Engineering Economy Lecture B

ENGINEERING ECONOMY by Nilo T. Aldon, ChE 1

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Preview Problems  What will be the equivalent amount at the end of five years of a uniform 5 yearly deposit

of P5,000. if the nominal annual interest rate is 12% compounded monthly?

 Determine the present value of 10 semi-annual payments of P10,000 , the first of

which to be paid 2 years from now. Money is worth 12% pa compounded semiannually.

 A bond issue of P100,000 redeemable at par in 10-years, in P1,000 units paying10%

interest per annum payments, must be retired by the use of sinking fund that earns 8% pa. What is the total annual expense?

 An economy is experiencing inflation at an annual rate of 7%. If the market interest rate

is also 5% per annum, what will be the real value of P500 two years from now ?

 A company purchased an equipment for P 110,000. It is estimated that it will have a

useful life of 10 years. The scrap value of the equipment is P10,000, a. Compute the book value of the equipment at the start of the 6th year using declining-balance method. b. Compute the book value at the end of the 5th year using Sinking Fund method, i=10% pa c. Compute the book value at the start of the 6th year using SYDM

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ENGINEERING ECONOMY  _ study of

economic theories and their applications to engineering problems with the concept of obtaining maximum benefit at the least cost.  Time value of money is central to this study.

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Course Objectives  After completing this course, the student must be able to:

1. Solve problems involving interest and the time value of money; 2. Evaluate project alternatives by applying engineering economic principles and methods and select the most economically efficient one; and 3. Deal with risk and uncertainty in project outcomes by applying the basic economic decision making concepts.

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 1. Introduction

Course Outline

 2. Money-Time Relationship  

  

  

   5

2.1. Time Value of Money 2.2. Types of Interest 2.3. Inflation/Deflation 2.4. Annuity 3. Depreciation 4. Capital Investments 5. Operational Costs 6. Accounting Fundamentals 7. Basic Methods of Profitability Analysis 8. Methods of Financial Analysis 9. Optimization

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References  Plant Design and Economics for Chemical Engineers, Max S. Peters and Klaus D.  

   

      6

Timmerhaus, 4th Ed 2001 Process Engineering Economics, Schweyer Engineering Economy, de Garmo, Sullivan, Canada, 7th Ed Engineering Economy, Arreola, 2nd Ed Engineering Economy Sta. Maria, 3rd Ed Engineering Economy, Sullivan, Bentadilli and Wichs, 12th Ed 2003 Contemporary Engineering Economics, Chan S. Park, 3rd Ed 2002 Engineering Economy by L.T. Blank and A.J. Tarquin, 6th ed., McGraw Hill, 2005. Engineering Economy by W.G. Sullivan, E.M. Wicks, and J.T. Luxhoj, 13th ed., Prentice Hall, 2006. Contemporary Engineering Economics by Chan S. Park, 4th ed., Prentice Hall, 2007. Excel for Engineering Economics by R.W. Larsen and Chan S. Park, Prentice Hall, 2003. Engineering Economy and the Decision Making Process by J.C. Hartman, Prentice Hall, 2007. Engineering Economic Analysis by D. G. Newman, T. G. Eschenbach, and J. P. Larelle, 9th ed., Oxford University Press, 2004.

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1. INTRODUCTION  Engineering Economy _ study of economic theories and

their applications to engineering problems with the concept of obtaining maximum benefit at the least cost.  “Economics_ is the study of scarcity. Resources are limited, and every society wants to figure out how to allocate its resources for maximum benefit.“_Jodie Beggs, PhD (Harvard U)

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Reasons for Studying Engineering Economy:  Engineering designs and operations must be equated with costs for practical applications  Engineers evolve into managers of their own or other enterprises Uses of Engineering Economy  Application on various fields of engineering  Determining of limiting factors  Tool in selection of alternates  Investment of capital  Tool in decision making 8

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Economists study topics such as:  How prices and quantities of items are determined in market     

  

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economies How much value markets create for society How taxes and regulation affect economic value Why some goods and services are under-supplied in a market economy How firms compete and maximize profit How households decide what to consume, how much to save, and how much to work (or, more generally, how people respond to incentives) Why some economies grow faster than others What effect monetary and fiscal policy has on economic wellbeing How interest rates are determined

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 It is NOT an economist’s job to tell

people what stocks and bonds they should be investing in.

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SELECTION AND EQUIVALENCE IN PRESENT ECONOMY

 Present economy involves the analysis of problems for

manufacturing a product or rendering a service upon the basis of present or immediate costs. It is highlighted when the effects of time such as interest and depreciation are negligible. Present economy is employed when the alternatives to be compared will provide the same result and the period involved in the study is relatively short.  When alternatives for accomplishing a specific task are being compared over one year or least-and influence of time on money can be ignored, engineering economic analyses are referred to as present economy studies.

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SELECTION AND EQUIVALENCE IN PRESENT ECONOMY

Present economy studies occur in the following situations:  a. Selection of material_ In many cases, economic selection among materials cannot be

based solely on the costs of materials. Frequently, a change in materials will affect the design and processing costs, and shipping costs may also be altered.

 b. Selection of method to be used_ In mechanical or chemical operations a product

may be made by two or more methods giving equivalent results. Some goods may be delivered by various methods such as using different capacity trucks, and the results would still be the same regardless of the truck used. These are but a few of the examples that may be cited to show that certain operations are capable of being done by two or more methods.

 c. Selection of design_ In the design of a machine to produce a certain product, the

engineer responsible for the work will usually make as many designs as possible and from which, by a process of elimination, he will select the design best fitted for the work to be done with particular care being given to the one which will do the work with most economy.

 d. Selection location or site for a project_ In the choice of a factory site many factors 12

are often considered such as the cost of the land, the cost of construction in the NTAldon different sites, and the difference in transportation cost, and many other factors.

 e. Comparison of proficiency among workers_ In industrial operations

where the efficiency of the workers is a factor affecting costs, it is usually observed that workers have varying efficiencies. In some occupations only those with better average proficiencies are acceptable. In teaching for example, other factors being equal, preference should be given to those teachers who did better than average in their studies.  f. Economy of tool and equipment maintenance_ In many activities, tools have to be sharpened from time to time, and equipment have to be kept in good operating condition all the time. In certain cases, experience will show the best time to perform certain operations to maintain equipment at the optimum operating efficiency.  g. Economy of number of laborers_ In certain industrial operations it is observed that a certain number of workers cooperating on a certain phase of work will lead to the highest efficiency. An increase beyond this number will usually cause the taking into effect of the law of diminishing returns. In certain cases, the excess of laborers will result in some laborers not working at certain times while waiting for the work of other laborers to be finished. 13

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SAMPLE PROBLEMS:  A machine part to be machined may be made either from an alloy of

aluminum or steel. There is an order for 8000 units. Steel costs P380/kg, while aluminum costs P870/kg. If steel is used, the steel per unit weighs 110 grams; for aluminum, 30 grams. When steel is used, 50 units can be produced per hour; for aluminum, 80 units per hour with the aid of a tool costing P64,000, which will be useless after 8,000 units are finished. The cost of the machine and the operator is P1080 per hour. If all other costs are identical, determine which material will be more economical.  Solution: Steel 0.11kg (P380/kg)= P41.80 P1,080/50 = P 21.60

Material Cost Labor and Machine Tool Cost per piece P63.40 Answer: Aluminum is cheaper!  14

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Aluminum 0.030 kg (P870) = P26.10 P1,080/80 = P13.50 P64,000/8,000 = P8.00 P47.60

•A company manufactures 1 million units of a product annually. A new design of the product will reduce material cost by 12%, but will increase processing cost by 2%. If materials cost is P 12/unit and processing will cost P4/unit, how much can the company afford to pay for the preparation of the new design and making changes in equipment? Solution: Decrease in materials Increase in processing costs Net Savings

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1,000,000 (0.12) (P12) = P 1,440,000 1,000,000 (0.02) (P4) = P 80,000 P 1,360,000

Time Value of Money  Time affects the cost of money.

A peso now is worth more than a peso a year from now because it can earn interest during the year.  Interest represents two things:

1.The compensation paid for the use of the borrowed capital 2. The risk taken in making the loan.  The rate at which interest will be paid is usually fixed at the time the

capital is borrowed, and a guarantee is made to return the capital at some set of time in the future or on an agreed-upon pay-off schedule.  Riskier loans require more interest to make them attractive. 16

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History of Interest  The concept of interest goes back to earliest recorded history.  Babylon 2000 B.C. – money paid for use of grain that was borrowed.  Typical rates were 6 to 25% per annum.

 Usury is prohibited in the Law of Moses, and in Islamic cultures.  In the middle ages, interest on loans was prohibited based on these

restrictions.  In 1536, John Calvin adopted a theory of what constituted usury that allowed interest.  Islamic conventions developed to allow those with money to buy a stake in a business in return for an portion of the profit from that business.  Interest and the cost of capital have become an essential part of doing business.

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INTEREST DEFINED  Interest

__ the time value of money __ money paid for the use of money __ compensation paid for the use of borrowed capital.

 Elements of Interest

1. Principal, 2. Interest,

P = the sum of money lent or borrowed I = the price paid or charge made for the use of money 3. Time, n = the period of time during which interest is charged, measured in some specific unit. The unit may be day, week, month, 3 months, 6 months, or a year. 4. Rate, i = the price paid for the use of money for a unit of time. It is given as a percentage of the original amount. 18

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CASH FLOW

Cash Flow _ is a systematic presentation of cash receipts and disbursements for a given operating period

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Cashflow Diagram: Investment Transaction

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Cashflow Diagram: Loan Transaction

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Types of Interest A. Simple Interest:The interest is proportional to the original amount of the loan I  Pin Requires compensation payment at a constant interest rate based only on the original amount The principal P must be repaid eventually; therefore the entire amount F, of principal plus simple interest due after n periods is;

PFI

In the payment of simple interest, it makes no difference whether interest is paid at the end of each time unit or after any number of time units. The same total amount of money is paid during a given length of time, no matter which method is used. Under these conditions, there is no incentive to pay the interest until the end of the total loan period.

1. Ordinary Simple Interest

I  Pin 

( P)(i)(d ) P i m  360 12

The time unit used to determine the number of interest period is usually one year, and the interest rate is expressed on a yearly basis. When an interest period of less than one year is involved, the ordinary way to determine the simple interest is to assume the year consists of twelve 30-day months, or 360 days.

2. Exact Simple Interest 23

I  Pin 

( P)(i)(d ) ( P)(i)(d ) ; or  365 366

The exact method accounts for the fact that there are 365 days in a normal year and 366 days in a leap year. NTAldon

Example: Determine the ordinary simple interest on P1000 for 8 months and 15 days if the rate of interest is 15%.

I  Pin

Solution:

For ordinary simple interest, it is assumed that 1 year = 12 months; n= 8.5 months P = 1000 i = 0.15/12

I  Pin

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 8.5  I  10000.15   P 106.25  12 

Example: Determine the exact simple interest on P1000 for the period January 1 to October 15, 2012 if the rate of interest is 15% pa. Solution: 2012 is a leap year = 366 days

Jan 1-31 February March April May June July

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Pid I  Pin  366 NTAldon

31 29 31 30 31 30 31 213

August September October

31 30 15

76

289 days

 10000.15289   P 118.44 366

3. Discounted Interest, id The interest for the money borrowed (discount) is deducted from the principal in advance.

I d  P id n  P = amount loaned P’ = actual amount received Id = interest payment deducted in advance

P'  P  I d Id i id   1 i P Effective Interest Rate, i 26

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id Id i  1  id P'

Example: Man borrowed P10,000 from a bank and agreed to pay the loan at the end of 1 year. The bank discounted the loan and gave him P8,000 1. What was the discounted rate?

I d 10,000  8,000 id    20% pa P 10,000 2. What was the effective rate of interest? I d 10,000  8,000 i   25% pa P' 8,000 id 0.20 i   0.25  25% pa 1  id 1  0.2 27

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Compound Interest: The interest is proportional to the balance at any point in time Stipulates that interest is due regularly at the end of each interest period. If payment is not made, the amount due is added to the principal, and the interest is charged on this converted principal during the following unit time. Thus an initial loan of P at an annual interest rate i would require payment of Pi as interest at the end of the first year. If this payment were not made, the interest for the second year would be ( P + Pi ) i and the total amount due for interest after 2 years would be :

IT2  Pi  ( P  Pi)i Therefore, the total amount of principal plus interest after 2 years equals

F2  P  Pi  ( P  Pi)i  P1  i 

2

Fn  P1  i  n n I  Fn  P  P1  i   P  P 1  i   1 n

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Future Worth





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1. Nominal Interest Rates, r Interests are compounded other than on annual basis. It always includes a qualifying statement indicating the compounding period. Example, 12% per annum compounded quarterly.

2. Effective Interest Rates, i Are always compounded on an annual basis. Conversion of Nominal Interest rate , r

to Effective Interest Rate, i : m

r  i  1    1  m where: r = nominal interest rate per year m = number of interest periods per year 30

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Compounding Periods 2

Compounded Semi-annually (every six months)

r  i  1    1 2  4

Compounded Quarterly (every three months)

 r i  1    1  4 12

Compounded Monthly 31

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r   i  1    1  12 

Continuous Interest The concept of continuous interest is that the cost or income due to interest flows regularly. If we let the change in the accumulated amount, F over the change in the unit period, n a function of both the accumulated amount F, and rate, r, then;

dF  rF dn F dF n P F  r 0 dn F Ln  rn P n Fn  Pern  P 1  i 

e r  1  i 

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Conversion of continuous interest rate to effective interest rate

i  er  1

F n Future Worth Factor  =  1+i  ; (F/P,i%,n) P Example: A person deposits P100,000 in the bank. a. How much would be his money in the bank after 5 years if interest is 6% per annum compounded annually? F=P  1+i  =100,000  1.06  =P 133,822.56 n

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b. How much would be his money in the bank after 5 years if interest is 6% per annum compounded monthly? F=P  1+i  33

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n

 0.06  =100,000  1+  12  

 5 12

=P 134,885.02

SAMPLE PROBLEMS: A person wishes to accumulate P100,000 in the bank after 5 years. a. How much is he going to deposit now assuming that his money earns 6% per annum ?

P 1 PresentWorth Factor  ; ( P / F , i %, n) n F 1  i 

P

F

1  i 

n



100, 000

1  0.06 

5

 P 74, 726

CASHFLOW-Annual

1 year 2 years 3 years 4 years 5 years 74,726) x 79,209.56 x 83,962.13 x 88,999.86 x 94,339.85 x (1.06) (1.06) (1.06) (1.06) (1.06) = 79,209.56 = 83,962.13 = 88,999.86 = 94,339.85 = 100,000

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SAMPLE PROBLEMS:

A person wishes to accumulate P100,000 in the bank after 5 years. b. How much is he going to deposit now assuming that his money earns 6% per annum ? compounded monthly

P

F

1  i 

n



100, 000  0.06  1   12  

 512 

 P 74,137.22

Alternative solution (compute first, i )

r  i  1    m

P

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F

1  i 

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n

m



12

 0.06  i  1    1  0.061677  6.1677% 12  

100, 000  5

1  0.061677 

 P 74,137.50

Example: Find the nominal interest compounded monthly which is equivalent to 12% pa compounded quarterly? Solution: m

12

4

r  r  0.12     i  1    1  1    1  1   1 m 12  4     r  11.88% pa compoundedmonthly

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INFLATION or DEFLATION: f Inflation is the increase in the price of goods and services from one year to the other, thus decreasing the purchasing power of money.

Deflation involves a decrease in the average price of goods and services resulting to the increase in the purchasing power of money. It is usually associated with a prolonged erosion of economic activity and high unemployment. Some measures of price changes in our economy are the Consumer Price Index (CPI) and Producer Price Index (PPI).

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Consumer Price Index (CPI) Consumer price index (CPI) measures changes in the price level of consumer goods and services purchased by households. The CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically. Sub-indexes and subsub-indexes are computed for different categories and sub-categories of goods and services, being combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the index. It is one of several price indices calculated by most national statistical agencies. The annual percentage change in a CPI is used as a measure of inflation. A CPI can be used to index (i.e., adjust for the effect of inflation) the real value of wages, salaries, pensions, for regulating prices and for deflating monetary magnitudes to show changes in real values. Annual Change Rate  f  38

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Indexn  Indexn 1 100% Indexn 1

Producer Price Index (PPI) Producer Price Index (PPI)_ is a family of indexes that measure the average change over time in the prices received by domestic producers of goods and services. PPIs measure price change from the perspective of the seller. The headline PPI (for finished goods) is a measure of the average price level for a fixed basket of capital and consumer goods for prices received by producers. The producer price index for finished goods is a major indicator of commodity prices in the manufacturing sector. These prices are more sensitive to supply and demand pressures than the more comprehensive consumer price index. Changes in the producer price index are considered a leading indicator for consumer price changes, although only a small portion of the PPI is directly connected to less than half of the CPI. 39

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Example: An economy is experiencing inflation at an annual rate of 5%. If this continues, what will P500 be worth two years from now in terms of today’s pesos? Solution: F 500

P

1  f 

n



1  0.05

2

 453.51

Example: An item presently costs P500. If inflation is at the rate of 5% per year, what will be the cost of the item in 2 years? Solution:

F  P 1  f   F2  P 1  f   500 1  0.05  551.25 n

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2

2

Sixteenth Rule: The cost of the equipment at a new capacity can be computed if the cost of the same equipment is known at a given capacity. The cost adjustment is the ratio of the two capacities raised to the power 0.6 S  CB  C A  B   SA 

0.6

Combination of Price Cost Index and Sixteenth Rule: I CB  C A  n  IK

 S B     S A 

0.6

Example: Six years ago, an 80-kw diesel electric generator costs P400,000. The cost index for this class of equipment six years ago was 187 and is now 194. Determine the cost of a 120 kw unit now? X

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 I  S   194  120  C B  C A  n  B   400 ,000    187  80   I K  S A   P 529 ,267

0 .6

Real Interest Rate,

i'

The real interest rate, i' would be the REAL value of your money’s actual earnings, i after considering the loss in its purchasing power due to inflation, f .

 1  i 1  i'  1  f 

1 i i'  1 1 f

Example IF you P100 deposit in the bank earning 8% pa, what would be the real interest rate if inflation is 5% pa. Solution: After a year your P100 will become

F  100 1.08  108 ( ACTUAL)

But after a year your P108 is only worth

F'

due to inflation.Therefore the real earnings is only



Therefore, the real interest rate is i'  42

i  f NTAldon 0.08  0.05   0.0286  2.86% 1 f 1  0.05

or

108 102.86 ( REAL) 1.05  102.86  100  2.86

2.86 x100%  2.86% 100

DIFFERENTIAL PRICE ESCALATION OR DEESCALATION RATE:

e

_ is a real price change in good or service caused by various factors in the market . It is the increment (%) of price change above or below the general inflation rate f, during a period (normally a year). The increase or decrease in price is in REAL pesos. 1 e  ' j

1 ej

1  f 

e  ' j

1 ej

1  f 

1

For example, if the unit price of the goods is P100 and after a year its price will be escalated or increased by 10% (ej ) , then its unit price will becomeP110 (ACTUAL increase in pesos). But during that time if inflation rate (f) is 5%, therefore the inflated cost should have been P110/1.05=104.76, then the differential price escalation or increase in REAL pesos is 104.76-100= P 4.76; e’j= 4.76% 43

1 ej

1.10 e  1   1  0.0476  4.76% 1  f  1.05

' NTAldonj

' j

ej

Total PRICE ESCALATION: _ The price escalation or deescalation rate is total rate (%) of price change in the unit price, or cost for a fixed amount during the period (normally) a year for good or service. It is the sum of the general price inflation rate and the differential inflation rate plus their product.The increase or decrease in price is in ACTUAL pesos.





1  e j  1  e 'j 1  f  For example, if the unit price of the goods is P100 and after a year its price will be escalated or increased by 10% (ej’ ) , then its unit price will becomeP110. But if inflation projected for the year of 5% is considered, then the actual unit selling price of the goods would be:





FC  PC 1  e j   PC 1  e 'j 1  f  44

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 100 1  0.10 1  0.05   P115 .50

N.2.4. Annuity  It is a series of equal PAYMENTS, A occurring at equal time

intervals. Interest is paid on all accumulated amounts, and the interest is compounded each payment period. The amount of an ANNUITY F, is the sum of all payments A, plus interest if allowed to accumulate at a definite rate of interest from the initial payment up to the end of the annuity term.  An annuity term, n is the time from the beginning of the first

payment period to the end of the last payment period.  It must be noted that the sum F, is expressed at the end of the

last payment period 45

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A. Ordinary Annuity The most common type of annuity. It involves the payment of amount, A at the end of each interest period.

Future Worth of Ordinary Annuity

P 0

1 A

2 A

 1  i n  1 Fn  A  i   3 A

4 A

n A

Fn Present Worth of Ordinary Annuity 46

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A P n 1  i 

 1  i n  1   i  

B. Annuity Due The uniform payments, A are made at the beginning of each interest period.

 1  i n 1  1  i   Fn  A  i  

Future Worth of Annuity Due

P 0 A

1

2 A

3 A

4 A

n A Fn

Present Worth of Annuity Due

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 1  i n 1  1  i  A P  n  i 1  i   

C. Deferred Annuity It is also an ordinary annuity but the payment of the first amount is deferred a certain number of periods after the first. For example, the first annuity payment could be made after 3 annuity terms instead of after the first annuity term.

 1  i n  1 Fn  A  i  

Future Worth of Deferred Annuity

m 0

P 0

1

2

1 A

2 A

3 A

4 A

n A

3 Fn

Present Worth of Deferred Annuity 48

NTAldon

A P 1  i n m

 1  i n  1   i  

D. Continuous Cash Flow Continuous Compounding Continuous flow of funds means a series of cash flows occurring at infinitesimally short intervals of time, corresponding to an annuity having an infinite number of short periods.

 1  i   1 Fn  A  i   n

r i m A A m

49

NTAldon

A= cash flow in a period A = sum of cash flows in a year m = number of periods in a year n = total number of periods

Continuous Cash Flow Continuous Compounding…..   r    1     A   m   Fn   r m m  

 mn  1     

As m approaches infinity,

 e 1   Fn  A   r  rn

50

Where NTAldon

A

  r    1       m   A r   

m    rn  r 

  1     

m r

  r  1   m   e   

A P  rn e

 e 1     r 

is the sum of continuous cash flows in one year

rn

Ordinary Annuity

 1  i n  1 Fn  A ; i  

A P n 1  i 

 1  i n  1   i  

Discrete Cash Flow -Continuous Compounding

 e rn  1 Fn  A r ;  e 1 

A P  rn e

 e rn  1  r   e 1 

Continuous Cash Flow- Continuous Compounding

51

 e rn  1 Fn  A ;  NTAldon  r 

rn  A e  1 P  rn   e  r 

Interest Factors 1. Single-Payment Future-Worth Factor; F= P (F/P, i%, n)

F n  1  i   F/P,i%, n  P 2. Single-Payment Present-Worth Factor; F= P (F/P, i%, n)

P 1   P/F,i%, n  n F 1  i  3. Future Worth Annuity Factor; F= A (F/A, i%, n)

F 1  i   1   F/A,i%, n  A i n

4. Present Worth Annuity Factor; F= A (P/A, i%, n)

52

n   P 1  i 1   P/A,i%, n  n ANTAldon 1  i  i

Example: 1. A loan of one million pesos is to paid in 10 years at an interest rate of 8.5% pa. a. How much should the 10 annual payments be? Solution: P 0

1 A

2 A

3 A

4 A

5 A

6 A

7 A

8 A

9 A

10 A F

 i 0.085  n 10    A  P1  i    1 , 000 , 000 1 . 085     152,407 .71 n 10  1  i   1  1.085   1 b. What would the balance be after the 6th payment ?  1  i n  1 n Balance  P1  i   A  i    1  0.085 6  1 1,000,000 (1.085)  152,407 .71   499,226 .13 0 . 085   6

2. If one million pesos is to be accumulated in 10 years at an interest rate of 8.5% pa, how much should the 10 annual payments be?

53

   0.085  i A  F   1,000,000    67,407 .70 n 10 NTAldon     1  i  1 1 . 085  1    

GRADIENT 1. Uniform Arithmetic Gradient It is also an ordinary annuity but disbursement or payment A increases or decreases by a uniform amount G each period. P 0

1 A

2 A+G

3 n A+2G A+(n-1)G FAn+FGn

Future Worth of Arithmetic Gradient, G : FGn n G  1  i   1  FGn    n i  i 

54

F  FAn  FGn

NTAldon n

 1  i n  1 FAn  A  i  

GRADIENT 2. Geometric Gradient It is also an ordinary annuity but disbursement or payment A increases or decreases by a uniform rate g each period

P 0

1 A

2 A(1+g)

3 n A(1+g)2 A(1+g)n-1 Fn

Future Worth of Geometric Gradient, G : Fn

 1  i n  1  g  n  Fn  A  ig  

When g=i 55

NTAldon

Fn  nA1  i 

n 1

SAMPLE PROBLEM 1.What is the accumulated amount of a series of payments when the initial payment of P1000 increases by P200 each period, until the third period if cost of money is 10% pa.

Required: Fn Solution: A= P1000 ,G =P200, and i =10% A 1 P1,000

0

CASH FLOW A+G 2 P1,200

A+2G 3 P1,400 F3

Fn  FAn  FGn  1  i n  1  G  1  i n  1  Fn  A   n   i i   i    1  0.10 3  1  200  1  0.10 3  1  Fn  1000   3  P3,930   0.10 0.10 0.10     Another way of solving this is to project individually the Future Worth of each payment. F3  1000 1.1  1200 1.1  1400  P 3,930 2

56

NTAldon

2. What is the accumulated amount of a series of payments when the initial

payment of P1,000 increases by 15% each period, until the third period if cost of money is 10% pa. Required: Fn Solution: A= P1,000 , g =15%, and i =10% A 1 P1000

0

CASH FLOW A(1+g) 2 P 1000(1.15)=1,150

A(1+g)2 3 2 P1000(1.15) = P1,725 F3

 1  i n  1  g  n   Fgn  A    ig   3  3  1  0.10   1  0.15   F  1, 000   P3, 798  g3 0.10  0.15    

Another way of solving it is to project individually the Future Worth of each payment. Fg 3  1000 1.1  1150 1.1  1725  P3,798 2

57

NTAldon

BONDS _is a certificate of indebtedness of a corporation usually for a period not less than ten years and guaranteed by a mortgage on certain assets of the corporation or its subsidiaries. Bonds are issued when there is a need for more capital such as for expansion of the plant or the services rendered by the corporation. The face or par value of a bond is the amount stated on the bond. When the face value has been repaid, the bond is said to have been retired or redeemed. The bond rate is the interest quoted on the bond. 58

NTAldon

Classification of Bonds 1. Registered Bonds _ The name of the owner of this bond is recorded on the record books of the corporation and interest payments are sent to the owner periodically without any action on his part. 2. Coupon Bonds _ Have a coupon attached to the bond for each interest payment that will come due during the life of the bond. The owner of the bond can collect the interest due by surrendering the coupon to the offices of the corporation or at specified banks.

59

NTAldon

BONDS…  Equipment obligation bonds _ refer primarily to bonds whose 

    

60

guarantee is a lien on equipment. Registered bonds _ the owner's name is recorded in the books of the corporation, and the interest is paid periodically to the owner without their asking for it. Joint bonds _ bonds which are issued by two or more corporations Par value of the bond or face value_ is the amount stated on the bond. Bond rate _ is the rate of interest quoted on the bond. Redemption or disposal price—usually equal to par value. Mortgage bonds _ bonds whose security is mortgaged on certain specified assets of the corporation. NTAldon

BONDS…  Debenture bonds _ bonds without security behind them except a

promise to pay by the issuing corporation  Callable bond _entitles the issuer to pay off the principal prior to the stated maturity date. Similarly, the owner of a putable bond _can force the issuer to pay off the principal before the maturity date.  Convertible bond _gives the bondholder the right to exchange the bond for shares of the issuer's common stock at a specified date.  Municipal bonds _are issued by state and local governments and other public entities, such as colleges and universities, hospitals, power authorities, resource recovery projects, toll roads, and gas and water utilities. Municipal bonds are often attractive to investors because the interest is exempt from federal income taxes and some local taxes. There are two types of municipal bonds: general obligation bonds and NTAldon 61 revenue bonds.

62

NTAldon

Retirement of Bonds  The corporation may issue another set of

bonds equal to the amount of bonds due for redemption.  The corporation may set up a sinking fund into which periodic deposits of equal amount are made. The accumulated amount in the sinking fund is equal to the amount needed to retire the bonds at the time they are due. 63

NTAldon

Bond Periodic Expense A = periodic deposit to the sinking fund I = interest on the bonds per period A+I = total periodic expense F = accumulated amount, (par value of the bond) needed to retire the bond i = rate of interest in the sinking fund r = bond rate per period 64

NTAldon

to the sinking fund, A

  i A  F  n  1  i   1

Interests on the Bonds per Period, I

I  Fr

Total Periodic Expense: A+I   i A  I  F   Fr n  1  i   1 i = rate of interest in the sinking fund r = bond rate per period n = number of periods 65

NTAldon

Bond Value, P  The present worth of all future amounts that are expected to be

received through ownership of the bond.

C P n 1  i 

 1  i n  1  Fr  n   i1  i  

P = value of the bond n periods before redemption F = amount needed to retire the bond C = redemption price, usually equal to F (also known as Principal, Face Value, Par Value) r = bond rate per period n = number of periods before redemption i = investment rate or yield period 66

NTAldon

Sample Problems-BONDS 1. A bond issue of P200,000, in 10-years, in P1,000 units paying 16% nominal interest in semi-annual payments, must be retired by the use of sinking fund that earns 12% pa compounded semi-annually. What is the total semi-annual expense?  Solution: F = P200,000 r = 16%/2= 8% per semi-annual

i = 12%/2 = 6% per semi-annual  Total semi-annual expense = A + I

67

  i Total Semi  annual Expense  F    Fr n  1  i   1    0.06  200, 000    200, 000  0.08  20  1  0.06   1  NTAldon P 21, 437

Sample Problems-Bonds 2. Find the current price of a 10-year bond paying 6% per year that is redeemable at par value, if bought by a purchaser to yield 10% per year. The face value of the bond is P100,000 Solution:

n 10      C 1  i  1 100,000 1  0.1  1  P  Fr    100,0000.06  n n  10 10  1  i   i1  i   1  0.1  0.101  0.10  P  38,554.33  38,867.40  75,421.73

68

NTAldon

Sample Problems-Bonds 3. Find the price of a 10-year bond , two years before its redemption, paying 6% per year that is redeemable at par value if bought by a purchaser to yield 10% per year. The face value of the bond is P100,000 Solution:  1  i n  1 100,000  1  0.12  1  C P  Fr    100,0000.06   n n  2 2 1  i   i1  i   1  0.1  0.10 1  0.10   P  82,644.83  10,413.22  93,058.05 69

NTAldon

Sample Problems-Bonds 4. A 10-year bond with a par value of P1,000 and with bond rate of 10% payable annually is sold now for P1080. If the yield is to be 12%, how much should the redemption price be at the end of 8 years? Solution:

 1  i n  1  1  0.128  1  C C P  Fr   1,0000.10   1080  n n 8 8  1  i        i 1  i 1  0.12 0.12 1  0.12     C  1,444.07

70

NTAldon

DISCOUNT FACTORS and EQUIVALENCE

71

NTAldon

DEPRECIATION

 The decrease in the value of equipment, building or other structures

due to the passage of time. The causes of depreciation may be physical or functional.

 Examples of physical depreciation are, wear and tear, corrosion, accident,

deterioration due to age or elements.

 The rest are functional depreciation and one good example is

obsolescence. This is caused by technological advances or developments which make an existing property obsolete. Even though the property has suffered no physical change, its economic serviceability is reduced because it is inferior to improved types of similar assets that have been made available through advancements in technology

 Depletion_ Another kind of depreciation is material loss due to 72

consumption or exploitation particularly applicable to natural resources. NTAldon

Purposes of Depreciation  To provide for the recovery of capital which has been invested in

physical property

 To enable the cost of depreciation to be charged to the cost of

producing products or services that results from the use of property.

 For engineers, depreciation is included as cost of production of

any product or the rendering of any service where equipment is used to provide for the replacement either at the end of its physical or economic life or at the time when its operation no longer results in satisfactory profit or to provide for the maintenance of capital to replace the decrease in the value of equipment

73

NTAldon

 Maintenance _conveys the idea of constantly keeping a property in good condition;  Repairs _connotes replacing or mending broken or worn parts of a property.  Service life of the property _is the period during which the use of property is economically

feasible. Both physical and functional depreciation are taken into consideration in determining service life. The term is synonymous with economic or useful life. In estimating the probable service life, it is assumed that a reasonable amount of maintenance and repairs will be carried out at the expense of the property owner.  Recovery Period_ The number of years over which the basis of the property is recovered through

the accounting process. For the classical methods of depreciation, this is normally the useful life. Under the MACRS, this period is the property class for the General Depreciation System (GDS), and it is the class life for the Alternative Depreciation System (ADS)  Present Value _ The value of the asset in its condition at the time of valuation  Salvage Value_ is the net amount of money obtainable from the sale of the used property over and

above any charges involved in removal and sale.  If a property is capable of further service, its salvage value may be higher. This is not necessarily true, however, because

other factors, such as location of the property, existing price levels, market supply and demand, and difficulty in dismantling, may have an effect. The term salvage value implies that the asset can give some type of further service and is worth more than merely its scrap or junk value.

74

NTAldon

 Scrap or junk value_ is the amount of money obtained when the property cannot





  



75

be disposed as a useful unit but rather dismantled and sold as junk to be used again as a manufacturing raw material. Book value _ also known as depreciated value, is the worth of the property as recorded in the books of account of the enterprise and is equal to the original cost less the amounts which have been charged to depreciation. It is sometimes called the unamortized value. Market value _ The price which could be obtained for an asset if it were placed on sale in the open market. Is the amount which a willing buyer will pay to a willing seller for the property when neither one is under compulsion to buy or sell. Fair Value _ The value is usually determined by a disinterested third party in order to establish a price that is fair to both the seller and the buyer Replacement value _ The cost necessary to replace an existing property at any given time with one at least equally capable of rendering the same service. Adjusted Cost basis_ The original cost of the asset, adjusted by allowable increases or decrease , is used to compute depreciation and depletion deductions. For example, the cost of any improvement to a capital asset with a useful life greater than one year increases the original cost basis, an d a casualty or theft loss decreases it. If the basis is altered , the depreciation deduction may need to be adjusted. Basis, or cost basis_ The initial cost of acquiring an asset (purchase price plus tax) , including transportation expenses and other normal costs of making an asset serviceable for its intended use. This amount is also called the unadjusted cost basis. NTAldon

Methods of Depreciation A. Uniform Depreciation 1.

Straight Line Method This is the simplest and most widely used method compared to any other method. It is based on uniform annual charge. It doesn’t take into account the interest or profit earned on accumulated depreciation fund. It is a standard accounting method acceptable by the Bureau of Internal Revenue.

d Tn  n d  FC  SV d L BVn  FC  n d  76

NTAldon

where:

d = periodic depreciation dTn= total depreciation after nth period FC = First cost SV= Salvage Value BVn= Book value after nth period L = Service Life n = nth period

2. Sinking Fund Method It is based on uniform annual charge. It is assumed that a sinking fund is created to replace the original cost of equipment. All amounts in the sinking fund (including interest) earn interest. The company uses the amount accumulated in its operations, and therefore assumed to earn interest. It is generally used for economy-study purposes.

  i d  FC  SV  L     1  i  1

d Tn 77

 1  i n  1  d  i  

BVn  FC  d Tn

NTAldon

B. Non-Uniform Depreciation 1. Declining-Balance-Method

Also known as Matheson formula. The annual depreciation cost is a constant percentage of the salvage value at the beginning of the year. The annual depreciation cost differs every year, and decreases in absolute value as time progresses. The salvage value of the property can never depreciate to zero. f = fractional depreciation

d n  FC1  f 

n 1

f 

BVn  FC1  f 

n

78

NTAldon

BVn n L  1  f  SV

SV  FC1  f 

L

1/ L

 SV  f  1    FC 

2. Double-Declining Balance Method This method is similar to the declining balance method except that the f is replaced by 2/L.

3. Sum-of-the-Years Digit Method The annual depreciation cost differs each year and decreases as time progresses. It provides for a rapid depreciation during the early years of life of property, hence faster recovery of capital

dn

 FC  SV L  1  n   L  1L / 2

d Tn  79

FC  SV 2L  1  nn L  1L

NTAldon

BVn  FC  dTn

4. Service-Output Method This method assumes that the total depreciation that has taken place is directly proportional to the quantity of output of the property up to that time. This method has the advantage of making the unit cost of depreciation constant and giving low depreciation expense during periods of low production.

FC = first cost of equipment SV = salvage value of equipment after its service life QT = total units of output up to its service life Qn = number of units of output during the nth year QTn = total number of units of output on the nth year dn = annual depreciation during the nth year dTn = total depreciation on the nth year

 Depreciation FC  SV  d  unit output QT dn

 FC  SV   Q QT

BVn  FC  dTn 80

NTAldon

n

dTn

 FC  SV   Q QT

Tn

5. Working Hours Method This method assumes that the total depreciation that has taken place is directly proportional to the operating time of the equipment. This method has the advantage of making the unit cost of depreciation constant and giving low depreciation expense during low operating or utilization period.

FC = first cost of equipment SV = salvage value of equipment after its service life HT = total hours of operation up to its service life Hn = hours of operation during the nth year HTn = total hours of operation on the nth year dn = annual depreciation during the nth year dTn = total depreciation on the nth year

FC  SV  Depreciation d  Operating Period HT

81

NTAldon

dn 

FC  SV  H

n

dTn 

FC  SV  H

Tn

HT

HT

C. Depletion This method is usually applicable to natural resources such as petroleum deposits, natural gas, mines, timberlands, etc. A depletion fund is provided for the recovery of the capital invested in the said undertaking. The annual charge set aside for the gradual extraction is called depletion cost. 1. Unit Method This method is similar to service output method of depreciation. The depletion charge depends upon the initial cost of the property and the number of units in the property.

dn

82

 Fc  SV   Q QT

n

2. Percentage Method This method allows a fixed percentage of the gross income received during the year to be the depletion charge. Considering that the total depletion charge may exceed the initial cost of the property, it is required that for any year the depletion charge should not exceed 50% of the net taxable income for that year obtained by deducting all expenses excluding depletion from the gross income. NTAldon

SAMPLE PROBLEMS 1. An asset for drilling was purchased and placed in service by a petroleum production

company. Its cost basis is P6M and has an estimated book value of P1.2 M at the end of an estimated useful life of 14 years. Compute the book value at the end of the fifth year of life by the straight-line method FC  SV 6  1.2   P 0.3429M L 14 BV5  6  0.3429 5  P 4.2855

d3 

2. The original cost of a certain piece of equipment is P500,000 and is depreciated by a 12% sinking fund method. Determine the annual depreciation charge if the book value of the equipment after 10 years is the same as if it had been depreciated at P40,000 each year by straight line formula.  Using straight line Method:

Total depreciation  40,000 (10)  400,000 SalvageValue  500,000  400,000  100,000  Using sinking fund Method:

83

   i  0.12   d  FC  SV   400 , 000    22,793.67 10    1  i  1   1  0 . 12  1     NTAldon

3. In order to make it worthwhile to purchase a piece of equipment, the annual depreciation costs for the equipment cannot exceed P295,000 at any time. The original cost of the equipment is P3M and a salvage value of P50,000. Determine the length of service life necessary if the equipment is depreciated by a. Sum-of-the-years-digit method

d1 

FC  SV L  1  n L  1L / 2

Maximum depreciation occurs on the 1st year: 295,000 

3,000,000  50,000 L  1  1 L  1L / 2

L  19 years

b. Straight-line method

3,000,000  50,000 FC  SV  295,000  L L L  10 years

d

84

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4. Solve, using the declining-balance- method, the depreciation cost of an equipment on the 8th year, if its book value on the 7th year is P250,000. The Book value of the equipment is computed to be P460,512 on the 5th year.  Soln: FC 

BV7 BV5 250,000 460,512 250,000 7 5    ;    1  f 1  f 7 1  f 5 1  f 7 1  f 5 460,512 1 2

 250,000  1 f     0.7368  460,512  f  0.2632 d8  BV7 f  250,0000.2632)   65,800

85

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5. An asset for drilling was purchased and placed in service by a petroleum production company. Its cost basis is P6M and has an estimated book value of P1.2 M at the end of an estimated useful life of 14 years. Compute the depreciation amount in the third year and the book value at the end of the fifth year of life by SYD method • Solution: d3  FC  SV 

L  1  n  6  1.2 14  1  3  P 0.5486 M L  1L/ 2 14  114/ 2

BVn  FC  dTn  FC 

FC  SV 2L  1  nn  6  6  1.2 214  1  55  3.257 L  1L 14  114

or BV5  FC  dT 5  6  6  1.2 86

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14  13  12  11  10  P 3.257 M 105

6. To develop an oil well containing an estimated 4M barrels of oil required an initial investment of P3B. in a certain year, 400,000 barrels were produced from this well. Determine the depletion charge during that year.

dn

 FC  SV   Q QT

n

 3x10  d 400,000  P300 M 9

4 x10

87

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6

88

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8.

An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and book value during the 8th year using a. Straight-line method b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

Solution: a. Straight line method

1,000,000  100,000   P 90,000 / year FC  SV d L 10 BVn  FC  dTn  FC  d (n)

d

 1,000,000  90,000 8  P 280,000

89

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An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and book value during the 8th year using a. Straight-line method b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

8.

Solution: b. Sinking fund method

90

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  i d  FC  SV   L  1  i   1   0.1  1,000000  100,000    P56,471 10  1  0.10   1  1  i n  1 BV8  FC  dT 8  FC  d   i    1  0.10 8  1  1,000,000  56,471   P534,204 0.10  

8.

An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and book value during the 8th year using a. Straight-line method b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

Solution: c. Declining balance method

d n  FC1  f 

n 1

1 L

 f ;

BVn  FC1  f   SV 1  f 

 100,000   SV  f 1     ;  1   FC   1,000,000  d n  FC 1  f 

n 1

n L

n

1 10

 0.2057

 f  d8  1, 000, 000 1  0.2057 

81

 0.2057   P 41, 032

BVn  FC 1  f  1, 000, 00 1  0.2057   P158, 444 n

91

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8

8.

An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and book value during the 8th year using a. Straight-line method b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

Solution: d. Sum-of-the-years-digit method (SYDM)

FC  SV L  1  n 2 d  1,000,000  100,000 10  1  8 2  P49,091 8 L  1L 10  110 FC  SV 2 L  1  n  n BVn  FC  dTn dTn  L  1L 1,000,000  100,000 210   1  88  P149,090 BV8  1,000,000  10  110

dn 

92

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C. Modified Accelerated Cost Recovery System (MACRS) The principal method for computing depreciation deductions for property in engineering projects in the U.S.. Unlike the conventional method of computing depreciation which requires estimates of useful life (L) and salvage value (SV) at the end of useful life, in MARCS, the SV is defined to be zero, and the useful life estimates are not used directly in calculating depreciation amounts. MACRS consists of two systems for computing depreciation deductions; The main system is called General Depreciation System (GDS), and the second system is called the Alternative Depreciation System (ADS). When an asset is depreciated under MACRS, the following information is needed before deductions can be calc:  The cost basis (B)  The date the property was placed in service  The property class and recovery period  The MACRS depreciation method to be used (GDS or ADS)  The time convention that applies (half-year)

Note: The depreciation period during the first year is only ½ year. The other ½ is extended after the last year of the recovery period: Example: Recovery period = 3 years 1st year = 0.5 year; 2nd year = 1 year; 3rd year = 1 year; 4th year = 0.5 year

dn 

2 for 3,5,7,10 L



1.5NTAldon for 15,20 L

93 dn

200% using Declining Balance method with switch-over to Straight-Linemethod (whichever is higher) 150% using Declining Balance method with switch-over to Straight-Line-method (whichever is higher)

3. Depreciation Methods, Time Convention, Recovery Rates  GDS 3,5,7 and 10-year personal property classes: The 200% DB 

  

 94

method, which switches to the SL method when that method provides a greater deduction. GDS 15 and 20-year personal property classes: The 150% DB method, which switches to the SL method when that method provides a greater deduction. GDS nonresidential real and residential rental property classes: SL method over the fixed GDS recovery periods. ADS: The SL method for both personal and real property over the fixed ADS recovery periods. Half-year time convention is used in depreciation calculations for tangible personal property. If asset is disposed of before the full recovery period is used, then only half of the normal depreciation deduction can be taken for that year. If the asset is disposed of in year n+1 the final BV of the asset will be zero. NTAldon

When are you going to Switch-over from DecliningBalance Method to Straight-Line?  Compare the value of recovery rate:  Once the value of SL recovery rate is equal or greater than DB, then you have to switch-

over to SL.

 For example for 7-year recovery period

The recovery rate=2/L (except the first year, 1/L)

DB

SL

1st year 2/2L= 1/L 1/7 2nd year 2/7=1/3.5 > (7-0.5 )= 1/6.5 1.5 3rd year =1/3.5 > 1/(7-1.5) =1/5.5 2.5 4th year =1/3.5 > 1/(7-2.5) = 1/4.5 3.5 5th year =1/3.5 = 1/(7-3.5) = 1/3.5 6th year =1/3.5 < 1/(7-4.5) = 1/2.5 7th year =1/3.5 < 1/(7-5.5) =1/1.5 8th year =1/3.5 1-(sum of 1 to 6)7.0 95

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period use DB use DB use DB use DB 4.5 5.5 6.5

switch-over to SL

• For a 5-year recovery period The DB recovery rate=2/L (except the first year, 1/L) The SL recovery rate=1/LREMAINING

DB 1st year 1/5=0.2 2nd year (1-0.2)(2/5)=0.32 3rd year (1-0.52)(2/5)=0.192 4th year (1-0.712)(2/5)=0.1152 5th year 6th year

96

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SL 0.2 (1-0.2)/4.5=0.1778 (1-0.52)/3.5=0.1371 (1-0.712)/2.5=0.1152 (1-0.8272)/1.5=0.1152 (1-0.9424) =0.0576

 Sample MACRS Problem

1. A firm purchased and placed in service a new piece of semiconductor manufacturing equipment. The cost basis for the equipment is P100,000. Using MACRS Method, determine (a) the depreciation charge permissible in the fourth year, (b) the cumulative depreciation through the third year, and (c) the BV at the end of the fourth year, (d) the BV at the end of the fifth year if the equipment is disposed of at that time. 97

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Solution: From Table N-1, the semi-conductor (electronic manufacturing equipment has a class life of six years and a GDS recovery period of five years (Asset Class 36).

d4  0.1152 (100,000)  P11,520

(a) The depreciation deduction, or cost-recovery allowance , that is allowable in year four (d4) is =0.1152 b) Accumulated depreciation through year three,d3, is the sum of depreciation amounts in years one through three:

dT3=d1+d2+d3

dT 3  100,000(0.20  0.32  0.192)  P71,200 c) The BV at the end of year four (BV4) is the cost basis less depreciation charges in years from one through four:

BV4  100,000 100,000 (0.20  0.32  0.192  0.1152)  P17,280

e) The depreciation deduction in year five when the equipment is disposed of prior to year six.

d5=(0.5)(0.1152)(100,00)= P5,760 BV5= BV4-d5 = 17,280-5,760 = P11,520 DB 1/5 =0.2000 (1-0.2)(2/5) =0.3200 (1-0.52)(2/5) =0.1920 (1-0.712)(2/5)=0.1152

1st year 2nd year 3rd year 4th year 5th year NTAldon 98 th 6 year

SL 0.2000 (1-0.2)/4.5=0.1778 (1-0.52)/3.5=0.1371 (1-0.712)/2.5=0.1152 1-0.8272)/1.5=0.1152 (1-0.9424) =0.0576

CAPITAL _

refers to wealth in the form of money or property that can be used to produce more wealth.

Two forms of capital, debt and equity 99

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CAPITAL INVESTMENT FIXED CAPITAL WORKING CAPITAL 100

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CAPITAL INVESTMENT  FIXED CAPITAL

The capital needed to supply the necessary manufacturing and plant facilities  WORKING CAPITAL

The capital necessary for the operation of the plant 101

NTAldon

TOTAL CAPITAL INVESTMENT  The sum of the fixed-capital investment

and the working capital is known as the total capital investment.

Fixed Capital Investment + Working Capital Total Capital Investment 102

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FIXED CAPITAL INVESTMENT  Before an industrial plant can be put into operation, a large

amount of money must be supplied to purchase and install the necessary machinery and equipment. Land and service facilities must be obtained, and the plant must be erected complete with all piping, controls and services. In addition, it is necessary to have money available for the payment of expenses involved in the plant operation. The fixed-capital portion may be further subdivided into  manufacturing fixed-capital investment and  non-manufacturing fixed-capital investment. 103

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FIXED CAPITAL INVESTMENT 

104

Manufacturing fixed-capital investment represents the capital necessary for the installed process equipment with all auxiliaries that are needed for complete process operation. Expenses for piping, instruments, insulation, foundations, and site preparation are typical examples of costs included in the manufacturing fixed-capital investment. NTAldon

FIXED CAPITAL INVESTMENT  Non-manufacturing fixed capital investments  are fixed capital required for construction overhead and for all plant

components that are not directly related to the process operation is designated as the non-manufacturing fixed-capital investment.  These plant components include the land, processing buildings, administrative and other offices, warehouse, laboratories, transportation, shipping and receiving facilities, utility and wastedisposal facilities, shops, and other permanent part of the plant.  The construction overhead cost consists of field-office and supervision expenses, home-office expenses, engineering expenses, miscellaneous construction costs, contractor’s fees, and contingencies. In some cases, construction overhead is proportioned between manufacturing and non-manufacturing fixed-capital investment. 105

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FIXED CAPITAL INVESTMENT 1. Direct Costs Process equipment, Instrumentation/controls, piping, electrical, buildings, yard improvements, service utilities, land

2. Indirect Costs Engineering and supervision, construction expenses of temporary facilities

106

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WORKING CAPITAL  The working capital for an industrial plant consists of the total

amount of money invested in 1. raw materials and supplies carried in stocks, 2. finished products in stock and semi-finished products in the process of being manufactured, 3. accounts receivable, 4. cash kept on hand for monthly payment of operating expenses, such as salaries, wages, and raw-materials purchases, 5. accounts payable, and 6. taxes payable.

107

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ACCOUNTING FUNDAMENTALS  All accounting is based on the fundamental accounting equation, which is ; 

 Assets = liabilities + owner’s equity 

 Where:

assets _are those things of monetary value that the firm possesses, liabilities _are those things of monetary value that the firm owes, and owner’s equity _is the worth of what the firm owes to the stockholders (also referred to as equities, net worth, etc.)  Basic Engineering Accounting Terms:     

108

Revenue = total income (or total savings) Net profits = Gross Profits - income tax Gross profits = Net sales – Costs of Sales Income tax = (Gross Profits) ( tax rate) Cash flow = Net Profits + Depreciation

NTAldon

Generally Accepted Accounting Principles GAAP is a codification of how CPA firms and corporations prepare and present their business income and expense, assets and liabilities on their financial statements. GAAP is not a single accounting rule, but rather the aggregate of many rules on how to account for various transactions. The basic principles underlying GAAP accounting are set forth below.  The Basic Principles 1. 2.

3. 4. 5.

109

Principle of regularity: Regularity can be defined as conformity to enforced rules and laws. Principle of consistency: This principle states that when a business has once fixed a method for the accounting treatment of an item, it will enter all similar items that follow in exactly the same way. Principle of sincerity: According to this principle, the accounting unit should reflect in good faith the reality of the company's financial status. Principle of the permanence of methods: This principle aims at allowing the coherence and comparison of the financial information published by the company. Principle of non-compensation: One should show the full details of the financial information and not seek to compensate a debt with an asset, revenue with an expense, etc. NTAldon

Generally Accepted Accounting Principles Principle of prudence: This principle aims at showing the reality "as is": one should not try to make things look prettier than they are. Typically, revenue should be recorded only when it is certain and a provision should be entered for an expense which is probable. 7. Principle of continuity: When stating financial information, one should assume that the business will not be interrupted. This principle mitigates the principle of prudence: assets do not have to be accounted at their disposable value, but it is accepted that they are at their historical value. 8. Principle of periodicity: Each accounting entry should be allocated to a given period, and split accordingly if it covers several periods. If a client pre-pays a subscription (or lease, etc.), the given revenue should be split to the entire time-span and not counted for entirely on the date of the transaction. 9. Principle of Full Disclosure/Materiality: All information and values pertaining to the financial position of a business must be disclosed in the records. 10. Principle of Utmost Good Faith: All the information regarding to the firm should be disclosed to the insurer before the insurance policy is taken 6.

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ACCRUAL  a method of accounting that counts income or expenses at the time they are earned or

incurred, irrespective of when money is received or paid

 when the business performs a service, makes a sale or incurs an expense, the

accountant enters the transaction into the books, whether or not cash has been received or paid.

 it measures the performance and position of a company by recognizing economic

events regardless of when cash transactions occur. The general idea is that economic events are recognized by matching revenues to expenses (the matching principle) at the time in which the transaction occurs rather than when payment is made (or received). This method allows the current cash inflows/outflows to be combined with future expected cash inflows/outflows to give a more accurate picture of a company's current financial condition

111

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FINANCIAL STATEMENTS A.

Income Statement

 The income statement is a computation of the project’s total

revenue and total costs for one period of fiscal year, thereby arriving at the concern’s net income or deficit within the period, together with its performance in terms of profitability and cost control. It differs from the “cash budget” in the sense that it follows the “actual concept” in accounting, by which revenues should be associated with the costs involved in realizing the former within the period of occurrence. A model format for income statement preparation is presented. An analysis of each account in the presentation follows:

 Profit (loss) = revenues – expenses  Gross Profit = net Sales – cost of Sales 112

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NET SALES Net sales_ in pesos are arrived at by subtracting sales returns, allowances, and discounts from gross sales.  Sales returns_ represent goods sold which could not meet

customer requirements and thus have been returned.  Allowance_ refer to goods which cannot be sold due to spoilage, wrong specification, and similar cause;  Sales discount_ are price reduction occasionally given in favor of customer. The latter items are to be considered as different from sales discount favoring the project, which are entered in the ”other income” account of the statement. 113

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COST OF SALES Cost of sales_ is a function of  raw materials used,  direct labor expenses, and  factory overhead accounts.

The factory overhead accounts are itemized as follows:  materials and labor expenses indirectly related with production;  heat, light, and power required for manufacturing;  maintenance costs associated with productive fixed assets supplies needed to produce fixed assets;  taxes associated with the manufacturing fixed assets;  and insurance expenses related to the productive operation. 114

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Operational costs A. Variable Costs

Raw materials, direct labor, utilities, direct supervision, laboratory charges, royalty, packaging, spoilage, losses A. Fixed costs Depreciation, taxes, insurance, interest, overhead, management expenses (GAE)

115

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Pro-f orma Income Statements Y ears ending: 31 December 1st year 308,000

2nd year

3rd year

300,000 (8,000) 308,000 (8,000) 300,000 789,000 (63,120) (15,780) 710,100

300,000 (8,000) 308,000 (8,000) 300,000 828,000 (66,240) (16,560) 745,200

56,160 441 56,601 5,000 61,601 (6,000) 55,601 18,144

58,890 463 59,353 6,000 65,353 (7,000) 58,353 19,051

(9,000) 306,035

118,659 13,860 25,162 7,126 11,010 43,010 2,600 3,819 298,991 9,000 (10,000) 297,991

124,632 14,553 26,764 7,126 11,471 43,010 2,600 2,887 310,447 10,000 (11,000) 309,447

Co sts o f sales

306,035 (20,000) 286,035

20,000 317,991 (21,000) 296,991

21,000 330,447 (22,000) 308,447

Gro ss pro fit

388,965

413,109

436,753

P ro ductio n (in Units) A dd: Invento ry, beginning Units available fo r sale Less: Invento ry investments Sales, gro ss Sales, gro ss (in P ) Less: sales returns and allo wances sales disco unts Sales, net

308,000 (8,000) 300,000 750,000 (60,000) (15,000) 675,000

Co st o f sales: Raw materials: P urchases A dd: freight in To tal purchases

57,500 420 57,920

A dd:invento ry beginning Co st o f raw materials available fo r use Less: Invento ry, ending Co st o f raw materials A dd:

Direct labo r

57,920 (5,000) 52,920 17,280

Overhead: Indirect materials Indirect labo r Heat, light and po wer M aintenance Supplies Depreciatio n Taxes Insurance, etc. M anufacturing co sts

113,009 13,200 50,640 7,126 10,499 43,010 2,600 4,751 315,035

A dd: Go o ds-in pro cess invento ry, begnng Less:Go o ds- inpro cess invento ry, ending Co sts o f go o ds available fo r sale

A dd: finished-go o ds invento ry, beginning Co sts o f go o ds available fo r sale Less: finished-go o ds invento ry, ending

116

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388,965 1s t year

413,109 2nd year

436,753 3rd year

General and administrative salaries36,480

38,304 6,794 189

40,220 7,051 198

3,600

3,600

5,520 114 768

6,012 120 806

6,550 126 846

700 90,260

700 56,525

700 59,291

7,439 16,620

7,794 17,451

8,168 18,324

43,188 13,500 80,747

45,435 14,202 84,882

47,681 14,904 89,077

Operating expenses

171,007

141,407

148,368

Operating pro fit

217,958

271,702

288,385

28,506

27,714

24,546

28,506

27,714

24,546

189,452

243,988

263,839

Gro ss pro fit Operating expenses: General and administrative salaries:

Fringe benefits Research and develo pment Engineering co sts Depreciatio n

6,511 180 36,387 3,600

Taxes Insurance Office supplies Heat, light and po wer Telepho ne Water supply M iscellaneo us: A mo rtizatio n To tal Selling expenses: Salaries Sto rage o f go o ds B illing Transpo rtatio n P ublic relatio ns A dvertisment, sales taxes M iscellaneo us: bad debts To tal

Financial expenses (net o f o ther inco me): Interest B o rro wing co sts To tal

P ro fit befo re inco me tax

P ro visio n fo r inco me tax

Net inco me (net lo st)

(56,308) 133,144

A dd: Retained earnings, beginning

117

NTAldonLess: Cash dividends, declared Retainend earnings, ending

(98,038) 35,106

(75,396)

(82,344)

168,592

181,495

35,106

105,660

(98,038) 105,660

(98,038) 189,117

CASH FLOW  The cash-flow statement or the” cash budget” is a systematic presentation of cash receipts

 



 

 118

and disbursements for a given operating period or fiscal year, taking for granted the” accrual concept “ in account illustrates a cash budget model , showing the inflow and presenting a large-scale schedule for the determination of ending cash balance sheet. The budget is used to estimate future loans or financing needs, optimize the timing of project financing, and maximize profitability by efficient cash utilization. a. Cash receipts are subdivided into those which flow from financing the project and those coming from sales revenues. Cash flow from financing may take the form of stocks issued including stock premium or discount being closed, the net of the latter two accounts being closed to the “paid-in surplus” account; bond issues: and long-terms loans. In computing for cash in-flows from sales revenues; the “profit – before-income tax” account is entered in the budget, and this is increased to the period such as depreciation and amortization. Other account which increase the entries are increases in account payable, accrued expenses, and deferred income. b. Under cash disbursement, out-of-pocket expenses on intangible assets acquisition are entered. Other account included here are decreases in account payable, notes payable, bankdrafts payable, accrued expenses, mortgage bonds payable and long-terms notes receivable, inventories, and investment. Cash dividends issued and income tax payments also comprise cash disbursements. The beginning cash balance for the period is then added to the net cash flow to arrive at ending cash balance in the balance sheet. It should be noted that all accounts entered in the cash budget should tally with the same account in the income statement and balance sheet. NTAldon

Pro-formal cash-flow statements Years ending 31 December CASH RECEIPTS: Common stocks issued Preffered stocks issued Paid-in surplus Mortgage bonds payable-increases Long-term notes payable-increases Total receipts from financing Profit before income tax Add: Depreciation of fixed assest Amortization of pre-paid expenses Amortization of deferred charges Amortization of intangible assets Other non-out-of-pocket expenses Accounts payable Notes payable-increases Bank drafts payable-increases Accrued expenses-increases Deferred income-increases Total inflow from production, operations and financial accounts TOTAL ASSUMED CASH RECEIPTS

119

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1st year 400,000 90,192

(in pesos) 2nd year

3rd year

11,151 200,000 701,343 189,452 46,610

243,988 46,610

263,839 46,610

700

700

700

291,298 291,298

311,149 311,149

6,394 20,000

263,156 964,499

TOTAL ASSUMED CASH RECEIPTS

964,499

CASH DISBURSEMENTS: 1st year Expenses on intangible assets (Out of Pocket) Good will Patents 500 Copyrights Leases Licenses 500 Franchises 500 Organization and pre-operating expenses 2,000 Acquisitions of fixed assets (out-of-pocket): Land 200,000 Buildings 60,000 Equipment 77,545 Machinery 100,000 Accounts payable-decreases Notes payable-decreases Bank drafts payable-decreases Accrued expenses-decreases Treasury stocks-increases Mortgage bonds payable-decreases Long-term notes payable-decreases Cash dividends issued Marketable securities-increases 85,507 Accounts receivable-increases 317,520 Notes receivable-increases Inventories-increases: Raw materials 5,000 Supplies 2,000 Goods in process 9,000 Finished goods 20,000 Income tax payments Investment-increases (pre-paid and deferred charges) 2,000 TOTAL CASH DISBURSEMENTS 882,072 NET CASH FLOW (Net cash deficit) = receipts - disbursements 82,427 Add: balance, beginning CASH BALANCE, ENDING 82,427

120

NTAldon

291,298 2nd year

1,394 25,000 98,038 78,196 16,511

1,000 1,000 1,000 1,000 56,308 2,000 281,447 9,851 82,427 92,278

311,149 3rd year

1,394 25,000 98,038 89,297 16,511

1,000 1,000 1,000 1,000 75,396 2,000 311,636 (487) 92,278 91,791

BALANCE SHEET The balance sheet shows the assets derived by the project from corresponding liabilities and equities (net worth).It is an overall picture of a film’s financial condition as of a certain time. Furthermore, it shows the major changes brought about by the project’s operation within the fiscal period. The assets are entered under the debit portion of the balance sheet while the liability and equity claims on these assets are found under the credit portion. Exhibit F-3 present a model balance sheet.

121



Comprising the asset portion of the statement are current asset, fixed asset, and intangible assets.



Current assets _ to those type with are either cash account or other account expected to be converted into cash with one year. The item listed in this division are of course cash, marketable securities, receivables, inventories, prepaid expense, and deferred change. The latter two accounts signify cash expenditures for the services of a creditor not yet received in full by the project in question, such as prepaid insurance.



Fixed assets _ are the tangible assets of an enterprise of an enterprise, the service life of which usually extends to over one year. Land, building, machinery, and equipment are typical example of fixed assets. The balance sheets or book value of these assets are derived by subtracting their accumulated depreciation from their cost of acquisition, depreciation being the portion of cost allocated to one fiscal period.



Intangible assets _service life, like fixed will, patents, copyrights, leases, licenses, franchises, and organization and pre-operation expenses fall under other assets. When an intangible asset is amortized, the accumulated amortization account is not entered in the balance sheet, which contains only the net book value of assets in this category.



Assets = liabilities + (beginning owner’s equity + revenue – expenses) NTAldon

 Intangible assets _ have not physical substance. Examples are,

goodwill, leaseholds, copyrights, patents, franchises, licenses, and trademarks. Accounting for an intangible asset is rendered somewhat difficult because the lack of physical substance makes evidence of its existence more elusive, may make its value debatable and its useful life may be questionable.

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LIABILITIES _ are

debts or claims anyone other than the owners of the property upon the assets of the company.

 Current liabilities:

Accounts payable ,Notes payable, Bank-drafts payable , Estimated tax liability, Accrued expenses (Dividends payable):  Other liabilities: 123

Mortgage bonds payable ,Long-term notes payable NTAldon

OWNER’S EQUITY  COMMON STOCK

124

_ represents the ownership of stockholders who have residual claim on the assets of the corporation after all other claims have been settled. No return is guaranteed on the investment of common stockholders. They have the right to call meetings, to vote, to elect members of the board of directors, amend charter and constitution and by-laws, inspect books of the corporation, receive dividends, share remaining assets if corporation is dissolved.  PREFERRED STOCK_ _ also represent ownership. And it possesses the same rights as common stock, but in addition, it enjoys certain preferences, not possessed by common stock. It has priority over common stock in receipt of dividends, and it is usually guaranteed a fixed annual dividend, regardless of the amount of the earnings of the corporation. In case the corporation is dissolved, the owner of the preferred stock, has priority over the common stockholders. They NTAldon may have right to vote in meetings.

(in pesos)

ASSETS:

1st year

2nd year

3rd year

Current assets Cash

82,427

92,278

91,791

M arketable securities

85,507

163,703

253,000

317,520

334,031

350,542

Raw materials

5,000

6,000

7,000

Supplies

2,000

3,000

4,000

Goods-in-process

9,000

10,000

11,000

20,000

21,000

22,000

Pre- paid expenses

1,000

2,000

3,000

Deferred charges

1,000

2,000

3,000

523,454

634,012

745,333

200,000

200,000

200,000

Building

60,000

60,000

60,000

Equipment

77,545

77,545

77,545

M achinery

100,000

100,000

100,000

437,545

437,545

437,545

(93,220)

(139,830)

344,325

297,715

Account receivable, net Notes receivable Inventories

Finished goods

Tota current assets

Fixed assets: Land

Total fixed assets,

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Less:accumulated depreciation Total fixed assets, net

(46,610) 390,935

1st year Other assets: Investments Intangible assets, net of amortization: Goodwill Patents Copyrights Lease Licenses Franchises Organization and pre-operating expenses Total other assets

2nd year

3rd year

400

300

200

400 400 1,600 2,800

300 300 1,200 2,100

200 200 800 1,400

917,189

980,437

1,044,448

6,394 20,000

6,394 20,000

6,394 20,000

56,308

75,396

82,344

98,038

98,038

98,038

180,740

199,828

206,776

Mortgage bonds payable

11,151

9,757

8,363

Long-term notes payable

200,000

175,000

150,000

211,151

184,757

158,363

391,891

384,585

365,139

Common stocks

400,000

400,000

400,000

Preferred stocks

90,192

90,192

90,192

35,106

105,660

189,117

TOTAL EQUITIES

525,298

595,852

679,309

TOTAL LIABILITIES AND EQUITY

917,189

980,437

1,044,448

TOTAL ASSETS (current, fixed, other) LIABILITIES AND EQUITY: Current liabilities Accounts payable Notes payable Bank-drafts payable Estimated tax liability Accrued expenses: Dividends payable Deferred income Total current liabilities Other liabilities:

Total other liabilities

TOTAL LIABILITIES

OWNER'S EQUITY:

Less:

treasury stocks

Paid-in surplus Retained earnings

126

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WHOLE-LIFE COSTS Total Cost of Ownership(TCO)  Refers to the total cost of ownership over the life of an asset. Also commonly

referred to as “cradle to grave” or “womb to tomb” costs.

Areas of expenditure:        

Planning Design Construction/acquisition Operations Maintenance Rehabilitation Financial Replacement/disposal

 These costs are converted into present value together with benefits in 127

order to compute the benefit-cost ratio. NTAldon

EBITDA  EBITDA_ an initialism for earnings before interest, taxes,

128

depreciation, and amortization. It is a non-GAAP (generally accepted accounting principles) metric that is measured exactly as stated. All interest, tax, depreciation and amortization entries in the income statement are reversed out from the bottom-line net income. It purports to measure cash earnings without accrual accounting, canceling tax-jurisdiction effects, and canceling the effects of different capital structures.  EBITDA differs from the operating cash flow in a cash flow statement primarily by excluding payments for taxes or interest as well as changes in working capital.  EBITDA also differs from free cash flow because it excludes cash requirements for replacing capital assets (capex). EBITDA margin refers to EBITDA divided by total revenue. EBITDA margin measures the extent to which cash operating expenses use up revenue.  Use by debtholders_EBITDA is widely used in loan covenants. The theory is that it measures the cash earnings that can be used to pay interest and repay the principal. Since interest is paid before income tax is calculated, the debtholder can ignore taxes. They are not interested in whether the business can replace its assets when they wear out, therefore can ignore capital amortization and depreciation. NTAldon

BASIC METHODS OF PROFITABILITY ANALYSIS 1. Return on Investment, ROI  Profit or savings (before income tax) divided by investment required.

Profit x 100% ROI  Investment Incremental Profit x 100% ROI  Incremental Investment

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Minimum Acceptable Rate o Return (MARR)  Also known as Minimum Attractive Rate of Return or known as hurdle

rate, the interest rate used in the valuation of profitability of a project in Present Worth, FutureWorth and Annual Worth Methods.

 It is usually a policy issue by the top management of an organization in view

of the following considerations:

 The amount of money available for investment,  Number of good projects available for investment,  The amount of perceived risk associated with investment opportunities available

and  Type of organization involved.

 In business and engineering, the minimum acceptable rate of return,

often abbreviated MARR, or hurdle rate is the minimum rate of return on a project a manager or company is willing to accept before starting a project, given its risk and the opportunity cost of forgoing other projects.

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Minimum Acceptable Rate of Return; Hurdle Rate  The hurdle rate is usually determined by evaluating existing opportunities in 









operations expansion, rate of return for investments, and other factors deemed relevant by management. A risk premium can also be attached to the hurdle rate if management feels that specific opportunities inherently contain more risk than others that could be pursued with the same resources. A common method for evaluating a hurdle rate is to apply the discounted cash flow method to the project, which is used in net present value models. The hurdle rate determines how rapidly the value of the dollar decreases out in time, which, parenthetically, is a significant factor in determining the payback period for the capital project when discounting forecast savings and spending back to present-day terms. Most companies use a 12% hurdle rate, which is based on the fact that the S&P 500 typically yields returns somewhere between 8% and 11% (annualized). Companies operating in industries with more volatile markets might use a slightly higher rate in order to offset risk and attract investors. The hurdle rate is frequently used as synonym of cutoff rate, benchmark and cost ofNTAldon capital.

131

SAMPLE PROBLEMS; ROI Given: Investment

Total Investment Net profit

1

P 100,000

P 23,000

2

P 150,000

P 28,000

3

P 180,000

P 37,000

Required: Select the best alternative if minimum acceptable return on investment required is 10% Solution: ROI based on initial total investment: ROI1 

132

 23, 000 100  23%  10%, ok 100, 000

ROI 2 

28,000 100  18.67%  10%, ok 150,000

ROI3 

37,000 100  19.05%  10%, ok 180,000

NTAldon

All three investments passed the MARR therefore evaluate the investments using ROI based on incremental investment:  Comparing 1 and 2

Additional investment of P50,000 will yield additional net profit of P5,000) ROI12 

•

150, 000  100, 000 

100  10%, ok

investment 2 is better than 1

Comparing 2 and 3; Additional investment of P30,000 will yield additional net profit of P9,000) ROI 23 

133

 28, 000  23, 000 

NTAldon

 37, 000  28, 000 

180, 000  150, 000 

100  30%  10%, ok

Therefore, select # 3

2. Annual Cost Method The annual cost of the alternatives including the minimum return on investment is determined. The alternative with the least annual cost is chosen. This method, like the rate of return on investment method, applies only to alternatives which have a uniform cost data for each year and a single investment of capital at the beginning of the project life. Typical cost factors

134

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a. Depreciation Costs(usually as sinking fund) b. Annual Operating Costs c. Annual Labor Costs d. Insurance and Taxes e. Other Costs f. Return on Investment or Cost of Money Total Annual Costs

Sample Problem A company is considering two types of equipment for its new plant. The following data are given. If the minimum return on investment is 15%, which equipment should be selected using Annual Cost Method.

Given: Equipment A P 2.0 M P 350,000 P 500,000 3.5% of First Cost 8% of first Cost P200,000 10 years

First Cost Annual Operating Cost/yr Annual Labor Cost/yr Insurance and Taxes/yr Other Cost/yr Salvage Value Estimated life

Equipment B P 3.0 M P 250,000 P 350,000 3.5% of First Cost 8% of First Cost P300,000 10 years

Solution: Annual Cost Method Annual Costs a. Depreciation Cost (Sinking fund) b. Annual Operating Cost c. Annual Labor Cost d. Insurance and Taxes,3.5% FC e. Other Cost, 8% FC f. Return on Investment,15% FC Total Annual Costs

Equipment A, Pesos 88,654 35,0000 50,0000 70,000 160,000 300,000 1,468,654

FC1  i   SV a  f  capital re cov ery  CR  1  i L  1 NTAldon i 135

Equipment B, Pesos 132,981 250,000 350,000 105,000 240,000 450,000 1,527,981

L

Since total annual cost of equipment A is less than equipment B, therefore chose A

3. Discounted Cash Flow, Internal Rate of Return (IRR)  The method of approach for discounted cash flow takes into account the time value of money

and is based on the amount of the investment that is unreturned at the end of each year during the estimated life of the equipment.

 A trial-and-error method is used to establish a rate of return which can be applied to yearly

cash flow so that the original investment is reduced to zero (or to salvage and land value plus working capital investment) during the project life.

 Thus, the rate of return by this method is equivalent to the maximum interest rate (normally

after taxes) at which money could be borrowed to finance the project over its life that would just be sufficient to pay all principal and interest accumulated on the outstanding principal.

 The discount rate reflects two things:

1. The time value of money - investors would rather have cash immediately than having to wait and must therefore be compensated by paying for the delay. 2. A risk premium - reflects the extra return investors demand because they want to be compensated for the risk that the cash flow might not materialize after all.NTAldon

136

3. Discounted Cash Flow, Internal Rate of Return (IRR)  Internal Rate of Return is the most widely used rate of return method for

performing engineering economic analyses. It is sometimes called by several names, such as the investor’s method, the discounted cash flow method, and the profitability index. Also means that the value of this measure depends only on the cash flows from an investment and not on any assumptions about reinvestment rates.

 The internal rate of return (IRR) is a rate of return used in capital budgeting to

measure and compare the profitability of investments. It is also called the discounted cash flow rate of return (DCFROR) or simply the rate of return (ROR). In the context of savings and loans the IRR is also called the effective interest rate. The term internal refers to the fact that its calculation does not incorporate environmental factors (e.g. the interest rate).  The internal rate of return is the rate of return promised by an investment project over its useful life. It is some time referred to simply as yield on project. The internal rate of return is computed by finding the discount rate that equates the present value of a project's cash out flow with the present value of its cash inflow In other words, the internal rate of return is that discount rate that will cause the net present value of a project to be equal to zero.

137

NTAldon

CFn CF1 CF2 Total Capital Investment    ...  1 2 1  i  1  i  1  i n

Sample Problem: Discounted Cash Flow Compute for the IRR given by the sequence of cash flows i=29%

1 2 3 4 5 6 7 8 138 9

A B year, n Cash Flow, Cn 0 -100 1 40 2 59 3 55 4 20 IRR 29% NTAldon

solving by trial and error

Solving using Excel program =IRR(B3:B7)

SAMPLE PROBLEM : Discounted Cash-flow IRR Given:

Initial Fixed-Capital Investment = P100,000 Working capital Investment = P10,000 Service life = 5 years Salvage value @ the end of service life = P10,000

Required: Internal Rate of Return (IRR) Solution: By Trial-and-Error: i = 0.207 (20.72%)

110,000 

139

0 1 2 3 4 5 IRRNTAldon

Cash-flow, P

1

30,000

2

31,000

3

36,000

4

40,000

5

43,000

30,000 31,000 36,000 40,000 43,000 10,000  10,000      1 2 3 4 5 1  i  1  i  1  i  1  i  1  i  1  i 5

Solving using Excel program YEAR

YEAR

Cash-flow, P

-110,000 30,000 31,000 36,000 40,000 63,000 20.72%

Pay-out Period, N This method determines the number of years within which the invested capital can be recovered out of the expected cash flow. It does not consider the possible earnings of the reinvested capital during the pay-put period.

A.Without Interest

B.With Interest

N

Depreciable Fixed Capital Investment AverageCashFlow / yr

N

Fixed Capital Investment  SalvageValue AverageNet Pr ofit / yr  AverageDepreciation / yr

N

Depreciable Fixed Capital Investment  Interest On Total Investment Average CashFlow / yr





DFCI  TCI 1  i   1 N AverageNet Pr ofit / yr  AverageDepreciation / yr as annuity

Note: 140

n

Depreciable Fixed Capital Investment= Fixed Capital Investment- Salvage Value TCI=Total capital Investment=Fixed Capital Investment +Working Capital

NTAldon

SAMPLE PROBLEM:

PAY-OUT PERIOD

Given: Total fixed capital P 100,000

Working capital P 11,000

Salvage Value

Service Life, years

P 10,000

6

Required: Pay-out Period, N, without interest Solution:

N=

Depreciable Fixed Capital Investment  Net Profit+ Depreciation ave year

Annual Dep  N

141

NTAldon

100,000  10,000  15,000 6

100,000  10,000   2.5 years 21,000 15,000 

Net Profit P21,000

SAMPLE PROBLEM: •

PAY-OUT PERIOD

Given: Total fixed capital

Working capital

P 100,000

P 11,000

Salvage Value

Service Life, years

P 10,000

Net Profit

6

P21,000

Required: Pay-out Period, N, with interest; i = 10% pa Solution:

N

Depreciable Fixed Capital Investment  Interest On Total Investment Average CashFlow / yr   i d  FC  SV   L  1  i   1  0.10   100,000  10,000    11,664 .66 6   1 . 10  1  

N

142

NTAldon

100, 000  10, 000   100, 000  11, 000  1.10  21, 000  11, 664.66

6

 1   5.4 years

SAMPLE PROBLEM: •

PAY-OUT PERIOD

Given: Total Fixed Capital P 100,000

Working capital P 11,000

Salvage Value

P10,000

Service life, years 6

Annual Cash flow P 36,000

Required: Pay-out Period, N, with interest; i = 10% pa Solution:

N

Depreciable Fixed Capital Investment  Interest On Total Investment Average CashFlow / yr

6   100,000  10,000   100,000  11,000  1.10   1 N  4.88

36,000

143

NTAldon

years

Present Worth (Net Present Worth) The difference between the present value of the annual cash flows (CF) and the total initial investment (TCI). If the present worth of the net cash flow is equal to or greater than zero, the project is justified economically.

CFn CF1 CF2 NPW    ..   TCI 2 n 1  i  1  i  1  i  SAMPLE PROBLEM GIVEN:

Total Fixed Capital P 100,000

Required: Net Present Value Solution:

Working capital P 11,000

Net Pr esent Worth 

Salvage Value P10,000

Service Annual life, years Cash flow 6 P 36,000

CFn CF1 CF2   ..   FC 2 n 1  i  1  i  1  i  

 1  0.12 6  1  11, 000  10, 000   36, 000   100, 000  11, 000   47, 650  6 6   0.12 1  0.12   1  0.12  144

NTAldon

Future Worth Method This method is comparable to the present worth method except that all cash inflows and outflows are compounded forward to a reference point in time called the future. If the future worth of the net cash flow is equal or greater than zero, the project is justified economically.

F  CF1 1  i 

n 1

145

NTAldon

 CF2 1  i 

n2

 ..  CFn  TCI 1  i 

n

Capitalized Cost, K The total amount of money that must be available initially to purchase the equipment and simultaneously provide funds for interest accumulation to permit perpetual replacement of the equipment. In perpetuity, the amount required for replacement must be earned as compounded interest over a given length of time. Let P be the amount of present principal or present worth which can accumulate to an amount F during the interest periods at periodic interest i. Then, F = P(1+i)n If perpetuation is to occur, the amount F accumulated after n periods minus cost for the replacement must equal the present worth P. If we let CR represent the replacement cost, n

I  CR  F  P  P1  i   P CR P 1  i n  1 K  FC  P K  FC 

CR 1  i n  1

where: FC = First Cost of the equipment CR = Replacement/Maintenance Cost of the equipment after certain period ,n K = Capitalized Costs = additional investment which interest will take care of the perpetual replacement of the equipment NTAldon 146P

Sample Problem

Working in millions K  FC  K  25 

147

NTAldon

CR

1  i 

n

1

2

1  0.12 

1

1

 41.67

Sample Problem: Given: The initial cost of the equipment is P100,000, a salvage vale of P20,000 after 5 years and a maintenance cost of P10,000 per year, and cost of money of 10% pa. Required: Capitalized Cost Solution:

100, 000  20, 000   10, 000 K  100, 000    P 331, 038 5 1 1  0.10   1 1  0.10   1

148

NTAldon

Capital Recovery, CR The minimum income that must be earned by the investor in order to recover the cost of depreciation of the equipment plus the interest earned by the initial investment made. FL  FC1  i 

L

 1  i L  1  CR   SV i  

FC1  i   SV CR   FC A/P,i%, n   SV  A/F,i%, n  L 1  i   1 i L

where: FC = First cost of the equipment SV = salvage value at the end of service life L = service life, i = periodic interest 149

NTAldon

Sample Problem: Capital Recovery Given:

Installed cost of Equipment = P400,000 Service life = 5 years Salvage value = P40.000 Cost of money = 10% p.a.

Required: Capital Recovery, CR Solution:

FC 1  i   SV L

CR 

1  i  i

L

1

400, 000 1.1  40, 000 5



1.1

5

1

 P 98,969

0.1

Explanation:

150

    i 0.10  annual dep  d   FC  SV      400, 000  40, 00     58,967.09 L 5  1  i   1   1  0.10   1  Interest   I  400, 000  0.10   40, 000 year Minimum NTAldon annual earnings=Capital Recovery  58,967.09  40, 000  98,967.09

SAMPLE PROBLEM: A company requires an initial fixed capital investment of P100,000 and a working capital of P10,000. The fixed capital investment has a salvage value of P10,000 after 5 years, The projected annual cash flow is P36,000 and annual expenses is P44,000. Assume a minimum yield on investment of 15% pa. Determine the ff. a. ROI b. Minimum pay-out period, w/o and w/ interest c. Present worth d. Capitalized costs

SOLUTION: a. ROI Profit = Cash flow – Annual depreciation Total Investment = FCI + working capital Annual depreciation = (100,000 – 10,000)/ 5 = P18,000 Total investment = 100,000 + 10,000 = P110,000 Profit = 36,000 – 18,000 = 18,000

Profit 18,000 ROI   100%  16.36% Investment 110,000 151

NTAldon

a.

Minimum pay-out period, without interest

Depreciable Fixed Capital Investment Cash Flow 100, 000  10, 000   2.5 years 36, 000

N

b. Minimum pay-out period, with interest

Depreciable Fixed Capital Investment  Interest on Total Investment N Cash Flow 5 100, 000  10, 000  110, 000 1  0.15   1    5.6 years  36, 000

152

NTAldon

c.

Net Present Worth

NPW 

CFn CF1 CF2   ..   FC 2 n 1  i  1  i  1  i 

 1  0.155  1  10, 000  10, 000   36, 000   110, 000  P20, 622  5 5  1  0.15  0.15  1  0.15

d. Capitalized Costs

K  FC 

CR 1  i n  1

 110, 000  153

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44, 000 100, 000  10, 000    P 492,322 5 0.15 1  0.15  1  

Break Even Analysis Break-even point _ level of production where the total income is equal to the total expenses

Basic Production Assumptions: 1. That the variable costs are substantially directly proportional to production rate over the range from 0 to 100% capacity. 2. That the fixed charges are constant regardless of the annual production. 3. That there are no financial costs. 4. That there is no income other than from operations. 5. That all units produced are sold at a constant price per unit. Gross Profit = net Sales – cost of Sales = net Sales – (Variable costs + Fixed Costs)

Z  nS  nV  F  0  nS  V   F F n S V 154

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Where:

Z= gross profit in pesos n = number of units sold per year S = nets sales, pesos/unit V= variable cost, pesos/unit F= annual fixed cost, pesos

Note: If S and V are in terms of total sales pesos and total variable cost pesos, respectively, at 100% capacity, then n is terms of fractional capacity.

SAMPLE PROBLEM A company has the capacity to produce one million units of product per year. At present it can only produce and sell 800 thousand units annually at a total sales of P800 million. Variable costs per unit is P500 with an annual fixed costs of P50 million. a. Calculate the company's annual profit or loss for this present production. b. What is its break-even point? Use analytical and graphical method Solution:

a. Profit  Sales  Cost of Sales Z  S-(FC  VC)   800 ,000 ,000  50 ,000 ,000  800 ,000 units  selling price/unit  s 

P 800 ,000 ,000 P 1,000  ; 800 ,000 unit

variable cost/unit  vc 

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b. BEP 

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P 500 unit

FC 50 ,000 ,000 n  100 ,000 units 1,000  500  s-vc

 500     P350 M unit  

SAMPLE PROBLEM: The annual fixed costs of a plant are P100,000, and the variable costs are P140,000 at 70% capacity with net sales of P280,000. What is the break-even point in units of production if the selling price per unit is P40? Solution: The variable costs and net sales are based on 70% capacity, therefore we express them based on 100% capacity:

V = P 140,000/0.7 = P200,000 ; S = P 280,000/0.7 = P400,000 FC = P 100,000

F 100, 000  100%  50% S  V 400, 000  200, 000 P 400, 000   0.50   5, 000 units NTAldon P 40 / unit n

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Graphical Solution 500 450

Thousand Pesos

400

Sales

350

BEP Sales=Cost of Sales

300 250

Costs of Sales FC+VC

200 150

VariableCosts

100

Fixed Costs

50 0 -50 -100 157

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10

20

30

40

50

60

% Capacity

70

80

90

100

OPTIMIZATION Sample Problem: The cost of operating a large ship (Co) varies as the square of its velocity (v); specifically, Co=kLv2, where L is the trip length in kilometers and k is a constant of proportionality. It is known that at 12 kilometers per hour the average cost of operation is P10,000 per kilometer. The owner of the ship wants to minimize the cost of operation, but it must be balanced against the cost of perishable cargo (Cc), which the customer has set at P150,000 per hour. At what velocity should the trip be planned to minimize the total cost (CT), which is the sum of the cost of operating the ship and the cost of perishable cargo? 158

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SOLUTION:

Co 2 2 k  kv  k 12   10,000; k  69.444 L L 2 CT  kLv   150,000; v 150,000 L 2 CT  69.444 Lv   ; v dCT 150,000 L  138.888 Lv   0; v  10.26km / h 2 dv v 150,000 L 2 CT  69.444 Lv   v 150,000 L 2 CT NTAldon  69.444 L10.26    21,930 159 10.26

 A company produces circuit boards used to update

outdated computer equipment The fixed cost is P2.0 M per month, and the variable cost is P2,700 per circuit board. The selling price is S=7500-2n. Where n is the number of units produced. Maximum plant capacity is 4,000 units a month. a. Determine the optimum demand for this product. b. What is the maximum profit per month c. At what volume does breakeven occurs 160

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a. Daily Profit Z  7500  2n   2,700 n   2.1x10 6  4,800 n  2n 2  2.0 x10 6 dZ  4,800  4n  0; n  1,200 dn

b. Maximum Profit per month 2 Z  4,8001200  21,2000   2.0 x10 6  P0.880 M c. BEP : Z  0  4,800 n  2n 2  2.0 x10 6  2n 2  4,800 n  2.0 x10 6 4,800  4,800 2  42 2 x10 6 n  1863; 537 22

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

 A plant produces a type of product at a rate of P units

per day. The variable costs per unit have been determined to be P4,773 + 10P1.2. The total daily fixed charges are P 175,000, and all other expenses are constant at P732,000 per day. If the selling price per unit of product is P17,300. a. Determine the daily profit at a production schedule giving the minimum cost per unit of product b. Determine the daily profit at a production schedule giving the maximum daily profit c. Determine the production schedule at the break-even 162

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Economic Order Quantity, EOQ

The order quantity which minimizes the inventory cost unit time.

2aK EOQ  h where:

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a= constant depletion rate (items/unit time) K= the fixed cost per order (peso) h= the inventory storage cost (peso/unit item)

Sample Problem Given: a= constant depletion rate (items/unit time) = 1000 kg/month K= the fixed cost per order (peso) = P 2,000 h= the inventory storage cost (peso/unit item) = P100/kg/month

2aK 21000 2000  EOQ    200 kg h 100

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FINANCIAL ANALYSIS 1. Test of Liquidity These measures are used to determine a firm’s ability to meet short-term obligations, and to remain solvent in the event of adversities.  Liquidity ratios are used to measure your enterprise's ability to pay its bills on time.  They can be overall measures of liquidity or measures of specific assets.

 Liquidity is the availability of liquid assets to an enterprise.  Liquid assets are those assets held in or easily converted into cash.

Current Assets 1. A. Current Ratio  Current Liabilities

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The ratio is mainly used to give an idea of the company's ability to pay back its shortterm liabilities (debt and payables) with its short-term assets (cash, inventory, receivables). The higher the current ratio, the more capable the company is of paying its obligations. A ratio under 1 suggests that the company would be unable to pay off its obligations if they came due at that point. While this shows the company is not in good financial health, it does not necessarily mean that it will go bankrupt - as there are many ways to access financing - but it is definitely not a good sign. NTAldon

Current Assets  Inventories Current Liabilities  A stringent indicator that determines whether a firm has enough shortterm assets to cover its immediate liabilities without selling inventory. The acid-test ratio is far more strenuous than the working capital ratio, primarily because the working capital ratio allows for the inclusion of inventory assets.  Companies with ratios of less than 1 cannot pay their current liabilities and should be looked at with extreme caution. Furthermore, if the acidtest ratio is much lower than the working capital ratio, it means current assets are highly dependent on inventory. Retail stores are examples of this type of business. The term comes from the way gold miners would test whether their findings were real gold nuggets. Unlike other metals, gold does not corrode in acid; if the nugget didn't dissolve when submerged in acid, it was said to have passed the acid test. If a company's financial statements pass the figurative acid test, this indicates its financial integrity.

1.B. Quick or Acid Test Ratio 

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1.C. Inventory Turn-Over Ratio 

Cost of Goods Average Inventory

 The liquidity of a firm's inventories is reflected in the number of time the firm's average

inventory is turned over during the year. The inventory ratio requires confirmation by other measures and a more thorough examination of contents because rapid turnover on a few items or a slow turnover on others could skew the results.

 Example:

Cost of Goods Sold = P 1,520,891 Inventory Beginning = P 139,725 Inventory Ending = P 141,410 Inventory Turn-Over Ratio 

Cost of Gods Sold 1,520,891   10.82 Average Inventory 139,725  141,410 2

 The company turns its inventory almost eleven times a year (almost every month). It's a good

strategy to mention in your plan the false assumptions associated with this conclusion.  Average inventory is the average of the beginning and ending inventories. Sales are sometimes used in the numerator of the inventory ratio rather than the cost of goods sold. This would include markup, a variable which fluctuates across different situations. 167

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Cash  Short Term or Marketable Securities 1.D. Cash Ratio  Current Liabilities  The cash ratio is the most conservative liquidity ratio of all. It

only measures the ability of a firm's cash, along with investments that are easily converted into cash, to pay its shortterm obligations. Along with the quick ratio, a higher cash ratio generally means the company is in better financial shape.

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2. Tests of Debt-Service These tests are employed to present the project’s ability to meet long-term obligations. Total Liabilities 2. A. Debt  to  Net Worth Ratio  Total Equities

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Measure used in the analysis of financial statements to show the amount of protection available to creditors. The ratio equals total liabilities divided by total stockholders' equity; also called debt to net worth ratio. A high ratio usually indicates that the business has a lot of risk because it must meet principal and interest on its obligations. Potential creditors are reluctant to give financing to a company with a high debt position. However, the magnitude of debt depends on the type of business. For example, a bank has a high debt ratio but its assets are generally liquid. A utility can afford a higher ratio than a manufacturer because its earnings can be controlled by rate adjustments. Usually, book value is used to measure a firm's debt and equity securities in calculating the ratio. Market value may be a more realistic measure, however, because it takes into account current NTAldon conditions. market

2.B. Total Capitalization Ratio 

Long term Liabilites Long term Liabilities  Equities

 The capitalization ratio measures the debt component of a

company's capital structure, or capitalization (i.e., the sum of long-term debt liabilities and shareholders' equity) to support a company's operations and growth.

 Long-term debt is divided by the sum of long-term debt and

shareholders' equity. This ratio is considered to be one of the more meaningful of the "debt" ratios - it delivers the key insight into a company's use of leverage. There is no right amount of debt. Leverage varies according to industries, a company's line of business and its stage of development. Nevertheless, common sense tells us that low debt and high equity levels in the capitalization ratio indicate investment quality.

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Earnings before Interest and Taxes 2.C. Debt Service Ratio  Interest  The ratio measures debts servicing capacity of a business so far as

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interest on long-term loans is concerned. This ratio shows how many times the interest charges are covered by the earnings. Debt service ratios is also known as interest coverage ratio.  The interest coverage ratio is used to determine how easily a company can pay interest expenses on outstanding debt. The ratio is calculated by dividing a company's earnings before interest and taxes (EBIT) by the company's interest expenses for the same period. The lower the ratio, the more the company is burdened by debt expense. When a company's interest coverage ratio is only 1.5 or lower, its ability to meet interest expenses may be questionable. The ability to stay current with interest payment obligations is absolutely critical for a company as a going concern. While the non-payment of debt principal is a seriously negative condition, a company finding itself in financial/operational difficulties can stay alive for quite some time as long as it is able to service its interest expenses. NTAldon

2.D. Fixed Ch arg e Coverage Ratio Earnings before Interest & Taxes  Lease Payments  Lease Payments  Interest Ch arg es

 Equation that indicates whether the company is able to meet its fixed commitments (i.e.,

interest) from its profits. A high ratio reflects favorably upon the firm's ability to refinance obligations as they mature. The ratio equals earnings available to meet fixed charges divided by fixed charges. Fixed charges include rent and interest. The fixed charge coverage ratio includes lease payments as well as interest payments. Lease payments, like interest payments, must be met on an annual basis. The fixed charge coverage ratio is especially important for firms that extensively lease equipment, for example.

Here is the calculation for the fixed charge coverage ratio: EBIT, Taxes, and Interest Expense are taken from the company's income statement. Lease Payments are taken from the balance sheet and are usually shown as a footnote on the balance sheet. The result of the fixed charge coverage ratio is the number of times the company can cover its fixed charges per year. The higher the number, the better the debt position of the firm, similar to the times interest earned ratio.  Like all ratios, you can only make a determination if the result of this ratio is good or bad if you use either historical data from the company or if you use comparable data from the industry. 

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 The above formula can be explained with the help of an example:

For example, a company has P13,000 as EBIT and P2,000 as lease payments and P1,000 as interest payments the fixed charge coverage ratio is measured as: Fixed charge coverage ratio



13,000  2,000 5 1,000  3,000

This means that the company has earned five times its fixed charges, the company is able to pay the fixed charges of the company. Therefore this means that by calculating the fixed charge coverage ratio, it helps in ascertaining the company’s ability to pay the various fixed costs of the company in case the business tends to fall. Every business would have its own share of risks involved and every company must be well prepared to handle all the expenses and losses that can occur to the company. This is why it is important to calculate the fixed charge coverage ratio and it enables a business to understand the loss or expense taking capacity of the business in case some misfortune strikes the company. This ratio like all other ratios can provide a basic idea of the standing of the company’s finances based on the historical data provided to you. Therefore it is important that you determine fixed charge coverage ratio to ascertain the standing of the company. 173

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 Amortization _ method of repaying a debt, the principal and interest

included, usually by a series of equal payments at periodic interval of time.  Assets _ anything of value possessed by a enterprise, classified as current, fixed and other assets (goodwill, copyrights, franchises, etc. )  Authorized capital_ The authorized capital of a company (sometimes referred to as the authorized share capital, registered capital or nominal capital, is the maximum amount of share capital that the company is authorized by its constitutional documents to issue (allocate) to shareholders. Part of the authorized capital can (and frequently does) remain unissued. This number can be changed by shareholders' approval  Average cost method _ all materials in the store room are mixed and no attempt is made to determine which materials came in first or last, and therefore all materials issued are to be priced at the average price of the all the materials in the store room at that time. 174

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Bond _ is a certificate of indebtedness of a corporation usually for a period not less than 10 years, and guaranteed by a mortgage on certain assets of the corporation or its subsidiaries. •Coupon bonds _ bonds which are attached coupons indicating the interest due and the date which such interest is to be paid. The owner of the bond can collect the interest due by surrendering the same to the officers of the corporation or the same may be cashed at specified banks. •Collateral bonds _ the corporation pledges securities which it owns, such as stocks or bonds of one of its subsidiaries •Equipment obligation bonds _ refer primarily to bonds whose guarantee is a lien on equipment. •Registered bonds _ the owner's name is recorded in the books of the corporation, and the interest is paid periodically to the owner without their asking for it. •Joint bonds _ bonds which are issued by two or more corporations •Mortgage bonds _ bonds whose security is mortgaged on certain specified assets of the corporation. 175

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•Debenture bonds _ bonds without security behind them except a promise to pay by the issuing corporation •Callable bond _entitles the issuer to pay off the principal prior to the stated maturity date. Similarly, the owner of a •putable bond _can force the issuer to pay off the principal before the maturity date. •Convertible bond _gives the bondholder the right to exchange the bond for shares of the issuer's common stock at a specified date. •Municipal bonds _are issued by state and local governments and other public entities, such as colleges and universities, hospitals, power authorities, resource recovery projects, toll roads, and gas and water utilities. Municipal bonds are often attractive to investors because the interest is exempt from

•Par value of the bond or face value_ is the amount stated on the bond. •Bond rate _ is the rate of interest quoted on the bond. NTAldon 176 •Redemption or disposal price—usually equal to par value.

 Leveraged _ company that raises funds by issuing bonds.  Book costs_ are those that do not involve cash payments, but rather represent the recovery of

past expenditures over a fixed period of time. The most common of which is the depreciation charge for the use of assets such as plant and equipment.  Book value _ also known as depreciated value, is the worth of the property as recorded in the books of account of the enterprise and is equal to the original cost less the amounts which have been charged to depreciation.  Bookkeeping _ is the systematic recording of all business transactions in financial terms.  Borrowed capital_ are those supplied by others on which a fixed rate of interest must be paid and the debt must be repaid at a specified time.  Break-even point _ level of production where the total income is equal to the total expenses  Break-even analysis_ a means of identifying the value of a particular project variable that causes the project to exactly break even.  Capacity or plant factor _ the ratio between the average load and the total available capacity.  Capitalized cost _ is the sum of the first cost and the additional investment necessary in order to take care of the replacement and operating costs of the equipment etc. to perpetually operate it. Only the interest of the additional investment will take care all the replacement and operating expenses. NTAldon 177

 1. Equity capital_ capital owned by individuals who have invested their money or property in 







a business project or venture in the hope of receiving profit. 2. Debt capital _ also known as borrowed capital. Capital obtained from lenders (e.g. obtained from sale of bonds) for investment. In return, the lenders receive interest from the borrowers. Capital_ collective term for a body of goods and monies from which future income can be derived. Land, buildings, equipment, inventory, and raw materials, as well as stocks, bonds, and bank balances available are considered as capital. Generally, consumer goods and monies spent for present needs and personal enjoyment are not included in the definition or economic theory of capital. Homes, furnishings, cars, and other goods that are consumed for personal enjoyment (or the money set aside for purchasing such goods) are not considered capital in the traditional sense. Paid-in-capital_ amount of money received from the sale of stock more than the par value of the stock. Outstanding stock is the number of shares issued that is actually held by the public. If the corporation buys back part of its own issued stock, it is listed as Treasury Stock on balance sheet. Subscribed capital_ also known as issued share capital_ the total of a company’s shares that are held by shareholders. A company can, at any time, issue new shares up to the full amount of authorized share capital. 178

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 Capital gains tax_ tax on sale of assets; a tax on profit above a fixed 

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179

level made from the sale of financial assets Capital Recovery_ The minimum income that must be earned by the investor in order to recover the cost of depreciation of the equipment plus the interest earned by the initial investment made. Cartel_ a group of businesses controlling market: an alliance of companies formed to control production, competition and prices. A formal organization of producers within industry forming perfect collusion purposely formed to increase profit and block new comers from the industry. Cash Costs_ are those that involves payment of cash (and results in cash flow). It is distinguished from non-cash costs or book costs like depreciation. Cash Flow _ is a systematic presentation of cash receipts and disbursements for a given operating period or fiscal year, taking for granted the accrual concept in accounting. It details how the company generated the cash and how the company used the cash during the reported period. NTAldon

 Common stock _ represents the ownership of stockholders who have residual

claim on the assets of the corporation after all other claims have been settled. No return is guaranteed on the investment of common stockholders. They have the right to call meetings, to vote, to elect members of the board of directors, amend charter and constitution and by-laws, inspect books of the corporation, receive dividends, share remaining assets if corporation is dissolved.  Consumer goods and services_ are those products or services that are directly used by people to satisfy their wants. Food, clothing, homes, cars, television sets, haircuts, cinema, and medical services are examples.  Consumer price index (CPI) _measures changes in the price level of consumer goods and services purchased by households. The CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically. Sub-indexes and sub-sub-indexes are computed for different categories and sub-categories of goods and services, being combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the index. It is one of several price indices calculated by most national statistical agencies. The annual percentage change in a CPI is used as a measure of inflation. A CPI can be used to index (i.e., adjust for the effect of inflation) the real value of wages, salaries, pensions, for regulating prices and for deflating monetary magnitudes to show NTAldon 180 changes in real values.

 Copyright _ is an exclusive right granted by the government to protect the

production and sale of literary or artistic works for a period of 50years.  Corporation _ is a distinct legal entity, separate from the individuals who own it, and which can engage in practically any business transaction which a real person could do. It may sue, or be sued in its own name. It is separate from its owners and managers. This separation gives the corporation four major advantages: 1) It can raise capital from large investors by issuing stocks and bonds; 2) it permits easy transfer of ownership interest by trading shares of stock; 3) it allows limited liability-personal liability is limited to the amount of the individual’s investment in the business; 4) it is taxed differently than the proprietorships and partnerships, and under certain conditions, the tax laws favor corporations. On the negative side, it is expensive to establish a corporation. Furthermore, a corporation is subject to numerous governmental requirements and regulations. Cost accounting _ is the process of determining the actual cost of manufacturing a product or of rendering a service. Methods used are, postmortem cost accounting, method of predicted cost, and method of standard cost. Elements of cost are materials, direct labor and overhead. 181

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 Current liabilities _ these are liabilities which mature within a short 

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182

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time, usually a year. Current or liquid assets - include cash, accounts receivables within a short period of time or at least within the present accounting period and inventories (Examples are, raw materials, goods in the process of production, and finished goods ready for sale). Types of current assets 1. Cash_ represents actual money. Cash equivalent like marketable securities and short term investments. 2. Accounts receivable_ money which is owed to the firm but has yet to be received. 3. Inventories_ money invested in raw materials, work-in-process, finished goods available. Demand _ is the quantity of a certain commodity bought at a certain price at a given place and time. Demand factor _ the ratio between the maximum power demand and NTAldon the sum of the connected loads of the system

 Depression _ in economics, a period in an industrial nation

characterized by low production and sales and a high rate of business failures and unemployment.  Depreciation and devaluation are sometimes incorrectly used interchangeably, but they always refer to values in terms of other currencies.  Inflation, on the other hand, refers to the value of the currency in goods and services (related to its purchasing power). Altering the face value of a currency without reducing its exchange rate is a redenomination, not a devaluation or revaluation.

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 Direct Costs_ are costs that can be reasonably measured and

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184

allocated to a specific output or work activity. The labor and material costs directly associated with a product, service, or construction activity are direct costs. Direct materials _ are materials which are used in the finished product itself. Discount _ the difference between the value of a negotiable paper between now and the future. Discounted interest_ The interest for the money borrowed (discount) is deducted from the principal in advance Disposal costs_ includes those nonrecurring costs of shutting down the operation and the retirement and disposal of assets at the end of the life cycle. NTAldon

 Discounting_ is a financial mechanism in which a debtor obtains the

right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. The discount, or charge, is simply the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt  Duopoly_ concentration of power in two forces: an economic situation in which two powerful groups or organizations dominate commerce in one business market or commodity.  Duopsony_ two rival buyers’ control over sellers: a situation in which two competing buyers exert controlling influence over many sellers.  Economic life_ is the length of time during which an equipment or property will operate at a satisfactory profit.  Effective interest _ is the actual rate of interest on the principal for one year. NTAldon 185 Efficiency _ output divided by input

 Elastic demand _ occurs when a decrease in selling price will

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186

cause greater than proportionate increase in sales. Usually applicable to luxury goods. Equipment obligation bonds _ refer primarily to bonds whose guarantee is a lien on equipment. Equities _ are the claims of anyone against the asset of the enterprise. It includes the liabilities to the creditors as well as the claims of the owners. Equity capital_ or ownership funds_ are those supplied and used by the owners of an enterprise in the expectation that a profit will be earned. Expense _ the cost of producing income or revenue, or the value of commodities and services needed in the operation of the business. Also classified as operating and non-operating expenses. NTAldon

 Fair value _ is the value which a disinterested third

party, different from the buyer or the seller, will determine in order to establish a price that is fair and acceptable to both the buyer and the seller.  FIFO _ first-in, first out method. The principle behind this method is that the materials issued at any time are taken from the oldest stock and should be priced at the cost when they are purchased. Ex food manufacturing.  First cost of property _ includes original purchase price, freight and transportation, installation, taxes, permits and all other expenses to put it into operation.  Fixed liabilities _ liabilities which are not due for payment until sometime in the future, usually after a period exceeding one year. NTAldon 187

 Franchise_ the right and privilege granted to an individual or corporation to 

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



do business in a certain region. Franchise value _ is an intangible item of value arising from the exclusive right of a company to provide a specific product or service in a stated region of the country. Going concern value_ The value of a company as an ongoing entity. This value differs from the value of a liquidated company's assets, because an ongoing operation has the ability to continue to earn profit, while a liquidated company does not. Goodwill_ an intangible value_ is that element of value which a business has earned through the favorable consideration and patronage of its customers arising from its well-known and well conducted policies and operation. Gratuitous_ an obligation with no condition attached.

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 Gross Domestic Product (GDP)_ measures the value of all goods and

services produced within a nation’s border’s regardless of the nationality of the producer. GDP measures a country’s economic activity regardless of who owns the productive assets in that country. For example, the output United Statesowned companies based in the Philippines is considered part of Philippine’s GDP rather than part of the U.S.. GDP may be calculated in three ways: (1) by adding up all the value of all goods and services produced (2) by adding up the expenditures on goods and services at the time of sale, or (3) by adding up producers’ incomes from the sale of goods or services .  GDP is usually divided by its population to arrive at GDP per head. The figure is then converted to dollars to allow for its comparison between countries. If GDP grows at a higher rate than the population, standards of living are said to be rising. If the population is growing higher than GDP, living of standards are said to be falling. GDP per head does not take the cost of living into account.  Gross National Product (GNP)_ used to describe in monetary value the total annual flow of goods and services in the economy of a nation. It is measured by totaling all personal spending, all government spending, and all investment spending by a nation’s industry both domestically and all over the world. In other words, the income earned by a U.S.-owned business based in the Philippines would be considered part of the U.S.  Gross Margin_ net sales less the cost of goods sold. 189

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 Hedge funds_ risk-taking investment company: an investment

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 190

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company that is organized as a limited partnership and uses highrisk techniques in the hope of making large profits Income _ the value of personal and professional services rendered or of goods sold in the operation of the business. Usually classified as operating and non-operating income. Income statement _ or a profit and loss statement, is a summary of the incomes and expenses of an individual or enterprise for a given period. The next in importance to the balance sheet. Incremental Costs _ are additional costs that result from increasing the output of a system by one (or more) units. Indirect Costs_ are costs that are difficult to attribute or allocate to a specific output or work activity. For example, the costs of common tools, general supplies, and equipment maintenance in plant are treated as indirect costs. Indirect materials _ are materials not directly part of the product being produced Inelastic demand _ occurs when a decrease in the selling price NTAldon will cause a little a less than proportionate increase in sales.

 Inflation_ is the increase in the prices of goods and services from one 

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year to another, thus decreasing the purchasing power of money. Intangible assets _ have not physical substance. Examples are, goodwill, leaseholds, copyrights, patents, franchises, licenses, and trademarks. Accounting for an intangible asset is rendered somewhat difficult because the lack of physical substance makes evidence of its existence more elusive, may make its value debatable and its useful life may be questionable. Inventory_ stock of goods; the merchandise or stock a store or company has on hand Investment Cost_ is the capital required for most of the activities in the acquisition phase. This cost is often called a capital investment. Joint bonds _ bonds which are issued by two or more corporations. Journal _ is an accounting book where the original record of all transaction is ordinarily recorded. It is the book of original entry NTAldon

 Kelvin's Law _ the most economical cross sectional area for a

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conductor is that one for which the investment cost just equals the annual cost of lost energy. Law of Diminishing returns _ when one of the factors of production is fixed in quantity or is difficult to increase, increasing the other factors of production will result in a less than proportionate increase in output. Law of diminishing utility _ an increase in the quantity of any good consumed or acquired by an individual will decrease the amount of satisfaction derived from that good. Ledger _ serves as a secondary record of business transactions. The ledger sheets are used as intermediates, between journal records, balance sheets, income statements, and general records. Examples are, cash, equipment, accounts receivables, inventory, accounts payable and manufacturing expense. Liabilities _ are debts or claims anyone other than the owners of theNTAldon property upon the assets of the company.

 Life-cycle cost_ refers to a summation of all costs, both recurring and

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non-recurring, related to a product, structure, system, or service during its life plan. Life cycle_ refers to the notion that a fair, holistic assessment requires the assessment of raw material production, manufacture, distribution, use and disposal including all intervening transportation steps necessary or caused by the product's existence. The sum of all those steps - or phases - is the life cycle of the product. The concept also can be used to optimize the environmental performance of a single product (ecodesign) or to optimize the environmental performance of a company. LIFO _ last-in. last out method. The materials last to obtained are the first to be issued. Ex sand and gravel industry Load factor _ the ratio between the average demand and the maximum demand. Luxuries_ are those products or services that are desired by humans and will be purchased if money is available after the required necessities have been obtained. NTAldon

 Marginal cost _ is the additional cost of producing one more  

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unit. Marginal revenue _ is the amount received from the sale of an additional unit of a product. Marginal utility _ is the utility of the last unit of the same commodity which is consumed or acquired. If a man has three shirts of the same kind of brand, the marginal utility of the 2nd unit is greater than the marginal utility of the fourth unit. Market - is a place where sellers and buyers come together Market value _ is the amount which a willing buyer will pay to a willing seller for the property when neither one is under compulsion to buy or sell.

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 Monopoly _ a unique product or service is available only from a

single supplier and entry of all other possible suppliers are prevented.  Monopsony_ single-customer market: a situation in which a product or service is only bought and used by one customer  Mortgage bonds _ bonds whose security is mortgaged on certain specified assets of the corporation.  Mutual Fund_ form of management-investment company that combines the money of its shareholders and invests those funds in a wide variety of stocks, bonds, and so-called money market instruments. The latter include short-term investments such as United States Treasury bills and other federal securities, commercial paper, and bank certificates of deposit. Mutual funds provide the investor with professional management of funds and diversification of investment among the securities offered by leading corporations, federal and state governments, and other entities. NTAldon 195

 Necessities _ are those products or services that are required to

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support human life activities that will be purchased in somewhat the same quantity even though the price varies considerably. Non-recurring costs_ are those which arte non-repetitive, even though the total expenditure may be cumulative over a relatively short period of time.. For example, the purchase of a real estate upon which the plant will be constructed is a non-recurring cost, as the cost of constructing the plant itself. Obsolescence - refers to the changes external to the equipment such as, decrease or disappearance of demand, invention of more efficient equipment or style of products may have changed considerably. Organization cost_ an intangible value_ is the amount of money spent in organizing a business and arranging for its financing and building. Oligopoly _ occurs when there are few suppliers and any action taken by one of them will definitely affect the course of action of the others. NTAldon

 Operation and maintenance cost_ includes many of the recurring

annual expenses associated with the operation phase of life cycle. The direct and indirect costs of operation associated with the five primary resource areas- people, machines, materials, energy, and information- are a major part of the costs in this category.  Opportunity Cost_ is incurred because of the use of limited resources, such as the opportunity to use those resources to monetary advantage in an alternative use is foregone.  Overhead expenses _ consist of those expenses which cannot be readily included under direct materials and direct labor. Also known as indirect costs or burden.  Ownership or proprietorship _ it represents the investment of a person or several persons in the enterprise. 197

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 Partnership _ is an association of two or more persons for the

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purpose of engaging in a business profit. Usually formed by the voluntary agreement of the partners either verbally or in writing. The agreement among the partners usually states the relations between partners on matters relating to the proportion in which profits or losses are to be shared, their investments , rights and duties of each partner, and provisions for the withdrawal of any partner or the dissolution of the partnership.  A partnership has many advantages, among which are its low cost and ease of formation. Because more than one person makes contributions, a partnership typically has larger amount of capital available for business use. Since the personal assets of all partners stand behind the business, a partnership can borrow money more easily from a bank. Each partner pays only personal income tax on his or her share of a partnership’s taxable income.  Patent _ is an exclusive right granted by the government for the manufacture, use, and sale of a specific product. When a company acquires a patent or copyright by purchase of from the owner, the purchase price is classified as an intangible asset. NTAldon

 Payout period _ the minimum period needed to recover an

investment. Depreciable fixed capital/ net cash flow  Perfect competition_ a situation where a commodity or service is supplied by a number of vendors and there is nothing to prevent additional vendors entering the market.  Perpetual Inventory _ consists of the preparation of inventory cards, and their being kept up-to-date for each type of equipment or materials used or issued, and for the products completed or in the process of manufacture.  Perpetuity _ is an annuity where the payments periods extend or in which the periodic payments continue indefinitely.

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 Physical Life of an equipment _ is the length of time during which it is

capable of performing the function for which was designed and manufactured.  Power factor _ ratio of the power output in watts and the product of volts and amperes  Preferred stock _ also represent ownership. And it possesses the same rights as common stock, but in addition, it enjoys certain preferences, not possessed by common stock. It has priority over common stock in receipt of dividends, and it is usually guaranteed a fixed annual dividend, regardless of the amount of the earnings of the corporation. In case the corporation is dissolved, the owner of the preferred stock, has priority over the common stockholders. They may have right to vote in meetings.

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 Prepaid expense _ assets in the form of money paid for certain

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materials not yet delivered or services not yet rendered to the company. Prepaid income _ these are liabilities representing income which have been paid to the enterprise but for which the goods have not been delivered or any service rendered to the payer. Present economy _ involves the analysis of problems for manufacturing a product or rendering a service upon basis of present or immediate costs. Present value _ is the amount which if invested now will give a value of F after n interest periods. It is also defined as projected cash inflows and outflows expressed or discounted to the present time. Price _ is defined as the amount of money or its equivalent which is given in exchange of the goods being sold. NTAldon

 Producer goods and services_ are used to produce consumer goods and services or

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other producer goods. Machine tools, factory buildings, buses, and farm machinery are examples. Project Risk_ the possibility that an investment project will not meet the minimum requirements for acceptability and success. Producer Price Index (PPI)_ is a family of indexes that measure the average change over time in the prices received by domestic producers of goods and services. PPIs measure price change from the perspective of the seller. The headline PPI (for finished goods) is a measure of the average price level for a fixed basket of capital and consumer goods for prices received by producers. The producer price index for finished goods is a major indicator of commodity prices in the manufacturing sector. These prices are more sensitive to supply and demand pressures than the more comprehensive consumer price index. Changes in the producer price index are considered a leading indicator for consumer price changes, although only a small portion of the PPI is directly connected to less than half of the CPI. Proprietorship_ the simplest form of business organization wherein the business is owned entirely by one person. Pyramid scheme_ a fraudulent scheme in which the perpetrators recruit people to pay money to those above them in a hierarchy on the expectation that they will get payments from those below. When the number of newly recruited people eventually dwindles, the payment structure collapses. Also known as Ponzi scheme. NTAldon

 Recurring Costs _are those that are repetitive and occur when an

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organization produces similar goods or services on a continuing basis. Variable costs are also recurring costs because they repeat with each unit of output. A fixed cost that is paid on a repeatable basis is also a recurring cost. REER (Real effective exchange rate)_ measures the competitiveness of a currency in terms of making exports more or less expensive. It takes into account the movement of one currency against several others, and the inflation rates in other countries. Inflation is taken into account to measure currency competitiveness in real terms because affordability of export goods is determined not just by the movement of an exchange rate, but also by movement of prices of raw materials. Replacement value _ The cost necessary to replace an existing property at any given time with one at least equally capable of rendering the same service. Retained earnings_ the cumulative net income of the firm since its beginning, less the total dividends that have been paid to stockholders. It indicate the amount of assets that have been financed by plowing profits back into the business. Therefore, these retained earnings belong to the stockholders. Revenue_ the price of goods sold and services rendered during a given accounting period. NTAldon

 Scenario analysis_ a means of comparing a “base-case” or expected

project measurement (such as NPW) to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes.  Sole proprietorship _ or individual ownership, is the simplest of business organization, wherein the business is owned entirely by one person who is responsible for the operation, firm’s policies, and is personally liable for its debts. The proprietorship has two major advantages. First, it can be formed easily and inexpensively. No legal and organizational requirements are associated with setting up a proprietorship, and organizational costs are therefore, virtually nil. Second, the earnings of a proprietorship are taxed at the owner’s personal tax rate, which may be lower than the rate at which corporate income is taxed. Apart from personal liability considerations, the disadvantage of a proprietorship is that it cannot issue stocks and bonds, making it difficult to raise capital for any business expansion.  Standard Costs _ are representative costs per unit of output that are established in advance of actual production or service delivery. The are developed from anticipated direct labor hours, materials, and overhead categories (with their established cost per unit). 204

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 Stock _ in business and finance, a share of ownership in a corporation. Shares in a

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corporation can be bought and sold, usually on a public stock exchange. Consequently, the owner of shares can realize a profit or capital gain if the stock is sold at a price above what the owner originally paid for it. Stock Exchange_ organized market for buying and selling financial instruments known as securities, which include stocks, bonds, options, and futures. Most stock exchanges have specific locations where the trades are completed. For the stock of a company to be traded at these exchanges, it must be listed, and to be listed, the company must satisfy certain requirements. But not all stocks are bought and sold at a specific site. Such stocks are referred to as unlisted. Many of these stocks are traded over the counter—that is, by telephone or by computer. Stock Holder_ share holder, owner of company stock, Stockholder’s Equity_ the amount available to the owners after all other debts have been paid Sunk cost _ money which has been spent or capital which has been invested and which cannot be recovered due to certain reasons. They are non-refundable cash outlay, such as earnest money on a house, capital that has been invested and cannot be retrieved or money spent on passport. Supply _ is the quantity of a certain commodity that is offered for sale at a certain NTAldon price at a given place and time.

 Income taxes_ expressed as a function of gross revenues minus allowable deductions.  Property taxes_ are assessed as a function of the value of property owned, such as land,

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buildings, equipment, and so on, and the applicable tax rates. They are independent of the income or profit of the company. Sales taxes_ are assessed on the basis of purchases of goods or services and are thus independent of gross income or profits. Excise Taxes_ assessed as a function of the sale of certain goods or services often considered non-necessities (alcohol, tobacco), and are hence independent of the income or profit of a business. The Law of Demand _ the demand for a commodity varies inversely as the price of commodity, though not proportionately. The Law of Supply _ the supply of commodity varies directly as the price of the commodity, though not proportionately. The Law of Supply and Demand _ when free competition exists, the price of a product will be that value where supply is equal to the demand. Time value of money_ is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory. For example, P100 of today's money invested for one year and earning 5% interest will be worth $105 after one year. Therefore, P100 paid now or P105 paid exactly one year from now both have the same value to the recipient who assumes 5% interest; using time value of money terminology, P100 invested for one year at 5% interest has a future value of P105.

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 Tort_ a wrongful act that causes injury to a person or property and for 

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which the law allows a claim by the injured party to recover damages. Unitary elasticity of demand _ occurs when the mathematical product of price and volume of sales remain constant regardless of any change in price. PV=C Utility _ is the capacity of a commodity to satisfy human wants and needs. Utility or use value _ is what it is worth to the owner of a property when in actual operation. Value_ the price that must be paid in order to obtain a particular item

 Valuation_ or appraisal_ is the process of determining the value of

certain property for specific reasons.  Variable Costs_ are those associated with an operation that vary in total with the quantity of output or other measures of activity level.  Working capital_ refers to the funds required for current assets (other than fixed assets) that are needed for the start-up and support of operational activities. Also known as the circulating capital, includes all funds which are required to make the enterprise a going concern. 207

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Thank You!

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