contribution → Gross Contribution – Specific Fixed Cost → It contributes to the common pool towards general fixed cost recovery and profit.

Step 4: Calculation of contribution per pack and ranking the leaflets Product A B C

Contribution/1,000 60 150 320

Packs per 1,000 leaflets 2 6 16

Contribution /pack 30 25 20

Rank 1 2 3

Step 5: Allocation of 170 packs Product A B C

Qty.in (‘000s) 10 10 5

No. of packs/1,000 2 6 16

Requirement 20 60 90

∑ 𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐦𝐞𝐧𝐭 20 80 160

After this allocation there remains 10 unutilized packs and unsatisfied demand of ‘C’ to the extent of 5,000. Step 6: Alternative Allocation We can try compromising the limiting factor ranking in order to use full capacity. We can sacrifice 1,000 leaflets of ‘B’ and release 6 packs which along with the 10 idle packs can be used to produce 1 more 1,000 leaflets of ‘C’. Product A B C

Contribution/1,000 60 150 320

Alternative 1 Numbers Gross Contribution 10 600 10 1,500 5 1,600 3,700

Alternative 2 Numbers Gross Contribution 10 600 9 1,350 6 1,920 3,870

Since 2nd alternative gives Rs.170 extra contribution it should be preferred. Alternatively, Benefit: Contribution from ‘C’ = Rs.320 Cost: Contribution lost from ‘B’ =Rs.150 Net Benefit = Rs.320 – Rs.150 = Rs.170 Notes: 1) In the previous sum it was observed that when specific fixed cost exists our aim is not to earn more contribution but to earn more profit. 2) In limiting factor allocation specific fixed costs is also considered. 3) In this sum while allocating 170 packs we have ignored the specific fixed costs and try to maximize contribution. Why?

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AMA-Notes Answer: Specific fixed costs is irrelevant because we have already committed to produce 50,000 leaflets of each product. Specific fixed cost becomes relevant only when we have an option to abandon a product line. Step 7: Commenting on profitability of the products as stand alone Particulars Selling Price Less: Variable Cost Contribution Fixed Cost Specific General Total Fixed Cost BEP Maximum Demand

A 100 40 60

B 220 70 150

C 450 130 220

2,400 4,000 6,400 6,400/60 = 107 leaflets 60 leaflets

4,000 4,000 8,000 8,000/150 = 54 leaflets 60 leaflets

9,500 4,000 13,500 13,500/220 = 43 leaflets 60 leaflets

Summary table: Product A B C

BEP (Standalone) 107 54 43

Rank (in standalone status) Not Possible 2 1

Notes: 1) Standalone product means when the demand for other products becomes ‘0’ can this product survive? 2) When a product becomes standalone it should recover it’s specific fixed cost and entire general fixed cost to break even. 3) ‘A’ can never be a standalone product because even at it’s maximum demand it cannot break-even. It can only co-exists with ‘B’ & ‘C’. 4) ‘C’ is a better standalone product because it’s break-even sooner and has high margin of safety. Step 8: Commenting on the profitability of the products as member of the group Product Specific Fixed Cost (Rs.) A 2,400 B 4,000 C 9,500

Contribution/1000 leaflets (Rs.) 60 150 320

BEP (‘000 leaflets) 40 27 30

Ranking III I II

Notes: 1) Product ‘B’ breaks-even sooner than minimum demand and thus surely contributes towards the general fixed cost. It is an asset to the group. 2) ‘C’ breaks-even exactly at minimum demand. It will surely recover it’s specific fixed cost and hence it will never be liability to the group. 3) ‘A’ should be printed only when we are certain that the demand will be more than 40,000 leaflets. Otherwise ‘B’ & ‘C’ will be made to recover ‘A’s fixed cost also. E M Reddy

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AMA-Notes 7.6. Shut down (or) Continue decisions

1) During the periods of lean demand management may consider temporary shutdown of operations. Such a decision is called “Shutdown Decision”. 2) The shutdown decision should be made after doing cost – benefit analysis. 3) Shutdown Decision i. Benefit → Avoidable Fixed Cost ii. Cost → Shut Down cost & Contribution lost on possible shut down period demand 4) Avoidable fixed cost are those fixed costs that can be avoided when the plant is shut down and shutdown costs are costs specifically incurred during the shutdown period to maintain the factory in working condition. 5) If the benefit exceeds cost shutdown else continue. 6) The shutdown decision greatly depends on the possible shutdown period. If the shutdown period demand is high continue, if it is low shutdown. 7) The volume at which the company is indifferent between shutting down or continuing is called ‘Shut Down Point’. It can be calculated as follows: i.

In Units →

ii.

In Value →

Avoidable Fixed Cost−Shutdown Cost Contribution per unit Avoidable Fixed Cost−Shutdown Cost PV Ratio

Question no 20: 3(a) A firm incurs a fixed cost of Rs.1,20,000 at 60% capacity. AT 60% capacity, fixed cost is only Rs.40,000. If its VC Ratio is 80%, find out the shutdown point. 3(b) A paint manufacturing company manufactures 2,00,000 per annum medium – sized tins of “Spray Lac Paint” when working at normal capacity. It incurs the following costs of manufacturing per unit: Solution: a) Total Fixed Cost = Rs.1,20,000 Less: Unavoidable Fixed Cost = (Rs.40,000) Avoidable Fixed Cost = Rs.80,000 PV Ratio = 100% - Variable Cost Ratio = 100% - 80% = 20% Shut down point =

Avoidable Fixed Cost−Shutdown Cost PV Ratio

=

1,20,000−40,000 20%

= Rs.4,00,000

Conclusion: Sales Range Less than Rs.4,00,000 At Rs.4,00,000 Greater than Rs.4,00,000

Decision Shutdown Shutdown (or) Continue Continue

b) Step 1: Contribution per unit Selling Price Less: Variable Cost Direct Materials E M Reddy

Rs.21 Rs.7.8 Page | 268

AMA-Notes Direct Labour Rs.2.1 Variable Overhead Rs.2.5 Variable selling & administration cost Rs.0.6 Rs.13 Contribution per unit R.s.8 Step 2: Avoidable fixed cost Fixed Cost per annum = Normal Capacity x Standard Rate = 2,00,000 x Rs.4 = Rs.8,00,000 Fixed Cost per quarter = Rs.8,00,000 x 3/12 = Rs.2,00,000 Unavoidable fixed cost = Rs.74,000 Avoidable fixed cost = Rs.2,00,000 – Rs.74,000 = Rs.1,26,000 Step 3: Shutdown Cost Shutdown cost (Given)

= Rs.14,000

Step 4: Shutdown Point Shutdown Point

= =

Avoidable Fixed Cost−Shutdown Cost Contribution per unit Rs.1,26,000−Rs.14,000

Step 5: Conclusion Shutdown period Demand Less than 14,000 Units At 14,000 Units Greater than 14,000 Units

Rs.8

= 14,000 Units

Decision Shutdown Shutdown (or) Continue Continue

Since the marketing team believes that in next quarter only 10,000 units could be sold it is recommended that plant should be shut down. Question no 21: Question no 2 Solution: a)

PV Ratio (or) Contribution to Sales Ratio: PV Ratio =

Change in Profit

4,000−2,000

= 30,000−20,000 = 20%

Change in Sales Change in Cost

26,000−18,000

Variable cost Ratio = Change in Sales = 30,000−20,000 = 80% b) Breakeven Sales: Particulars Contribution (Sales x PV Ratio) Less: Profit Fixed Cost Fixed Cost

Breakeven Sales = PV Ratio = c) Sales to earn Rs.6,000 profit

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2002 4,000 (20,000 x 20%) (20000) 2,000

Rs.2,000 20%

2003 3,000 (30,000 x 20%) (4000) 2,000

= Rs.10,000

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AMA-Notes Profit Add: Fixed Cost Contribution

= Rs.6,000 = Rs.2,000 = Rs.8,000

Sales Alternatively,

=

Contribution PV Ratio Profit

=

Rs.8,000 20%

= Rs.40,000

Rs.6,000

Margin of Safety = PV Ratio = 20% = Rs.30,000 Sales = Margin of Safety + Breakeven Sales = Rs.30,000 + Rs.10,000 = Rs.40,000 d) Profit when the sales is Rs.12,000 Contribution (Sales x PV Ratio) = Rs.12,000 x 20% = Rs.2,400 Less: Fixed Cost = Rs.2,000 Profit = Rs.400 Alternatively, Margin of Safety = Sales – Breakeven Sales = Rs.12,000 – Rs.10,000 = Rs.2,000 Profit = Margin of Safety x PV Ratio = Rs.2,000 x 20% = Rs.400 7.7. Differential Costing

Question no 22: Question no 18 Solution: Part A: Determination of optimum output: Sales 60,000 70,000 80,000 90,000 1,00,000

Selling price/Unit (Rs.) 0.9 0.8 0.75 0.67 0.61

Sales 54,000 56,000 60,000 60,300 61,000

Incremental Revenue 2,000 4,000 300 700

Incremental Cost 1,500 (10,000 x 15) 1,500 (10,000 x 15) 1,500 (10,000 x 15) 1,500 (10,000 x 15)

Net 500 2,500 (1,200) (800)

Notes: 1) Cost accountant assumes linearity in sales and cost function. 2) When linearity is assumed it means selling price is constant, variable cost per unit is constant and fixed cost in total is constant at all output levels. 3) In case of linearity the optimum output is the maximum output. 4) In this problem the linearity is assumption is broken due to price elasticity of demand. 5) Advantage of low volume is higher selling price and high volume is more units. Optimum output is the output where the profit is highest. It need not be maximum output. 6) In such scenario compare marginal revenue with marginal cost (Incremental revenue with incremental cost/Differential revenue with differential cost). Keep increasing the output as long as the marginal revenue exceeds the marginal cost. In this problem the optimum output level is 80,000 units beyond which the marginal cost exceeds marginal revenue. Part B: Acceptance of export order

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AMA-Notes Selling price Less: Variable cost Contribution per unit Contribution from the order

= Rs.0.50 = Rs.0.15 = Rs.0.35 = 20,000 Units x Rs.0.35 = Rs.7,000

Instead of keeping the capacity idle it is better to earn Rs.7,000 contribution. Notes: 1) We had rejected a selling price of Rs.0.61. Then how come we accept a selling price of Rs.0.50? Answer: It is improper to compare the two selling prices. The selling price of Rs.0.61 is for cumulative 1,00,000 units but the selling price of Rs.0.50 is only for incremental 20,000 units i.e. we can sell locally 80,000 units at Rs.0.75 (Optimum output) and in addition sell 20,000 units at Rs.0.50 Question no 23: Question no 19 Solution: Units

Additional Units 70,000 80,000 10,000 90,000 10,000 1,00,000 10,000

Cost per unit (Rs.) 97 92 87 82

Total Cost (Rs.) 67,90,000 73,90,000 78,30,000 82,00,000

Incremental Cost (Rs.) 5,70,000 4,70,000 3,70,000

Incremental cost per unit (Rs.) 57 47 37

The orders will be independently rejected because the selling price is less than incremental cost per unit. May be accepting all the three together will push the factory to different capacity level which may be feasible. Order A B C All

Units 5,000 10,000 10,000 25,000

Operating Capacity 70% - 80% 70% - 80% 70% - 80% 90% - 100%

Incremental Cost 57 57 57 12,25,000 (WN – 1)

Offer price 55 52 51 13,05,000 (WN – 2)

Conclusion Reject Reject Reject Accept

WN – 1: 5,70,000 + 4,70,000 + ½ of 3,70,000 = 12,25,000 WN – 2: (5,000 x 55) + (10,000 x 52) + (10,000 x 51) = 13,05,000 Question no 24: Question no 32 Solution: Step 1: Calculation of contribution per unit Particulars Selling Price Less: Production Cost Less: Distribution cost Contribution per unit

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Area 1 (Rs.) 100 80 10 10

Area 2 (Rs.) 100 80 8 12

Area 3 (Rs.) 100 80 6 14

Area 4 (Rs.) 100 80 4 16

Area 5 (Rs.) 100 80 2 18

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AMA-Notes Step 2: Analysis of 2001 profits Area Units Contribution per unit (Rs.) 1 6,500 10 2 6,500 12 3 6,500 14 4 6,500 16 5 6,500 18 Total Contribution Less: Fixed Cost (Sales Man Salary) (35 Men x Rs.8,000) Profit

Contribution (Rs.) 65,000 78,000 91,000 1,04,000 1,17,000 4,55,000 2,80,00 1,70,000

Step 3: Analysis of 2002 profits Area Units Contribution per unit (Rs.) 1 5,000 10 2 5,000 12 3 5,000 14 4 7,800 16 5 7,800 18 Total Contribution Less: Fixed Cost (Sales Man Salary) (35 Men x Rs.8,000) Profit

Contribution (Rs.) 50,000 60,000 70,000 1,24,800 1,40,400 4,45,200 2,80,00 1,65,200

Notes: 1) Instead of giving equal sales man to all five areas the company gave minimum penetration of 5 sales men to all 5 areas and the balance 10 they gave to two high contributing areas ‘A4’ and ‘A5’. Instead of improving the profit the strategy resulted in drop in profits. Why? 2) The volume achieved with 7 sales in each men area was 32,500 units but in the new strategy in 2002 the volume dropped to 30,600 units resulting in 1,900 units drop. 3) Cost-Benefit analysis of this strategy as follows: i. Benefit A4 – 1,300 Units x Rs.16 A5 – 1,300 Units x Rs.16 Contribution gained = Rs.44,200 ii. Cost A1 – 1,500 Units x Rs.10 A2 – 1,500 Units x Rs.12 A3 – 1,500 Units x Rs.14 Contribution lost = Rs.54,000 4) The volume lost from A1, A2, A3 is more than the volume gained in A4 and A5. The sales force is not reduced but only transferred. Then why there is a volume drops? 5) The volume drops because the sales man and penetration relationship is non-linear which means when more sales men is allocated to an area the volume increases but at decreasing rate. Step 4: Calculation of contribution and marginal contribution for all this areas at different levels

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AMA-Notes Men Units A1 Cn 5 5,000 50,000 6 5,800 58,000 7 6,500 65,000 8 7,100 71,000 9 7,600 76,000 10 7,800 78,000 11 8,000 80,000

MCn 8,000 7,000 6,000 5,000 2,000 2,000

A2 Cn 60,000 69,600 78,000 85,200 91,200 93,600 96,000

MCn 9,600 8,400 7,200 6,000 2,400 2,400

A3 Cn 70,000 81,200 91,000 99,400 1,06,400 1,09,200 1,12,000

MCn 11,200 9,800 8,400 7,000 2,800 2,800

A4 Cn 80,000 92,800 1,04,000 1,13,600 1,21,600 1,24,800 1,28,000

MCn 12,800 11,200 9,600 8,000 3,200 3,200

A5 Cn 90,000 1,04,400 1,17,000 1,27,800 1,36,800 1,40,400 1,44,000

MCn 14,400 12,600 10,800 9,000 3,600 3,600

Step 5: Allocation of the additional 10 sales men Sales Men 26th Sales Men 27th Sales Men 28th Sales Men 29th Sales Men 30th Sales Men 31st Sales Men 32nd Sales Men 33rd Sales Men 34th Sales Men 35th Sales Men

Area A5 A4 A5 A3 A4 A5 A3 A2 A4 A5

Summary of Sales Men allocated to each area: Area A1 A2 A3 A4 A5 Total

Sales Men Allocated 5 6 7 8 9 35

Step 6: Calculation of the maximum profit with 35 sales men Area Units Contribution/Unit (Rs.) A1 5,000 10 A2 5,800 12 A3 6,500 14 A4 7,100 16 A5 7,600 18 Total Contribution Less: Fixed Cost Profit

Contribution (Rs.) 50,000 69,600 91,000 1,13,600 1,36,800 4,61,000 2,80,000 1,81,000

Notes: When we have asked to allocate the limiting factor for a non-linear data where the rankings frequently change do the allocation stage by stage using tick (√) technique.

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AMA-Notes Question no 24: Question no 5, pricing chapter, page no.56 Solution: Step 1: Calculation of Variable cost per unit Fixed Cost = 200% of Variable Cost. Therefore, FC:VC = 2:1 Therefore Variable Cost = 1/3 of total cost Product A B C

Variable cost per unit 6 (1/3 x 18) 8 (1/3 x 24) 10 (1/3 x 30)

Step 2: Calculation of Contribution and Marginal Contribution of product ‘A’ Units 2,000 4,000 6,000 8,000 10,000 12,000 14,000

Contribution/Unit 18.5 17.5 16.5 15.5 14.5 13.5 12.5

Contribution 37,000 70,000 99,000 1,24,000 1,45,000 1,62,000 1,75,000

Incremental Contribution/2000 Hours 37,000 33,000 29,000 25,000 21,000 17,000 13,000

Step 3: Calculation of Contribution and Marginal Contribution of product ‘B’ Units 2,000 4,000 6,000 8,000 10,000 12,000 14,000

Contribution/Unit 26 25 24 23 22 21 20

Contribution 52,000 1,00,000 1,44,000 1,84,000 2,20,000 2,52,000 2,80,000

Incremental Contribution/2000 Hours 52,000 48,000 44,000 40,000 36,000 32,000 28,000

Step 4: Calculation of Contribution and Marginal Contribution of product ‘C’ Units

Contribution/Unit Contribution Incremental Contribution/4000 Hours 2,000 29 58,000 58,000 4,000 28 1,12,000 54,000 6,000 27 1,62,000 50,000 8,000 26 2,08,000 46,000 10,000 25 2,50,000 42,000 12,000 24 2,88,000 38,000 14,000 23 3,22,000 34,000

Incremental Contribution/2000 Hours 29,000 27,000 25,000 23,000 21,000 19,000 17,000

Step 5: Allocation of limiting factor E M Reddy

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AMA-Notes Hours 2,000 4,000 6,000 8,000 10,000 12,000 13,500

A 37,000 37,000 37,000 37,000 37,000 33,000 33,000

B 52,000 48,000 44,000 40,000 36,000 36,000 32,000

C 29,000 29,000 29,000 29,000 29,000 29,000 29,000

Select B B B B A B A

Conclusion: The 13,500 hours should be allocated as follows: A = 3,500 Hours → 3,500 Units → Selling price = Rs.23.50 B = 10,000 Hours → 10,000 Units → Selling Price = Rs.30.00 Step 6: Calculation of net profit for the above plan Products Units Contribution per unit (Rs.) A 3,500 17.5 B 10,000 22 Total Contribution Less: Fixed Cost (WN) Profit

Contribution (Rs.) 61,250 2,20,000 2,81,250 (1,83,000) 98,250

WN: Calculation of fixed cost A: 2/3 x Rs.18 = Rs.12 x 6,000 Units = Rs.72,000 B: 2/3 x Rs.24 = Rs.16 x 6,000 Units = Rs.96,000 C: 2/3 x Rs.30 = Rs.20 x 750 Units = 15,000 Total Fixed Cost = Rs.72,000 + Rs.96,000 + Rs.15,000 = Rs.1,83,000 Question no 25: Question no 12, Relevant Costing, page no.56 Solution: Step 1: Analysis of production is strike is allowed Total Production Capacity = 27,500 Machines - 46 Weeks – 25,300 Machines - 4 Weeks – 2,200 Machines - Demand lost due to competition – 650 Machines - OT Production – 1,550 Machines Step 2: Profitability when the strike is allowed and when not allowed Particulars Sales (-) Wages (-) Other Production Cost E M Reddy

Not Allow Strike (‘000s) 66,000 (27,500 Machines x Rs.2,400) 21,186 (WN – 1) 29,700 (27,500 Machines x Rs.1,080)

Allow Strike (‘000s) 64,440 (26,850 Machines x Rs.2,400) 21,079.80 (WN – 1) 28,998 (26,850 Machines x Rs.1,080) Page | 275

AMA-Notes (-) Distribution Cost (-) Overhaul Expenses (-) Additional Fixed Cost Profit

2,750 (27,500 Machines x Rs.100) 100 12,264

2,685 (26,850 Machines x Rs.100) 25 10 11,642.20

WN – 1: Wages Calculation Variable Production Cost = Rs.1,800 per Machine - Wages = Rs.1,800 x 40% = Rs.720 per Machine - Other Production expenses = Rs.1,080 per Machine Wages when strike is allowed = Rs.720 x 107% x27,500 Machines = Rs.21,186,000 Wages when the strike is allowed: Normal time wages = Rs.720 x 105% x 25,300 Machines = Rs.19,126,800 Overtime Wages = Rs.720 x 105% x 150% x 1,550 Machines/90% = Rs.19,53,000 Total Wages = Rs.19,126,800 + Rs.19,53,000 = Rs.21,079,800 If we decide to allow the strike the profit is likely to drop by Rs.6,21,800 (Rs.1,22,64,000 – Rs.1,16,42,200). Hence recommended not to allow strike. Step 3: Analysis of production after strike takes place Total Production Capacity = 27,500 Machines - 47 Weeks – 25,850 Machines - 3 Weeks – 1,650 Machines - Demand lost due to competition – 650 Machines - OT Production – 1,000 Machines Step 4: Profitability after the strike takes place Particulars Sales (-) Wages Normal (-) Wages Normal (-) Other Production Cost (-) Distribution Cost (-) Overhaul Expenses (-) Additional Fixed Cost Profit

Computation 26,850 Machines x Rs.2,400 Rs.720 x 106% x 25,850 Machines Rs.720 x 106% x 150%x 1,000 Machines/90% 26,850 Machines x Rs.1,080 26,850 Machines x Rs.100

Amount (‘000s) 64,440 19,728.72 1,272 28,998 2,685 25 10 11,721.28

Due to allowing strike the profit lost by the management is Rs.5,42,720 (Rs.1,22,64,000 – Rs.1,17,21,280) Step 5: Checking the viability of Overtime Particulars Selling Price (-) Other Production Cost E M Reddy

Amount (Rs.) 2,400 1,080 Page | 276

AMA-Notes (-) Distribution Cost 100 Contribution excluding wage cost 1,220 Benefit: Contribution = 100 Machines x Rs.1,220 = Rs.12,20,000 Cost: Wages = Rs.720 x 106% x 150 x 1,000 Machines/90% = Rs.12,72,000 Additional Fixed Cost = Rs.10,000 Net Benefit/(Cost) = Rs.12,20,000 – Rs.12,82,000 = (Rs.62,000) It is not viable to work overtime because the cost exceeds benefit by Rs.62,000 Conclusion: The cost of strike earlier calculated of Rs.5,42,720 is wrong because included in it is Rs.62,000 lost due to the wrong decision of working overtime. The real cost of strike is Rs.4,80,720 (Rs.5,42,720 – Rs.62,000) Question no 26: Question no 29 (1:02:00) Solution: Step 1: Types of Cost 1) Material i. Company to contractor 110% (100 + 10) → Company get 10% ii. Contractor to customer 137.5% = 110 + (25% of 110) (Charge by contractor) → Contractor gets 27.5% 2) Labour i. Maintenance 90% of list price is contractor share → Company gets 10% ii. Ad-hoc 85% of list price is contractor share → Company gets 15% Step 2: Calculation of incremental income if the entire work is done on own Particulars

Income to company when sub-contract (Rs.) 30,000

Labour – Maintenance Labour – Ad- 12,000 hoc Material18,000 Maintenance Material-Ad6,000 hoc Total Additional Income

Company get %

Bill Amount (Rs.)

Income to company when own (Rs.)

Additional income (Rs.)

10%

3,00,000

3,00,000

2,70,000

15%

80,000

80,000

68,000

10%/137.5%

2,47,500

49,500

10%/137.5%

82,500

67,500 (2,47,500 x 37.5/137.5) 22,500 (82,500 x 37.5/137.5)

16,500 4,04,000

If the company does the entire work on its own it will earn an additional income of Rs.4,04,000 (without considering specific fixed cost for different options). E M Reddy

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AMA-Notes Note: Labour cost is included in fixed cost. So, total bill amount is considered for calculating incremental revenue. Step 3: Evaluation of different options Option 1 Own 40% Contract 60% Increase in income (Rs.4,04,000 x Own%) Rs.1,61,600 Cost (Includes labour cost) (Rs.1,48,000) Net Benefit/(Cost) Rs.13,600

Option 2 60% 40% Rs.2,42,400 (Rs.2,85,000) (Rs.42,600)

Option 3 100% Rs.4,04,000 (Rs.3,85,000) Rs.19,000

It is recommended to choose option 3 i.e. fully do on our own because that gives us the maximum net benefit.

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AMA-Notes 8. SIMULATION

1) There are various models that supports decision making. 2) Most of the models has underlying assumptions and the model will work only when the underlying assumptions are satisfied in real world situation. 3) Where no model can be applied in a decision making situation, then we should make decision based on chance. The scientific way of making decision based on chance is called ‘Simulation’. 4) Simulation is a process through which we build a model and test it through random numbers to understand how it works. 5) Random numbers represent the chance factor and is closely related to probabilities of events. 6) In any simulation problem there are two steps: (i) Random Number Coding → Each event is coded with a range of Random Numbers based on its probability. (ii) Simulation Work Sheet (or) Fitting Random Numbers → The Random Numbers selected is fitted to the code to identify the decision. 7) The above process is popularly called “Monti Carlo Simulation”. Question no 1: The occurrence of rain in a day is dependent upon whether it rained in the previous day. If it rained in the previous day, the rain distribution is given by: Event Probability No rain 0.50 1 cm 0.25 2 cm 0.15 3 cm 0.05 4 cm 0.03 5 cm 0.02 If it did not rain in the previous day, the rain distribution is given by: Event Probability No rain 0.75 1 cm 0.15 2 cm 0.06 3 cm 0.04 Simulate the city’s whether for 10 days and determine by simulation the total days without rain as well as the total rainfall during the period. Use the following random numbers: 76 78 84 75 02 86 02 78 07 63 Assume that for the first day of simulation it has not rained on the previous day. Solution: Step 1: Random Number Coding Table 1: Random Number Coding (Rained Previous Day) Event No rain 1 cm 2 cm

Probability 0.50 0.25 0.15

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Cumulative Probability 0.50 0.75 0.90

Random Number Interval 00 – 49 50 – 74 75 – 89

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AMA-Notes 3 cm 4 cm 5 cm

0.05 0.03 0.02

0.95 0.98 1.00

90 – 94 95 – 97 98 – 99

Table 2: Random Number Coding (No Rain Previous Day) Event No rain 1 cm 2 cm 3 cm

Probability 0.75 0.15 0.06 0.04

Cumulative Probability 0.75 0.90 0.96 1.00

Random Number Interval 00 – 74 74 - 89 90 – 95 96 – 99

Step 2: Fitting Random Numbers (or) Simulation Worksheet Day 1 2 3 4 5 6 7 8 9 10

Random Number 76 78 84 75 02 86 02 78 07 63

Table Reference Table 2 Table 1 Table 1 Table 1 Table 1 Table 2 Table 1 Table 2 Table 1 Table 2

Rainfall (Cm) 1 Cm 2 Cm 2 Cm 2 Cm No rain 1 Cm No rain 1 Cm No rain No rain

Conclusion: Total days without rain are 4 days and total rain is 9 Cm. Question no 2: Dr. Strong is a dentist who schedules all her patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending on the type of dental work to be done. The following summary shows the various categories of the work, their probabilities and time requires completing them: Category Filling Crown Cleaning Extraction Check Up Time Required (Minutes) 45 60 15 45 15 Probability 0.40 0.15 0.15 0.10 0.20 Simulate the dentist clinic for 4 hours and determine the average waiting for the patients as well as idleness of the doctor. Arrival time of 1st patient is 8 AM. Random numbers are as follows: 40 82 11 34 25 66 17 79 Solution: Step 1: Random Number Coding Types Filling Crown Cleaning Extraction Check Up E M Reddy

Time (Minutes) 45 60 15 45 15

Probability 0.40 0.15 0.15 0.10 0.20

Cumulative Probability 0.40 0.55 0.70 0.80 1.00

Random Number Interval 00 – 39 40 – 54 55 – 69 70 – 79 80 – 99 Page | 280

AMA-Notes Step 2: Fitting Random Numbers (or) Simulation Worksheet Simulation Random Run Number 1 40 2 82 3 11 4 34 5 25 6 66 7 17 8 79 Total Waiting time

Type

Time Required Crown 60 Minutes Checkup 15 Minutes Filling 45 Minutes Filling 45 Minutes Filling 45 Minutes Cleaning 15 Minutes Filling 45 Minutes Extraction 45 Minutes

Arrival Time 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30

Waiting Time 0 30 Minutes 15 Minutes 30 Minutes 45 Minutes 60 Minutes 45 Minutes 60 Minutes 285 Minutes

Entry Time 8:00 9:00 9:15 10:00 10:45 11:30 11:45 12:30

Exit Time 9:00 9:15 10:00 10:45 11:30 11:45 12:30 01:15

The average waiting time per patient = 285/8 = 35.62 Minutes. The doctor is never idle during the 4 hours period. Question no 3: Arial ltd. trades in a perishable commodity, each day it receives supplies of the goods from a wholesaler but the quantity supplied random variable, as is subsequent retail customer demand for commodity. Both supply and demand are expressed in batches 50 units and over the past working year (consider 300 days) company has kept records of supplies and demands. The rates are given in the following table: Wholesaler 50 100 150 200

No.of days 60 90 90 60

Customer Demand 50 100 150 200

No.of days occurring 60 60 150 30

Buys the commodity Rs.6 p.u. and sells at Rs.10 p.u. at present there are no storage facilities and unsold units at the end of the day are worthless. Arial estimates that each unit of unsatisfied demand on any day costs them Rs.2. Use the following random number for supply – 8,4,8,0,3,3, and for demand 4,7,9,6,1,5. Simulate six days trading and estimate annual profit, return the exercise to estimate value of storage facilities. Solution: Step 1: Random Number Coding Purchase/ Sales in Batches 1 2 3 4

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Purchase Probability

Sales Probability

60/300=0.2 90/300=0.3 90/300=0.3 60/300=0.2

60/300=0.2 60/300=0.2 150/300=0.5 30/300=0.1

Purchases ∑ 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 Random Number 0.2 0–1 0.5 2–4 0.8 5–7 1.0 8–9

Sales ∑ 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 Random Number 0.2 0–1 0.4 2–3 0.9 4–8 1.0 9–9

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AMA-Notes Step 2: Fitting Random Numbers (or) Simulation Work Sheet Simulation Run 1 2 3 4 5 6

Purchases Random Number 8 4 8 0 3 3

Purchases 4 2 4 1 2 2

Sales Random Number 4 7 9 6 1 5

Sales 3 3 4 3 1 3

Step 3: Understanding the financial details There are 3 situations: - Satisfied Demand → Profit per batch = (Rs.10 – Rs.6) x 50 Units = Rs.200 - Excess Stock → Cost per Batch = Rs.6 x 50 Units = Rs300 - Stock Out → Cost per batch = Rs.2 x 50 Units = Rs.100 Step 4: Calculation of weekly profit and annual profit without storage facility Day Purchase Sales Excess Stock – loss 1 4 3 1 2 2 3 3 4 4 4 1 3 5 2 1 1 6 2 3 Total 2

Short Stock – Loss 1 2 1 4

Profit producing sales (Demands satisfied) 3 2 4 1 1 2 13

Profitability statement – 6 Days Cycle: Profit (13 Batches x Rs.200) Less: Stock out cost (4 Batches x Rs.100) Less: Excess stock loss (2 Batches x Rs.300) Profit/(Loss) Estimated Annual profit =

Rs.1,600 6 Days

= Rs.2,600 = (Rs.400) = (Rs.600) = Rs.1,600

x 300 Days = Rs.80,000

Step 5: Calculation of weekly and annual profits with storage facilities Day 1 2 3 4 5 6 Total

Opening Stock 1 1

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Purchases 4 2 4 1 2 2

Sales 3 3 4 3 but 1 1 3

Closing Stock Sales Lost 1 2 1 2

Demand Satisfied 3 3 4 1 1 2 15

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AMA-Notes Profitability statement – 6 Days Cycle: Profit (15 Batches x Rs.200) Less: Stock out cost (2 Batches x Rs.100) Profit/(Loss) Estimated Annual profit =

Rs.2,800 6 Days

= Rs.3,000 = (Rs.200) = Rs.2,800

x 300 Days = Rs.1,40,000

Conclusion: Due to storage facility the company could earn extra profit of Rs.60,000 (Rs.1,40,000 – Rs.80,000). This is the value of storage facilities. The company can maximum pay Rs.60,000 per annum towards the storage facilities. **Question no 4: A plant has a large number of similar machines. The machines breakdown random and the breakdowns are independent of each other. Once a machine breaks down, it has to be taken out of production till the time it is repaired. On the basis of the past data, the following distributions have been constructed. No.of breakdowns per Probability No.of hours required for repair per Probability hour breakdown 0 0.900 1 0.100 1 0.085 2 0.240 2 0.012 3 0.450 3 0.03 4 0.165 5 0.040 6 0.005 Each hour that a machine remains idle due to being, or waiting to be repaired, it costs the plant, Rs.80 per hour by way of lost production. If a repairman is paid at Rs.8 per hour, how many repairmen should be hired by the company to service the machine breakdowns? For the purpose, simulate the system for a 50-hour period and use the following random numbers, reading row-wise starting with the NW corner. For Breakdowns: 100 375 084 990 128 660 310 852 635 737 985 118 834 886 995 654 801 743 699 098 914 803 441 125 636 611 154 945 424 235 044 005 353 598 460 321 692 195 451 948 980 331 809 797 185 740 541 116 483 690 For Repair times: 765 648 196 093 801 340 455 020 053 035 672 121 099 195 981 783 389 421 125 623 Solution: Step 1: Random Number Coding (Number of Breakdowns) Number of Breakdowns 0 1 2 3 E M Reddy

Probability 0.900 0.085 0.012 0.03

Cumulative Probability 0.900 0.985 0.997 1.000

Class Intervals 000 – 899 900 – 984 985 – 996 997 – 999 Page | 283

AMA-Notes Step 2: Random Number Coding (Repair time) Number of hours taken for repair 1 2 3 4 5 6

Probability 0.100 0.240 0.450 0.165 0.040 0.005

Cumulative Probability 0.100 0.340 0.790 0.955 0.995 1.000

Class Intervals 000 – 099 100 – 339 340 – 789 790 – 954 955 – 994 995 – 999

Step 3: Simulation Worksheet Breakdown Hours: Random Numbers 990 985 995 914 945 948 980

No.of Breakdowns 2 2 2 1 1 1 1 10

Hour of Breakdown 4 11 15 21 28 40 41

Repair time (Only one repair man): Breakdown Numbers B1 B2 B3 B4 B5 B6 B7 B8 B9 B10

Hour of Breakdown 4 4 11 11 15 15 21 28 40 41

Random no.of repairs 765 648 196 093 801 340 455 020 053 035

Time Taken 3 3 2 1 4 3 3 1 1 1

Entry time for repair 4 7 11 13 15 19 22 28 40 41

Finish time 7 10 13 14 19 22 25 29 41 42

Waiting time Nil 3 Nil 2 Nil 4 1 Nil Nil Nil

Step 4: 1 Repair Man: Repairman Cost (Rs.8 x 50 Hours) Idle time cost (Rs.80 x 10 Hours) Total

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= Rs.400 = Rs.800 = Rs.1,200

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AMA-Notes 2 Repair Men: Repairmen Cost (Rs.8 x 50 Hours x 2) = Rs.800 Idle time cost = Nil Total = Rs.800 Notes: 1) With respect to number of breakdowns all Radom numbers below 900 represents ‘0’ breakdowns. Hence those numbers are ignored. 2) We didn’t consider 3 repair men option because as per the indication given by random number the maximum number of simultaneous breakdown is ‘2’. Hence the 3rd repair man will always remain idle. 3) The company loses Rs.80 per hour on hour’s lost due to repairing and waiting to be repaired time. We have ignored the opportunity cost of repairing time. Why? Answer: This is because the number of repair men decision will not alter the cost. Question no 5: The tit-fit scientific laboratories is engaged in producing different types of Highclass equipment’s for use in science labs. The company has two difference assembly line to produce its popular product ‘P’. Processing time (min) 10 11 12 13 14 Assembly A1 0.10 0.15 0.40 0.25 0.10 Assembly A2 0.20 0.40 0.20 0.14 0.05 Use the following random numbers, generate data on the process times for 15 units of the item and compute the expected process time for the product. 4134 8343 3602 7505 7428 7476 1185 9445 0089 3424 4943 1915 5415 0880 9390 Solution: Step 1: Random Number Coding Time Assembly A1 Probability ∑ 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 Random Numbers 10 0.10 0.10 0000 – 0999 11 0.15 0.25 1000 – 2499 12 0.40 0.65 2500 – 6499 13 0.25 0.90 6500 – 8999 14 0.10 1.00 9000 – 9999

Assembly A2 Probability ∑ 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 Random Numbers 0.20 0.20 0000 – 1999 0.40 0.60 2000 – 5999 0.20 0.80 6000 – 7999 0.15 0.95 8000 – 9499 0.05 1.00 9500 – 9999

Step 2: Simulation Worksheet (or) Fitting Random Numbers Simulation Run 1 2 3 4

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Random Number 4134 8343 3602 7505

Assembly A1 Time 12 13 12 13

Assembly A2 Time 11 13 11 12

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AMA-Notes 5 6 7 8 9 10 11 12 13 14 15

7428 7476 1185 9445 0089 3424 4943 1915 5415 0880 9390

13 13 11 14 10 12 12 11 12 10 14

12 12 10 13 10 11 11 10 11 10 13

Step 3: Expected process time for the product Simulation Run Simulation Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time Required Assembly A1 Time 12 13 12 13 13 13 11 14 10 12 12 11 12 10 14

∑ 𝐓𝐢𝐦𝐞 12 25 37 50 63 76 87 101 111 123 135 146 158 168 182

Total Time

The expected average time per unit = No.of Units =

Assembly A2 Time 11 13 11 12 12 12 10 13 10 11 11 10 11 10 13

195 Minutes 15

∑ 𝐓𝐢𝐦𝐞 12 + 11 = 23 25 + 13 = 38 38 + 11 = 49 50 + 12 = 62 63 + 12 = 75 76 +12 = 88 88 + 10 = 98 101 + 13 = 114 114 + 10 = 124 124 + 11 = 135 135 + 11= 146 146 + 10 = 156 158 + 11 = 169 169 + 10 = 179 182 + 13 = 195

= 13 Minutes per unit

Note: The minimum spent by a unit in each assembly is 10 minutes. Therefore, to produce one unit we will minimum take 20 minutes. Hence, for 15 units the minimum time should have been 300 minutes. Then how it is completed in 195 minutes? Answer: This is because of simultaneous activates i.e. when we are processing the 10th unit of A2 we will simultaneously process 11th unit’s A1. Question no 6: Process involves the production of a particular component, which is then installed into an end product. Past observation has indicated that the average production time for the component is 4 minutes but fluctuations about the average do occur. The following probability distribution has been derived: Production time (min) 2 3 4 5 6 7 Probability 0.10 0.25 0.40 0.10 0.10 0.05

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AMA-Notes Average time taken to install a component is 3 minutes but it also fluctuations and the following probability distribution has been derived: Production time (min) 2 3 4 5 Probability 0.30 0.45 0.15 0.10 The current system uses an operative for installation but the company is considering employing another operative for installation but the company is considering employing another operative on the installation process. Simulate 10 times the current system, using the following 2 digit random numbers: 20, 74, 94, 22, 93, 45, 44, 16, 04, 32 and 03, 62, 61, 89, 01, 27, 49, 50, 90, 98. Solution: Step 1: Random Number Coding (Production Time) Production Time 2 3 4 5 6 7

Probability 0.10 0.25 0.40 0.10 0.10 0.05

∑ 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 0.10 0.35 0.75 0.85 0.95 1.00

Random Number 00 – 09 10 – 34 35 – 74 75 – 84 85 – 94 99 – 99

Step 2: Random Number Coding (Installation Time) Production Time 2 3 4 5

Probability 0.30 0.45 0.15 0.10

∑ 𝐏𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲 0.30 0.75 0.90 1.00

Random Number 00 – 29 30 – 74 75 – 89 90 – 99

Step 3: Simulation Worksheet (or) Fitting Random Numbers [Installation time] Simulation Run 1 2 3 4 5 6 7 8 9 10

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Random Number 03 62 61 89 01 27 49 50 90 98

Installation time 2 3 3 4 2 2 3 3 5 5

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AMA-Notes Step 4: Simulation Worksheet (or) Fitting Random Numbers Simulation Run 1 2 3 4 5 6 7 8 9 10

Random Number 20 74 94 22 93 45 44 16 04 32

Production time 3 4 6 3 6 4 4 3 2 3

∑ 𝐏𝐫𝐨𝐝𝐮𝐜𝐭𝐢𝐨𝐧 𝐭𝐢𝐦𝐞 Installation time 3 2 7 3 13 3 16 4 22 2 26 2 30 3 33 3 35 5 38 5

Cumulative time 3+2=5 7 + 3 = 10 13 + 3 = 16 16 + 4 = 20 22 + 2 = 24 26 + 2 = 28 30 + 3 = 33 33 + 3 = 36 36 + 5 = 41 41 + 5 = 46

Conclusion: Out of 10 simulation runs only 2 times the production was over and the units are waiting to get installed due to installation machine being busy. In remaining 8 times the installation was completed and the machine is waiting for the next unit to get produced. Hence, it is recommended not to have one more operative in installation department.

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AMA-Notes 9. MATERIALS REQUIREMENT PLANNING (MRP) 9.1. Introduction

9.2. Planning Order Release

Question no 1: The product structure and the lead times for a finished product ‘X’ are given in figure below. If 100 units of ‘X’ are required in week 12 and if none of the components, sub-assembles and the end product are either on hand or on order. Compute the amounts and sub-assemblies. Assume that there is no particulars order size and therefore all the order quantities are lot for lot.

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AMA-Notes

Solution:

Summary: Product Planned Order Release X 10th Week 6th Week P 7th Week Q 9th Week 3rd Week R 4th Week 3rd Week S 4th Week

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Units 100 40 100 200 1,200 300 800 200

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AMA-Notes 9.3. Construction of Product Tree

Question no 2: The manufacture of product ‘x’, requires the assembly of modules ‘a’, ‘b’ and ‘c’. Two modules, each of ‘a’ & ‘c’ and only one module of ‘b’ is needed to make one unit of ‘x’. Module ‘a’ is made from components ‘i’, ‘j’ and ‘k’. To make one sub-assembly of ‘d’, two components each of ‘j’ and ‘i’ are required and 1 component of ‘k’. Sub-assembly ‘f’ needs components ‘i’ and ‘m’ (one each). Module ‘c’ needs sub-modules of ‘g’ and ‘h’ in quantities of two units and one unit, respectively. Sub-module ‘g’ is, in turn, assembled from five units each of components ‘i’ and ‘j’. Item ‘i’ need 1 unit each of components ‘n’ and ‘o’. Draw the product structure based on the above information. If 100 units of x are to be produced, what are the requirements at the various levels of the product? Write an indented bill of materials and calculate the requirements of materials at the various intervals? Calculate the net requirements if the quantities on hand and/or on order are as shown below. A safety stock of ‘i’ of 400 is seen as essential as it is used sometimes in another product ‘y’ whose demand is not all that predictable. Item On Hand On Order D 70 E 100 F 50 100 I 500 500 Solution: Step 1: Product Structure tree

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AMA-Notes Step 2: Planning Order Release

9.4. Preparation of MRP

Question no 3: Given the following information, how many units are on hand at the end of week 9? Which are the weeks in which the orders may be accepted? Order Quantity = 200 Week Lead Time = 2 Weeks 1 2 3 4 5 6 7 8 9 Requirements 90 10 140 55 5 15 115 95 100 Scheduled Receipts On the hand at the end of the period 110 Planned Order Release Solution: Particulars

Week 0 1 Requirements 90 Scheduled Receipts Closing Stock 110 20 Planned Order Release 200

2 10 10 -

3 140 200 70 -

4 55 15 200

5 5 10 -

6 15 200 195 200

7 115 80 -

8 95 200 185 -

9 100 85 -

9.5. Preparation of MRP with safety stock

Question no 4: Geetha industries uses MRP for its production materials planning. The table below provides the information about a particular component X. The demand for this component is somewhat uncertain and in order to take care of a sudden spurt in the demand, a safety stock of 50 items is recommended.

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AMA-Notes Order Quantity = 250 Week Lead Time = 3 Weeks 1 2 3 4 5 6 7 8 9 Requirements 40 100 70 150 20 20 50 100 70 Scheduled Receipts 250 On the hand at the end of the period 150 Planned Order Release Solution: Particulars

Week 0 1 Requirements 40 Scheduled Receipts Closing Stock 150 110 Planned Order Release 250

2 100 250 260 -

3 70 190 -

4 150 250 290 -

5 20 270 -

6 20 250 250

7 50 200 -

8 100 100 -

9 70 250 280 -

9.6. Material Purchase Budget and Economic Order Quantity [EOQ]

Question no 5: A company is engaged in manufacturing two products A and B. Product A uses one unit of component X and two units of component Y. Product B uses two units of component X, one unit of component Y and two units of component Z. Component Z which is assembled in the factory uses one unit of component Y. Components X and Y are purchased from the market. The company has prepared the following forecast of sales and inventory for the next year: Particulars Sales Stock at the end of the year Stock at the beginning of the year

Product A [Units] 80,000 10,000 30,000

Product B [Units] 1,50,000 20,000 50,000

The production of both the products and the assembling of the component Z will be spread out uniformly throughout the year. The company at present orders its inventory of X and Y in quantities equivalent to 3 months’ production. The company has compiled the following data related to the two components. Particulars Price per unit (Rs.) Order placing cost per order (Rs.) Carrying cost per annum

Product A [Units] 20 1,500 20%

Product B [Units] 8 1,500 20%

Required: (i) Prepare a budget for production and requirements of components for the year. (ii) Suggest the optimal order quantity of components X and Y.

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AMA-Notes Solution: Step 1: Product Structure Tree

Step 2: Production Particulars Sales Add: Closing Stock Less: Opening Stock Production

A 80,000 10,000 (30,000) 60,000

B 1,50,000 20,000 (50,000) 1,20,000

Step 3: Annual Consumption of ‘X’ A: 60,000 Units x 1 = 60,000 Units B: 1,20,000 Units x 2 = 2,40,000 Units Total Units of ‘X’ required = 60,000 Units + 2,40,000 Units = 3,00,000 Units Step 4: Annual Consumption of ‘Y’ A: 60,000 Units x 2 = 1,20,000 Units B: 1,20,000 Units x 1 = 1,20,000 Units Z: 2,40,000 Units x 2 = 2,40,000 Units Total Units of ‘X’ required = 1,20,000 Units + 1,20,000 Units + 2,40,000 Units = 4,80,000 Units Step 5: Calculation of EOQ of ‘X’ A (Annual Consumption) B (Ordering Cost) C (Carrying Cost) 2AB

EOQ = √

C

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2 x 3,00,000 x 1,500

=√

Ordering cost =

= 3,00,000 Units = Rs.1,500 = Rs.20% x Rs.20 = Rs.4 per unit per annum

4

Annual Consumption EOQ

= 15,000 Units x Ordering Cost =

3,00,000 15,000

x Rs.1,500 = Rs.30,000 per annum

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AMA-Notes 1

1

Carrying Cost = 2 x EOQ x Carrying Cost = 2 x 15,000 Units x Rs.4 = Rs.30,000 per annum Step 6: Calculation of EOQ of ‘Y’ A (Annual Consumption) B (Ordering Cost) C (Carrying Cost) 2AB

EOQ = √

C

2 x 4,80,000 x 1,500

=√

Ordering cost =

= 4,80,000 Units = Rs.1,500 = Rs.20% x Rs.8 = Rs.1.6 per unit per annum

1.6

Annual Consumption EOQ 1

= 30,000 Units x Ordering Cost =

4,80,000 30,000

x Rs.1,500 = Rs.24,000 per annum

1

Carrying Cost = 2 x EOQ x Carrying Cost = 2 x 30,000 Units x Rs.1.6 = Rs.30,000 per annum

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AMA-Notes 10. NETWORK ANALYSIS 10.1. Learning Objectives

1) Understanding some basic terms used in Network 2) Learning to draw a network diagram and appropriately use dummy activates 3) Forward Pass and Backward Pass Procedure 4) Calculating EST, LST, EFT and LFT of each activity 5) Total float, free float and independent float 6) Identification of critical activates and critical path 7) Program evaluation review technique 8) Network Crashing 9) Resource allocation with loading chart 10) Resource leveling or smoothing with time scale network 11) Network updating 10.2. Introduction

A. B. C. D.

Projects involves huge investments, complex activities and a longer time frame. To avoid time & cost over-run it is necessary to properly plan & control the project implementation. One of the popular techniques used in project planning and control is “Network Analysis”. In Network Analysis we, a) Break the projects into number of activities b) Sequence the activities c) Present the same in the form of a network diagram which is a pictorial representation of the entire project. d) Estimate the time and resource required for each activity and fit it into the network diagram. e) Then use techniques like crashing, resource allocation etc., to manage the network.

10.3. Understanding some basic terms used in Network

1) 2) 3) 4) 5) 6)

Activities Events Types of Activities Types of Events Errors in drawing a Network Conventions in Network Diagram

10.3.1. Activities & Events

1)

a) Activity is something that consumes time and resource. b) It is represented as a straight line in the Network. c) Here Activity ‘A’ is covered by 2 circles ① and ②. They are called “Events”.

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AMA-Notes d) Event ① is the starting event of Activity ‘A’ and called “Tail Event” and event ② is the ending event of an activity and called “Head Event”. 2) Types of Activities:

The diagram shows Activity ‘A’ should be done first and when Activity ‘A’ is over Activity ‘B’ and Activity ‘C’ can start. Here there are 3 types of activities: a) Preceding Activities → For Activity ‘B’ and Activity ‘C’, Activity ‘A’ is proceeding. b) Succeeding Activities → For Activity ‘A’, Activity ‘B’ and Activity ‘C’ are succeeding. c) Simultaneous Activities → For Activity ‘B’ Activity ‘C’ is simultaneous and vice-versa. 3) Events:

a) When an event is a starting event for more than one activity it is called “Burst Event”. Here Event ② is starting event for Activity ‘B’ and Activity ‘C’. b) If an event is ending event of more than one activity it is called “Merge Event”. Event ⑤ represents completion of Activity ‘D’ and Activity ‘E’. 10.3.2. Errors in Networking

1) Looping Error 2) Dangling Error 3) Mistake in Succeeding, Preceding relationship 10.3.2.1. Looping Error

1) When Activity ‘A’ is over Activity ‘B’ will starts, when Activity ‘B’ is over Activity ‘C’ starts, on completion of Activity ‘C’ again Activity ‘B’ starts. Thus a loop is formed. 2) This project will never end. 3) In real world there are situations where finite loops can be formed which is supported by flowcharting and programming techniques. However, in network looping is not possible because with loops we cannot perform the Forward and Backward Pass procedures.

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AMA-Notes 10.3.2.2. Dangling Error

1) A project can have only one starting event and one ending event. 2) In the above diagram if we call event ③ as the completing event of the project then Activity ‘B’ becomes irrelevant for the project completion and vice-versa. 3) This error is called Dangling error. Every activity should either be connected to next Activity or to the last event. 4) The error can be removed by using ‘Dummy Activity’. 5) Dummy activity is an activity that consumes ‘0’ time and ‘0’ resource. It is represented by dotted lines.

6) Event ④ has now become merge event. It represents the completion of activities ‘B’ and dummy. Since dummy takes ‘0’ time it gets completed as soon as Activity ‘C’ is completed. Hence event ④ represents completion of Activity ‘B’ and Activity ‘C’. 10.3.2.3. Mistake in Preceding, Succeeding relationship

Example: A = 1st activity. B & C can start once A is completed. D can start once B & C is over. ‘E’ can start once B is over. 1) Wrong Diagram:

There are two mistakes in this diagram. i) Two Activities can have a common tail event or can have common head event but cannot have the same head and tail events as it creates problems in Forward, Backward pass computations. ii) For staring of Activity ‘D’, Activity ‘B’ and Activity ‘C’ should merge and for starting of activity ‘E’ activity ‘B’ alone should be completed. The above can be resolved using dummy activity.

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AMA-Notes

10.3.3. Conventions in Network Drawing

1) 2) 3) 4)

Time moves from left to right. Activities are represented as straight lines. Head event number should be greater than tail event number. Try to avoid crossing of lines while drawing network. If necessary, use gates.

10.4. Floats, Forward Pass, Backward Pass and Critical Path

Question no 1: With the help of activities given below draw a network and find out: (a) Earliest start time (b) Earliest finish time (c) Latest start time (d) Latest finish time (e) Total float (f) Free float (g) Independent float. The following are the activities and their duration: Activity Duration 1–2 6 2–3 8 2–4 10 3–4 0 3–5 6 4–5 20 5–6 16 Solution: Step 1: Network Diagram

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AMA-Notes Step 2: Forward Pass Procedure (Earliest Start Time – EST)

Step 3: Backward Pass Procedure (Latest Finish Time – LFT)

Forward Pass Procedure: 1) Forward Pass is a procedure through which we find out earliest start time for every activity. 2) It is done as follows: a. Put “E” of event 1 as “0”. b. “E” of head event = “E” of tail event + Duration c. Where the head event is merge event it will have multiple tails. In such case it is “E” of each tail event + Duration whichever is higher. E M Reddy

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AMA-Notes Backward Pass Procedure: 1) Through this procedure we find out latest finish time of each activity. 2) It is done as follows: a. Assign “L” of the last event as “E” of last event. b. “L” of tail event = “L” of Head event – Duration c. If the tail event is burst event, it will have multiple heads. In such case it is “L” of each head event – Duration whichever is lower. Step 4: Calculation of EST, EFT, LST, LFT and Total Float Activity 𝐭 𝐧 – Duration Start E L 1–2 6 0 0 2–3 8 6 8 2–4 10 6 6 3–4 0 14 16 3–5 6 14 30 4–5 20 16 16 5–6 16 36 36

Finish E L 6 6 14 16 16 16 14 16 20 36 36 36 52 52

Total Float 0 2 0 2 16 0 0

Calculation of time estimates: 1) 2) 3) 4)

EST = “E” of Tail Event LFT = “L” of Head Event LST = “LFT – Duration EFT = EST + Duration

Step 5: Network with Critical Paths

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AMA-Notes Total Float, Critical Activity and Critical Path: 1) Total Float = LFT – EFT (or) LST – EST 2) Total Float indicates by how many days we can postpone an activity without affecting the project duration. 3) The total float of activity ‘2 – 3’ days. This means instead of starting activity ‘2 – 3’ on 6th day if we start on 8th day, still we can complete on time. 4) Those activities having total float as ‘0’ cannot be postponed and are referred as “Critical Activity”. 5) The path in which all the activities are critical activates is called “Critical Path”. 6) Critical path is the longest path in the Network and all the activities in the path are critical activates. Paths Duration 1–2–3–5–6 6 + 8 + 6 + 16 = 36 1 – 2 – 3 – 4 – 5 – 6 6 + 8 + 0 + 20 + 16 = 50 Critical Path 1–2–4–5–6 6 + 10 + 20 + 16 = 52 Step 6: Calculation of Free Float and Independent Float Activity Total Float 1–2 0 2–3 2 2–4 0 3–4 2 3–5 16 4–5 0 5–6 0

Free Float (Total Float – Head event slack) 0–0=0 2–2=0 0–0=0 2 – 0= 0 16 – 0 = 16 0–0=0 0–0=0

Independent Float (Free Float – Tale event slack) 0–0=0 0–0=0 0–0=0 2–2=0 16 – 2 = 14 0–0=0 0–0=0

Notes: 1) Concept of free float: a) Free float = Total Float – Head Event Slack b) It is that part of total float which does not affect the float of succeeding activity. c) For example, activity ‘2 – 3’ is having total float of 2 days and activity ‘3 – 5’ is having a total float f 16 days. If we postpone activity ‘2 – 3’ by 2 days, we can postpone activity ‘3 – 5’ only by 14 days. That means using activity ‘2 – 3’ floats affect the float of succeeding activity ‘3 – 5’. Thus activity ‘2 – 3’ has ‘0’ free float. 2) Concept of independent float: a) Independent Float = Free Float – Tail Event Slack b) It is that part of that total float which does not affect the float of succeeding and preceding activity. c) For example, activity ‘3 – 5’ has a total float of 16 days Postponing it by 16 days results in reduction of float of activity ‘2 – 3’ but if we postpone by 14 days (Independent Float), it does not affect the float of activity ‘2 – 3’.

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AMA-Notes 10.5. Network Crashing

1) Crashing is a process through which we try to reduce duration of a project. 2) The network crashing affects the project cost in two ways: (i) Benefit → Savings in Overhead Cost → Overhead costs are those costs which are linked to project duration (ii) Cost → To reduce the project duration we should reduce activity duration for which we should employ more resources in the activities. The cost involved is called “Crash Cost”. 3) Keep Crashing the network as long as the benefit of crashing exceeds the cost of crashing. When this reverses stop crashing. 4) The project length (duration) at which the total cost is minimum is called “Optimum Project Length/Duration”. 5) If the problem asks “Minimum Project Length/Shortest Project Duration”, continue crashing till we reach a stage where further crashing not possible. Question no 2: A small maintenance project consists of jobs in the table below. With each job is listed its normal time and a minimum or crash time in days. The cost in Rs. Per day of each job is also given: Job (i – j) Normal Days Crash Days Crash Cost per Day 1–2 9 6 20 1–3 8 5 25 1–4 15 10 30 2–4 5 3 10 3–4 10 6 15 4–5 2 1 40 a) What is the normal project length and minimum project length? b) Determine the minimum crashing cost of schedule ranging from normal length down to, and including, the minimum length schedule. c) Overhead costs total Rs.60 per day. What is the optimum length schedule in terms of both crashing and overhead cost? Solution: Step 1: Network Diagram

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AMA-Notes Step 2: Network Crashing Network Diagram:

Paths Table: Paths 1–2–4–5 1–4–5 1–3–4–5

0 16 17 20

3 16 17 17

4 15 16 16

5 15 15 15

7 13 13 13

8 12 12 12

Slash Table: Activity 1–2 1–3 1–4 2–4 3–4 4–5

Crash Days Possible 3/2 3/1/0 5/4/2/1 2/0 4/1/0 1/0

Crash Cost/Day 20 25 30 10 15 40

Cost Table: Duration 20 17 16 15 13 12

Crash Cost Nil 45 85 130 260 335

Overhead @ 60 per Day 1,200 1,020 960 900 780 720

Total Cost 1,200 1,065 1,045 1,030 1,040 1,055

Evaluation Table: Stages Activities Possible

Remarks

Crash Cost

A

Crash ‘3 – 4’ by 3 days

Rs.15 x 3 Days = 45

1 – 3, 3 – 4, 4 – 5

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∑ 𝐂𝐫𝐚𝐬𝐡 𝐂𝐨𝐬𝐭 (Rs.) 45

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AMA-Notes B

D

[1 – 3, 1 – 4, 3 – 4]; [1 – 4, 4 – 5] [1 – 3, 1 – 4, 3 – 4]; [1 – 4, 4 – 5] 1 – 2, 2 – 4, 1 – 4, 1 – 3

E

1 – 2, 1 – 4, 1 – 3

F

1 – 2, 1 – 4,

C

Crash ‘4 – 5’ by 1 day Crash ‘3 – 4’ & ‘1 – 4’ by 1 day Crash 2 – 4, 1- 4, 1-3 by 1 day Crash 1 – 2, 1 – 4, 1 – 3 by 1 day Not possible to crash

Rs.40 x 1 Day = Rs.40 Rs.45 x 1 Day = Rs.45 Rs.65 x 2 Days = Rs.130 Rs.75 x 1 Day = Rs.75

85 130 260 335

Final Solution: Duration Normal Optimum Shortest

Days 20 Days 15 Days 12 Days

Cost (Rs.) 1,200 1,030 1,055

Notes: 1) When decision regarding crashing is made in the remarks column in evaluation table. 2) There are two aspects to be decide: (i) What activity to be crashed (ii) How many days to crash. 3) Always crash only critical activities because crashing non-critical activities does not result in reduction of project duration. It is a wasteful expenditure. 4) While selecting select least cost critical activity. 5) If there are more than one critical paths, all the paths should be simultaneously crashed. Here we have two options: (i) Crash an activity common to all the parts (ii) Crash one activity each from every critical path That option that gives lowest crash cost should be selected. 6) In deciding the number of days to be crashed we should consider 2 tables: (i) Slash Table → To see how many crash days are available (ii) Paths Table → To ensure that the path that being is crashed retains it’s criticality. For example, in stage A we decided to crash ‘3 – 4’ by 3 days even though ‘3 – 4’ days available to crash? Answer: This is because if we crash ‘3 – 4’ by 4 days the critical path ‘1 – 3 – 4 – 5’ becomes 16 days while ‘1 – 4- 5’ continues to be 17 days. Inspire of 4 days crashing the project duration gets reduced only 3 days making the 4th day expenditure wasteful. The rule is “A path once critical should always be critical”. 7) Till 15 days crashing we can see the total cost getting reduced beyond which it begins to increase. Hence the optimum duration is 15 days. 8) Continue crashing till we reach a stage where we don’t have crash days available in any one of the critical path. For example, in stage F there are 3 critical paths but we do not have any critical activity to crash in the critical path ‘1 – 3 – 4 – 5’. 9) Situation 1: If the problem requires us to find out normal and shortest duration without requiring any cost detail the question can be answered simply as follows: Answer:

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AMA-Notes

Paths 1–2–4–5 1–4–5 1–3–4–5

Normal Duration 16 17 ⑳

Shortest Duration 10 11 ⑫

10) Situation 2: Network Crashing when the problem requires us to calculate normal and shortest duration with their associated costs Step 1: Draw Network with Normal & Shortest Duration

Step 2: Prepare Slash Table Activity 1–2 1–3 1–4 2–4 3–4 4–5

Crash Days Possible 3 3 5 2 4 1

Crash Cost/Day 20 25 30 10 15 40

Step 3: Crashing Table Path

Normal Shortest Activities Crash Days Duration Duration Available 1 – 2 – 4 – 5 16 10 1–2 3 2–4 2 4–5 1 1–4–5 17 11 1–4 5 4–5 1 1 – 3 – 4 – 5 20 12 1–3 3 3–4 4 4–5 1 Total Crash Days Cost

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Crash Days 1 2 1 4 1 3 4 1

Cost 1 x 20 = 20 2 x 10 =20 4 x 30 = 120 3 x 25 = 75 4 x 15 =60 1 x 40 = 40 335

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AMA-Notes (i) The Critical Path for the shortest duration is ‘1 – 3 – 4 – 5’. Thus we can understand that, that path is crashed fully i.e. all the activities in that path has been crashed to the extent of crash days available. (ii) The path ‘1 – 4 – 5’ can be crashed by 6 days and ‘1 – 2 – 4 – 5’ also by 6 days but we have decided to crash them by 5 days & 4 days respectively. Why? Answer: Any effort to crash these paths below 12 days is wasteful expenditure as it will have no impact on project duration. (iii) When we crash ‘4 – 5’ by 1 day, the other two paths also get crashed by 1 day because ‘4 – 5’ is present in those paths also. (iv) Thus the second path ‘1 – 4 – 5’ should now be crashed by 4 days which we do it by crashing path ‘1 – 4’. (v) Similarly, the path ‘1 – 2 – 4 – 5’ should now being crashed by 3 days for which we first crash path ‘2 – 4’ due it’s low crash cost and next path ‘1 – 2’. (vi) Final Solution: Time Duration Overhead Cost @ 60 /day Crash Cost Total Cost Normal 20 Days Rs.1,200 Rs.1,200 Shortest 12 Days Rs.720 Rs.335 Rs.1,055 Question no 3: The following table shows for each activity needed to complete the project the normal time, the shortest time in which the activity can be completed of a building contract and the cost per day for reducing the time of activity. The contract includes a penalty clause of Rs.100 per day over 17 days. The overhead cost per day is Rs.160. Activity 1–2 1–3 1–4 2–4 2–5 3–6 4–6 5–6

Normal time (in days) 6 8 5 3 5 12 8 6

Shortest time (in days) 4 4 3 3 3 8 5 6

Cost of reduction per day 80 90 30 40 200 50 -

The cost of completing the eight activities in normal time is Rs.6,500. 1) Calculate the normal duration of the project, its cost and the critical path. 2) Calculate and plot on graph the cost time function for the project and state. (i) The lowest cost and associated time. (ii) The shortest time and associated cost.

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AMA-Notes Solution: Step 1: Network Diagram

Step 2: Network Crashing Network Diagram:

Paths Table: Paths 1–2–5–6 1–2–4–6 1–4–6 1–3–6

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0 17 17 13 20

3 17 17 13 17

4 16 16 13 16

5 15 15 13 15

7 13 13 11 13

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AMA-Notes Slash Table: Activity 1–2 1–3 1–4 2–4 2–5 3–6 4–6 5–6

Crash Days Possible 2/1/0 4/1/0 2 0 2/0 4/3/1 3/1 0

Crash Cost/Day 80 90 30 40 200 50 -

Cost Table: Duration 20 17 16 15 13

Normal Cost 6,500 6,500 6,500 6,500 6,500

Overhead @ Rs.160 per Day 3,200 2,720 2,560 2,400 2,080

Crash Cost 270 440 720 1,300

Penalty Cost 300 -

Total Cost 10,000 9,490 9,500 9,620 9,880

Evaluation Table: Stages Activities Possible

Remarks

A

1 – 3, 3 – 6

Crash ‘1 – 3’ by 3 days

B

[1 – 3, 3 – 6], [1 – 2, 2 – 5], [1 – 2, 4 – 6] [3 – 6], [1 – 2, 2 – 5], [1 – 2, 4 – 6] [3 – 6], [2 – 5], [4 – 6]

Crash ‘1 – 2’ & ‘1 – 3’ by 1 day Crash ‘1 – 2’ & ‘3 – 6’ by 1 day Crash ‘3 – 6’, ‘2 – 5’, ‘4 – 6’ by 2 days

C D

Crash Cost

∑ 𝐂𝐫𝐚𝐬𝐡 𝐂𝐨𝐬𝐭 (Rs.) Rs.90 x 3 Days = 270 Rs.270 Rs.170 x 1 day = 440 Rs.170 Rs.280 x 1 day = 720 Rs.280 Rs.290 x 2 days 1,300 = Rs.580

Final Solution: Duration Normal Optimum Shortest

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Days 20 Days 17 Days 13 Days

Associated Cost (Rs.) 10,000 9,490 9,880

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AMA-Notes Graphical Representation:

10.6. Program Evaluation Review Technique

1) When the activity times for a project could not be estimated with certainty, Project Evaluation Review Technique should be used. 2) In Project Evaluation Review Technique 3 time estimates are made for every activity namely Optimistic, Pessimistic and Most likely time. 3) These estimates are assumed to fall into Normal Probability Distribution. 4) For Drawing the network which time should be taken? Is it optimistic, pessimistic or most likely? Answer: Neither of the 3. We should take expected time for the network. 5) Expected time is the average time where the weights for optimistic and pessimistic is ‘1’ and most likely ‘4’. te =

to +4tm +tp 6

where

t e = Expected time t o = Optimistic time t m = Most likely time t p = Pessimistic time 6) When the time is expected (Mean) there should be a variance around mean. The variance of expected time = (

tp −to 2 ) 6

**Question no 4: A small project network is composed of 7 activities whose time estimates are listed in the table below. a) Draw the project network and identify all the paths through it. b) Find the expected duration and variance for each activity. What is the expected project length? c) Calculate the variance and the standard deviation of project length. What is the probability that E M Reddy

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AMA-Notes the project will be completed i) At least 3 weeks earlier than expected ii) Not more than 3 weeks later than expected d) If the project due date is 18 weeks what is the probability of not meeting it? e) What due date has about 90% chance of being met? f) Find probability of reaching event – 5 in 9 weeks g) Also find the event variances. Activities (I – J) 𝐭 𝐨 (Optimistic Time) 𝐭 𝐦 (Most Likely Time) 𝐓𝐏 (Pessimistic Time) 1–2 1 1 7 1–3 1 4 7 1–4 2 2 8 2–5 1 1 1 3–5 2 5 14 4–6 2 5 8 5–6 3 6 15 Solution: Step 1: Calculation of expected time and variance for each activity Activities (I – J) 𝐭 𝐞 (Expected Time) Variance 7−1 1+(4 x 1)+7 1–2 ( 6 )2 = 1 =2 1–3

6 1+(4 x 4)+7

1–4

6 2+(4 x 2)+8

2–5

6 1+(4 x 1)+1

3–5

6 2+(4 x 5)+14

4–6

6 2+(4 x 5)+8

5–6

6 3+(4 x 6)+15 6

=4 =3 =1 =6

=5 =7

7−1 2 ) =1 6 8−2 2 ( 6 ) =1 1−1 ( 6 )2 = 0 14−2 ( 6 )2 = 4 8−2 ( 6 )2 = 1 15−3 ( 6 )2 = 4

(

Step 2: Drawing Network using expected times

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AMA-Notes Step 3: Identification of the critical path using the expected projected length Paths 1–2–5–6 1–3–5–6 1–4–6

Duration 2 + 1 + 7 = 10 4 + 6 + 7 = 17 3+5=8

Critical Path

Expected project length = 17 Weeks Step 4: Variance and standard deviation of project length 1) Variance of project length is the total of variances of all the activities in the critical path of the project. 2) Standard Deviation if the square root of the variance. Activities 1–3 3–5 5–6

Duration Variance 4 1 6 4 7 4 17 9

Standard Deviation of project = √9 = 3 Step 5: Probability of completing the project within 14 weeks

X−X

14−17

a) Z = σ = 3 = -1 b) Normal Table (Z) = NT (1) = 0.3413 Note: 0.3413 means 34.13% chance of completing the project between 14 and 17 weeks. c) Probability = 0.5 – 0.3413 = 0.1587. This means there is 15.87% chance of completing the project within 14 weeks. Step 6: Probability of completing the project within 20 weeks

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AMA-Notes X−X

20−17

a) Z = σ = 3 = 1 b) Normal Table (Z) = NT (1) = 0.3413 c) Probability = 0.5 + 0.3413 = 0.8413. This means there is 84.13% chance of completing the project within 20 weeks. Step 7: Probability of not meeting the due date of 18 weeks

X−X

18−17

a) Z = σ = 3 = 0.33 b) Normal Table (Z) = NT (0.33) = 0.1293 c) Probability = 0.5 – 0.1293 = 0.3707. This means there is 37.07% chance of exceeding the due date of 18 weeks. Step 8: The due date that has 90% chance of being met

0.40 is the normal table value of Z which is 1.28. Z

=

X−X σ X−17

1.28 = 3 X = 3.84 + 17 = 20.84 20.84 weeks has got chance of 90% being met. Step 9: Probability of reaching event 5 in 9 weeks The longest leading to event 5 is ‘1 – 3 – 5’. The expected time in reaching event 5 is 10 weeks (4 weeks + 6 weeks). The variance of this expected time is the total of the variances of the longest path leading to this event. Activity Variance 1–3 1 3–5 4 Variance 5 Standard Deviation = √5 = 2.24 E M Reddy

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AMA-Notes

X−X

9−10

a) Z = σ = 2.24 = - 0.45 b) Normal Table (Z) = NT (0.45) = 0.1736 c) Probability = 0.5 – 0.1736 = 0.3264. This means there is 32.64% chance of reaching event-5 in 9 weeks. Step 10: Calculation of event variances Event 6 5 4 3 2 1

Longest Path 1–3–5–6 1–3–5 1–4 1–3 1–2 Nil

Computation 1+4+4 1+4 1 1 1 0

Variance 9 5 1 1 1 0

10.7. Resource Allocation

Question no 5: Find out the time required to complete the project. No. of persons 4. Job 1–2 1–3 1–5 2–3 2–6 3–4 4–7 5–6 6–7

Time 10 6 5 0 8 10 10 7 5

Men 1 2 3 0 1 2 3 1 2

Solution: Step 1: Network Diagram

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AMA-Notes

Step 2: Calculation of EST, LFT, LST, LFT and Total Float Activity Duration Start E L 1–2 10 0 0 1–3 6 0 4 1–5 5 0 13 2–3 0 10 10 2–6 8 10 17 3–4 10 10 10 4–7 10 20 20 5–6 7 5 18 6–7 5 18 25

Finish E L 10 10 6 10 5 18 10 10 18 25 20 20 30 30 12 25 23 30

Total Float 0 4 13 0 7 0 0 13 7

Step 3: Resource Allocation table Halt Resources Time Available 0 R1, R2, R3 & R4 6 10 11

R2, R3 & R4 R1 R2, R3 & R4

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Activities Available 1–2 1–3 1–5 1–5 2–3 2–6 3–4 3–4 5–6

Total Float 0 4 13 7 0 7 0 0 13

Men x Days 1 x 10 2x6 3x5 3x5 Dummy 1x8 2 x 10 2 x 10 1x7

Ra nk 1 2 3 1

Allocated Men R1 R2 & R3 Not Possible R2, R3, R4

2 1 1 2

R1 Not Possible R2 & R3 R4

Idle

R4 -

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AMA-Notes 18 21 23

R1 & R4 R2 & R3 R1, R2, R3 & R4

6–7 4–7 4–7

7 0 0

2x5 3 x 10 3 x 10

1 1 1

R1 & R4 Not Possible R1, R2 & R3

R2 & R3 R4

The Project can be completed with 4 persons only in 33 days. Two times we postponed critical activities, first ‘3 – 4’ by 1 day and next ‘3 – 4’ by 2 days. Step 4: Loading Chart (or) Gantt Chart

1) Loading Chart indicates at different points of time how the resources are loaded and what resource is idle. 2) The loading chart is also called “Gantt Chart”. 10.8. Resource Leveling (or) Resource Smoothing

Question no 6: Job 1–2 1–3 3–5 2–4 3–6 4–7 5–7 6–7

Time 4 6 5 5 4 5 3 7

Men 3 6 7 5 5 4 3 4

Calculate the minimum number of men required to complete the above project in time.

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AMA-Notes Solution: Step 1: Network Diagram

Step 2: Calculation of EST, LFT, LST, LFT and Total Float Activity Duration Start E L 1–2 4 0 3 1–3 6 0 0 3–5 5 6 9 2–4 5 4 7 3–6 4 6 6 4–7 5 9 12 5–7 3 11 14 6–7 7 10 10

Finish E L 4 7 6 6 11 14 9 12 10 10 14 17 14 17 17 17

Total Float Free Float 3 0 3 3 0 3 3 0

0 0 0 0 0 3 3 0

Step 3: Before resource smoothening Halting time 0 4 6 9 10 11 14 17

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In 3+6 5 7+5 4 4 3 -

Out 0 -3 -6 -5 -5 -7 -4-3 -4

Strength 9 11 17 16 15 11 4 -

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AMA-Notes From the above table it can be seen that we require 17 persons on a single day for doing the project. It occurs during day 6. Step 4: Post pone 3 – 5 by 3 days Halting time 0 4 6 9 10 14 17

In 3+6 5 5 4+7 4 3 -

Out 0 -3 -6 -5 -5 -7-4 -3-4

Strength 9 11 10 16 15 7 -

Notes: 1) 17 persons were required on day 6 when we are starting ‘3 – 5’ & ‘3 – 6’ activities. 2) ‘3 – 6’ cannot be postponed as it is a critical activity. Hence we postponed ‘3 – 5’ in order to level peak requirement. 3) By postponing ‘3 – 5’ by 3 days we are able to complete the project with 16 persons. 4) The peak requirement of 16 occurs on day 9. On that day we are starting activities ‘3 – 5’ & ‘4 – 7’. 5) ‘3 – 5’ cannot be postponed because it’s float is fully used but ‘4 – 7’ can be postponed by 3 days i.e. start on 12th day. Step 5: Post-pone ‘4 – 7’ by 3 days Halting time 0 4 6 9 10 12 14 17

In 3+6 5 5 7 4 4 3 -

Out 0 -3 -6 -5 -5 0 -7 -4-3-4

Strength 9 11 10 12 11 15 11 -

Notes: 1) Due to postponing ‘4 – 7’ by 3 days we are able to the project with 15 persons. 2) On 12th day when the peak requirement happens we are starting activity ‘4 – 7’ which cannot be further postponed. Hence the resource leveling stops. Step 6: Time scale diagram Before Resource Smoothening Dotted line represents “Float”.

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AMA-Notes

After Resource Smoothening:

How to draw time scale network diagram: 1) In a normal network diagram there is no link between the length of the line and the duration of the activity. 2) In a time-scale diagram, the network will be drawn on a time scale where activities with longer duration will have longer lines and vice-versa. In other words, the length of the line is proportioned to duration of the activity. 3) First we should draw the longest path i.e. critical path around which other paths should be drawn. 4) The other paths will obviously complete before the critical path and then wait till for the critical path to complete. The difference is called “Float” and is represented by dotted lines. 5) The activity ‘4 – 7’ is completed on day 14 but event 7 occurs only on day 17.

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AMA-Notes 6) Instead of finishing early and waiting we used the float and started late and then completed on time due to which we are able to level the resources. It is called resource leveling (or) resource smoothening. Same logic for ‘3 – 5’ also. 10.9. Understanding to draw a network & use dummy activities

Situation 1: P and Q has the same tail event and also are joint preceding activity Condition a) P is not repeated as preceding activity and Q also is not repeated as preceding activity b) P is repeated as preceding activity and not Q c) Q is repeated as preceding activity and not P c) P is repeated and Q also repeated

To be done Dummy from P to Q or Q to P Dummy from P to Q Dummy from Q to P Two dummies. P to a new event and Q to a new event

Example 1: Activity Preceding A P A Q A R P, Q S R Network Diagram:

Example 2: Activity Preceding A P A Q A R P, Q S P

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AMA-Notes Network Diagram:

Example 3: Activity Preceding A P A Q A R P, Q S Q Network Diagram:

Example 4: Activity Preceding A P A Q A R P, Q S P T Q

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AMA-Notes Network Diagram:

Situation 2: P and Q has different tail events and are joint preceding activity Condition a) P is not repeated as preceding activity and Q also is not repeated as preceding activity b) P is repeated as preceding activity and not Q c) Q is repeated as preceding activity and not P c) P is repeated and Q also repeated

To be done No dummy. Merge P and Q to start next activity Dummy from P to Q Dummy from Q to P Two dummies. P to a new event and Q to a new event

Example 1: Activity Preceding A B P A Q B R P, Q S R Network Diagram:

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AMA-Notes Example 2: Activity Preceding A B P A Q B R P, Q S P Network Diagram:

Example 3: Activity Preceding A B P A Q B R P, Q S Q Network Diagram:

Example 4: Activity Preceding A B -

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AMA-Notes P Q R S T

A B P, Q P Q

Network Diagram: Question no 7: Draw a network for the following data: Task Immediate predecessor A -B A C A D B E A F B, E G C H D, F I G J H, I Solution:

Question no 8: Draw a network for the following data: Task Immediate predecessor A -B -C B D B

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AMA-Notes E F G

B E A, D, C

Solution:

**Question no 9: The production manager at Gemini Machines ltd. has been asked to present information about the times and costs for the development of a new machine that the company may choose to manufacture. The Managing Director requires accurate time and cost estimates since the project will involve a fixed fee contract offering no provision for later re-generation, even in the event of modifications. Activity Preceding Activities Duration (Weeks) Cost Rs.’000 A Obtain engineering quotes I 1 4 B Sub-contract specifications A, J 4 8 C Purchase of raw materials -3 24 D Construct prototype I 5 15 E Final Drawings I 2 6 F Fabrication H 6 30 G Special Machine Study -4 12 H Sub-contract work B, E 8 40 I Preliminary design G 2 8 J Vendor evaluation C, D 3 3 The production manager has been asked to identify the critical activities, to determine the shortest project duration and to provide a week-by-week cost schedule. Required:

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AMA-Notes (a) Draw a network to represent the inter-relationships between the activities indicated, and insert earliest and latest event times throughout. (b) Determine the critical path and the shortest possible duration of the project. (c) Assuming each activity commences at the earliest start date and that for each activity the cost is incurred evenly over its duration construct a week-by-week schedule of cash flows. (d) The project is to financed by Rs.50,000 available initially, a further Rs.50,000 available at the start of week 9 and the final Rs.50,000 available from week 20. Identify any particular problems and suggest solutions. Solution: Step 1: Network Diagram

Step 2: Identification of the critical path Paths 1–4–5–6–7–8 1–2–3–4–5–6–7–8 1–2–3–5–6–7–8 1–2–3–6–7–8

Duration 3 + 3 + 4 + 8 + 6 = 24 4 + 2+ 5 + 3 + 4 + 8 + 6 = 32 4 + 2 + 1 + 4 + 8 + 6 = 25 4 + 2 + 2 + 8 + 6 = 22

Step 3: Calculation of cost per week A B C D E F G H I J

Activity Obtain engineering quotes Sub-contract specifications Purchase of raw materials Construct prototype Final Drawings Fabrication Special Machine Study Sub-contract work Preliminary design Vendor evaluation

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Duration (Weeks) 1 4 3 5 2 6 4 8 2 3

Cost Rs.’000 4 8 24 15 6 30 12 40 8 3

Cost Rs.’000/week 4 2 8 3 3 5 3 5 4 1 Page | 326

AMA-Notes Step 4: Calculation of EST, EFT, LST, LFT and Total Floats Activities 1–2 1–4 2–3 3–4 3–5 3–6 4–5 5–6 6–7 7–8

Activity G C I D A E J B H F

Duration 4 3 2 5 1 2 3 4 8 6

EST 0 0 4 6 6 6 11 14 18 26

LST 0 8 4 6 13 16 11 14 18 26

EFT 4 3 6 11 7 8 14 18 26 32

LFT 4 11 6 11 14 18 14 18 26 32

Total Float 0 8 0 0 7 10 0 0 0 0

Step 5: Cash requirement schedule Halting time 0 3 4 6 7 8 11 14 18 26

In 8+3 -4 4+3+3 --1 2 5 5

Out -8 3 4 4 3 3 1 2 5

Balance 11 3 4 10 6 3 1 2 5 5

Activity C, G G I A, D, E D, E D J B H F

Step 6: Week by week schedule of cash flow Week Cash Week Cash

1 11 17 2

2 11 18 2

3 11 19 5

4 3 20 5

5 4 21 5

6 4 22 5

7 10 23 5

8 6 24 5

9 3 25 5

10 3 26 5

11 3 27 5

12 1 28 5

13 1 29 5

14 1 30 5

15 2 31 5

16 2 32 5

Step 7: Cash flow Management 1) Availability and Requirement:

2) It is evident that we do not have enough cash to do all the activities planned in 1st 8 weeks. Hence we should post-pone some activities to the next slot so that a cost of Rs.10,000 can be post-poned.

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AMA-Notes 3) The activities we are doing in the first 8 weeks are C, G, I, A, D, E. In these activities we cannot postpone G, D, I because these are critical activities. 4)

Question no 10: Solution: (i) Simple Critical Path Method (CPM) (ii) Critical Path Method with Crashing (iii) Program Evaluation Revaluation Technique (iv) Critical Path Method with resource allocation (v) Program Evaluation Review Technique Question no 11: A project consists of 7 activities. The time for performance of each of the activity s as follows: Activity A

Immediate --

B C D

-A B, C

E

D

F

D

G

E, F

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Time 3 4 5 4 1 4 5 3 4 5 6 5 7 2 3

Probability 0.2 0.6 0.2 1.0 1.0 0.8 0.2 0.1 0.3 0.3 0.3 0.2 0.8 0.5 0.5 Page | 328

AMA-Notes a) Draw a network and identify critical path using expected time. b) Simulate the project for 5 times using random number and find the critical paths. 68 13 09 20 73 07 72 99 93 18 24 22 07 29 57 33 49 65 92 98 00 57 12 31 96 85 92 91 77 37 34 11 27 10 59 Solution: Step 1: Network Diagram

From the above diagram we can generalize the critical path as follows: {‘A + C’ or B} → D → {E or F} → G Step 2: Calculation of expected time Activity A B C D E F G

Computation (0.2 x 3) + (0.6 x 4) + (0.2 x 5) 1x4 1x1 (0.8 x 4) + (0.2 x 5) (0.1 x 3) + (0.3 x 4) + (0.3 x 5) + (0.3 x 6) (0.2 x 5) +(0.8 x 7) (0.5 x 2) + (0.5 x 3)

Expected Time 4 4 1 4.2 4.8 6.6 2.5

Critical Path = A → C → D → F → G Duration = 4 + 4 + 1 + 4.2 + 4.8 + 6.6 + 2.5 = 18.3 E M Reddy

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AMA-Notes Step 3: Random Number Coding Activity Time Probability A 3 0.2 4 0.6 5 0.2 B 4 1.0 C 1 1.0 D 4 0.8 5 0.2 E 3 0.1 4 0.3 5 0.3 6 0.3 F 5 0.2 7 0.8 G 2 0.5 3 0.5

Cumulative Probability 0.2 0.8 1.0 1.0 1.0 0.8 1.0 0.1 0.4 0.7 1.0 0.2 1.0 0.5 1.0

Random Numbers 00 – 19 20 – 79 80 – 99 00 – 99 00 – 99 00 – 79 80 – 99 00 – 99 10 – 39 40 – 69 70 – 99 00 – 19 20 – 99 00 – 49 50 – 99

C No. 09 18 49 31 34

E No. 73 22 92 85 27

Step 4: Simulation Worksheet Run A No. 1 68 2 99 3 57 4 57 5 77

Time 4 5 4 4 4

Simulation Run 1 2 3 4 5

B No. 13 93 33 12 37

Time 4 4 4 4 4

Time 1 1 1 1 1

Critical Path A→C→D→E→G A→C→D→F→G A→C→D→F→G A→C→D→F→G A→C→D→E→G

D No. 20 24 65 96 11

Time 4 4 4 5 4

Time 6 4 6 6 4

F No. 07 07 98 92 10

Time 5 5 7 7 5

G No. 72 29 00 91 59

Time 3 2 2 3 3

Duration 4 + 1 + 4 + 6 + 3 = 18 5 + 1 + 4 + 5 + 2 = 17 4 + 1 + 4 + 7 + 2 = 18 4 + 1 + 5 + 7 + 3 = 20 4 + 1 + 4 + 5 + 3 = 17

10.10. Network Updation

Question no 12: After 15 days of working the following progress is notes for the network of an erection job. a) Activity 1 – 2, 1 – 3 and 1 – 4 completed as per original schedule. b) Activity 2 – 4 is in progress and will be completed in 3 more days. c) Activity 3 – 6 is in progress and will need 18 days more for completion. d) Activity 6 – 7 appears to present some problem and its new estimated time of completion is 12 days. e) Activity 6 – 8 can be completed in 5 days instead of originally planned for 7 days.

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AMA-Notes

You are required to: (i) Update the above diagram after 15 days of the start of work based on the assumptions given above. (ii) Write down the critical path with total project duration. Solution: Paths 1–2–5–7–8 1–2–4–7–8 1–4–7–8 1–3–4–7–8 1–3–6–7–8 1–3–6–8

Duration (Days) 9 + 18 + 8 + 6 = 41 9 + 9 + 20 + 6 = 44 6 + 20 + 6 = 32 10 + 5 + 20 + 6 = 41 10 + 23 + 12 + 6 = 51 10 + 23 + 5 = 38

Critical Path is ‘1 – 3 – 6 – 7 – 8’

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AMA-Notes 11. TRANSFER PRICING 11.1. Introduction

1) In a decentralized form of organization, the companies will be having divisions which can be categorized as follows:

2)

3) Division X manufactures Intermediate Product (IP) and transfers to Division Y which further process it and sell to outsiders as final product. 4) Basically the supplying division is a cost center. However, to promote inter-divisional competition and improve efficiency companies may treat the supplying division as profit center. 5) The transfer of intermediate product will be deemed to be sales of the supplying division and the transfer is made at a price higher than cost which is called “Transfer Price”. 6) Transfer price is selling price to supplying division, purchase cost to receiving division and neither selling price nor purchase cost for the company. 7) Thus transfer price will affect divisional profits but prima facie does not affect company’s profit. 8) Transfer price affects the company’s profits through output decision of divisions. 11.2. Transfer Price - Variable Cost

Question no 1: A company with two manufacturing divisions is organized on profit center basis. Division 'A' is the only source for the supply of a component that is used in Division ‘B’ in the manufacture of a product KLIM. One such part is used in each unit of the product KLIM. As the demand for the product is not steady, division ‘B’ can obtain order in increased quantities only by spending more on sale promotion and by reducing the selling prices. The Manager of Division B has accordingly prepared the following forecast of sales quantities and selling prices.

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AMA-Notes Sales in units per day Average selling price per unit of Klim (Rs.) 1,000 5.25 2,000 3.98 3,000 3.30 4,000 2.78 5,000 2.40 6,000 2.01 The manufacturing cost of KLIM in Division ‘B’ is Rs.3,750 for first 1000 units and Rs.750 per 1000 units in excess of 1000 units. Division A incurs a total cost of Rs.500 per day for an output up to 1000 components and the total costs will increase by Rs.900 per day for every additional 1000 components manufactured. The manager of Division A state that the operating results of his division will be optimized if the transfer price of Component is set at Rs.1.20 per unit and he has accordingly set the aforesaid transfer price for his supplies of the component to Division B. Required: A) Prepare a schedule showing the profitability at each level of output of Division A & Division B. B) Find the Profitability of the Company as a whole at the output level at which: I. Division A's net profit is maximum; II. Division B's net profit is maximum. C) If the Company is not organized on profit center basis, what level of output will be chosen to yield the maximum profit? Solution: Step 1: Statement of profitability – Division A (Supplying Division) Units 1,000 2,000 3,000 4,000 5,000 6,000

Sales (Rs.) 1,200 2,400 3,600 4,800 6,000 7,200

Cost (Rs.) 1,500 2,400 3,300 4,200 5,100 6,000

Profit(Rs.) - 300 -300 600 900 1,200

Step 2: Statement of profitability – Division B (Receiving Division) Units 1,000 2,000 3,000 4,000 5,000 6,000

Sales (Rs.) 5,250 7,960 9,900 11,120 12,000 12,060

IP Purchase Cost (Rs.) 1,200 2,400 3,600 4,800 6,000 7,200

Further Processing Cost (Rs.) 3,750 4,500 5,250 6,000 6,750 7,500

Profit(Rs.) 300 1,060 1,050 320 -750 -2640

Step 3: Statement of profitability – Company Units Sales (Rs.) IP Production Cost (Rs.) Further Processing Cost (Rs.) Profit(Rs.) 1,000 5,250 1,500 3,750 0 2,000 7,960 2,400 4,500 1,060

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AMA-Notes 3,000 4,000 5,000 6,000

9,900 11,120 12,000 12,060

3,300 4,200 5,100 6,000

5,250 6,000 6,750 7,500

1,350 920 150 -1,440

Notes: 1) 2) 3) 4) 5) 6) 7) 8)

9)

The profit of Division ‘A’ is maximum at an output level of 6,000 Units. The profit of Division ‘B’ is maximum at an output level of 2,000 Units. The Company profit is maximum at an output level of 3,000 Units. Even though Division ‘A’ wants to transfer 6,000 Units, it can transfer only what the Division ‘B’ is willing to take i.e. 2,000 Units. Thus the Division ‘B’ determines the output of the company which is against the company’s optimum output level. Thus there exists a conflict in goals between the Company and Division ‘B’ which is due to Transfer Price. Can the company order the Division ‘B’ to produce 3,000 units? Answer: No, because Divisional autonomy should be protected. No decision whether output or transfer price should be thrust on a division. A goods transfer price should ensure the following: i. Avoid Goal Conflict ii. Ensure Divisional Autonomy iii. Evaluates fairly the Divisional performance The Transfer Price of Rs.1.2 is incorrect because it creates Goal Conflict

Step 4: Optimum Output – Organization View Units Revenue Further Processing Cost 1,000 5,250 3,750 2,000 7,960 4,500 3,000 9,900 5,250 4,000 11,120 6,000 5,000 12,000 6,750 6,000 12,060 7,500

Net Revenue 1,500 3,460 4,650 5,120 5,250 4,560

Net Marginal Revenue -1,960 1,190 470 130 - 690

Marginal Cost of Intermediary Product -900 900 900 900 900

Fixation of Transfer Price:

Since the transfer price is fixed as Rs.1.2 it resulted in Goal Conflict. E M Reddy

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AMA-Notes Question no 2: A company has two divisions. South division manufactures an intermediate product for which there is no immediate external market. North division incorporates this intermediate product into a final product, which it sells. One unit of the intermediate product is used in the production of the final product. The expected units of the final product, which North division estimates it can sell at various selling prices, are as follows: Net Selling Price (Rs.) Quantity Sold (Units) 100 1,000 90 2,000 80 3,000 70 4,000 60 5,000 50 6,000 The costs of each division are as follows: Particulars South Division (Rs.) North Division (Rs.) Variable cost per unit 11 7 Fixed costs per annum 60,000 90,000 The transfer price is Rs.35 for the intermediate products, and is determined on a full cost-plus basis. You are required to: (a) Prepare profit statements for each division and the company as a whole for the various selling prices. (b) State which selling price maximizes the profit of north division and the company as a whole and comment on why the latter selling price is not selected by north division. (c) State which transfer pricing policy will maximize the company's profit under a divisional organization. Assume that there is no capacity constraint. (d) State the implications of transfer pricing policy in (c) above on south division's profitability. Solution: Step 1: Statement of profitability – South Division (Supplying Division) Units 1,000 2,000 3,000 4,000 5,000 6,000

Sales (Rs.) 35,000 70,000 1,05,000 1,40,000 1,75,000 2,10,000

Cost (Rs.) 11,000 22,000 33,000 44,000 55,000 66,000

Profit(Rs.) 24,000 48,000 72,000 96,000 1,20,000 1,44,000

Step 2: Statement of profitability – North Division (Receiving Division) Units 1,000 2,000 3,000 4,000 5,000 6,000

Sales (Rs.) 1,00,000 1,80,000 2,40,000 2,80,000 3,00,000 3,00,000

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IP Purchase Cost (Rs.) 35,000 70,000 1,05,000 1,40,000 1,75,000 2,10,000

Further Processing Cost (Rs.) 7,000 14,000 21,000 28,000 35,000 42,000

Profit(Rs.) 58,000 96,000 1,14,000 1,12,000 90,000 48,000 Page | 335

AMA-Notes Step 3: Statement of profitability – Company Units 1,000 2,000 3,000 4,000 5,000 6,000

Sales (Rs.) 1,00,000 1,80,000 2,40,000 2,80,000 3,00,000 3,00,000

IP Production Cost (Rs.) 11,000 22,000 33,000 44,000 55,000 66,000

Further Processing Cost (FPC) (Rs.) 7,000 14,000 21,000 28,000 35,000 42,000

Profit(Rs.) 82,000 1,44,000 1,86,000 2,08,000 2,10,000 1,92,000

Step 4: Optimum output level – Organization view Units Revenue (Rs.) FPC (Rs.) Net Revenue 1,000 1,00,000 7,000 93,000 2,000 1,80,000 14,000 1,66,000 3,000 2,40,000 21,000 2,19,000 4,000 2,80,000 28,000 2,52,000 5,000 3,00,000 35,000 2,65,000 6,000 3,00,000 42,000 2,58,000 The profit Can be understood as follows: Units Computation Profit (Rs.) 1,000 82,000 2,000 82,000 + 73,000 – 11,000 1,44,000 3,000 1,44,000 + 53,000 – 11,000 1,86,000 4,000 1,86,000 + 33,000 – 11,000 2,08,000 5,000 2,08,000 + 13,000 – 11,000 2,10,000 6,000 2,10,000 – 7,000 – 11,000 1,92,000

Net Marginal Revenue -73,000 53,000 33,000 13,000 -7,000

Marginal Cost (Rs.) 11,000 11,000 11,000 11,000 11,000

Notes: 1) The Optimum output for the company is 5,000 units because till that output level the marginal revenue exceeds the marginal cost. 2) For division North the statement looks similar except that the marginal cost is Rs.35,000 per 1,000 units instead of Rs.11,000. This made North division stop at 3,000 Units output level. 3) Thus it is evident that transfer price is the reason for Goal Conflict. 4) If the transfer price is fixed as variable cost of intermediate product i.e. Rs.11, then the north & company will select the same output level. Is this transfer price is correct? Answer: Wrong, because the supplying division will not have any motivation to transfer since it just recovers it’s variable cost. Therefore, transfer price should be more than Rs.11. 5) The transfer price should not exceed Rs.13. If it exceeds the north division will not be selecting 5,000 units as it’s output. For the north division to go from 4,000 units to 5,000 units can spend only maximum Rs.13,000 towards the Intermediate Product (IP). 6) Transfer price Range:

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AMA-Notes

Question no 3: Division ‘A’ of a large divisionalised organization manufactures a single standardized product. Some of the output is sold externally whilst the remainder is transferred to Division ‘B’ where it is a sub-assembly in the manufacture of that division's product. The unit costs of Division A's product are as follows: Particulars Rs. Direct Material 4 Direct Labour 2 Direct Expense 2 Variable Manufacturing overheads 2 Fixed Manufacturing overheads 4 Selling and packaging expenses – variable 1 Total 15 Annually 10,000 units of the product are sold externally at the standard price of Rs.30. In addition to the external sales, 5,000 units are transferred annually to Division B it an internal transfer charge of Rs. 29 per unit. This transfer price is obtained by deducting variable selling and packing expense from the external price since this expense is not incurred for internal transfers. Division B incorporates the transferred in goods into a more advanced product. The unit costs of this product are as follows: Particulars Rs. Transferred in item (from Division A) 29 Direct Material and components 23 Direct Labour 3 Variable overheads 12 Fixed overheads 12 Selling and packaging expenses – variable 1 Total 80 Division B's manager disagrees with the basis used to set the transfer price. He argues that the transfers should be made at variable cost plus an agreed (minimal) mark-up since he claims that his division is taking output that division ‘A’ would be unable to sell at the price of Rs. 30. Partly because of this disagreement, the company's sales director has recently make a study of the relationship between selling price and demand for each division. The resulting report contains the following table: Customer demand at various selling prices:

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AMA-Notes Division A: Selling Price Rs.20 Rs.30 Rs.40 Demand 15,000 10,000 5,000 Division B: Selling Price Rs.80 Rs.90 Rs.100 Demand 7,200 5,000 2,800 The manager of Division B claims that this study supports his case. He suggests that a transfer price of Rs.12 would give Division ‘A’ a reasonable contribution to its fixed overheads while allowing Division B to earn a reasonable profit. He also believes that it would lead to an increase of output and an improvement in the overall level of company profits: You are required: (a) To calculate the effect that the transfer pricing system has had on the company's profits, and (b) To establish the likely effect on profit of adopting the suggestion by the manager of Division B of a transfer price of Rs. 12. Solution: Step 1: Optimum output for Division A for external Sales Units 5,000 10,000 15,000

Revenue 2,00,000 3,00,000 3,00,000

Cost @ Rs.11 55,000 1,10,000 1,65,000

Marginal Revenue -1,00,000 --

Marginal Cost -55,000 55,000

Step 2: Optimum output for Division B Units 2,800 5,000 7,200

Revenue 2,80,000 4,50,000 5,76,000

FPC @ Rs.39 1,09,200 1,95,000 2,80,800

Net Revenue 1,70,800 2,55,000 2,95,200

Marginal Revenue -84,200 40,200

Marginal Cost @ Rs.29 -63,800 63,800

Net Revenue 1,70,800 2,55,000 2,95,200

Marginal Revenue -84,200 40,200

Marginal Cost @ Rs.29 -22,000 22,000

Step 3: Optimum output for company Units 2,800 5,000 7,200

Revenue 2,80,000 4,50,000 5,76,000

FPC @ Rs.39 1,09,200 1,95,000 2,80,800

Notes: 1) Reason for Division ‘A’ fixing Rs.29 as transfer price: The Market pays Rs.30 for the intermediary product and internal transfers does not have selling cost of Rs.1 hence Division ‘B’ should pay Rs.29. 2) Is this Rs.29 transfer justified? No, because a. Division ‘A’ transfers only those units which it is unable to sell in the external market at Rs.30. b. Further this transfer price creates Goal Conflict as it makes Division ‘B’ select 5,000 units as it’s output while for the company the optimum output is 7,200 units.

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AMA-Notes 3) What should be the transfer price? The transfer price should be within the following range:

4) Can the Rs.12 recommended transfer price be accepted? Yes, because it falls within the range. It gives Division ‘A’ a Rs.2 contributions for the capacity which otherwise would remain idle and for Division ‘B’ since it is within Rs.18.27 makes it select 7,200 units output level inconformity with the company. 11.3. Transfer Price – Specific Fixed Cost

***Question no 4: A group of highly integrated divisions wishes to be advised as to how it should set transfer prices for the following interdivisional transactions: Division L sells all its output of product LX to Division M. To 1 Kg of LX, Division M adds other direct materials and processes it to produce 2 Kg of product MX that it sells outside the group. The price of MX is influenced by volume offered and the following cost and revenue data are available: Division L: The variable costs of LX are (per kg) at 50,000 Kg. Direct Materials 4.00 Direct Labour 2.00 Total 6.00 The following cost increases are expected at different levels of production per annum: Direct Materials At 60,000 kg p.a. increases Rs.5.00 per kg At 90,000 kg p.a. increases Rs.5.50 per kg At 1,00,000 kg p.a. increases Rs.6.00 per kg Direct Labour At 80,000 kg p.a. increases Rs.2.50 per kg At 1,00,000 kg p.a. increases Rs.3.00 per kg Fixed Overhead Under 70,000 kg 2,10,000 p.a. 70,000 – 79,999 Kg 2,60,000 p.a. 80,000 – 89,999 kg 2,80,000 p.a. 90,000 or more kg 3,10,000 p.a. Division M: To produce 1 kg of product MX, the following variable cost incurred for each 0.5 kg of LX used (at 1,00,000 kg of MX):

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AMA-Notes Other Direct Materials Rs.1.50 Processing Cost Rs.3.50 The following cost increases are expected at different levels of production of MX per annum: Other Direct Materials At 1,40,000 kg p.a. increases Rs.1.75 per kg At 1,60,000 kg p.a. increases Rs.2.00 per kg At 1,80,000 kg p.a. increases Rs.4.00 per kg Fixed Overhead: Under 1,20,000 Kg 2,50,000 p.a. 1,20,000 – 1,39,999 Kg 2,80,000 p.a. 1,40,000 – 1,59,999 Kg 2,90,000 p.a. 1,60,000 – 1,99,999 Kg 3,20,000 p.a. 2,00,000 or more kg 3,60,000 p.a. Selling Price: Up to 1,99,999 kg? Rs.16.00 per kg 2,00,000 or more kg Rs.15.50 per kg You are required to: Recommend, with supporting calculations and explanations, the most appropriate narrow range of transfer price per kg for product LX as between the two divisions; assume that any changes in output are steps of 10,000 kg of product LX and 20,000 kg of product MX. Solution: Step 1: Calculation of ‘LX’ cost Output 50,000 60,000 70,000 80,000 90,000 1,00,000

Direct Material 2,00,000 3,00,000 3,50,000 4,00,000 4,95,000 6,00,000

Direct Labour 1,00,000 1,20,000 1,40,000 2,00,000 2,25,000 3,00,000

Fixed Overhead 2,10,000 2,10,000 2,60,000 2,80,000 3,10,000 3,10,000

Total Cost 5,10,000 6,30,000 7,50,000 8,80,000 10,30,000 12,10,000

Step 2: Calculation of further processing cost of ‘MX’ Output 1,00,000 1,20,000 1,40,000 1,60,000 1,80,000 2,00,000

Other Direct Material 1,50,000 1,80,000 2,45,000 3,20,000 3,60,000 4,00,000

Processing Cost 3,50,000 4,20,000 4,90,000 5,60,000 7,20,000 8,00,000

Fixed Overhead 2,50,000 2,80,000 2,90,000 3,20,000 3,20,000 3,60,000

Total Cost 7,50,000 8,80,000 10,25,000 12,00,000 14,00,000 15,60,000

Step 3: Determination of Optimum Output Level LX Units 50,000 60,000 70,000 80,000

MX Total Cost Marginal Cost Units 5,10,000 -1,00,000 6,30,000 1,20,000 1,20,000 7,50,000 1,20,000 1,40,000 8,80,000 1,30,000 1,60,000

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Revenue 16,00,000 19,20,000 22,40,000 25,60,000

FPC 7,50,000 8,80,000 10,25,000 12,00,000

Net Revenue 8,50,000 10,40,000 12,15,000 13,60,000

NMR -1,90,000 1,75,000 1,45,000 Page | 340

AMA-Notes 90,000 10,30,000 1,00,000 12,10,000

1,50,000 1,80,000

1,80,000 28,80,000 14,00,000 14,80,000 2,00,000 31,00,000 15,60,000 15,40,000

1,20,000 60,000

The transfer price should be fixed in such a way that both the division selects the Optimum Output Level. Step 4: Transfer Price Fixation A. From Receiving Division’s View Point

Notes: 1) What happens if transfer price more than Rs.14.5 say Rs.15? a) If transfer price is Rs.15, for every 10,000 Kgs of ‘LX’ Division M has to pay Rs.1,50,000. b) The Net Marginal Revenue (NMR) exceeds Rs.1,50,000 only up to 70,000 Kgs of further processing ‘LX’. c) Thus anything above Rs.14.5 will make Division M stop before the optimum output level of 80,000 Kgs. 2) What happens if transfer price is below Rs.12 say Rs.11? a) For every 10,000 Kgs of ‘LX’ the receiving division has to pay Rs.1,10,000. b) The Net Marginal Revenue (NMR) exceeds the Marginal Cost of Rs.1,10,00 up to 90,000 Kgs of further processing ‘LX’. c) To prevent Division ‘M’ in further processing up to 90,000 Kgs the transfer price should be more than Rs.12. B. Transfer Price from Supplying Division View Point

Notes: 1) What happens if transfer price is less than Rs13 say Rs.12.5? a) When transfer price is Rs.12.5 ‘LX’ earns Rs.1,25,000 for every 10,000 Kgs transferred. b) This revenue of Rs.1,25,000 exceeds the marginal cost only up to 70,000 Kgs. Beyond which the cost is more than revenue.

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AMA-Notes c) To make ‘LX’ reach optimum output of 80,000 Kgs transfer price should be more than Rs.13. 2) What happens if transfer price exceeds Rs.15 say Rs.16? a) For every 10,000 Kgs transferred ‘LX’ earns Rs.1,60,000. b) Up to 90,000 Kgs of transfer this Rs.1,60,000 exceeds the marginal cost. c) To prevent ‘LX’ from crossing 80,000 units the transfer price should be less than Rs.15. C. Narrow Range ‘MX’ Range : Rs.12 < Transfer Price < Rs.14.5 ‘LX’ Range : Rs.13 < Transfer Price < Rs.15 Narrow Range : Rs.13 < Transfer Price < Rs.14.5 11.4. Linear Programming Method of Transfer Price fixation

Question no 5: Black and Brown are two divisions in a group of companies and both require intermediate products Alpha and Beta which are available from Divisions A and B respectively. Black and Brown divisions convert the intermediate products into products Blackalls and Brownalls respectively. The market demand for Blackalls and Brownalls considerably exceeds the production possible, because of the limited availability of intermediate products Alpha and Beta. No external market exists for Alpha and Beta and no other intermediate product market is available to Black and Brown divisions. Other data are as follows: Black Division: Blackalls Selling price per unit Rs.45 Processing cost per unit Rs.12 Intermediate products required per unit: Alpha: 3 Units Beta: 2 Units Brown Division: Brownalls: Selling price per unit Rs.54 Processing cost per unit Rs.14 Intermediate products required per unit: Alpha: 2 Units Beta: 4 Units A Division: Alpha Variable cost per unit Rs.6 Maximum production capacity 1,200 Units B Division: Beta Variable cost per unit Rs.4 Maximum production capacity 1,600 Units The solution to a linear programing model of the situation shows that the imputed scarcity value (shadow price) of Alpha and Beta is Rs.0.50 and Rs.2.75 per unit respectively and indicates that the intermediate products be transferred such that 200 units of Blackalls and 300 units of Brownalls are produced and sold. Required: (a) Calculate the contribution earned by the group if the sales pattern indicated by the linear programming model is implemented.

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AMA-Notes (b) Where the transfer prices are set on the basis variable cost plus shadow price, show detailed calculations for: (i) The contribution per unit of intermediate product earned y divisions A and B and (ii) The contribution per unit of final product produced by Black and Brown divisions. (c) Comment on the results derived in (b) and on the possible attitude of management of the various divisions to the proposed transfer pricing and product deployment policy. (d) In the following year the capacities of divisions A and B have each doubled and the following changes have taken place. (i) Alpha: There is still no external market for the product, but A division has a large demand for other products which could use the capacity and earn contribution of 5% over cost. Variable cost per unit for the other products would be the same as that for Alpha and such products would use the capacity at the same rate as Alpha. (ii) Beta: An intermediate market for this product now exists and beta can be bought and sold in unlimited amounts at Rs.7.50 per unit. External sales of beta would incur additional transport costs of Rs.0.50 per unit, which are not incurred in inter-division transfers. The market demand for Blackalls and Brownalls will still exceed the production availability of Alpha and Beta. (i) Calculate the transfer prices at which Alpha and Beta should now be offered to Black and Brown divisions in order that the transfer policy implemented will lead to the maximization of group profit. (ii) Determine the production and sales pattern for Alpha, Beta, Blackalls and Brownalls, which will now maximize the given contribution and calculate the group contribution that could be achieved. It may be assumed that divisions will make decisions consistent with the financial data available. Solution: Step 1: Profit per unit of Black and Brown (Company Level) Particulars Selling Price Less: Variable Cost Alpha Beta Further Processing Cost Total Variable Cost Contribution per unit

Black (Rs.) Brown (Rs.) 45 54 18 8 12 38 7

12 16 14 42 12

Step 2: Formulating Situation into LPP to find out optimum output Let X1 = Number of Units of Blackalls & X2 = Number of Units of Brownalls Maximize Z = 7X1 + 12X2 Subject to 3X1 + 2X2 < 1,200 2X1 + 4X2 < 1,600 Where X1 & X2 > 0 E M Reddy

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AMA-Notes Step 3: Final Solution to LPP FR – Fixed Ratio Program Quantity 200 X1 300 X2 Cj Zj NER (Cj − Zj )

X1 1 0 7 7 0

X2 S1 S1 RR – Replacement Ratio 0 1 12 0 0 12 0.5 2.75 0 -0.5 -2.75

Notes: 1) Through the simplex we determined the optimum output for the company. It is 200 units of Blackalls and 300 units of Brownalls. 2) The shadow cost of Alpha and Beta is 0.5 and 2.75. It is nothing but S1, S2 in the NER (Net Evaluation Row) in the final simplex table where S1 reprints unused Alpha Capacity and S2 unused Beta capacity. 3) When we introduce S1 as basic variable (Plan to keep 1 unit of Alpha unused), then the profit drops by Rs.0.50 i.e. every alpha is capable of generating Rs.0.50 profit. Same for Beta also. Step 4: Calculation of the Division’s profitability when transfer price is equal to variable cost Items Selling Price Less: Variable Cost Alpha Beta Processing Cost Contribution per unit Units Sold Contribution

A (Rs.) B (Rs.) Black (Rs.) Brown (Rs.) 6 4 45 54 6 1,200 -

4 1,600 -

18 8 12 7 200 1,400

12 16 14 12 300 3,600

Step 5: Division’s profitability when transfer price is equal to variable cost plus Shadow Cost Alpha = Rs.6 + Rs.0.5 = Rs.6.5 Beta = Rs.4 + Rs.2.75 = Rs.6.75 Items Selling Price Less: Variable Cost Alpha Beta Processing Cost Contribution per unit Units Sold Contribution

A (Rs.) B (Rs.) Black (Rs.) Brown (Rs.) 6.5 6.75 45 54 6 0.5 1,200 600

4 2.75 1,600 4,400

19.5 13.5 12 200 -

13 27 14 300 -

Notes: 1) The Company’s profit of Rs.5,000 represents efforts of all 4 divisions.

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AMA-Notes 2) At the first instance the profits are receiving division because they are the profit centers. 3) The profit gets transferred from receiving divisions to supplying divisions through transfer price i.e. always transfer price acts as between divisions. 4) If we fix transfer price as variable cost of Intermediate product then no profit is transferred between receiving and supplying divisions and entire profit is cornered by receiving divisions. 5) If transfer price = Variable Cost + Opportunity cost, then the entire profit through the opportunity cost is transferred from receiving to supplying divisions. 6) Thus the transfer price should be between variable cost and ‘Variable Cost + Opportunity cost’

Transfer Price Alpha

Beta

Rs.6 < Transfer Price < Rs.6.5

Rs.4 < Transfer Price < Rs.6.75

Step 6: Fixation of Transfer Price for Alpha and Beta in the changed scenario 1) Capacity constraint continues and alternative uses emerges. In this case transfer price should not be a range but a single price. 2) Transfer Price

Alpha

Beta

Variable Cost + Opportunity Cost

External Market Price – Selling Cost

Rs.6 + (Rs.6 x 5%) = Rs.6.30

Rs.7.5 – Rs.0.5 = Rs.7

Variable Cost + Opportunity Cost Rs.4 + (Rs.7.5 – Rs0.5 – Rs.4) Rs.4 + Rs.3 = Rs.7

3) When Black and Brown uses Alpha it has the duty to recover 2 things for the company: (i) It’s variable manufacturing cost of Rs.6

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AMA-Notes (ii) The contribution the company loses from other revenues due to use of Alpha for Black and Brown i.e. Rs.0.30 If Black and Brown selling price is unable to recover Rs.6.3 it is better to Alpha for other purposes. 4) If we fix transfer price more than Rs.6.3 there is a risk of Goal Conflict. For example, the Black can afford recovery up to Rs.6.32 and when transfer price is fixed as Rs.6.35 Black division may incur losses but still from organization’s view point it is a better product compared to other uses as it gives Rs.0.32 above Rs.6. This results in Goal Conflict. 5) Similarly, when Beta is used internally the company loses external price of Rs.7.50 but saves a selling cost of Rs.0.50 resulting in Rs.7 loss which Black and Brown should recover. 6) An interim chart for transfer price fixation:

Step 7: Profitability of Black and Brown in the revised scenario Items Selling Price Less: Variable Cost Alpha Beta Processing Cost Total Variable Cost Contribution per unit

Black (Rs.) Brown (Rs.) 45 54 18.9 14 12 44.9 0.10

12.6 29 14 54.6 -0.60

Notes: 1) We should transfer Alpha & Beta for Black production because it gives Rs.0.10 extra contribution competed to the next alternative. This can be understood as follows: Contribution earned = Rs.7 Contribution lost:

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AMA-Notes Alpha (3 Units x Rs.0.3) = Rs.0.9 Beta (2 Units x Rs.3) = Rs.6 Incremental Contribution = Rs.0.10 2) By using Alpha and Beta for Brown we earned Rs.0.60 less than the next possible alternative which can be understood as follows: Contribution earned = Rs.12 Contribution lost: Alpha (2 Units x Rs.0.3) = Rs.0.6 Beta (4 Units x Rs.3) = Rs.12 Decrease in Contribution = Rs.0.60 3) Conclusion if Black should be produced and Brown should be abandoned. Step 8: Optimum production plan for the company Particulars Available Units Required for 1 Blackalls Possible Blackalls production Output can be produced

Alpha 2,400 Units 3 Units 800 Units 800 Units

Beta 3,200 Units 2 Units 1,600 Units

Beta Balance = 3,200 Units – (800 Units x 2) = 1,600 Units. Sell this unused of 1,600 units to outside market. The contribution from the above plan is as follows: Black: 800 Units x Rs.7 = Rs.5,600 Beta: 1,600 Units x Rs.3 = Rs.4,800 Profit = Rs.5,600 + Rs.4,800 = Rs.10,400 11.5. Limiting Factor and Transfer Pricing

**Question no 6: Question no 11 Solution: Step 1: Contribution per limiting factor Particulars Selling Price (Rs.) Less: Variable Cost (Rs.) Contribution per units (Rs.0 Hours per unit Contribution per hour (Rs.) Rank

A 150 130 20 3 6.67 IV

B 146 100 46 4 11.5 III

C 140 90 50 2 25 I

D 130 85 45 3 15 II

Step 2: Allocation of 20,000 labour hours Product Units Hours/Unit Hours ∑ 𝐇𝐨𝐮𝐫𝐬 C 2,300 2 4,600 4,600 D 1,600 3 4,800 9,400

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AMA-Notes B A

2,500 200

4 3

10,000 600

19,400 600

Step 3: Allocation of 30,000 hours Product C D B A Idle Capacity

Units 2,300 1,600 2,500 2,800 -

Hours/Unit 2 3 4 3 -

Hours 4,600 4,800 10,000 8,400 2,200

∑ 𝐇𝐨𝐮𝐫𝐬 4,600 9,400 19,400 27,800 30,000

Step 4: Transfer Price fixation when capacity is 20,000 hours    

Division Z is having capacity constraint. It does not have enough hours to manufacture units both for external sales and internal transfer. Producing 2,500 units of D for internal transfer requires 2,500 Units x 3 Hours = 7,500 Hours. These 7,500 hours can be obtained only by releasing 600 hours from A and 6,900 hours from B. Transfer price = Variable Cost + Opportunity Cost of Department Z. Variable Cost 2,500 Units x Rs.85 Add: Opportunity Cost A 600 Hours x Rs.6.67 B 6,900 Hours x Rs.11.5 Total Cost

Transfer price =

Rs.2,95,850 2,500 Units

2,12,500 4,000 79,350 2,95,850

= Rs.118.34/Unit

Step 5: Transfer price fixation when capacity is 30,000 hours     

Division Z is having capacity constraint. It does not have enough hours to manufacture units both for external sales and internal transfer. Producing 2,500 units of D for internal transfer requires 2,500 Units x 3 Hours = 7,500 Hours. These 7,500 hours can be obtained only by using 2,200 hours of idle time and releasing 5,300 hours from A. Opportunity cost of idle time is nil and balance 5,300 hours, it is the contribution lost from product A. Transfer price = Variable Cost + Opportunity Cost of Department Z. Variable Cost 2,500 Units x Rs.85 Add: Opportunity Cost Idle 2,200 Hours x Rs.0 A 5,300 Hours x Rs.6.67 Total Cost

2,12,500 0 35,350 2,47,850

Rs.2,47,850

Transfer price = 2,500 Units = Rs.99.14/Unit Notes:

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AMA-Notes 1) When supplying division is a single product division having capacity constraint the transfer price is “Variable Cost + Opportunity Cost of Intermediate Product”. 2) If the supplying division is a multi-product division having capacity constraint, then transfer price is equal to “Variable Cost + Opportunity Cost of Supplying Division”. In this problem for internally transferring ‘D’ we don’t lose D’s external demand but lose the demand of Demand of ‘A’ & ‘B’ based on limiting factor ranking. Hence it is not D’s contribution lost but supplying division contribution lost which is the opportunity cost. 3) The Intermediate Product can be purchased at Rs.125. Here we can have 2 situations: (i) “Variable Cost + Opportunity Cost” > Rs.125 – Do not Transfer as it cheaper to Buy. Hence no need to fix transfer price. (ii) “Variable Cost + Opportunity Cost” < Rs.125 – Transfer is good from the company’s view point. Ensure that transfer price is not greater than Rs.125 as it will make receiving division purchase from outside creating Goal Conflict. Question no 7: Question no 12 Solution: Step 1: Calculation of contribution per unit Items Selling Price (Rs.) Less: Variable Cost (Rs.) Contribution per unit (Rs.) Hours Per unit Contribution per hour Rank

X 800 620 180 4 45 I

Y 160 140 20 1 20 II

Z 1,450 1,320 130 ----

Step 2: Allocation of 96,000 Hours Product Units Hours/Unit Hours ∑ 𝐇𝐨𝐮𝐫𝐬 X 15,000 4 60,000 60,000 Y 36,000 1 36,000 96,000 Step 3: Calculation of Divisional profit and Company profit when component imported A. Division A Profit Particulars Computation Amount (Rs.) Contribution from ‘X’ 15,000 Units x Rs.180 27,00,000 Contribution from ‘Y’ 36,000 Units x Rs.20 7,20,000 Total Contribution 34,20,000 Less: Fixed Cost (30,00,000) Profit 4,20,000 B. Division B Profit Particulars Computation Amount (Rs.) Contribution from ‘Z’ 5,000 Units x Rs.130 6,50,000

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AMA-Notes Less: Fixed Cost Profit

(5,00,000) 1,50,000

C. Company Profit Company Profit = Rs.4,20,000 + Rs.1,50,000 = Rs.5,70,000 Step 4: Calculation of Divisional profit and Company profit when division B purchases at Rs.800 from division A A. Division A Profit Particulars Computation Amount (Rs.) Contribution from ‘X’ 20,000 Units x Rs.180 36,00,000 Contribution from ‘Y’ 16,000 Units x Rs.20 3,20,000 Total Contribution 39,20,000 Less: Fixed Cost (30,00,000) Profit 9,20,000 B. Division B Profit Particulars Sales Less: Variable Cost (Excluding transfer price) Less: Transfer Price Less: Modification Cost Contribution Less: Fixed Cost Profit/(Loss)

Computation 5,000 Units x Rs.1,450 5,000 Units x Rs.520 5,000 Units x Rs.800 5,000 Units x Rs.80

Amount (Rs.) 72,50,000 26,00,000 40,00,000 4,00,000 2,50,000 (5,00,000) (2,50,000)

C. Company Profit Company Profit = Rs.9,20,000 – Rs.2,50,000 = Rs.6,70,000 Notes: 1) The import substitution increases the company’s profits by Rs.1,00,000. Hence, it is a good decision. 2) How the company profit increased by Rs.1,00,000? Cost of ‘X’ manufactured and transferred: Variable Cost = Rs.620 Opportunity cost of Division A = Rs.80 (20,000 Units x Rs.20/5,000 Units) Modification Cost = Rs.80 Total Cost = Rs.780 Cost of Import = Rs.800 Savings per unit = Rs.20 Increase in profit (20,000 Units x Rs.20) = Rs.1,00,000 3) Import substitution decrease division B profit by Rs.4,00,000 (Rs.1,50,000 – (-Rs.2,50,000). Why the profit has decreased? a) Transfer price paid to division A = Rs.800 E M Reddy

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AMA-Notes Modification Cost = Rs.80 Cost of Using ‘X’ = Rs.880 Imported Cost = Rs.800 Extra cost per unit = Rs.80 Decrease in profit (5,000 Units x Rs.80) = Rs.4,00,000 4) Is the transfer price of Rs.800 correct? Answer: No, because it creates Goal Conflict. Company decides to substitutes import while division B prefers imports. Step 5: Calculation of Divisional profits and company profit when division B purchase @ Rs.720 from division A A. Division A Profit Particulars Computation Contribution from ‘X’ [15,000 Units x Rs.180] + [5,000 Units x Rs.100] Contribution from ‘Y’ 16,000 Units x Rs.20 Total Contribution Less: Fixed Cost Profit

Amount (Rs.) 32,00,000 3,20,000 35,20,000 (30,00,000) 5,20,000

B. Division B Profit Particulars Sales Less: Variable Cost (Excluding transfer price) Less: Transfer Price Less: Modification Cost Contribution Less: Fixed Cost Profit/(Loss)

Computation 5,000 Units x Rs.1,450 5,000 Units x Rs.520 5,000 Units x Rs.720 5,000 Units x Rs.80

Amount (Rs.) 72,50,000 26,00,000 36,00,000 4,00,000 6,50,000 (5,00,000) 1,50,000

C. Company Profit Company Profit = Rs.5,20,000 + Rs.1,50,000 = Rs.6,70,000 Notes: 1) Transfer price of Rs.720 is also wrong because the incremental profit due to import substitution is fully cornered by division A. 2) Division B manager may feel that it can earn the same Rs.1,50,000 profit by importing and avoid modification work. 3) The transfer price should be fixed as follows:

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AMA-Notes Transfer Price Minimum

Maximum

VC + OC of Supplying Division

Purchase Cost – Modification Cost

Rs.620 + Rs.80 = Rs.700

Rs.800 – Rs.80 = Rs.720

11.6. Multi-Division range fixations

***Question no 8: Question no 13 Solution: Step 1: Transfer Price fixation for Product ‘X’

Capacity 20,000 Units External Demand – 14,000 Units

Idle Capacity – 6,000 Units

TP = EMP – SC 110 – 15 = 95

Min TP = VC Rs.40 + Rs.30 = Rs.70

No Transfer

Max TP = EP – Delivery Cost Rs.85 – Rs.6 = Rs.79

Rs.70 < TP < Rs.79 Notes: 1) When external demand of ‘X’ is sacrificed and transfer made the company loses Rs.110 selling price but saves Rs.15 agent’s commission. The net loss to the company is Rs.95. 2) If the company purchases the ‘X’ from outside it has to pay only Rs.85 purchase cost. It is better to pay Rs.85 than lose Rs.95. Hence we should not transfer by sacrificing external demand. When there is no transfer no need to fix transfer price. 3) The real cost of transferring is not Rs.95 but Rs.101 i.e. we lose Rs.95 and also incurring Rs.6 pickup cost. Buying is cheaper as long as it is less than Rs.101.

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AMA-Notes 4) Regarding idle capacity there is no opportunity cost. The transfer price should minimum recover the variable cost of intermediate product. 5) Transfer price should not exceed Rs.79 (Rs.85 – Rs.6) because in that case division Y will prefer to buy from outside which creates Goal Conflict. 6) The Goal Conflict is because in company’s interest using idle capacity costs only Rs.76 but buying cost is Rs.85. Company would like to transfer while division Y would like to purchase if Transfer price exceeds Rs.79. Step 2: Transfer Price fixation for product Y Particulars Product X Pick up cost of X Labour Delivery Cost – Internal Total Variable Cost for Internal transfer

When TP = Rs.70 Rs.70 Rs.6 Rs.50 Rs.8 Rs.134

When TP = Rs.79 Rs.79 Rs.6 Rs.50 Rs.8 Rs.143

Capacity 30,000 Units External Demand – 26,000 Units

Idle Capacity – 4,000 Units

TP = EMP – SC – Extra Delivery Cost 170 – 15 – 2 = 153

Min TP = VC = Rs.134

No Transfer

Max TP = EP = Rs.135 Rs.134 < TP < Rs.135

Notes: 1) When we sacrifice external demand of ‘Y’ and transfer to ‘Z’ the company loses a selling price of Rs.170 and saves & extra delivery cost of Rs.15 & Rs.2 (Rs.10 – Rs.8) respectively thereby losing net Rs.153. 2) It is better for the company to buy ‘Y’ from outside at Rs.135 rather than lose Rs.153 on internal transfer. Thus no transfer should be made by sacrificing external demand. Since no transfer made, no need to fix transfer price. 3) In company’s interest idle capacity should be used and transfer should be made and the variable cost of ‘Y’ is Rs.134 which should be minimum transfer price. 4) Any transfer price above Rs.135 will make division ‘Z’ purchase ‘Y’ which creates Goal Conflict. 5) Hence transfer price for ‘Y’ should be between Rs.134 and Rs.135. To have this range ‘X’ transfer price should be between Rs.70 and Rs.71 (Rs.135 – Rs.8 – Rs.50 – Rs.6)

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AMA-Notes 6) Produce 6,000 units of ‘X’ using the idle capacity and transfer to ‘Y’ at a transfer price of Rs.70 to Rs.71 and produce 4,000 units of ‘Y’ using idle capacity and transfer to ‘Z’ at a transfer price of Rs.134 to Rs.135. 7) It should be observed that manufacturing ‘Y’ and transferring to ‘Z’ is feasible only when ‘X’ is manufactured and transferred to ‘Y’. Buying ‘X’ and manufacturing ‘Y’ costs the company Rs.143 which is more than Y’s buying cost of Rs.135. 8) We can conclude that Y to Z transfer can happen only for so many units transferred from ‘X’ to ‘Y’. Suppose ‘X’ idle capacity is 4,000 units and ‘Y’ idle capacity 6,000 units, in this case ‘Y’ to ‘Z’ we can transfer only 4,000 units keeping 2,000 units idle. 11.7. Lump Sum Consideration Method

Question no 9: Question no 4 Solution: Step 1: Calculation of ROCE before recommendation Particulars A. Revenues External Sales Internal Transfer Total Revenues B. Cost Own Variable Cost Own Fixed Cost Transfer Price Total Cost C. Profit (A – B) D. Capital Employed E. ROCE (C/D)

Division A

Division B

30,00,000 (1,00,000 Units x Rs.30) 12,50,000 (25,000 Units x Rs.50) 7,50,000 (25,000 Units x Rs.30) -37,50,000 12,50,000 18,75,000 (1,25,000 Units x Rs.15) 5,00,000 -23,75,000 13,75,000 66,25,000 20.75%

2,50,000 (25,000 Units x Rs.10) 2,25,000 7,50,000 (25,000 Units x Rs.30) 12,25,000 25,000 12,50,000 2%

Notes: 1) Division B reports a very low ROCE which it blames on transfer price. 2) Division A states that transfer price of Rs.30 is market determined, hence correct. Is this correct? Answer: No, because A transfers only those units which it is unable to sell in outside market at Rs.30. 3) The transfer price should recover variable cost of intermediary product and contributes some towards fixed cost. 4) Fixed Cost of Division A = Rs.5,00,000 1,00,000

a) Share attributable to outsiders – Rs.4,00,000 (Rs.5,00,000 x 1,25,000) 20,000

b) Share attributable to Division ‘B’ – Rs.1,00,000 (Rs.5,00,000 x 1,25,000) 5) Transfer price = Rs.15 per unit + A lump sum of Rs.1,00,000. Step 2: Calculation of ROCE after recommendation Particulars

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Division A

Division B

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AMA-Notes A. Revenues External Sales Internal Transfer Total Revenues B. Cost Own Variable Cost Own Fixed Cost Transfer Price Total Cost C. Profit (A – B) D. Capital Employed E. ROCE (C/D)

30,00,000 (1,00,000 Units x Rs.30) 12,50,000 (25,000 Units x Rs.50) 4,75,000 (25,000 Units x Rs.15 + Rs.1,00,000) -34,75,000 12,50,000 18,75,000 (1,25,000 Units x Rs.15) 5,00,000 -23,75,000 11,00,000 66,25,000 16.60%

2,50,000 (25,000 Units x Rs.10) 2,25,000 4,75,000 9,50,000 3,00,000 12,50,000 24%

Notes: 1) This method is good it contributes Rs.1,00,000 to division A for using it’s idle capacity and also improves ROCE of division B. 2) If the division B actually creates a demand of 30,000 units should the lump sum consideration increase? If the demand falls to 10,000 units should the lump sum consideration decrease? Answer: In both the cases Rs.1,00,000 should not change. ‘B’ has paid Rs.1,00,000 for capacity of 25,000 units. If it overuses the capacity, it is favourable fixed overhead volume variable and if it under uses the capacity it results in adverse fixed overhead volume variance. When we change the consideration then it becomes variable. 3) If the demand for B exceeds 30,000 units, then capacity constraint arises in division A. For those excess units transfer price should be ‘Variable Cost + Opportunity Cost’ or External Market Price of Rs.30 in this case. *****Question no 10: Question no 9 Solution: Eshwar (Rs. in ‘000s) Units Revenue Cost 100 204 115 200 362 185 300 486 261 400 598 344 500 703 435 600 803 535 700 898 645 800 988 766 Units 100 200 300 400

MR 204 158 124 124

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NMR 133 133 133 122

Brahma (Rs. in ‘000s) MR MC Revenue FPC NR 204 115 703 570 133 158 70 1,375 1,120 255 124 76 2,036 1,670 366 112 83 2,676 2,220 456 105 91 3,305 2,770 535 100 100 3,923 3,320 603 95 110 4,530 3,870 660 90 121 5,126 4,420 706

MC 115 70 76 83

Yes/No Y Y Y Y

NMR 133 122 111 90 79 68 57 46

Internal/External E E I E

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AMA-Notes 500 600 700 800

112 112 105 105

122 111 111 90

91 100 110 121

Y Y Y N

I E I --

Conclusion: Produce 700 engines and sell as engines 400 & sell as dories 300. Optimum output for brahma 300 units, Eshwar 700 units. Fixation of transfer price: A. Receiving Division Range (Brahma):

B. Supplying Division Range (Eshwar):

C. Narrow Range: Receiving Division: Rs.900 < Transfer Price < Rs.1,110 Receiving Division: Rs.1,100 < Transfer Price < Rs.1,210 Narrow Range: Rs.1,100 < Transfer Price < Rs.1,110 Question no 11: Question no 5 Solution: Step 1: Real Cost of Company B

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AMA-Notes

Step 2: Real Cost of ‘RS’

Real Cost of RS quotation = Rs.3,000 + Rs.11,000 + Rs.9,100 + Rs.6,300 = Rs.29,300

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AMA-Notes Conclusion: RT should purchase it’s component from RS in the group interest. The transfer price should be fixed in such a way that there is no Goal Conflict. Working Note 1: Own Cost of RS for Company B Contract RS wants to earn 25% profit on it’s own cost. Own Cost = Rs.5,500/125 x 100 = Rs.4,400 Profit = Rs.5,500 x 25/125 = Rs.1,100 Cost of Company B Contract = Rs.22,000 + Rs.,7,500 + Rs.3,080 = Rs.32,580 Working Note 2: Calculation of profit in RT’s price Profit = 20% on total Cost. Selling Price = 100% + 20% (100 x 20%) = 120% Profit = 30,000 x 20/120 = Rs.5,000 Own Cost = Rs.19,000 – Rs.5,000 = Rs.4,000 Working Note 3: Calculation of Own Cost and Profit of ‘RS’ Transfer Price = Rs.48,000 – Total Cost = Rs.48,000 – Rs.42,000 = Rs.6,000 Own Cost = Total Cost – Cost of Bought in Components from RR & RT = Rs.42,000 – Rs.33,000 = Rs.9,000 11.8. Transfer Pricing Fixation Chart

1)

2)

3)

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AMA-Notes

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AMA-Notes 12. PRICING 12.1. Pricing Using Calculus

Question no 1: Question no 1 Solution: Step 1: Current Period Cost at Previous period price level Current Period Cost = Rs.1077.44 Increase in price level during the period = 4% Current period cost at previous period price level = 1077.44/1.04 = 1036 Step 2: Segregation into variable and fixed at previous period price level Particulars Previous Year Current Year Units (‘000) 100 106 Cost (‘000) 1000 1036 Variable Cost = Change in Cost/Change in units = (1036 – 1000)/(106 – 100) = 6 per unit Fixed Cost = Total Cost – Variable Cost = 1000 – (6 x 100) = 400 Step 3: Variable and fixed cost at next year price level Variable Cost = 6 x 104% x 106% = 6.6144 per unit Fixed Cost = 400 x 104% x 106% = 440.96 Part A: Budgeted position when Selling price is Rs.13 Particulars Computation Sales 1,06,000 Units x 109% x Rs.13 Less: Variable Cost 1,06,000 Units x 109% x Rs.6.6144 Contribution Less: Fixed Cost Profit

Amount Rs.15,02,020 Rs.7,64,228 Rs.7,37,792 Rs.4,40,960 Rs.2,96,832

Part B: Budgeted position when Selling price is Rs.13.78 (Increased by 6%) Particulars Computation Amount Sales 1,06,000 Units x Rs.13 Rs.14,60,680 Less: Variable Cost 1,06,000 Units x Rs.6.6144 Rs.7,01,126 Contribution Rs.7,59,554 Less: Fixed Cost Rs.4,40,960 Profit Rs.3,18,594 Part C:

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AMA-Notes The option of increase in selling price is recommended because it gives the highest budget profit. In the option 1, keeping selling price constant helps to increase the volume but the volume increase also increases the variable cost. Part D: Assumptions 1) 2) 3) 4)

Price is the sole factor influencing the demand. The price elasticity is accurately estimated. Both variable and fixed cost has the same rate of inflation. Decision is made purely on the basis of economic factors.

Question no 2: Question no 2 Solution: Part A: Calculation of Profit at Current Selling Price Particulars Computation Sales 50 Units x Rs.150 Less: Cost (Rs.0.5 x 502) + (Rs.20 x 50 Units) + Rs.4,000 Profit

Amount (Rs.) 7,500 6,250 1,250

Part B: Optimum Output and Best Selling Price Step 1: Revenue & Cost Functions Selling Price = 300 – 3Q Revenue = Units Sold x Selling Price = Q x (300 – 3Q) = 300Q – 3Q2 Cost = 0.5Q2 + 20Q + 4,000 (Given) Step 2: Marginal Revenue & Marginal Cost dR

dR

Marginal Revenue (dQ) = dQ (300Q − 3Q2 ) = 300 – 6Q dC

Marginal Cost (dQ)

dC

= dQ (0.5Q2 + 20Q + 4,000) = Q + 20

Step 3: Optimum Output Optimum Output is the level at which marginal revenue equals marginal cost. 300 – 6Q = Q + 20 → 7Q = 280 → Q = 40 Units Step 4: Best Selling Price Selling Price = 300 – 3Q → 300 – (3 x 40) = Rs.180 Step 5: Profit at Optimum Output Particulars Computation Sales 40 Units x Rs.180

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Amount (Rs.) 7,200

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AMA-Notes (Rs.0.5 x 402) + (Rs.20 x 40 Units) + Rs.4,000 5,600 1,600

Less: Cost Profit Notes:

1) Understanding the first derivative: a) Variable Cost = Rs.5 per unit and Fixed Cost = Rs.10,000. The Cost function is Y = 5X + 10,000.

2) 3) 4) 5) 6) 7) 8)

dY

dY

= 5X 0 = 5. This means when ‘X’ changes by ‘1’ unit the ‘Y’ changes by Rs.5. The dX means dX change in ‘Y’ with respect to ‘X’. When price is elastic to demand then the concept of optimum output will emerge. The optimum output is the output at which marginal revenue equals marginal cost. The first step is to construct a price function. Selling Price = Selling Price at ‘0’ demand – Elasticity times quantity. Next step is to construct revenue function by multiplying price with quantity. Differentiate with respect to quantity which is called Marginal Revenue and cost with respect to quantity which is called ‘Marginal Cost. Equate Marginal Revenue and Marginal Cost to identify optimum output. Determine the best selling price using the optimum output. b)

***Question no 3: Question no 3 Solution: Part A: Optimum Output and Best Selling Price when there is no tax Step 1: Revenue & Cost function Selling Price = 157 – 3X Revenue = (157 – 3X) X = 157X - 3X 2 Cost = 1064 + 5X + 0.04X 2 Step 2: Marginal Revenue & Marginal Cost dR

dR

Marginal Revenue (dQ) = dQ (157X − 3X 2 ) = 157 – 6X dC

Marginal Cost (dQ)

dC

= dQ (1064 + 5X + 0.04X 2 ) = 5 + 0.08X

Step 3: Optimum Output Optimum Output is the level at which marginal revenue equals marginal cost. 157 – 6X = 5 + 0.08X → 6.08X = 152 → X = 25 Units Step 4: Fixation of Selling Price Selling Price = 157 – 3X = 157 – 3 x 25 = 82 i.e. Optimum selling price is Rs.82,000.

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AMA-Notes Step 5: Maximum Profit Particulars Computation Sales 25 Units x 82 Less: Cost 1,064 + (5x 25 Units) + (0.04 x 252) Profit

Amount (Rs.)(‘000s) 2,050 1,214 836

The profit is Rs.8,36,000 Part B: Optimum Output and Selling Price with tax Step 1: Revenue & Cost function Revenue function will not change but the cost function changes as follows: Selling Price = 157 – 3X Revenue = (157 – 3X) X = 157X - 3X 2 Cost = 1064 + 5X + 0.04X 2 + tX Step 2: Marginal Revenue & Marginal Cost dR

dR

Marginal Revenue (dQ) = dQ (157X − 3X 2 ) = 157 – 6X dC

Marginal Cost (dQ)

dC

= dQ (1064 + 5X + 0.04X 2 + tx) = 5 + 0.08X + t

Step 3: Optimum Output Optimum Output is the level at which marginal revenue equals marginal cost. 157 – 6X = 5 + 0.08X + t → 6.08X = 152 – t → X = 25 – 0.1645t Step 4: Fixation of Selling Price Selling Price = 157 – 3X = 157 – 3 x (25 – 0.1645t) = 157 – 75 + 0.4935t → 82 + 0.4935t Part C: Without tax the selling price is Rs.82 and when we have tax we increase the selling price by Rs.0.4935t which means 49.35% of tax is passed on to the customer. Part D: Profit when tax is Rs.4,000 Step 1: Revenue & Cost function Selling Price = 157 – 3X Revenue = (157 – 3X) X = 157X - 3X 2 Cost = 1064 + 5X + 0.04X 2 + 4X Step 2: Marginal Revenue & Marginal Cost E M Reddy

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AMA-Notes dR

dR

Marginal Revenue (dQ) = dQ (157X − 3X 2 ) = 157 – 6X dC

Marginal Cost (dQ)

dC

= dQ (1064 + 5X + 0.04X 2 + 4x) = 5 + 0.08X + 4 = 9 + 0.08X

Step 3: Optimum Output Optimum Output is the level at which marginal revenue equals marginal cost. 157 – 6X = 9 + 0.08X → 6.08X = 148 → X = 24.34 Step 4: Fixation of Selling Price Selling Price = 157 – 3X = 157 – 3 x (24.34) = 157 – 73 = Rs.84 Step 5: Maximum Profit Particulars Computation Sales 24.34 Units x 84 Less: Cost 1,064 + (5 x 24.34 Units) + (0.04 x 24.342) + (4 x 24.34) Profit

Amount (Rs.)(‘000s) 2,044.56 1306.76 737.8

The profit is Rs.7,37,800 12.2. Pricing Under Uncertainty and Expected Value of Perfect Information (EVPI)

Question no 4: Question no 8, pg. no.61 Solution: Step 1: Calculation of Material Cost under all Options Demand

Selling Price = Rs.15 Option 1 Option 2 Optimistic (Rs.) 3,24,000 2,97,500 Most Likely (Rs.) 2,52,000 2,31,000 Pessimistic (Rs.) 1,62,000 1,48,500

Selling Price = Rs.20 Option 3 Option 4 Option 5 2,70,000 2,52,000 2,31,000 2,10,000 2,07,000 1,89,750 1,59,000 (W-1) 1,17,000 1,26,500 (W-2)

Option 6 2,10,000 1,74,000(W-3) 1,44,000 (W-4)

WN – 1: Material Cost when selling price is Rs.15, demand is Pessimistic and Purchase Price is Rs.2.5 Consumption of Materials (18,000 Units x 3 Kgs) = 54,000 Kgs Purchase Cost (70,000 Kgs x Rs.2.5) = Rs.1,75,000 Less: Realizable value of unused materials (16,000 x 1) = Rs.16,000 Net Material Cost (Rs.1,75,000 – Rs.16,000) = Rs.1,59,000 WN – 2: Material Cost when selling price is Rs.20, demand is Pessimistic and Purchase Price is Rs.2.75 Consumption of Materials (13,000 Units x 3 Kgs) Purchase Cost (39,000 Kgs x Rs.2.75)

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= 39,000 Kgs = Rs.1,37,500

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AMA-Notes Less: Realizable value of unused materials (11,000 x 1) = Rs.11,000 Net Material Cost (Rs.1,37,500 – Rs.11,000) = Rs.1,26,500 WN – 3: Material Cost when selling price is Rs.20 and demand is Most likely and Purchase Price is Rs.2.5 Consumption of Materials (23,000 Units x 3 Kgs) Purchase Cost (70,000 Kgs x Rs.2.5) Less: Realizable value of unused materials (1,000 x 1) Net Material Cost (Rs.1,75,000 – Rs.1,000)

= 69,000 Kgs = Rs.1,75,000 = Rs.1,000 = Rs.1,74000

WN – 4: Material Cost when selling price is Rs.20 and demand is Pessimistic and Purchase Price is Rs.2.5 Consumption of Materials (13,000 Units x 3 Kgs) = 39,000 Kgs Purchase Cost (70,000 Kgs x Rs.2.5) = Rs.1,75,000 Less: Realizable value of unused materials (31,000 x 1) = Rs.31,000 Net Material Cost (Rs.1,75,000 – Rs.31,000) = Rs.1,44,000 Step 2: Profit Table Demand

Probability

Selling Price = Rs.15 Option 1 Option 2 Optimistic (Rs.) 0.3 83,000 1,10,000 Most Likely (Rs.) 0.5 59,000 80,000 Pessimistic (Rs.) 0.2 29,000 42,500 Expected Profit (Weighted Avg.) 60,200 81,500

Option 3 1,37,000 1,01,000 32,000 98,000

Selling Price = Rs.20 Option 4 Option 5 1,28,000 1,49,000 88,000 1,05,250 8,000 -1,500 84,000 97,025

Option 6 1,70,000 1,21,000 -19,000 1,07,700

Conclusion: Option 6 gives highest expected profit. Hence select option 6 and fix selling price as Rs.20 and negotiate for a purchase price of Rs.2.5 per kg with a minimum 70 Kgs quantity. Step 3: Expected Value of Perfect Information 1) Expected Profit with perfect information: Optimistic = Rs.1,70,000 x 0.3 Most Likely = Rs.1,21,000 x 0.50 Pessimistic = Rs.42,500 x 0.20 Expected Profit = Rs.1,20,000 2) Expected Profit Without Perfect Information is Rs.1,07,700 3) Expected Value of perfect Information (1 – 2) = Rs.1,20,000 – Rs.1,07,700 = Rs.12,300 This is the price we can pay to get perfect information about the demand. Question no 5: Question no 6, pg. no.61 Solution: Step 1: Identification of Maximum production part A

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AMA-Notes Line S = 4000 Hours/0.6 = 6,666 Units Line T = 4,500 Hours/0.5 = 9,000 Units Materials = 13,000 Kilos/1.6 = 8,125 Units The company can produce 6,666 units of part A and the limiting factor is Line S. Step 2: Identification of Maximum production part A Line S = 4000 Hours/0.25 = 16,000 Units Line T = 4,500 Hours/0.55 = 8,181 Units Materials = 13,000 Kilos/1.6 = 8,125 Units The company can produce 8,125 units of part B and the limiting factor is Materials. Part A: Which part to Manufacture Particulars Part A: Sales - Materials -Line S -Line T Contribution Part B: Sales -Materials -Line S -Line T Contribution

Computation

Amount (Rs.)

6,666 Units x Rs.145 6,666 Units x 1.6 Kgs x Rs.12.5 6,666 Units x 0.6 Hours x Rs.80 6,666 Units x 0.5 Hours x Rs.100

9,66,570 -1,33,320 -3,19,968 -3,33,300 1,79,982

8,125 Units x Rs.115 8,125 Units x 1.6 Kgs x Rs.12.5 8,125 Units x 0.25 Hours x Rs.80 8,125 Units x 0.55 Hours x Rs.100

9,34,375 -1,62,500 -1,62,500 -4,46,875 1,62,500

Part A should be manufactured as it gives highest contribution. Part B: The company earns the maximum profit of Rs.1,79,982 and it could not meet the maximum call off unit because of non-availability of Line S hours. Part C: Particulars Part A: Sales -Cost Contribution + Payment for unused hours Total Contribution Part B: Sales E M Reddy

Computation

Amount (Rs.)

Rs.9,66,570 x 90% Rs.1,33,320+Rs.3,19,968+Rs.3,33,300

8,69,913 -7,86588 83,325

Line S: Nil Line T: [4,500 – 6,666 x 0.5] x Rs.60 Rs.9,34,375 x 90%

70,020 1,53,345 8,40,937 Page | 366

AMA-Notes -Cost Rs.1,62,500+ Rs.1,62,500+Rs.4,46,875 Contribution + Payment for unused hours Line S: [4,000 – 8,125 x 0.25] x Rs.60 Line T: [4,500 – 8,125 x 0.55] x Rs.60 Contribution In case of this offer the company should manufacture and sell Part B.

-7,71,875 1,18,125 1,875 1,89,062

12.3. ROI (Return on Investment) Pricing

Question no 6: Question no 10 Solution: Step 1: Cost of Production per unit of Product M Particulars Direct Materials

Computation Dept A: 4 x Rs.6 = Rs.24 Dept B: 8 x Rs.2.5 = Rs.20 Direct Labour Dept A: 2 x Rs.4 = Rs.8 Dept B: 3 x Rs.3 = Rs.9 Variable Overhead Dept A: Rs.24 x Rs.0.8 = Rs.19.2 Dept B: 3 Hours x Rs.2 = Rs.6 Total Variable Cost Fixed Overheads Dept A: Rs.24 x Rs.2.2 = Rs.19.2 Dept B: 3 Hours x Rs.2 = Rs.6

Amount (Rs.) 44 17 25.20 86.20

Question no 7: Question no 11 Solution: Question no 8: Question no 14 Solution:

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AMA-Notes 13. DEVELOPMENTS IN COST ACCOUNTING (STRAGETIC COST MANAGEMENT 13.1. Learning Objectives

1) Throughput Costing 2) Theory of Constraints (TOC) 3) Just-In-Time System (JIT) 4) Backflush Costing System 5) Total Quality Management (TQM) 6) Life Cycle Costing (LCC) 7) Target Costing 8) Activity Based Costing (ABC) 9) Value Chain Analysis 10) Balance Score Card 13.2. Through Put Costing

Question no 1: Emerson corporations, which uses throughput costing, just completed its first year of operations, planned and actual production equaled 10,000 units, and sales totaled 9,600 units at Rs.72 per unit. Cost data for the year are as follows: Direct Material (per unit) Rs.12 Conversion Cost: Direct Labour Rs.45,000 Variable Manufacturing Overhead Rs.65,000 Fixed Manufacturing Overhead Rs.2,20,000 Selling and administrative costs: Variable (per unit) Rs.8 Fixed Rs.1,18,000 The company classified only direct material as a throughput cost. Required: 1. Compute the company’s total cost for the year assuming that variable manufacturing costs are driven by the number of units produced, and variable selling and administrative costs are driven by the number of units sold. 2. How much of this costs would be held in year-end inventory under (a) absorption costing (b) Variable Costing, and (c) Throughput costing 3. Prepare Emerson’s throughput costing income statement. Solution: Part 1: Calculation of total cost Particulars Direct Materials Direct Wages Variable Manufacturing Overhead Fixed Manufacturing Overhead Variable Selling Overheads Fixed Selling Overheads Total Cost

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Computation 10,000 Units x Rs.12 Given Given Given 9,600 Units x Rs.8 Given

Amount (Rs.) 1,20,000 45,000 65,000 2,20,000 76,800 1,18,000 6,44,800

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AMA-Notes Part 2: Stock Valuation under three systems Items Direct Materials Direct Wages Variable Manufacturing Overhead Fixed Manufacturing Overhead Product Cost Production Cost per unit Closing Stock Closing Stock Value

Absorption Costing 1,20,000 45,000 65,000 2,20,000 4,50,000 10,000 45 400 18,000

Marginal Costing 1,20,000 45,000 65,000 -2,30,000 10,000 23 400 9,200

Throughput Costing 1,20,000 ---1,20,000 10,000 12 400 4,800

Part 3: Income statement under three systems Items Sales (9,600 Units x Rs.72) Less: CGS/ VCGS/ TCGS GP/GC/GTC Less: Period Cost: Direct Wages Variable Manufacturing Overhead Fixed Manufacturing Overhead Variable Selling Overhead Fixed Selling Overhead Total Period Cost Profit

Absorption Costing 6,91,200 4,32,000 (9,600 x 45) 2,59,200

Marginal Costing 6,91,200 2,20,800 (9,600 x 23) 4,70,400

Throughput Costing 6,91,200 1,15,200 (9,600 x 12) 5,76,000

---76,800 1,18,000 1,94,800 64,400

--2,20,000 76,800 1,18,000 4,14,800 55,600

45,000 65,000 2,20,000 76,800 1,18,000 5,24,800 51,200

Part 4: Reconciling Profits Particulars Computation Throughput Profit Add: Difference stock in value (Marginal vs. Throughput) (Rs.9,200 – Rs.4,800) Marginal Costing in Profit Add: Difference stock in value (Absorption vs. Marginal) (Rs.180200 – Rs.9,200) Absorption Costing Profit

Amount (Rs.) Rs.51,200 Rs.4,800 Rs.55,600 Rs.8,800 Rs.64,400

Part 5: Understanding Expired & Unexpired Cost Particulars Total Cost Less: Unexpired Cost (Closing Stock Value) Expired Cost

Absorption Costing 6,44,800 18,000

Marginal Costing 6,44,800 9,200

Throughput Costing 6,44,800 4,800

6,26,800

6,35,600

6,40,000

CGS/VCGS/TCGS Add: Period Cost Expired Cost

4,32,000 1,94,800 6,26,800

2,20,800 4,14,800 6,35,600

1,15,200 5,24,800 6,40,000

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AMA-Notes Notes: 1) Product costs are those costs considered for stock valuation and period costs are ignored for stock valuation. 2) There are 3 types of costing systems:

Absorption Costing System

Marginal Costing System

Throughput Costing

Values Stock at Full Manufacturing Cost including unitized fixed cost

Values Stock at Variable Manufacturing Cost

Values Stock at Raw Material Cost

3) It was earlier discussed that Absorption Costing hides inefficiency by allowing fixed manufacturing overhead to go to next year through stock (for more details refer Marginal Costing). Fixed Cost will anyhow be incurred whether or not the production take place. Hence should not go into stock valuation. 4) Throughput costing states that wages and variable overheads also should not enter stock value What is tangible transferred through stock is only raw materials. We cannot transfer a labour time or a power consumption from one period to another period. 5) Even if the finished good is unsalable we can still scrap the raw materials but not labour or variable overhead. 6) Contribution = Sales – Variable Cost under Marginal Costing. In throughput costing we used a term ‘Throughput Contribution’ which is ‘Sales – Material Cost of Goods Sold’. 7) CGS = Cost of Goods Sold, VCGS = Variable Cost of Goods Sold, TCGS = Throughput Cost of Goods Sold 8) GP = Gross Profit, GC = Gross Contribution, GTC = Gross Throughput Contribution 13.3. Theory of Constraints

**Question no 2: The Wellesley corporation makes printed cloth in two operations, weaving and printing. Direct Material costs are Wellesley’s only variable costs. It sells at Rs.1,250 per roll to a distributor who markets, distributes and provided customer service for the product. Weaving Printing Monthly Capacity 10,000 rolls 15,000 rolls Monthly Production 9,500 rolls 8,550 rolls Direct Materials cost per roll of cloth processed at each operation Rs.500 Rs.100 Fixed operating costs Rs.28,50,000 Rs.4,27,500 Fixed operating cost per roll (Rs.28,50,000/9,500; Rs.4,27,500/8,550) Rs.300/roll Rs.50/roll Wellesley can start only 10,000 rolls of cloth in the weaving department because of capacity constraints of the weaving machines. If the weaving operation produces defective cloth, the cloth must be scrapped and yields zero net revenue. Of the 10,000 rolls of cloth started at the weaving operation, 500 rolls (5%) are scrapped. Scrap costs per roll, based on total (fixed and variable) manufacturing costs per roll incurred up to the end of the weaving operation, equal Rs.785 per roll as follows: Direct materials cost per roll (variable) Rs.500

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AMA-Notes Fixed operating costs per roll (Rs.28,50,000/10,000 rolls Rs.285 Total manufacturing costs per roll in weaving department Rs.785 The good rolls from the weaving department (called grey cloth) are sent to the printing department. Of the 9,500 good rolls started at the printing operation, 950 rolls (10%) are scrapped and yield Zero net revenue. Scrap costs, based on total (fixed and variable) manufacturing costs per unit up to the end of the printing decisions, equal Rs.930 per roll calculated as follows: Total manufacturing costs per roll in weaving department Rs.785 Printing department manufacturing costs Direct materials costs per roll (variable) Rs.100 Fixed operating costs per roll (Rs.4,27,500/9,500) Rs.45 Rs.145 Total manufacturing costs per roll Rs.930 Wellesley corporation’s total monthly sales of printed cloth equals the printing department’s output. Required: 1. The printing department is considering buying 5,000 additional rolls of grey cloth from an outside supplier at Rs.900 per roll. The printing department manager is concerned that the cost of purchasing the grey cloth is much higher than Wellesley’s cost of manufacturing the grey cloth. The quality of the grey cloth acquired from outside is very similar to that manufactured in-house. The printing department expects that 10% of the rolls obtained from the outside supplier will be scrapped. Should the printing department buy the grey cloth from the outside supplier? Show your calculations. 2. Wellesley’s engineers have developed a method that would lower the printing department’s scrap rate to 6% at the printing operations. Implementing the new method would cost Rs.3,50,000 per month. Should Wellesley implement the change? Show your calculations. 3. The design engineering team has proposed a modification that would lower the weaving department’s scrap rate to 3%. The modification would cost the company Rs.1,75,000 per month. Should Wellesley implement the change? Show your calculations. Solution: Part 1: Viability of Purchasing 5,000 rolls of Gray cloth from outside Particulars Computation Sales 5,000 x 90% x Rs.1,250 Less: Purchase Cost 5,000 x Rs.900 Less: Further Processing Cost 5,000 x Rs.100 Incremental Profit This suggestion is viable as it increase profit.

Amount (Rs.) 56,25,000 (45,00,000) (5,00,000) 6,25,000

Part 2: Feasibility of scrap reduction in printing department Particulars Existing Scrap Scrap after new method Reduction of Scrap Sales Less: New Method Cost Incremental Profit

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Computation Amount 9,500 x 10% 950 rolls 9,500 x 10% 570 rolls 380 rolls 380 x Rs.1250 Rs.4,75,000 (Rs.3,50,000) Rs.1,25,000

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AMA-Notes Scrap reduction is feasible as it improves the profit. Part 3: Feasibility of scrap reduction in weaving department Particulars Computation Existing Scrap 10,000 x 5% Scrap after new method 10,000 x 3% Reduction of Scrap Sales 200 x 90% x Rs.1250 Less: FPC & New Method Cost [200 x Rs.100] + Rs.1,75,000 Incremental Profit This option is also good as it improves profit.

Amount 500 rolls 300 rolls 200 rolls Rs.2,25,000 (Rs.1,95,000) Rs.30,000

Notes:

1) The Output of the factory is determined by the speed of the slowest Machine or Operation. That Machine (or) Operation is called Bottle Neck Machine (or) Bottle Neck Operation. 2) TOC (Theory of Constraints) is all about managing Bottle Necks. 3) The following things should be kept in mind while managing Bottle Necks: a) The Production of all the operations should be sub-ordinated to Bottle Neck Operation. b) For example, M1 can produce 10,000 units per day but the production should take place only for 8,000 units because if the full capacity is operated it leads to build up of work-in-progress inventories which involves holding costs. c) The Company should strive to take measures to remove bottle necks. d) Some measures that can be undertaken to remove bottle necks are: i) Sub-contract portion of Bottleneck Operation ii) Improve the capacity of the Bottleneck Operation by adding additional machines. iii) Upgrade the technology to improve the speed of Bottleneck Machines iv) Try for methods to reduce scrap (Both Bottleneck & Non-Bottleneck Machines) 4) The company should not spend any money that improves the output of non-bottle neck operations because it is a wasteful expenditure having no impact on the factory output. Similar to crashing a noncritical activity.

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AMA-Notes 13.3.1. Theory of Constraints Measures (TOC Measures)

Throughput Contribution (Money Into)

Investments (Money tied up)

Operating Cost (Money going out)

Sales – Material cost of goods sold

Sum of materials in direct materials, WIP and FG, R&D, and cost of equipments and buildings

All operating costs excluding materials like wages, VOH, rent, utilities, deprecation etc.

Notes: 1) There are 3 cash flows while running a business: a) Income → Money Coming into business b) Expense → Money going out of business c) Asset → Money tied in the business 2) Company should spend (or) tie up money only when if it improves throughput contribution. Otherwise such expenses and investments should be avoided. 3) For example, investment in R&D to improve efficiency of Bottleneck operations increases throughput contribution. Hence, it is a value added investment. 4) On the other hand, incurring expenses like power, wages etc., to run non-bottleneck operations at full capacity is wasteful expenditure. Investment in stocks unproductive investment as these will not improve ‘Throughput contribution’. 5) When we manage Bottleneck ensure that it does not get shifted to another operation. Question no 3: Vikram Ltd produces 4 products using 3 different machines. Machine capacity is limited to 3,000 hours for each machine. The following information is available for February 2009: Products A B C D Contribution (sales-direct material) Rs. 1,500 1,200 1,000 600 Machine Hours required/unit: Machine 1 10 6 2 1 Machine 2 10 9 3 1.5 Machine 3 10 3 1 0.5 Estimated demand (units) 200 200 200 200 Required: From the above information identify the bottleneck activity and allocate the machine time. Solution: Step 1: Calculation of requirement of machine hours Machine A B C D Total Machine 1 (Hours) 2,000 1,200 400 200 3,800 Machine 2 (Hours) 2,000 1,800 600 300 4,700 Machine 3 (Hours) 2,000 600 200 100 2,900

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AMA-Notes Step 2: Calculation of Throughput Accounting Ratio (TAR) Machine Requirement Availability TAR Machine 1 (Hours) 3,800 3,000 126.67% Machine 2 (Hours) 4,700 3,000 156.67% Machine 3 (Hours) 2,900 3,000 96.67% 1) Throughput Accounting Ratio =

Requirement Avaibility

2) That Machine which is having the highest throughput accounting ratio is called “Bottleneck Machine. When we allocate the bottleneck machine all the other machines stands automatically allocated. Step 3: Calculation of throughput contribution per bottleneck hour Particulars A B C D Throughput Contribution (Rs.) 1,500 1,200 1,000 600 Machine 2 Hours 10 9 3 1.5 Contribution per hour (Rs.) 150 133.33 333.33 400 Rank III IV II I Step 4: Allocation of Machine 2 hours Product Units Hours per unit Hours Cumulative Hours D 200 1.5 300 300 C 200 3 600 900 A 200 10 2000 2900 B 11 9 100 3000 Question no 4: A company produces three products A, B and C. The following information is available for a period: Particulars A B C Contribution (Rs. p.u.) (Sales – Direct Materials) 30 25 15 Machine hours required per unit of production: Particulars Hours Throughput A B C Accounting Ratio Machine 1 10 2 4 133.33% Machine 2 15 3 6 200% Machine 3 5 1 2 66.67% Estimated sales demand for A, B and C is 500 units each and machine capacity is limited to 6,000 hours for each machine. Required: (a) Analyze the above information and apply theory of constraints process to remove the constraints. (b) How many units of each product will be made? Solution: Step 1: Calculation of requirement of machine hours Machine

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A

B

C

Total

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AMA-Notes Machine 1 (Hours) 5,000 1,000 2,000 8,000 Machine 2 (Hours) 7,500 1,500 3,000 12,000 Machine 3 (Hours) 2,500 500 1,000 4,000 Step 2: Calculation of Throughput Accounting Ratio (TAR) Machine Requirement Availability TAR Machine 1 (Hours) 8,000 6,000 133.33% Machine 2 (Hours) 12,000 6,000 200% Machine 3 (Hours) 4,000 6,000 66.67% Machine 2 has highest throughput accounting ratio and hence it is bottleneck machine. Step 3: Calculation of throughput contribution per bottleneck hour Particulars A B C Throughput Contribution (Rs.) 30 25 15 Machine 2 Hours 15 3 6 Contribution per hour (Rs.) 2 8.33 2.5 Rank III I II Step 4: Allocation of Machine 2 hours Product Units Hours per unit Hours Cumulative Hours B 500 3 1,500 1,500 C 500 6 3,000 4,500 A 100 15 1,500 6,000 Question no 5: Guptha ltd produces 4 products P, Q, R and S by using 3 different machines X, Y and Z. Each machine capacity is limited to 6,000 hours per month. The details given below are for July 2013: Particulars P Q R S Selling price p.u. 10,000 8,000 6,000 4,000 Variable cost p.u. 7,000 5,600 4,000 2,800 Machine hours p.u. X 20 12 4 2 Y 20 18 6 3 Z 20 6 Expected demand (units) 200 200 200 200 Required:  Find out bottleneck activity  Allocate the machine hours on the basis of bottleneck  Ascertain the profit expected in the month if the monthly fixed cost amounts to Rs.9,50,000.  Calculate the unused spare hours of each machine. Solution: Step 1: Calculation of requirement of machine hours Machine

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P

Q

R

S

Total

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AMA-Notes X Y Z

4,000 2,400 800 400 7,600 4,000 3,600 1,200 600 9,400 4,000 1,200 400 200 5,800

Step 2: Calculation of Throughput Accounting Ratio (TAR) Machine Requirement Availability TAR X 7,600 6,000 126.67% Y 9,400 6,000 156.67% Z 5,800 6,000 96.67% Machine Y is bottleneck machine as it has highest throughput accounting ratio. Step 3: Calculation of contribution per bottleneck hour Particulars P Q R S Throughput Contribution (Rs.) 3,000 2,400 2,000 1,200 Machine Y Hours 20 18 6 3 Contribution per hour (Rs.) 150 133.33 333.3 400 Rank III IV II I Step 4: Allocation of Machine 2 hours Product Units Hours per unit Hours Cumulative Hours S 200 3 600 600 R 200 6 1,200 1,800 P 200 20 4,000 5,800 Q 11 18 200 6,000 Step 5: Calculation of Profit Product Units Contribution per unit (Rs.) Contribution (Rs.) P 200 3,000 6,00,000 Q 11 2,400 2,64,00 R 200 2,000 4,00,000 S 200 1,200 2,40,000 Total Contribution 12,66,400 Less: Fixed Cost (9,50,000) Profit 3,16,400 Step 6: Unused capacity of X and Z Machine P Q R S Total Units 200 11 200 200 X (Hours) 4,000 132 800 400 5,332 Z (Hours) 4,000 66 400 200 4,666 Machine Available Used Idle X (Hours) 6,000 5,332 668 Z (Hours) 6,000 4,666 1,334

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AMA-Notes 13.4. Just-in-Time System (JIT)

1) Push Approach:

a) The stores purchases Raw Material on reaching re-order level (or) the purchasing time. The Raw Material is issued to the factory when it is required for production. The factory produces at it’s full capacity and transfers the finished goods to the warehouse where it is sold when the demand arises. b) In this approach we don’t purchase Raw Material for requirement and we don’t produce for the demand due to which inventories build up in different stages. c) The Money tied up on these inventories does not increase the throughput. Hence are non value added investments. 2) Pull Approach (JIT System):

a) Here customer orders finished goods which triggers production in the factory which results in Raw Material Purchase. b) As soon as materials are purchased it gets consumed and as soon as production is complete it gets sold. c) Hence, there is no buildup of inventories in the system. 3) Pre-requisites for a JIT System: a) Reliable Supplier – Supplier should be willing to delivery any quantity ordered at the right quality on right time. b) Order and Receiving Facility – Ordering Procedure and Receiving Procedure should be simple and fast (automated) (or) EDI (Electronic Data Interchange) with the supplier. Delivery should be straight away to Machine instead of stores from the supplier. c) Flexible Manufacturing System – The setup time & setup cost should be ‘0’. The cost for producing even ’1’ unit and ‘10,000’ units should be same. d) Production flow based on bottleneck operation (Refer Theory of Constraints_ e) Kanban Card or Machine Cells – ‘Kanban Card’ is a request from Upstream Department to Downstream department to produce and send goods. ‘Machine Cells’ are those which contains the all type of machines for production of a goods. Suppose a product has to be passed through 3 big machines (30,000 capacity) to become finished good, we can have 3 cells with 3 machines (10,000 capacity). This helps in fixation of responsibility very easily. f) Task force rearrangement – People should be capable of doing multi-tasking

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AMA-Notes g) Change in accounting system – We should maintain less books of accounts instead of so many cost control accounts (Backflush Costing). 4) Impact of JIT on Costs: Reduction in Overhead Material Handling, inspection and facilities Most overhead cost becomes Depreciation direct cost due to Machine Cells Electricity Material Handling Consumable and Supplies Repairs and Maintenance Supervision Reduction in inventory carrying Warehouse Rent cost Insurance Obsolete Stores Cost of stores equipments Employee cost of stores department Reduction in capital investment Number of Small machines in place of big machines Reduction in working capital Simplified accounting procedures Backflush Costing

5) Performance Measures in JIT: What are not performance measures Some performance measures

Machine Utilization Piece work wages schemes Inventory Turnover Ratio (COGS/Stock) (Should be very minimum) Setup time reduction (Should be low) Customer complaints (Should be low) Scrap (Should be reduced) Cost of Quality Ideas Generated

Question no 6: The management of Alliance Enterprises recently decided to adopt a just-In-time inventory policy to curb steadily rising costs and free up cash for purposes of investment. The company anticipates that Inventory will decrease from Rs.36,00,000 to Rs.6,00,000, with the released funds to be invested at a 12 percent return for the firm. Additional data are as follows: • Reduced Inventories should produce savings in Insurance and property taxes of Rs.27,000. • Alliance will lease 75% of an existing warehouse to another firm for Rs.2 per square foot. The warehouse has 30,000 square feet. • Because of the need to handle an increased number of small shipments from suppliers, alliance will remodel production and receiving - dock facilities at a cost of Rs.6,00,000. The construction costs will be depreciated over a 10-year life. • A shift in suppliers is expected to result in the purchase and use of more expensive raw materials. However, these materials should give rise to fewer warranty and repair a net savings for the firm of Rs.25,000. • Three employees who currently earn Rs.30,000 each will be directly affected by the just-in-time adoption decision. Two employees will be transferred to other positions with Alliance; one will be

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AMA-Notes terminated. • Reduced raw material inventory levels and accompanying stock outs will cost Alliance Rs.70,000. Required: Compute the annual financial impact of Alliance's decision to adopt a just-in-time inventory system. Solution: Cost – Benefit Analysis: Particulars A) Benefit: Interest on fund released due to reduction of inventories Rental income on warehouse released Savings in Insurance and property tax Reduction in Materials Cost due to supplier change Savings in wages Total Benefit B) Cost: Construction cost Depreciation Stock Out cost Total Cost C) Net Benefit (A – B)

Computation

Amount (Rs.)

(Rs.36,00,000 – Rs.6,00,000) x 12% 3,60,000 30,000 Sq. feet x 75% x Rs.2 Given Given

45,000 27,000 25,000

3 employees x Rs.30,000

90,000 5,47,000

Rs.6,00,000/10 Years Given

60,000 70,000 1,30,000 4,70,000

Since net benefit is positive Just-in-Time should be implemented. Question no 7: Steel Tech ltd., is an automotive supplier that uses automatic screw machines to manufacture precision parts from steel bars. Steel Tech's Inventory of raw steel averages Rs.6,00,000 with a turnover rate of four times per year. John, president of Steel Tech, is concerned about the costs of carrying Inventory. He is considering the adoption of just-in-time inventory procedures in order to eliminate the need to carry any raw steel Inventory. John asked the company's financial controller, to evaluate the feasibility of JIT for the corporation. He has identified the following effects of adopting JIT. • Without scheduling any overtime, lost sales due to stock outs would increase by 35,000 units per year. However, by incurring overtime premiums of Rs.40,000 per year, the increase in lost sales could be reduced to 20,000 units. This would be the maximum amount of overtime that would be feasible for Steel Tech. • Two warehouses presently used for steel bar storage would no longer be needed. Steel Tech rents one warehouse from another company at an annual cost of Rs.60,000. The other warehouse is owned by Steel Tech and contains 12,000 square feet. Three-forth of the space in the owned warehouse could be rented out for Rs.1.50 per square foot per year. • Insurance totaling Rs.14,000 per year would be eliminated. Steel Tech's projected operating result for 2008 are as follows. Long - term capital investments by Steel Tech are expected to produce a rate of return of 20 percent before taxes.

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AMA-Notes STEEL TECH, INC. Budgeted Income Statement For the year ended December 31, 2008 (in thousands) Sales (9,00,000 units) Rs.10,800 Cost of goods sold: Variable Rs.4,050 Fixed Rs.1,450 Rs.5,500 Gross Margin Rs.5,300 Selling and administrative expenses: Variable Rs.900 Fixed Rs.1,500 Rs.2,400 Income before interest and taxes Rs.2,900 Interest expenses Rs.900 Income before taxed Rs.2,000 Required: Calculate the estimated savings or loss for Steel Tech, Ltd that would result in 2008 from the adoption of just-in-time inventory methods. Ignore income taxes. Solution: Step 1: Calculation of contribution per unit Particulars Sales -Variable cost of goods sold -Variable selling and administrative expenses Contribution

Amount (Rs.) 1,08,00,000 -40,50,000 -15,00,000 58,50,000

Rs.58,50,000

Contribution per unit = 9,00,000 Units = Rs.6.5 Step 2: Viability of Overtime

Recommended to work overtime because benefit exceeds costs. Step 3: Just-in-Time Cost Benefit Analysis Particulars A) Benefit: Interest saved due to reduction in inventory E M Reddy

Computation

Amount (Rs.)

Rs.6,00,000 x 20%

1,20,000 Page | 380

AMA-Notes Rent Saved in Warehouse Rental Income on Warehouse space released Savings in Insurance Total Benefit B) Cost: Stock Out Cost Overtime Premium Total Cost C) Net Benefit (A – B)

Given 60,000 12,000 Sq. feet x 3/4 x Rs.1.5 13,500 Given 14,000 2,07,500 25,000 Units x Rs.6.5 Given

1,30,000 40,000 1,70,000 37,500

It is recommended to implement Just-In-Time system and also work to overtime to reduce stock outs arising due to Just-in-Time. 13.5. Backflush Costing 13.5.1. Backflush Costing – Version 1

Question no 8: Road warrior corporation, assembles hand-held computers that have scaled-down capabilities of laptop computers. Each hand-held computer takes 6 hours to assemble. Road warrior uses a JIT production system and a back flush costing system with three trigger points:  Purchase of direct (Raw) materials  Completion of finished units of product  Sale of finished goods There are no beginning inventories of materials or finished goods. The following data are for August 2008: Direct (raw) materials purchased Rs.27,54,000 Direct (raw) materials used Rs.27,33,600 Conversion cost incurred Rs.7,23,600 Conversion cost allocated Rs.7,50,400 Road warrior records direct materials purchased and conversion costs incurred at actual costs. When finished goods are sold, the back flush costing system “pulls through” standard direct materials costs (Rs.102 per unit) and standard conversion costs (Rs.28 per unit). It produced 26,800 finished goods units in Augusts 2008 and sold 26,400 units. The actual direct material cost per unit in August 2008 was Rs.102 while the actual conversion costs per unit was Rs.27. Required: Prepare necessary ledger accounts for August 2008. Solution: Raw Material and In-process Control A/c Particulars Amount (Rs.) To Cash 27,54,000 Total Finished Goods Control A/c Particulars E M Reddy

27,54,000 Amount (Rs.)

Particulars By FG A/c (26,800 Units x Rs.102) By Closing Balance Total Particulars

Amount (Rs.) 27,33,600 20,400 27,54,000 Amount (Rs.) Page | 381

AMA-Notes To RM A/c (26,800 Units x Rs.102) To CC A/c (26,800 Units x Rs.28) Total

27,33,600 7,50,400 34,84,000

Cost of Sales A/c Particulars To FG A/c (26,400 Units x Rs.130) Total

Amount (Rs.) Particulars 34,32,000 By Costing P&L a/c 34,32,000 Total

Conversion Cost A/c (Wages & Overheads) Particulars Amount (Rs.) To Cash 7,23,600 To Costing P&L a/c Total

26,800 7,50,400

By Cost of Sales a/c By Closing Balance Total

34,32,000 52,000 34,84,000 Amount (Rs.) 34,32,000 34,32,000

Particulars By FG A/c (26,800 Units x Rs.28)

Amount (Rs.) 7,50,400

Total

7,50,400

13.5.2. Backflush Costing – Version 2

Assume the same facts in question no 5, except for the following change. Road Warrior Corporation, now used a back flush costing system with the following two trigger points:  Purchase of direct (raw) materials  Sale of finished goods. The inventory control account here will include direct materials purchased but not yet in production, materials in work in process, and materials in finished goods but not sold. No conversion costs are inventoried. Any under-or over allocated conversion costs are written off monthly to costing P&L account. Required: Prepare necessary ledger accounts for August 2008. Solution: Raw Material and In-process Control A/c Particulars Amount (Rs.) To Cash 27,54,000 Total Cost of Sales A/c Particulars To RM A/c (26,400 Units x Rs.102) To CC A/c (26,400 Units x Rs.102) Total

27,54,000

Amount (Rs.) Particulars 26,92,800 By Costing P&L a/c 7,39,200 34,32,000 Total

Conversion Cost A/c (Wages & Overheads) Particulars Amount (Rs.) To Cash 7,23,600 To Costing P&L a/c

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Particulars By COS A/c (26,400 Units x Rs.102) By Closing Balance Total

Particulars By COS A/c (26,400 Units x Rs.28)

Amount (Rs.) 26,92,800 61,200 27,54,000 Amount (Rs.) 34,32,000 34,32,000 Amount (Rs.) 7,39,200

15,600

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AMA-Notes Total

7,50,400

Total

7,50,400

13.5.3. Backflush Costing – Version 3

Assume the same facts in question no 5, except now Road Warrior uses only two trigger points, the completion of finished unit of product and the sale of finished goods. Any under or over allocated costs are written off monthly to costing P&L account. Required: Prepare necessary ledger accounts for August 2008. Solution: Finished Goods Control A/c Particulars To Cash A/c (26,800 Units x Rs.102) To CC A/c (26,800 Units x Rs.28)

Amount (Rs.) 27,33,600

Particulars By Cost of Sales a/c

Amount (Rs.) 34,32,000

7,50,400

By Closing Balance (400 Units x Rs.130) Total

52,000

Total

34,84,000

Cost of Sales A/c Particulars To FG A/c (26,400 Units x Rs.130) Total

Amount (Rs.) Particulars 34,32,000 By Costing P&L a/c 34,32,000 Total

Conversion Cost A/c (Wages & Overheads) Particulars Amount (Rs.) To Cash 7,23,600 To Costing P&L a/c Total

26,800 7,50,400

34,84,000

Amount (Rs.) 34,32,000 34,32,000

Particulars By FG A/c (26,800 Units x Rs.28)

Amount (Rs.) 7,50,400

Total

7,50,400

Notes: 1) Traditional Costing System meticulously traces the various cost items into inventories. The system ensures high degree of inventory control. 2) The Traditional Costing System operates with 4 trigger points. A trigger point is an event which makes cost accounting system to pass journal entries. 3) The 4 trigger points are: a) Purchase of Raw Materials b) Issue for Production c) Completion of Finished Goods d) Sale of Finished Goods The accounts maintained are Raw Material Control A/c, WIP Control A/c, Finished Goods Control A/c and Cost of Sales A/c.

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AMA-Notes 4) Companies operating Just-In-Time (JIT) system ideally will have no inventories (or) very negligible inventory. Hence there is no necessity to have an elaborate cost accounting system that traces costs to the stocks and control stocks. A simplified is called ‘Backflush Costing System’. 5) There are 3 versions in Backflush Costing System:

Version 1

Version 2

Version 3

3 Trigger Points: a) Purchase of Raw Materials b) Completion of Finished Goods c) Sale of Finished Goods

2 Trigger Points: a) Purchase of Raw Materials b) Sale of Finished Goods

2 Trigger Points: a) Completion of Finished Goods b) Sale of Finished Goods

Accounts: a) Raw Material & In process A/c b) Finished Goods A/c c) Cost of Sales A/c There is no WIP A/c

Accounts: a) Raw Material & In process A/c c) Cost of Sales A/c There is no Finished Goods A/c & WIP A/c

Accounts: a) Finished Goods A/c c) Cost of Sales A/c There is no Raw Material A/c & WIP A/c

6) In Version 1 Consumption of Raw Materials and charging of Conversion Cost happens not during Production bure recognized only on completion of goods. The completed goods pulls the Standard Cost of Raw Materials Consumed & Conversion Cost into Production. 7) In an ideal Just-In-Time System there should be no Price Variance because negotiation with supplier happens at the beginning of the period itself. There should also be no usage variance because in Just-InTime System there is no time available to re-work Scrap & Defectives. Still if it arises a separate Scrap Reporting System should capture it and transfer to Abnormal Loss Account. 8) In Version 3 the suppliers are paid only for standard consumption. Any excess consumption reported in scrap reporting system should be analyzed with reasons. If it is due to poor quality Raw Material the supplier will not be paid and if it is due to other reasons they will be paid and the cost booked to Abnormal Loss a/c. 9) In Version 1 the Rs.20,400 closing balance of Raw Material represents “Raw Material as Raw Material & Raw Material in Work-in-Progress”. In Version 2 the Rs.61,200 Raw Material closing balance represents “Raw Material as Raw Material, Raw Material in Work-in-Progress and Raw Material in Finished Goods”.

10) Conversion Cost treatment differs between the versions: a) Version 1 & Version 3 → Treated as Product Cost → Expires only to the extent of Cost of Goods Sold b) Version 2 → Treated as Period Cost → Expires Fully E M Reddy

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AMA-Notes 11) The above can be understood as follows (Version 1 & Version 3):

In Version 1 & Version 3, the conversion cost debited net to costing P&L is Rs.7,12,400 (Rs.7,39,200 – Rs.26,800). The balance transferred to next year. 12) The above can be understood as follows (Version 2):

Thus the entire Rs.7,23,600 gets debited in current year’s costing P&L and no part of it is inventoried and transferred to next year. Question no 9: Little field company uses a backflush costing system with three trigger points:  Purchase of Direct Material  Completion of good finished units of product  Sale of finished goods There are no beginning inventories. Information for March 2008 is: Direct Material Purchased Rs.4,40,000 Conversion Cost Allocated Rs.2,00,000 Direct Material Used Rs.4,25,000 Cost transferred to finished goods Rs.6,25,000 Conversion Cost Incurred Rs.2,11,000 Cost of goods sold Rs.5,95,000 Required: 1. Prepare journal entries for April [without disposing of under allocated or over allocated conversion cost]. Assume there are no direct materials variances. 2. Under an ideal JIT production system, how would the amounts in your journal entries differ for the journal entries in requirement 1. Solution: Part 1:

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AMA-Notes Particulars To Cash Total

Raw Material and In-process Control A/c Amount (Rs.) Particulars 4,40,000 By Finished Goods a/c By Closing Balance 4,40,000 Total

Particulars To RM & In process control a/c To Conversion Cost a/c Total Particulars To Finished Goods a/c Total Particulars To Cash Total

Amount (Rs.) 4,25,000 15,000 4,40,000

Finished Goods Control A/c Amount (Rs.) Particulars 4,25,000 By Cost of Sales a/c 2,00,000 By Closing Balance 6,25,000 Total

Amount (Rs.) 5,95,000 30,000 6,25,000

Cost of Sales A/c Amount (Rs.) Particulars 5,95,000 By Costing P&L a/c 5,95,000 Total

Amount (Rs.) 5,95,000 5,95,000

Conversion Cost A/c (Wages & Overheads) Amount (Rs.) Particulars 2,11,000 By Finished Goods a/c By Closing Balance (Under absorption) 2,10,000 Total

Amount (Rs.) 2,00,000 11,000 2,10,000

Part 2: Journal entries under an ideal Just-in-Time System Step 1: Calculation of Cost of Production and materials purchased 1) Ideal Just-in-time system will have no inventories (Raw Material or Finished Goods). 2) If finished goods inventory has to be ‘nil’ then cost of finished goods produced should be equal to cost of goods sold. Cost of Finished Goods Produced = Rs.5,95,000 Rs.4,25,000

a) Raw Material Used → Rs.5,95,000 x Rs.6,25,000 = Rs.4,04,600 Rs.2,00,000

b) Conversion Cost Allocated → Rs.5,95,000 x Rs.6,25,000 = Rs.1,90,400 3) When Raw Material stock has to be ‘nil’ then Raw Material used should be equal to Raw Material purchased i.e. Rs.4,04,600 Step 2: Preparation of Ledger Accounts Raw Material and In-process Control A/c Particulars Amount (Rs.) Particulars To Cash 4,04,600 By Finished Goods a/c Total 4,40,000 Total Particulars To RM & In process control a/c To Conversion Cost a/c Total

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Finished Goods Control A/c Amount (Rs.) Particulars 4,04,600 By Cost of Sales a/c 1,90,400 5,95,000 Total

Amount (Rs.) 4,04,600 4,40,000 Amount (Rs.) 5,95,000 5,95,000

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AMA-Notes Particulars To Finished Goods a/c Total Particulars To Cash Total

Cost of Sales A/c Amount (Rs.) Particulars 5,95,000 By Costing P&L a/c 5,95,000 Total Conversion Cost A/c (Wages & Overheads) Amount (Rs.) Particulars 2,11,000 By Finished Goods a/c By Closing Balance (Under absorption) 2,10,000 Total

Amount (Rs.) 5,95,000 5,95,000 Amount (Rs.) 1,90,4000 20,600 2,10,000

13.6. Total Quality Management (TQM)

1) Quality is what differentiates our product from others. 2) “Quality in Design” & “Quality in Performance” gives total quality of a given product (or) service. 3) Quality is a commitment given by a chance and the commitment is not compulsory. The quality commitment given once should be adhered. 4) Quality costs are those costs which are incurred by the company to adhere to it’s quality commitment. 5) There are 4 types of quality costs: a) Preventive Cost → Prevention costs are those costs incurred to prevent below quality goods from being purchased or produced. E.g.; - Quality training program given to employees b) Appraisal Cost → Appraisal cost is the cost spent to check whether the units produced (or) units purchased to adhered (or) confirmed the quality. E.g.; - Inspection Cost c) Internal failure Cost → Internal failure cost if the cost of producing a defective product before it reaches the customers. E.g.; - Rectification Cost → Curative in Nature d) External failure Cost → External failure cost if the cost of producing a defective product after it reaches the customers. E.g.; - Warranty Cost → Curative in Nature Question no 10: Calton Ltd. Makes and sell a single product. The existing product unit specifications are as follows: Direct Material X: 8 sq. meters at Rs.4 per sp. Meter Machine time: 0.6 running hours Machine cost per gross hour: Rs.40 Selling Price: Rs.100 Calton Ltd., require fulfilling orders for 5,000 product units per period. There are no stocks of product units at the beginning or end of the period under review. The stock level of material X remains unchanged throughout the period. The following additional information affects the costs and revenues: 1. 5% of incoming material from suppliers is scrapped due to poor receipt and storage organization. 2. 4% of material X input to the machine process is wasted due to processing problems. 3. Inspection and storage of material X costs Rs.0.10 paisa per sq. meter purchased. 4. Inspection during the production cycle, calibration checks on inspection equipment, vendor rating and other checks costs Rs.25,000 per period.

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AMA-Notes 5. Production quantity is increased to allow for the downgrading of 12.5% of product units at the final inspection stage. Downgraded units are sold as 'second quality' units at a discount of 30% on the standard selling price. 6. Production quantity is increased to allow for returns from customers which are replaced free of charge. Returns are due to specification failure and account for 5% of units initially delivered to customers. Replacement units incur a delivery cost of Rs.8 per unit. 80% of the returns from customers are rectified using 0.2 hours of machine running time per unit and are re-sold as ‘third quality’ products at a discount of 50% on the standard selling price. The remaining returned units are sold as scrap for Rs.5 per unit. 7. Product liability and other claims by customers is estimated at 3% of sales revenue from standard product sales. 8. Machine idle time is 20% of gross machine hours used (i.e. running hours = 80% of gross hours). 9. Sundry costs of administration, selling and distribution total Rs.60,000 per period. 10. Calton Ltd is aware of the problem of excess costs and currently spends Rs.20,000 per period in efforts to prevent a number of such problems from occurring. Calton Ltd. is planning a quality management programme which will increase its excess cost prevention expenditure from Rs.20,000 to Rs.60,000 per period. It is estimated that this will have the following impact. 1. A reduction in stores losses or material X to 3% of incoming material. 2. A reduction in the downgrading of product units at Inspection to 7.5% of units inspected. 3. A reduction in material X losses in process to 2.5% of input to the machine process. 4. A reduction in returns of products from customers to 2.5% of units delivered. 5. A reduction in machine idle time to 12.5% of gross hours used. 6. A reduction in product liability and other claims to 1% of sales revenue from standard product sales. 7. A reduction in inspection, calibration, vendor rating and other checks by 40% of existing figure. 8. A reduction in sundry administration, selling and distribution costs by 10% of the existing figure. 9. A reduction in machine running time required per product unit to 0.5 hours. Required: (a) Prepare summaries showing the calculation of (i) total production units (pre-Inspection), (ii) purchases of material X (sq. meters), (iii) gross machine hours. In each the figures are required for the situation both before and after the implementation of the additional quality management programme, in order that the orders for 5,000 product units may be fulfilled. (b) Prepare profit and loss account for Calton Ltd for the period showing the profit earned both before and after the implementation of the additional quality management programme. (c) Comment on the relevance of a quality management programme and explain the meaning of the terms Internal failure costs, appraisal costs and prevention costs giving examples for each, taken where possible from the information in the question. Solution: Step 1: Calculation of Production Units Particulars

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Before (Units)

After (Units)

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AMA-Notes Demand 5,000 5,000 Add: Returns 250 (5,000 x 5%) 125 (5,000 x 2.5%) Post Inspection Production 5,250 5,125 Add: Downgrading 750 (5,250/87.5x12.5) 416 (5,125/92.5x7.5) Pre Inspection Production 6,000 5,541 Step 2: Raw Materials Purchases in Meters Particulars Before (Sq. Mts.) After (Sq. Mts.) Requirements 48,000 (6,000 x 8) 44,328 (5,541 x 8) Add: Process Loss 2,000 (48,000/96x4) 1,137 (44,328/97.5x2.5) Input 50,000 45,465 Add: Loss on receipt 2,632 (50,000/95x5) 1,406 (45,465/97x3) Purchase of Raw Materials 52,632 46,871 Step 3: Gross Machine Hours Particulars Before (Hours) After (Hours) Running Hours 3,600 (6,000 x 0.6) 2,771 (5,541 x 0.5) Add: Rectification time 40 (250 x 80% x 0.2) 20 (125 x 80% x 0.2) Total Running Hours 3,640 2,791 Add: idle time 910 (3,640/80x20) 399 (2,791/87.5x12.5) Gross Machine Hours 4,550 3,190 Step 4: Income before and after the production Particulars Before (Rs.) After (Rs.) A. Revenues First Quality 5,00,000 (5,000 x 100) 5,00,000 (5,000 x 100) Second Quality 52,500 (750 x 70) 29,120 (416 x 70) Third Quality 10,000 (250 x 80% x 50) 5,000 (125 x 80% x 50) Scrap Sales 250 (250 x 20% x 5) 125 (125 x 20% x 5) Total 5,62,750 5,34,245 B. Cost Material 2,10,528 (52,632 x 4) 1,87,484 (46,871 x 4) Machine running cost 1,82,000 (4,550 x 40) 1,27,600 (3,190 x 40) Inspection Cost 5,263 (52,632 x 0.10) 4,687 (46,871 x 0.10) Vendor Rating 25,000 15,000 (25,000 x 60%) Delivery Cost 2,000 (250 x 8) 1,000 (125 x 8) Product liability claims 15,000 (5,00,000 x 3%) 5,000 (5,00,000 x 1%) Administration & Other expenses 60,000 54,000 (60,000 x 90%) Quality Program Cost 20,000 60,000 Total Cost 5,19,791 4,54,771 C. Profit 42,959 79,474 It is recommended to go for enhanced quality control program. Step 4: Examples for different quality costs

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AMA-Notes Quality Costs Prevention Cost Appraisal Cost Internal Failure Cost External Failure Cost

Example Quality Program Cost Inspection Cost Cost spent on downgraded units Liability Claims

Question no 11: TQ Ltd implemented a quality programme and had the following results: Particulars 2007 2008 Rs. in ‘000s Sales 6,000 6,000 Scrap 600 300 Rework 500 400 Production Inspection 200 240 Product Warranty 300 150 Quality Training 75 150 Material Inspection 80 60 You are required to: 1. Classify the quality costs as prevention, appraisal, internal failure and external failure and express each class as a percentage of sales. 2. Compute the amount of increase in proms due to quality Improvement. Solution: Particulars

2007 % Amount 100 6,000

A. Sales B. Cost 1. Prevention Cost Quality Training 1.25 2. Appraisal Cost Production Inspection 3.33 Material Inspection 1.33 Total 4.66 3. Internal failure Cost Scrap 10 Rework 8.33 Total 18.33 4. External failure Cost Product Warranty 5 Total Cost (1 + 2 + 3 + 4) 29.25 C. Profit 70.75

2008 % Amount 100 6,000

75

2.5

150

200 80 280

4 1 5

240 60 300

600 500 1,100

5 6.67 11.67

300 400 700

300 1,755 4,245

2.5 21.67 78.33

150 1,300 4,700

1) In 2007 the company spent 5.91% in prevention and appraisal cost resulting in a spending of 23.33% on failure costs. 2) In 2008 it increased the spending on prevention and appraisal cost to 7.5% resulting in reduction of failure costs to 14.17%.

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AMA-Notes Question no 12: X video company sells package of blank video tapes to its customers. It purchases video tapes from Y Tape Company @ Rs.140 a packet. Y Tape Company pays all freight to X video company. No incoming inspection is necessary because Y Tape Company has a superb reputation for delivery of quality merchandise. Annual demand of X video company is 13,000 packages. X video company requires 15% annual return on investment. The purchase order lead time is two weeks. The purchase order is passed through internet and it costs Rs.2 per order. The relevant material handling, insurance cost etc. is Rs.3.10 per package per year. X video company has to decide whether or not to shift to JIT purchasing. Y Tape Company agrees to deliver 100 packages of video tapes 130 times per year (5 times every two weeks) instead of existing delivery system of 1,000 packages 13 times a year with additional amount of Rs.0.02 per package. X video company incurs no stock out under its current purchasing policy. It is estimated X video company incurs stock out cost on 50 video tape packages under a JIT purchasing policy. In the event of stock out X video company has to rush order tape packages which costs Rs.4 per package. Required: Comment whether X video company should implement JIT purchasing system. Z Co. also supplies video tapes. It agrees to supply at Rs.136 per package under JIT delivery system. If video tape purchased from Z Co. relevant carrying cost would be Rs.3 per package against Rs.3.10 in case of purchasing from Y tape company. However, Z Co. does not enjoy so sterling reputation for quality. X video Co. anticipates the following negative aspects of purchasing tapes from Z Co. (a) To incur additional inspection cost of 5 paisa per package. Average stock out of 360 tapes package per year would occur largely resulting from late deliveries. Z Co. cannot rush order at short notice. X Video Co. anticipates lost contribution margin per package of Rs.8 from stock out. (b) Customer would likely return 2% of all packages due to poor quality of the tape and to handle this return an additional cost of Rs.25 per package. Required: Comment whether X Video Co. places order to Z Co. Solution: Part 1: Existing vs. Just-in-Time System Step 1: Total Annual Cost under existing system Particulars Purchase Cost Ordering Cost Interest Cost Material Handling Cost

Computation Amount (Rs.) 13,000 Packs x Rs.140 18,20,000 13 Orders x Rs.2 26 1,000 Packs x ½ x Rs.140 x 15% 10,500 1,000 Packs x ½ x Rs.3.10 1,550 Total Cost 18,32,076

Step 2: Total Annual Cost under Just-in-Time system Particulars Purchase Cost Ordering Cost Interest Cost Material Handling Cost E M Reddy

Computation Amount (Rs.) 13,000 Packs x Rs.140.02 18,20,260 130 Orders x Rs.2 260 100 Packs x ½ x Rs.140.02 x 15% 1,050 100 Packs x ½ x Rs.3.10 155 Page | 391

AMA-Notes Stock out Costs

50 Packs x Rs.4 Total Cost

200 18,21,925

It is recommended to shift to Just-in-Time purchasing since there is a reduction in cost. Part 2: Calculation of annual cost due to Just-in-Time purchase with Z Particulars Computation Amount (Rs.) Purchase Cost 13,000 Packs x Rs.136 17,68,000 Ordering Cost 130 Orders x Rs.2 260 Interest Cost 100 Packs x ½ x Rs.136 x 15% 1,020 Material Handling Cost 100 Packs x ½ x Rs.3 150 Stock out Costs 360 Packs x Rs.8 2,880 Inspection Cost 13,000 Packs x Rs.0.05 1,650 Return Cost 13,000 Packs x 2% x Rs.25 6,500 Total Cost 17,79,460 It is recommended to go for supplier Z in spite of poor quality due to reduction in cost. However nonfinancial aspect like brand value erosion etc., should be considered while making the decision. Question no 13: Classify the following items under appropriate categories of quality cost viz. Prevention Costs, Appraisal Costs, Internal Failure Costs and External Failure Costs: (i) Rework (ii) Disposal of scrap (iii) Warranty Repairs (iv) Revenue loss (v) Repair to manufacturing equipment (vi) Discount on defective sale (vii) Raw material inspection (viii) Finished product Inspection (ix) Establishment of quality circles (x) Packaging inspection Solution: Particulars (i) Rework (ii) Disposal of Scrap (iii) Warranty Repairs (iv) Revenue Loss (v) Repair to Manufacturing Equipment (vi) Discount on Defective Sale (vii) Raw Material Inspection (viii) Finished Product Inspection (ix) Establishment of Quality Circles (x) Packaging Inspection

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Classification Internal Failure Cost Internal Failure Cost External Failure Cost Internal Failure Cost Internal Failure Cost Internal Failure Cost Appraisal Cost Appraisal Cost Prevention Cost Appraisal Cost

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AMA-Notes 13.7. Life Cycle Costing (LCC)

1) The Product life cycle is classified as follows: a) Infinite Phase b) Growth Phase c) Maturity Phase d) Decline Phase 2) Infinite Phase a) It is the phase where the product is getting introduced (or) developed. b) Revenue will be very less in this phase when compared to cost. c) In this phase Fixed Overhead Cost & R&D cost are more and variable costs are less. d) The Product will be reporting losses at this infant phase. 3) Growth Phase a) It is the phase where the market share of a product rapidly increases. b) Revenue growth is high. c) Marketing cost and variable costs are very high and fixed cost is recovered. 4) Maturity Phase a) In this phase the product marker share grows at declining rate. b) Company builds-up loyal customers and company will have stable market share. c) Costs are mostly heavy manufacturing costs and moderate marketing cost. d) This is the longest phase in most of the products life cycles. 5) Decline Phase a) In this phase the company share gets reduced b) The company should try to extend the product life through some cost reduction techniques. Another way of understanding the product life cycle: 1) Stages in Product Life Cycle i) Market Research Product is a bundle of features that customer wants. Company should do the market research and should understand the customer needs. ii) Design Based on the customer requirements the company should design the product. The company should redesign the product to make it feasible for manufacturing. iii) Development Based on the design the product is developed and the design is freeze at the end of development stage. iv) Prototype Prototype means a model of the product and do simulation, testing under real conditions by doing marketing etc., v) Commissioning Once the prototype is working effectively, all the infrastructure costs are incurred (PreManufacturing Costs). vi) Manufacturing vii) Marketing viii) Distribution

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AMA-Notes ix) Customer Support x) Decommissioning Costs incurred to exit the market. Question no 14: Destin Products makes digital watches. Destin is preparing a product life-cycle budget for a new watch, MX3. Development on the new watch is to start shortly. Estimates about MX3 are as follows: Life-cycle units manufactured and sold 4,00,000 Selling price per watch Rs.40 Life-Cycle Costs: R&D and design costs Rs.10,00,000

Manufacturing:

Variable costs per watch Variable costs per batch Watches per batch Fixed Costs

Rs.15 Rs.600 500 Rs.18,00,000

Variable costs per batch Fixed Costs

Rs.3.20 Rs.10,00,000

Marketing:

Distribution:

Variable cost per batch Rs.280 Watches per batch 160 Fixed Costs Rs.7,20,000 Customer-service costs per watch Rs.1.50 Ignore the time value of money. Required: 1) Calculate the budgeted life-cycle operating income for the new watch. 2) What percentage of the budgeted total product life-cycle costs at the end of the R&D and design stages will incur? 3) An analysis reveals that 80% of the budgeted total product life-cycle costs of the new watch will be locked in at the end of the R & D and design stages. What implications do these findings have for managing MX3's costs? 4) Destin's Market Research Department estimates that reducing MX3's price by Rs.3 will increase life-cycle unit sales by 10 percent. If unit sales increase by 10%, Destin plans to increase manufacturing and distribution batch sizes by 10% as well. Assume that all variable costs per watch, variable costs per batch, and fixed costs will remain the same. Should Destin reduce MX3's price by Rs.3? Show your calculations. Solution: Part 1: Budgeted Life Cycle Income Statement Particulars A. Revenues Sales B. Cost R&D Design Cost

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Computation 4,00,000 Watches x Rs.40 Given

Amount (Rs.) 1,60,00,000 10,00,000

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AMA-Notes Variable Manufacturing Cost (Unit Level) 4,00,000 Watches x Rs.15 Variable Manufacturing Cost (Batch Level) 4,00,000 Watches/500 x Rs.600 Fixed Manufacturing Costs Given Variable Marketing Cost (Unit Level) 4,00,000 Watches x Rs.3.20 Fixed Marketing Cost Given Variable Distribution Cost (Batch Level) 4,00,000 Watches/160 x Rs.280 Fixed Distribution Cost Given Customer Service Cost (Unit level) 4,00,000 Watches x Rs.1.50 Total Cost C. Budgeted Life Cycle Income (A – B)

60,00,000 4,80,000 18,00,000 12,80,000 10,00,000 7,00,000 7,20,000 6,00,000 1,35,80,000 24,20,000

Part 2: Concept of Locked in Cost % of R&D Cost to total cost =

Rs.10,00,000 Rs.1,35,80,000

= 7.36%

1) R&D cost constitutes just 7.36% of the total life cycle cost. Hence it is not a major activity like manufacturing, marketing etc., Is it true? 2) It is not, because at the end of R&D the company commits itself to a given type of production facility, a required labour time, a raw material of a given quality and a particular marketing strategy. 3) All these costs may be spent tomorrow but is locked at the end of R&D stage itself. In this problem 80% of the cost is locked. 4) A poor R&D activity will result in negligible cost reduction possibility for the remaining 80% of cost. 13.8. Target Costing

Question no 15: For many years, Leno Corporation has used a straightforward cost-plus pricing system, marking its goods up approximately 25 percent of total cost. The company has been profitable; however, it has recently lost considerable business to foreign compellers that have become very aggressive in the marketplace. These firms appear to be using target costing. An example of Leno's problem is typified by Item no. 8976, which has the following unit-cost characteristics: Direct Material Rs.30 Direct Labour 75 Manufacturing Overhead 50 Selling and administrative expenses 25 The going market price of an Identical product of comparable quality is Rs.195, which is significantly below what Leno is charging. Required: 1) Contrast cost-plus pricing and target costing. Which of the two approaches could be aptly labeled price-led costing? Why? 2) What is Leno's current selling price of item no.8976 3) If Leno used target costing for item no.8976, what must happen to costs if the company desires to meet the market price and maintain its current rate of profit on sales? By how much? 4) Would the identification of value-added and non-value added costs assist Leno in this situation? Briefly explain.

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AMA-Notes 5) Suppose that by previous cost-cutting drives, costs had already been "pared to the bone" on Item no.8976. What might Leno be forced to do with its markup on cost to remain competitive? By how much? Solution: Step 1: Calculation of Leno’s current selling price Particulars Amount (Rs.) Product Cost 180 Add: Markup (Rs.180 x 25%) 45 Selling Price 225 Step 2: Target Cost 1) If Leno adopts cost plus pricing and sells the product at Rs.225 the following things happens: a) The Demand reduces because of higher price b) The unit cost increases because the same fixed cost is shared by fewer units. c) When the unit cost increases the selling price increases due to cost plus pricing. d) Which further triggers demand drop and this becomes vicious cycle. e) After some time, the product will be pushed out of the market. 2) An alternative is to go for target costing where the equation becomes Target Cost = Selling Price – Profit 3) This is not change in equation but the change in attitude. Target costing recopies that selling price is market determined and company has no control over it but what can be really controlled is cost. 4) Cost plus pricing is cost led pricing but target costing is price led costing. 5)

Particulars Amount (Rs.) Market determined price 195 Less: Markup (Rs.195 x 20%) 39 Target Cost 156

Step 3: Value Engineering 1) The company should try to reduce the current cost of Rs.180 to Rs.156 i.e. the target cost reduction is Rs.24 (Rs.180 – Rs.156). 2) To do this it should start value engineering program. Value engineering is a process through which the costs are classified as value added and non-value added. 3) Value engineering process has 2 aspects: a) Design engineering → A design of a product is nothing but bundle of features which can be classified into 2: i. Function features → Defined the utility of the product and is always value added. ii. Aesthetic features → Adds appeal to the product and is value added only when customer is willing to pay for it. b) Process engineering → Once design is finalized analyses the production and selling process and eliminate the non-value added process. This can be done when the company continuously seeks to improve it’s process which is called “Kaizen Approach”.

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AMA-Notes 4) When non-value added features are eliminated the activities required to have those features can be avoided thereby saving Activity Based Cost (ABC). To know how much, we saved we required Activity Based Costing (ABC) System. Same for process engineering also. 5) Even after value engineering i.e. after the cost is “pared to the bone”, still target cost not achieved then the company has to compromise on margin. Even after that if target cost could not be achieved the company should quit the market but never should be increased the selling price, otherwise it would be pushed out of the market. Question no 16: Danish Furniture (DF) manufactures easy-to-assemble wooden furniture for home and office. The firm is considering modification of a table to make it more attractive to individuals and businesses. The table is small, can be used to hold a computer printer or a fax machine, and has several shelves for storage. The company's marketing department surveyed potential buyers of the table regarding five proposed modifications. The 200 survey participants were asked to evaluate the modifications by using a five-point scale that ranged from 1 (strongly disagree) to 5 (strongly agree). Their responses, along DF's related unit costs for the modifications, follow. 1 2 3 4 5 Strongly Dis- Neutral Agree Strongly Disagree agree Agree Add cabinet doors in storage (Rs.6.00) 10 20 30 60 80 Expand storage area (Rs.2.50) 10 40 70 50 30 Add security lock to storage area (Rs.1.65) 30 60 50 40 20 Give table top a more rich, marble appearance 10 20 50 60 60 (Rs.4.25) Extend warranty to five years (Rs.1.50) 40 70 30 35 25 The table currently costs Rs.64 to produce and distribute and DFs selling price for this unit averages Rs.80. The current selling price for these tables with all or some or the aforesaid features averages Rs.95. Required: 1. Why is there a need in target costing to (a) focus on the customer and (b) have a marketing team become involved with product design? 2. DF's marketing team will evaluate the survey responses by computing a weighted-average rating of each of the modifications. This will be accomplished by weighting (multiplying) the point values (1, 2, etc.) by the frequency of responses, summing the results, and dividing by 200. Rank the popularity of the five modifications using this approach. 3. Management desires to earn approximately the same rate of profit on sales that is being earned with the current design. a. If DF uses target costing and desires to meet the current competitive selling price, what is the maximum cost of the modified table? b. Which of the modifications should DF consider? 4. Assume that DF wanted to add a modification or two that you excluded in your answer to requirement 3(b). What process might management adopt to allow the company to make its target profit for the table? Briefly explain. Solution: Step 1: Calculation of the desired profit margin for DF

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AMA-Notes Current Selling Price = Rs.80 Less: Cost = Rs.64 Profit = Rs.16 16

% of profit on Selling Price = 80 = 20% 16

% of profit on Cost = 64 = 25% Step 2: Calculation of target cost of modified table Market determined selling price Less: Desired margin @ 20% Target cost of modified table

= Rs.95 = Rs.19 = Rs.76

Step 3: Ranking the modifications based on the customer preferences 1) Current cost is Rs.64 and target cost is Rs.76. Hence the company can maximum spent Rs.12 towards modification. 2) It is not possible to have all modifications within Rs.12. Hence only some of them can be added. 3) What should be selected depends on the customer preferences obtained through the survey of 200 customers. 4) Ranking the customer preferences based on weights: Modification Computation Weighted Point Rank (10x1)+(20x2)+(30x3)+(60x4)+(80x5) Cabinet Doors 3.9 I Storage Area

200 (10x1)+(40x2)+(70x3)+(50x4)+(30x5)

3.25

III

Security Lock

200 (30x1)+(60x2)+(50x3)+(40x4)+(20x5)

2.8

IV

Rich Appearance

200 (10x1)+(20x2)+(50x3)+(60x4)+(60x5)

3.7

II

Extended Warranty

200 (40x1)+(70x2)+(30x3)+(35x4)+(25x5)

2.67

V

200

Step 4: Selection of modification within available Rs.12 cost Modification Cost (Rs.) Cumulative Cost (Rs.) Cabinet Doors 6.00 6.00 Rich Appearance 4.25 10.25 Storage Area Not Possible 10.25 Security Lock 1.65 11.9 The company should select the following features namely Cabinet Doors, Rich Appearance and Security Lock. Step 5: Strategy to include all features 1) To include the remaining 2 features, we need to spend Rs.7.6 but we already have Rs.0.1 and needs to reduce the cost by Rs.7.5. 2) This can be done by value engineering. (See previous question for notes) 3) Still if target cost reduction is not achieved compromise on margin. Never should selling price be increased.

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AMA-Notes Question no 20: Vijay associates, a small structural design firm prepares architectural drawings for various clients to ensure the structural safety of buildings. The architectural plans are then submitted to local government departments for approval. Vijay’s income statement for 2001 follows: Revenues Rs.6,80,000 Salaries of professional staff (8,000 Hours x Rs.50 per hour) Rs.4,00,000 Travel Rs.18,000 Administration and support Rs.1,60,000 Total Costs Rs.5,78,000 Operating Income Rs.1,02,000 An analysis of the parentage of time spent by professional staff on various activities gives this data: Doing calculations and preparing drawings for clients 75% Checking calculations and drawings 4% Correcting errors found in drawings (not billed to clients) 7% Making changes in response to client requests (billed to clients) 6% Correction errors to meet government building code requirements (not billed to clients) 8% Total 100% Assume administration and support costs vary with professional labour costs. Required: Consider each requirement independently. There is no connection between the requirements. 1. How much of the total costs in 2001 are value-added, non-value-added, or in the gray area in between? Explain your answers briefly what act ions can Vijay take to reduce its costs? 2. Suppose Vijay continued to check all calculations and drawings but, could eliminate all errors so that it did not need to spend any time making corrections and, as a result could proportionately reduce professional labour costs. Calculate Vijay's operating Income. 3. Now suppose Vijay could take on as much business as it could get done, but it could not add more professional staff. Assume, as in requirement 2, that Vijay could eliminate all errors so that it does not need to spend any time making corrections. Suppose Vijay could use the time saved to increase revenues proportionately. Assume travel costs will remain at Rs.18,000. Calculate Vijay's operating Income. Solution: Step 1: Analyzing the proportion of time to Value Added, Non-value added and Gray Area Particulars Value Added Gray Area Non-value added Doing calculations and preparing drawings for clients 75% --Checking calculations and drawings -4% -Correcting errors found in drawings --7% Making changes on client’s requests 6% --Correction errors to meet government code --8% Total 81% 4% 15% Step 2: Analyzing the total cost of Rs.5,78,000 in to value added, non-value added and Gray area Particulars Value Added Gray Area Non-value added Salaries of professional staff 3,24,000 16,000 60,000 Travel Costs 18,000 --Administration and support (same % as salary) 1,29,600 6,400 24,000 Total 4,71,600 22,400 84,000 E M Reddy

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AMA-Notes Step 3: Cost savings When Vijay associates eliminates all errors it could save the non-value added hours to the extent of 1,200 (8,000 Hours x 15%). Due to this the non-value added cost of Rs.84,000 could be saved and the operating income becomes Rs.1,86,000 (Rs.1,02,000 + Rs.84,000). Step 4: Increasing profit through increased revenue Revenue Productive Hours

= Rs.6,80,000 = 8,000 Hours – 1,200 Hours = 6,800 Hours

Revenue/Productive Hour

= 6,800 Hours = Rs.100 per hour

Rs.6,80,000

Increase in productive hours due to elimination of corrections = 1,200 Hours Increase in revenue = Rs.100 x 1,200 Hours = Rs.1,20,000 The above Rs.1,20,000 is both increase in revenue as well as increase in profit because cost does not increase. Operating Profit = Rs.1,02,000 + Rs.1,20,000 = Rs.2,22,000 13.9. Activity Based Costing (ABC) 13.9.1. Activity Based Costing (ABC) - Introduction

1) For what we collect cost that is called cost object. E.g.: Product, Service, division etc., 2) Costs are classified into 2 types: a. Direct Costs → If a costs is solely for a cost object that is called Direct Cost. b. Indirect Cost → A cost incurred for common cost objects is called Indirect Cost. 3) The cost object which generates revenue is called Ultimate Object. Example: Overhead Cost = Rs.1,00,000 Machine Hours = 10,000 Hours Product A = 5,000 Hours; 200 Units Product B = 5,000 Hours; 100 Units Calculate Overhead cost per unit of A and B. Solution: Machine Hour Rate =

Overhead Machine Hours

=

Rs.10,00,000 10,000 Hours

= Rs.10 per Machine Hour

Overhead = Rs.1,00,000 Product A = 5,000 Hours x Rs.10 = Rs.50,000 → Overhead/Unit = Rs.250 Product B = 5,000 Hours x Rs.10 = Rs.50,000 → Overhead/Unit = Rs.500 Notes: 1) When we use machine hour rate to charge overheads to the products we assume that all the overheads vary with machine hours.

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AMA-Notes 2) This means the cost driver is machine hours and overheads are apportioned in the ratio of this cost driver. More facts: Machine Running activity = Rs.60,000 Setup Activity = Rs.15,000 Inspection activity = Rs.25,00 Total Overhead = Rs.1,00,000 Cost Drivers A B Machine hours 5,000 5,000 Setup Hours 3,000 2,000 Inspection time 1,500 3,500 Activity Based Costing System: Step 1: Calculation of Cost driver rate Activity Cost Pool Machine hours 60,000 Setup Hours 15,000 Inspection time 25,000

Cost Driver Name Cost Driver Quantity Cost Driver Rate Machine hours 10,000 6 Setup Hours 5,000 3 Inspection time 5,000 5

Step 2: Apportionment of Overhead Costs Activity

Product A Product B Cost Driver Quantity Amount (Rs.) Cost Driver Quantity Amount (Rs.) Machine hours 5,000 30,000 5,000 30,000 Setup Hours 3,000 9,000 2,000 6,000 Inspection time 1,500 7,500 3,500 17,500 Total 46,500 53,500 Units 200 100 Overhead/Unit 232.50 535 Question no 21: Having attended a CIMA course on activity-based costing (ABC) you decide an experiment by applying the principles of ABC to the four products currently made and sold by your company. Details of the four products and relevant information are given below for one period: Product A B C D Output in units 120 100 80 120 Costs per unit: (Rs.) (Rs.) (Rs.) (Rs.) Direct Material 40 50 30 60 Direct Labour 28 21 14 21 Machine hours (per unit) 4 3 2 3 The four products are similar and are usually produced in production runs of 20 units and sold in batches of 10 units. Using a machine hour rate currently absorbs the production overhead, and the total of the production overhead for the period has been analyzed as follows: (Rs.)

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AMA-Notes Machine department costs (rent, depreciation and supervision) 10,430 Setup Costs 5,250 Stores receiving 3,600 Inspection/Quality Control 2,100 Materials handling and dispatch 4,620 Total 26,000 You have ascertained that the cost drivers to be used are as listed below for the overhead cost shown: Cost Cost Driver Setup Costs Number of production runs Stores Receiving Requisition raised Inspection/Quality Control Number of production runs Material Handling and dispatch Orders executed The number of requisition raised on the stores was 20 for each product and the number of orders executed was 42, each orders being for a batch of 10 of a product. You are required: (a) To calculate the total costs for each product if all overhead costs are absorbed on a machine hour basis; (b) To calculate the total costs for each product, using activity based costing; (c) To calculate and list the unit product cost from your figures in (a) and (b) above, to show the differences and to comment briefly on any conclusions, which may be drawn which could have pricing and profit implications. Solution: Part 1: Calculation of product cost using Traditional Costing System Particulars A B Direct Materials 40 50 Direct Labour 28 21 Prime Cost 68 71 Overheads (WN – 1) 80 60 Total Cost 148 131

C D 30 60 14 21 44 81 40 60 84 141

Part 2: Activity Based Costing System Step 1: Calculation of Cost driver rate Activity Cost Pool Machine Running 10,430 Setup 5,250 Stores Receding 3,600 Inspection 2,100 Material Handling 4,620

Cost Driver Name Cost Driver Quantity Cost Driver Rate (Rs.) Machine hours 1,300 8.02/ Hour Production runs 21 (WN – 2) 250/Production Run Requisitions raised 80 (20 x 4) 45/Requisition Production runs 21 (WN – 2) 100/Production Run Orders executed 42 (WN – 3) 110/Order

Step 2: Apportionment of Overhead Costs Activity

A B C D CDQ Amount CDQ Amount CDQ Amount CDQ Amount Machine Running 480 3,850 300 2,406 160 1,283 360 2,891

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AMA-Notes Setup Stores Receding Inspection Material Handling Total Cost Units Overhead/Unit

6 20 6 12

1,500 900 600 1,320 8,170 120 68.08

5 20 5 10

1,250 900 500 1,100 6,156 100 61.56

4 20 4 8

1,000 900 400 880 4,463 80 55.79

6 20 6 12

1,500 900 600 1,320 7,211 120 60.09

Step 3: Calculation of total cost under Activity Based Costing System (ABC) Particulars A B C D Prime Cost 68 71 44 81 Overheads 68.08 61.56 55.79 60.09 Total Cost 136.08 132.56 99.79 141.09 WN 1: Calculation of Machine hour rate Items Units Hours/Unit Hours A 120 4 480 B 100 3 300 C 80 2 160 D 120 3 360 Total Hours 1,300 Overhead Cost

Machine Hour rate = Machine Hours =

Rs.26,000 1,300

= Rs.20/Hour

WN 2: Calculation of production runs Items Units Computation Runs A 120 120/20 6 B 100 100/20 5 C 80 80/20 4 D 120 120/20 6 Total Production Runs 21 WN 3: Calculation of Number of orders executed Items Units Computation Orders A 120 120/10 12 B 100 100/10 10 C 80 80/10 8 D 120 120/10 12 Total Production Runs 42 Question no 22: KL currently manufactures over 100 products of varying levels of design complexity. A single, plant-wide overhead absorption rate (OAR), based on direct labour hour is used to absorb overhead costs. In the quarter-ended march, KL's manufacturing overhead costs were:

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AMA-Notes (Rs.000) Equipment operation expenses 125 Equipment maintenance expenses 25 Wages paid to technicians 85 Wages paid to stores men 35 Wages paid to dispatch staff 40 Total 310 During the quarter, RAM Management Consultants were engaged to conduct a review of KL's cost accounting systems. RAM report includes the following statement: In KL's circumstances, absorbing overhead costs individual products on a labour hour absorption basis is meaningless. Overhead costs should be attributed to products using an activity based costing (ABC) system. We have identified the following as being the most significant activities: (1) Receiving component consignments from suppliers (2) Setting up equipment for production runs (3) Quality inspections (4) Dispatching goods orders to customers. Our research has indicated that, in the short term, KL's overheads are 40% fixed costs and 60% variable. Approximately half the variable overheads vary in relation to direct labour hours worked and half vary in relation to the number of quality inspections. This model applies only to relatively small changes in the level of output during a period of two years or less. Equipments operation and maintenance expenses are apportionable as follows:  Component stores (15%), manufacturing (70%) and goods dispatch (15%).  Technician wages are apportionable as follows: Equipment maintenance (30%), setting up equipment for production runs (40%) and quality inspection (30%). During the quarter  A total of 2,000 direct labour hours were worked (paid at Rs.12 per hour),  980 component consignments were received from suppliers,  1,020 production runs were set up,  640 quality inspections were carried out, and  420 goods orders were dispatched to customers. KL's production during the quarter included components R, S and T. the following information is available: Component R Component S Component T Direct labour hours worked 25 480 50 Direct material costs Rs.1,200 Rs.2,900 Rs.1,800 Component consignments received 42 24 28 Production runs 16 18 12 Quality inspections 10 8 18 Goods orders dispatched 22 85 46 Quality produced 560 12,000 2,400 In April 2008 a potential customer asked KL to quote for the supply of a new component (Z) to a given specification. 1,000 units of Z are to be supplied each quarter for a two-year period. They will be paid for in equal installments on the last day of each quarter. The job will involve an initial design cost of Rs.40,000 and production will involve 80 direct labour hours, Rs.2,000 materials, 20 component consignments, 15 production runs, 30 quality inspections and 4 goods dispatches per E M Reddy

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AMA-Notes quarter. KL's Sales Director comments: Now we have a modern ABC system, we can quote selling prices with confidence. The quarterly charge we quote should be the forecast ABC production cost of the units plus the design cost of the Z depreciated on a straight-line basis over the two years of the job-to which we should add a 25% mark-up for profit. We can base our forecast on costs experienced in the quarter-ended march. Requirements: (a) Calculate the unit cost of components R, S and T using KL's existing cost accounting system (single factory labour OAR). (b) Explain how an ABC system would be developed using the information given. Calculate the unit cost of components R, S and T, using this ABC system. (c) Calculate the charge per quarter that should be quoted for supply of components Z in a manner consistent with the Sales Director's comments. Advise KL's management on the merits of this selling price, having regard to factor you consider relevant. Note: KL’s cost of capital is 3% per quarter. Solution: Part 1: Calculation of cost per unit using traditional costing system Step 1: Calculation of overhead absorption rate Absorption rate used ‘labour hour rate used’. Labour Rate =

Overheads Hours

Rs.3,10,000

= 2,000 Hours = Rs.155/Labour Hour

Step 2: Calculation of cost per unit Particulars Component R (Rs.) Component S (Rs.) Component T (Rs.) Direct Material Costs 1,200 2,900 1,800 Add: Direct Labour @ 12 per hour 300 (25 x 12) 5,760 (480 x 12) 600 (50 x 12) Prime Cost 1500 8,660 2,400 Add: Overheads @ 155 per hour 3,875 (25 x 155) 74,400 (480 x 155) 7,750 (50 x 155) Total Cost 5,375 83,060 10,150 Units Produced 560 12,000 2,400 Cost per unit 9.60 6.92 4.23 Part 2: Activity Based Costing System Step 1: Calculation of Cost driver rate Activity Cost Pool Manufacturing 1,22,850 Stores Receiving 61,325 Setup 34,000 Quality Inspection 25,500 Dispatch 66,325

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Cost Driver Name Cost Driver Quantity Cost Driver Rate (Rs.) Labour Hours 2,000 61.425/Hour Consignments 980 62.576/Consignment Production Runs 1,020 33.33/Production Run Inspections 640 39.84/Inspection Orders executed 420 157.92/Order

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AMA-Notes Step 2: Cost per unit f R, S and T Activity Direct Material Direct labour @ 12 Prime Cost Add: Overheads Manufacturing @ Rs.61.425 Stores Receiving @ Rs.62.576 Setup @ Rs.33.33 Quality Inspection @ Rs.39.84 Dispatch @ Rs.157.92 Total Cost Units Cost/Unit

Component R Component S Component T CDQ Amount CDQ Amount CDQ Amount 1,200 2,900 1,800 300 5,760 2,400 1,500 8,660 2,400 25 42 16 10 22

1,536 2,628 533 398 3,474 10,069 560 18

480 24 18 8 85

29,484 1,502 600 319 13,423 53,988 12,000 4.5

50 28 12 18 46

3,072 1,752 400 717 7,264 15,605 2,400 6.5

WN 1: Technician Wages

Rs.85,000

Equipment Maintenance(30 %) = Rs.25,500

Overhead Cost

Setup (40%) = Rs.34,000

Inspection (30%) = Rs.25,500

Activity Cost

WN 2: Equipment Operation and maintenance expenses

Rs.1,25,000 + Rs.25,000 + Rs.25,500 = Rs.1,75,500

Stores (15%) = Rs.26,325

Manufacturin g (70%) = Rs.1,22,850

Dispatch (15%) = Rs.26,325

WN 3: Constructing activity cost pool Items Manufacturing Stores Setup Inspection Dispatch Equipment Operation & Maintenance 1,22,850 26,325 --26,325 Technician Wages --34,000 25,500 -Stores Wages -35,000 ---E M Reddy

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AMA-Notes Dispatch Wages Total

-1,22,850

--61,325 34,000

-25,500

40,000 66,325

Part 3: Accept Z order or not Step 1: Fixation of Selling Price Particulars Direct Materials Direct Wages Prime Cost Add: Overheads Manufacturing @ Rs.61.425 Stores Receiving @ Rs.62.576 Setup @ Rs.33.33 Quality Inspection @ Rs.39.84 Dispatch @ Rs.157.92 Depreciation Total Cost Add: Profit Sales Selling Price

Computation Given 80 Hours x Rs.12 80 Hours x Rs.61.425 20 x Rs.62.576 15 Runs x s.33.33 30 x Rs.39.84 4 x Rs.157.92 40,000/8 Rs.16,454 x 20% 20,568/1,000

Amount (Rs.) 2,000 960 2,960 4,915 1,252 500 1,195 632 5,000 16,454 4,114 20,568 20.568

Every quarter the cash flow from this order is Rs.20,568 – Rs.11,454 = 9,114 Step 2: Calculation of NPV Period Cash flow (Rs.) PVF@3% Discounted Cash flow (Rs.) 1–8 9,114 7.0197 63,977 Less: Discounted cash outflow -40,000 Net Present Value 23,977 Recommended to accept the order since NPV is positive. Question no 23: Repack Ltd is a Warehousing and Distribution Company, which receives products from customers, stores the products and then re-packs them for distribution as required. There are three customers for whom the services are provided - John ltd, George Ltd and Paul Ltd. The products from all three customers are similar in nature but have varying degrees of fragility. Basic budget information has been gathered for the year to 30 June and is shown in the following table: Product handled (cubic meters) John Ltd 30,000 George Ltd 45,000 Paul Ltd 25,000 Cost Packaging materials (see note 1) 19,50,000 Labour – Basic 3,50,000 – Overtime 30,000 Occupancy 5,00,000 Administration and management 60,000 E M Reddy

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AMA-Notes Note 1: Packing materials are used in re-packing each cubic meter of product for John ltd, George ltd and Paul Ltd in the ratio 1:2:3 respectively. This ratio is linked to the relative fragility of the good for each customer. Additional information has been obtained in order to enable unit costs to be prepared for each of the three customers using an activity-based costing approach. The additional information for the year to 30 June has been estimated as follows: (i) Labour and overhead costs have been identified as attributable to each of three work centersreceipts and Inspection, storage and packing as follows: Cost allocation proportions Rectification & Inspection Storage Packing % % % Labour – Basic 15 10 75 – Overtime 50 15 35 Occupancy 20 60 20 Administration and Management 40 10 50 (ii) Studies have revealed that the fragility of different goods affects the receipt and Inspection time needed for the products for each customer. Storage required is related to the average size of the basic incoming product units from each customer. The re-packing of goods for distribution is related to the complexity of packaging required by each customer. The relevant requirements per cubic meter of product for each customer have been evaluated as follows: John ltd. George ltd. Paul ltd. Receipt and inspection (minutes) 5 9 15 Storage (square meters) 0.3 0.3 0.2 Packing (minutes) 36 45 60 Required Calculate the budgeted average cost per cubic meter of packaged products for each customer each of the following two circumstances: (i) Where only the basic budget information is to be used, (ii) Where the additional information enables an activity-based costing approach to be applied. Solution: Part 1: Cost per cubic meter using basic budgeted information (Traditional Costing System) Particulars John Ltd (Rs.) George Ltd (Rs.) Paul ltd (Rs.) Packaging Material Cost 3,00,000 9,00,000 7,50,000 Labour – Basic 1,05,000 1,57,500 87,500 Labour – Overtime 9,000 13,500 7,500 Occupancy 1,50,000 2,25,000 1,25,000 Administration 18,000 27,000 15,000 Total Cost 5,82,000 13,23,000 9,85,000 Cubic Meters 30,000 45,000 25,000 Cost per cubic meter 19.4 29.4 39.4

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AMA-Notes Part 2: Cost per cubic meter using basic budgeted information (Traditional Costing System) Step 1: Calculation of Cost driver rate Activity Receipt and inspection Storage Packing

Cost Pool 1,91,500

Cost Driver Name Inspection time

3,45,500 4,03,000

Square meters Packing time

Cost Driver Quantity 15,500

Cost Driver Rate (Rs.) 12.3548/Hour

27,500 76,750

12.5636/Sq. mtr. 5.2508/Hour

Step 2: Apportionment of overhead cost Activity

John Ltd George Ltd Paul Ltd CDQ Amount (Rs.) CDQ Amount (Rs.) CDQ Amount (Rs.) Receipt and inspection 2,500 30,887 6,750 83,395 6,250 77,218 Storage 9,000 1,13,072 13,500 1,69,609 5,000 62,818 Packing 18,000 94,515 33,750 1,77,215 25,000 1,31,270 Total Cost 2,38,474 4,30,219 2,71,306 Step 3: Calculation of cost per cubic meter Particulars John Ltd George Ltd Paul Ltd Indirect cost 2,38,474 4,30,219 2,71,306 Add: Packing 3,00,000 9,00,000 7,50,000 Total Cost 5,38,474 13,30,219 10,21,306 Cubic Meters 30,000 45,000 25,000 Cost/Cubic Meter 17.95 29.56 40.85 WN 1: Packaging Material Cost Particulars John Ltd George Ltd Paul ltd Ratio 1 2 3 Cubic Meters 30,000 45,000 25,000 Weighted Ratio 30,000 90,000 75,000 30,000

John Ltd: Rs.19,50,000 x 1,95,000 = Rs.3,00,000 90,000

George Ltd: Rs.19,50,000 x 1,95,000 = Rs.9,00,000 Paul Ltd: Rs.19,50,000 x

75,000 1,95,000

= Rs.7,50,000

WN 2: Other Cost Customer John ltd

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Labour – Basic Rs.3,50,000 x 30,000 = 1,05,000 Rs.1,05,000

Labour – Occupancy Overtime 30,000 Rs.30,000 x Rs.5,00,000 x 1,05,000 30,000 = Rs.9,000 = Rs.1,50,000 1,05,000

Administration 30,000

Rs.60,000 x 1,05,000 = Rs.18,000

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AMA-Notes George ltd Paul ltd

Rs.3,50,000 x 45,000 = 1,05,000 Rs.1,57,500 Rs.3,50,000 x 25,000 = Rs.87,500 1,05,000

Rs.30,000 x 45,000 = 1,05,000 Rs.13,500 Rs.30,000 x 25,000 = Rs.7,500 1,05,000

45,000

Rs.60,000 x 1,05,000 = Rs.27,000

25,000

Rs.60,000 x 1,05,000 = Rs.15,000

Rs.5,00,000 x 1,05,000 = Rs.2,25,000 Rs.5,00,000 x 1,05,000 = Rs.1,25,0500

45,000

25,000

WN 3: Construction of cost pool Cost

Receipt % Amount Labour – Basic 15 52,500 Labour – Overtime 50 15,000 Occupancy 20 1,00,000 Administration and Management 40 24,000 Cost Pool Total 1,91,500

Storage % Amount 10 35,000 15 4,500 60 3,00,000 10 6,000 3,45,500

Packing % Amount 75 2,62,500 35 10,500 20 1,00,000 50 30,000 4,03,000

WN 4: Calculation of Receipts and Inspection time Customer Computation Time in minutes Time in hours John ltd 30,000 x 5 Minutes 1,50,000 2,500 George ltd 45,000 x 9 Minutes 4,05,000 6,750 Paul ltd 25,000 x 15 Minutes 3,75,000 6,250 Total Inspection time 15,500 WN 5: Calculation of Storage Space Customer Computation Square Meters John ltd 30,000 x 0.3 Square Meters 9,000 George ltd 45,000 x 0.3 Square Meters 13,500 Paul ltd 25,000 x 0.2 Square Meters 5,000 Total Storage Space 27,500 WN 6: Calculation of packing time Customer Computation Time in minutes Time in hours John ltd 30,000 x 36 Minutes 10,80,000 18,000 George ltd 45,000 x 45 Minutes 20,25,000 33,750 Paul ltd 25,000 x 60 Minutes 15,00,000 25,000 Total Inspection time 76,750 Question no 24: Tropicana Ltd.· has decided to increase the size of its store. It wants information about the profitability of individual product lines: Orange juice, Apple juice and Mango juice. Tropicana ltd. provides the following data for 2008 for each product line: Particulars Orange Juice Apple Juice Mango Juice Revenues Rs.3,17,400 Rs.8,40,240 Rs.4,83,960 Cost of goods sold Rs.2,40,000 Rs.6,00,000 Rs.3,60,000 Cost of bottles returned Rs.4,800 Rs.0 Rs.0 Number of purchase orders placed 144 336 144 Number of deliveries received 120 876 264 E M Reddy

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AMA-Notes Hours of shelf-stocking time 216 2,160 1,080 Items sold 50,400 4,41,600 1,22,400 Tropicana ltd. also provides the following information for 2008: Sr.No. Activity (1) Description of Activity (2) Total Costs Cost allocation (3) base (4) 1 Bottle Returning of empty bottles Rs.4,800 Direct tracking to returns soft drink line 2 Ordering Placing of orders for purchases Rs.62,400 624 purchase orders 3 Delivery Physical delivery and receipts of Rs.1,00,800 1,260 deliveries merchandise 4 ShelfStocking of merchandise on store Rs.69,120 3,456 hours of shelfStocking shelves and ongoing restocking stocking time 5 Customer Assistance provided to customers Rs.1,22,880 6,14,400 items sold Support including bagging and checkout Total Rs.3,60,000 Required: (a) Tropicana Ltd. currently allocates store support costs (all costs other than cost of goods sold) to product lines on the basis of cost of goods sold of each product. Calculate operating income and operating income as a percentage of revenues for each product line. (b) If Tropicana Ltd. allocates store support costs (all costs other than cost of goods sold) to product lines using ABC system, calculate operating income and operating income as a percentage of revenues for each product line. (c) Compare both the systems. Solution: Part 1: Product line profitability under existing system Particulars Orange Juice (Rs.) Apple Juice (Rs.) Mango Juice (Rs.) Revenues 3,17,400 8,40,240 4,83,960 Less: Cost of goods sold 2,40,000 6,00,000 3,60,000 Less: Stores Support 76,800 (72,000 + 4,800) 1,80,000 1,08,000 Profit 600 60,240 15,960 Profit as % of sales 0.19% 7.17% 3.29% Part 2: Product line profitability under ABC System Step 1: Calculation of Cost-Driver Rate Activity Ordering Delivery ShelfStocking Customer Support

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Cost Pool (Rs.) 62,400 1,00,800 69,120 1,22,880

Cost Driver Name Placing of orders for purchases Physical delivery and receipts of merchandise Stocking of merchandise on store shelves and ongoing restocking Assistance provided to customers including bagging and checkout

Cost Driver Quantity 624 1,260

Cost Driver Rate (Rs.) 100/Order 80/Deliver

3,456

20/Stocking time

6,14,400

0.2/Unit

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AMA-Notes Step 2: Apportionment of Overhead Activity

Orange Juice Apple Juice Mango Juice CDQ Amount (Rs.) CDQ Amount (Rs.) CDQ Amount (Rs.) Bottle return -4,800 ----Ordering 144 14,400 336 33,600 144 14,400 Delivery 120 9,600 876 70,080 264 21,120 Shelf-Stocking 216 4,320 2,160 43,200 1,080 21,600 Customer Support 50,400 10,080 4,41,600 88,320 1,22,400 24,480 Total Cost 43,200 2,35,000 81,600 Step 3: Product line profitability Particulars Orange Juice (Rs.) Apple Juice (Rs.) Mango Juice (Rs.) Revenues 3,17,400 8,40,240 4,83,960 Less: Cost of goods sold 2,40,000 6,00,000 3,60,000 Less: Stores Support 43,200 2,35,000 81,600 Profit 34,200 5,240 42,360 Profit as % of sales 10.78% 0.62% 8.75% WN 1: Apportionment of stores support cost Rs.3,60,000

% of indirect cost to cost of goods sold = Rs.12,00,000 = 30% Orange Juice = Rs.2,40,000 x 30% = Rs.72,000 Apple Juice = Rs.6,00,000 x 30% = Rs.1,80,000 Mango Juice = Rs.3,60,000 x 30% = Rs.1,08,000 13.9.2. Activity Based Costing (ABC) & Target Costing

Question no 25: Cauvery ltd. manufactures two component parts for the television industry: • T: Annual production and sales of 50,000 units at a selling price of Rs.40.60 per unit. • Premia: Annual production and sales of 25,000 units at a selling price of Rs.60 per unit. Cauvery includes all R&D and design costs in engineering costs. Assume that Cauvery has no marketing, distribution, or customer-service costs. The direct and indirect costs incurred by Cauvery on T and Premia are as follows: T Premia Total Direct Material Costs (Variable) 8,50,000 6,00,000 14,50,000 Direct Manufacturing Labour Costs (Variable) 3,00,000 2,00,000 5,00,000 Direct Machining Costs (Fixed) 1,50,000 1,00,000 2,50,000 Indirect Manufacturing Costs: Machine Setup Costs 86,250 Testing Costs 4,87,500 Engineering Costs 4,50,000 Total Indirect Manufacturing Costs 10,23,750 Total Costs 32,23,750 Cauvery's management Identifies the following activity cost pools, cost drivers for each activity, and the cost per unit of cost driver for each overhead cost pool:

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AMA-Notes Manufacturing Activity 1. Setup

Description of Activity

Cost Driver

Cost per unit of cost driver Rs.25 per setup hours Rs.2 per testing hour

Preparing machine to manufacture Setup hours a new batch of products 2. Testing Testing components and final Testing Hours product (Cauvery tests each unit of T and Premia individually) 3. Engineering Designing products and processes Complexity of Cost assigned to and ensuring their smooth product and products by functioning process special study Over a long-run horizon, Cauvery's management views direct materials costs and direct manufacturing labour costs as variable with respect to the units of T and Premia produced, and overhead costs as variable with respect to their chosen cost drivers. For example, setup costs vary with the number of setup-hours. Direct machining costs represent the cost of machine capacity dedicated to the production of each product (50,000 hours at Rs.3 per hour for T). These costs are fixed and are not expected to vary over the long run horizon. Additional Information is as follows: T Premia 1. Production batch sizes 500 Units 200 Units 2. Setup time per batch 12 Hours 18 Hours 3. Testing and inspection time per unit of product produced 2.5 Hours 4.75 Hours 4. Engineering cost incurred on each product Rs.1,70,000 Rs.2,80,000 Cauvery is facing competitive pressure to reduce the price of T and has set a target price of Rs.34.80, well below its current price of Rs.40.60. The challenge of Cauvery is to reduce the cost of T. Cauvery’s engineers have proposed new product design and process improvements for the "New T" to replace T. The new design would improve product quality, and reduce scrap and waste. The reduction in prices will not enable Cauvery to increase its current unit sales. (However, if Cauvery does not reduce prices, it will lose sales). The expected effect of new design relative to T as follows: a. Direct materials costs for New T are expected to decrease by Rs.2.00 per unit. b. Direct manufacturing labour costs for New T are expected to decrease by Rs.0.50 per unit. c. Machining time required to make New T is expected to decrease by 20 minutes. It currently takes 1 hour to manufacture 1 unit of T. The machines will be dedicated to the production of New T. d. New T will take 7 setup-hours for each setup. e. Time required for testing each unit of New T is expected to be reduced by 0.5 hour. f. Engineering costs will be unchanged. Assume that the batch sizes are the same for New T as for T. If Cauvery required additional resources to implement the new design, it can acquire these additional resources in the quantities needed. Further assume the costs per unit of cost drivers for the New T are the same as those for T. Required: 1. Calculate the full cost per unit for T and Premia using activity based costing. 2. What is the markup on the full cost per unit for T? 3. What is Cauvery's target cost per unit for New T if it is to maintain the same markup percentage on the full cost per unit as it had for T?

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AMA-Notes 4. Will the New T design achieve the cost reduction targets that Cauvery has set? Explain. 5. What price will Cauvery charge for New T if it uses the same markup percentage on the full cost per unit for New T as it did for T? 6. What price should Cauvery charge for New T? Specify any other management action that Cauvery should take regarding New T. Solution: Part 1: Full Cost of T and Premia under ABC System Step 1: Apportionment of Overhead Costs Activities

T Premia Cost Driver Quantity Amount Cost Driver Quantity Amount Setup 1,200 Hours 30,000 2,250 Hours 56,250 Testing 1,25,000 Hours 2,50,000 1,18,750 Hours 2,37,500 Engineering -1,70,000 -2,80,000 Total Overhead Cost 4,50,000 5,73,750 Step 2: Calculation of total cost Particulars T (Rs.) Premia (Rs.) Direct Material Costs 8,50,000 6,00,000 Direct Manufacturing Labour Costs 3,00,000 2,00,000 Direct Machining Costs 1,50,000 1,00,000 Indirect Manufacturing Costs 4,50,000 5,73,750 Total Cost 17,50,000 14,73,750 Units 50,000 Units 25,000 Units Cost per unit 35 58.75 Part 2: Markup on full cost of T Selling Price Less: Total Cost Markup % Markup on Selling Price % Markup on Cost

Rs.40.60 Rs.35 Rs.5.60 Rs.5.6/Rs.40.6 = 13.79% Rs.5.6/Rs.35 = 16%

Part 3: Target Cost for “New T” Selling Price (Market Determined) Rs.34.8 Less: Markup @ 13.79% (Rs.34.8 x 13.79%) Rs.4.80 Target Cost Rs.30 Part 4: Calculation of “New T” Cost Particulars Computation Cost (Rs.) Direct Material Costs (8,50,000/50,000 – 2) x 50,000 7,50,000 Direct Manufacturing Labour Costs (3,00,000/50,000 – 0.5) x 50,000 2,75,000 Direct Machining Costs 1,50,000 Setup Cost 100 Batches x 7 Hours x Rs.25 17,500 E M Reddy

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AMA-Notes Testing Cost Engineering Cost

50,000 Units x 2 Hours x Rs.2 Total Cost

Units Cost per unit

Rs.15,62,500/50,000 Units

2,00,000 1,70,000 15,62,500 50,000 31.25

The new design has reduced cost but fall short of target cost by Rs.1.25 (Rs.31.25 – Rs.30). Part 5: Selling price using the Same markup Cost of New T = Rs.31.25 Add: Markup @ 16% = Rs.5 (Rs.31.25 x 16%) Selling Price = Rs.36.25 Part 6: We should not increase the selling price beyond Rs.34.8. For reasons see target costing introduction notes. The strategy is to compromise on margin. If it is not possible, exit from the market. WN 1: Calculation of Setup Hours Particulars T Premia Production 50,000 Units 25,000 Units Batch Size 500 Units 200 Units No. of batches 100 Batches 125 Batches Setup time per batch 12 Hours 14 Hours Setup Hours 1,200 Hours 2,250 Hours WN 2: Calculation of Testing Hours Particulars T Premia Production 50,000 Units 25,000 Units Testing hours per unit 2.5 Hours 4.75 Hours Total Hours 1,25,000 Hours 1,18,750 Hours Notes: 1) Direct Machining time has reduced by 20 Minutes but has no impact on cost due to following reasons: a) The Machine cost if fixed for which the cost driver is capacity and not the actual hours. Hence it will not reduce. b) With reduced time can’t we increase volume and decrease per unit cost? Answer: No, because there is no demand. It is better to keep capacity idle than build up inventory c) Can’t the idle capacity be diverted to Premia which has demand? d) Answer: No, because the machine is specific to “New T”. 2) Activities of an organization can be classified into 4 types: a) Unit Level Activity b) Batch Level Activity c) Product Level Activity E M Reddy

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AMA-Notes d) Facility Level Activity Activity

Unit Level Activity

Batch Level Activity

Product Level Activity

Facility Level Activity

The activities which are performed for each unit are called Unit level activities and cost drivers are called Unit level cost drivers. E.g.: Testing Activity in above problem

The activities which are performed for each batch/lot of units are called Batch level activities and cost drivers are called Batch level cost drivers. E.g.: Setup Activity in above problem

The activities which are performed specially for one product are called Product level activities. E.g. Marketing Activity on introduction of a new product

The activities which are performed for entire company (or) all products are Facility level activities. E.g.: Brand Building

Overhead allocation is similar under both ABC System & Traditional Costing System

Overhead allocation is different under both ABC System & Traditional Costing System. ABC system is superior in overhead allocation

Overhead allocation is similar under both ABC System & Traditional Costing System

Question no 26: State with a brief reason whether you would recommend an activity based system of costing in each of the following Independent situations:  Company K produces one product. The overhead costs mainly consist of depredation.  Company L produces 5 different products using different production facilities.  A consultancy firm consisting of lawyers accountants and computer engineers provides management consultancy services to clients.  Company S produces two different labour intensive products. The contribution per unit In both products is very high. The SEP Is very low. All the work Is carried on efficiently to meet the target costs. Solution:  Only one product – ABC System is not required  Most of the costs are directly traceable as different products are manufactured using different facilities – ABC System is not required.  ABC System is required  Breakeven Point low means variable costs are low and variable costs are high. Variable costs high means most costs are unit level activity costs – ABC System is not required Question no 27: State whether each of the following independent activities is value-added or nonvalue-added:  Polishing of furniture used by systems engineer in a software for a banking company.  Maintenance by a software company of receivables management software for a banking company  Painting of pencils manufactured by a pencil factory.  Cleaning of customer's computer key boards by a computer repair center.  Providing, brake adjustments in cars received for service by a car service station.

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AMA-Notes Solution:     

Non-Value Added Value Added Value Added Value Added Value Added

13.9.3. Activity Based Costing (ABC) with Variance Analysis

Question no 28: X uses traditional standard costing system. The inspection and setup costs are actually Rs.1,760 against a budget of Rs.2,000. ABC system is being implemented and accordingly, the number of batches is identified as the cost driver for inspection and setup costs. The budgeted production is 10,000 units in batches of 1,000 units, whereas actually, 8,800 units were produced in 11 batches. (i) Find the volume and total fixed overhead variance under the traditional standard costing system. (ii) Find the total fixed overhead cost variance under the ABC system. Solution: Part 1: Calculation of fixed overhead variances under traditional costing system Step 1: Calculation of Standard Rate SR/ Unit =

BFO BO

Rs.2,000

= 10,000 Units = Rs.0.2/Unit

Step 2: Computation table [1] [2] [3] AO x SR AFO BFO 8,800 Units x Rs.0.2 Rs.1,760 Rs.2,000 Rs.1,760 Rs.1,760 Rs.2,000 Step 3: Variance Computation Fixed Overhead Cost Variance (1 – 2) = Rs.1,760 – Rs.1,760 = Rs.0

Fixed Overhead Expenditure Variance (3 – 2) = Rs.2,000 – Rs.1,760 = Rs.240 (Favourable)

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Fixed Overhead Volume Variance (1 – 3) = Rs.1,760 – Rs.2,000 = Rs.240 (Adverse)

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AMA-Notes Part 2: Calculation of variances under ABC system Step 1: Calculation of Standard Rate Budgeted Output = 10,000 Units; Batch Size = 1,000 Units Budgeted Batches =

10,000 Units

= 10 Batches

1,000 Units Budgeted Fixed Overheads

Standard Rate/Batch =

Budgeted Batches

Rs.2,000

= 10 Batches = Rs.200/Batch

Step 2: Computation table [1] [2] [3] [4] `SB x SR AFO BFO AB x SR 9 Batches x Rs.200 Rs.1,760 Rs.2,000 11 Batches x Rs.200 Rs.1,800 Rs.1,760 Rs.2,000 Rs.2,200 WN: Standard Batch (Standard Batch for actual output Input Output 1 Batch 1,000 Units 9 Batches 8,800 Units Step 3: Variance Calculation

Fixed Overhead Cost Variance (1 – 2) = Rs.1,800 – Rs.1,760 = Rs.40 (Favourable) Fixed Overhead Expenditure Variance (3 – 2) = Rs.2,000 – Rs.1,760 = Rs.240 (Favourable)

Fixed Overhead Volume Variance (1 – 3) = Rs.1,800 – Rs.2,000 = Rs.200 (Adverse)

Fixed Overhead Capacity Variance (4 – 3) = Rs.2,200 – Rs.2,000 = Rs.200 (Favourable)

Fixed Overhead Expenditure Variance (1 – 4) = Rs.1,800 – Rs.2,200 = Rs.400 (Adverse)

Notes: 1) Understanding Capacity Variance: Plan to setup 10 batches but actually setup 11 batches resulting in over absorption of 1 Batch x Rs.200 = Rs.200 (Favourable)

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AMA-Notes 2) Understanding efficiency variance: 3) For the output of 8,800 units the batches allowed is 9 batches but actually dine in 11 batches. Hence there is adverse efficiency of 2 batches x Rs.200 = Rs.400 (Adverse) Question no 26: Toy master ltd produces a plastic toy car, TGC in batches. To manufacture a batch of TGCs, Toy master must set up the machines. Setup costs are batch-level costs. A separate setup department is responsible for setting up machines for TGC. Setup overhead costs consists of some costs that are variable and some that are fixed with respect to the number of set-up hours. The following information pertains to 2007. Static-Budget Amount Actual Amounts Units of TGC produced and sold 30,000 22,500 Batch size (number of units per batch) 250 225 Setup hours per batch 5 5.25 Variable overhead cost per setup hour Rs.250 Rs.240 Total fixed setup overhead costs Rs.1,80,000 Rs.1,75,350 Required: 1. For variable setup overhead costs, compute the efficiency and spending variances. Comment on the results. 2. For fixed setup overhead costs, compute the spending and the production-volume variances. Comment on the results. Solution: Step 1: Calculation of Standard Rate Standard Rate/Batch = Rs.250 x 5 Hours = Rs.1,250/Batch Standard Rate/Setup Hour = Rs.250 Step 2: Computation Table [1] [2] [3] SH x SR (or) SB x SR AVO AH x SR 450 Hours x Rs.250 (or) 90 Batches x Rs.1,250 525 Hours x Rs.240 525 Hours x Rs.250 Rs.1,12,500 Rs.1,26,000 Rs.1,31,250 WN 1: Standard Hours (Standard Setup hours for actual output) Input Output 1 Batch 250 Units 90 Batches 22,500 Units Standard Hours = 90 Batches x 5 Hours = 450 Hours WN 2: Calculation of AVO Input Output 1 Batch 225 Units 100 Batches 22,500 Units Actual Hours = 100 Batches x 5.25 Hours = 525 Hours

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AMA-Notes Step 3: Variance Calculation

Variable Overhead Cost Variance (1 – 2) = Rs.1,12,500 – Rs.1,26,060 = Rs.13,500 (Adverse) Fixed Overhead Expenditure Variance (3 – 2) = Rs.1,31,250 – Rs.1,26,060 = Rs.5,250 (Favourable)

Fixed Overhead Efficiency Variance (1 – 3) = Rs.1,12,500 – Rs.1,31,250 = Rs.18,750 (Adverse)

Due to Batch Size = (100 Batches – 90 Batches) x Rs.1,250 = Rs.12,500 (Adverse)

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Due to Setup time = (5.25 Hours – 5 Hours) x 100 Batches x Rs.250 = Rs.6,250

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