Engineering Economy_lecture6 (1)

Engineering Economy

Ryan Jeffrey P. Curbano, CIE

BREAK EVEN ANALYSIS

Break even Analysis Break even analysis - is used to determine the break even cost, which is the cost at which the total income is exactly equal to the total expenses incurred in the business.

Break-Even Chart 50,000 –

Revenue

Dollars

40,000 –

Break-even point

30,000 –

Total costs

20,000 –

Fixed costs

10,000 – | – 0

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2,000

4,000

6,000

8,000

10,000

Units

Break-Even Analysis BEPx = break-even point in units BEP$ = break-even point in dollars P = price per unit (after all discounts)

x = number of units produced TR F V TC

= = = =

total revenue = Px fixed costs variable cost per unit total costs = F + Vx

Break-even point occurs when

TR = TC or Px = F + Vx

F BEPx = P-V

Break-Even Analysis BEPx = break-even point in units BEP$ = break-even point in dollars P = price per unit (after all discounts)

BEP$ = BEPx P F = P P-V F = (P - V)/P F = 1 - V/P

x = number of units produced TR F V TC

= = = =

total revenue = Px fixed costs variable cost per unit total costs = F + Vx

Profit = TR - TC = Px - (F + Vx) = Px - F - Vx = (P - V)x - F

Example 1.0 • A manufacturer produces certain items at a labor cost of P115 each, material cost P76 each and variable cost of P2.32 each. If the item has a unit price of P600. how many number of units must be manufactured each month for the manufacturer to break even if the monthly overhead is P428,000

Example 2.0 • A company which manufactures electric motors has a production capacity of 200 motors a month. The variable cost are P150.00 per motor. The average selling price of the motors is P275.00. Fixed cost of the company amount to P20,000 per month which includes taxes. Find the number of motors that must be sold each month to break even.

Example 3.0 • A factory engaged in the fabrication of an automobile part with a production capacity of 700,000 units per year is only operating at 62% of capacity due to unavailability of the necessary foreign currency to finance the importation of their raw materials. The annual income is P430,000.00. Annual fixed cost are P190,000.00 and variable cost are P0.348 per unit – What is the current profit or loss? – What is the break even point?

Example 4.0 • The Asian Transmission Co. makes and sell certain automotive parts. Present sales volume is 500,000 units per year at a selling price of P0.50 per unit. Fixed expenses total P80,000 per year. – What is the present total profit for a year – What is the present break even point in pesos and in units.

Example 5.0 • The following data for year 2000 are available for Cagayan Automotive Company which manufactures and sell a single automotive product line. – Unit selling price P40.00 – Unit variable cost P20.00 – Unit contribution margin P20.00 – Total Fixed Cost P200,000.00 • What is the breakeven point in units for the current year?

DEPRECIATION

Depreciation • Depreciation – Is the reduction of fall in the value of an asset or physical property during the course of its working life and due to the passage of time

Types of Depreciation • Physical Depreciation – Is due to the reduction of the physical ability of an equipment or asset to produce result.

• Functional Depreciation – Is due to the reduction in the demand for the function that the equipment or asset was designed to render. This type of depreciation is often called obsolescence.

Methods of Computing Depreciation • Straight line Method – In this method of computing depreciation, it is assumed that the loss in value is directly proportional to the age of the equipment or asset.

Formula – Straight line method • Annual depreciation charge, d d = Co - Cn n Where: Co = first cost Cn = cost after “n” years (salvage/scrap value) • Book value at the end of “m” years of using, Cm Cm = Co – Dm Where: Dm = total depreciation after “m” years Dm = d(m)

• Sinking Fund Method – In this method of computing depreciation, it is assumed that sinking fund is established in which funds will accumulate for replacement purposes

Formula – Sinking Fund • Annual depreciation charge, d d = (Co – Cn)i n (1 + i) – 1 Where: Co = first cost Cn = cost after “n” years (SV) n = life of the property • Book value at the end of “m” years of using , Cm Cm = Co – Dm Where: Dm = total depreciation after “m” years n Dm = d[(1+i) - 1] i

• Declining Balance Method – In this method of computing depreciation, it is assumed that the annual cost of depreciation is fixed percentage of the book value at the beginning of the year. This method is sometimes known as constant percentage method or the Matheson Formula

Formula – Double Balance Method k = 1 – n Cn Co k = 1 – m Cm Co

Book Value = FC (1-k)

m

Depreciation at the end of “m years” d = (FC)(1-k)

m -1

k

Note: the value of k is the constant percentage. Hence k must be decimal and a value less than 1. In this method, salvage or scrap value must not be zero.

• Sum of Years Digit (SYD) Method – First year d1 = (Co – Cn) n ∑ years - Second year d2 = (Co – Cn) n-1 ∑ years - Third year d3 = (Co – Cn) n – 2 and so on… ∑ years Book value at the end of “m” years of using, Cm Cm = Co – (d1 + d2 +…+dm) Sum of year’s digit ∑years = n(n+1) 2

Double Declining Balance Method • In this method the depreciation during any year is a constant ratio of the book value at the beginning of the year. • Formula: k = 2/n m Book value = (FC)(1-k) m-1 Depreciation = (FC)(1-k) (k)

Service Output Method • In this method it is assumed that the total depreciation that has taken place is directly proportional to the quantity of the output of the property up to the time.

Formula – Service Output Method • Depreciation per unit output is d1 = Co – Cn T • Depreciation charge during “m” year Where: Dm = Qmd1 T = total units of output produced M = age in years of the property at any = (Co – Cn)Qm time Qm = total units of output during year “m” T

Dm = depreciation charge during year m Co = original cost of the property Cn = book value at the end of life, n years

Working Hours or Machine Hour Method • Formula Depreciation per hour = FC – SV Total number of hrs

Example 1.0 • In order to established the comparison between the depreciation methods mentioned above, let us consider the following data: • First cost (Co) = P10,000 • Salvage value, Cn = P500 • Life of property = 5 years Solve using the Straight line method, Sinking Fund at 10%, Matheson Formula and SYD method

Example 2.0 • A certain company makes it the policy that for any new piece of equipment that annual depreciation cost should not exceed 10% of the original cost at any time with no salvage value or scrap value. Determine the length of service life necessary if the depreciation method used is (a) the straight line formula (b) sinking fund at 8% ( c) SYD method

Straight line Method • A machine has an initial cost of P50,000 and a salvage value of P10,000 after 10 years. What is the book value after 5 years using straight line depreciation.

Straight line Method • An asset is purchased for P500,000. the salvage value in 25 years is P100,000. what is the total depreciation in the first three years using SLM

Straight line Method A manufacturing plant was built at a cost of P5M and is estimated to have a life of 20 years with a salvage value of P1M. A certain equipment worth P570,000 was installed at a cost of P80,000 is expected to operate economically for 15 years with a salvage value of P50,000. Determine the book value of the plant and equipment after ten years, Use Straight line method

Straight line Method The cost of the printing equipment is P500,000 and cost of handling and installation is P30,000. if the book value of the equipment at the end of the 3rd year is P242,000 and the life of the equipment is assumed to be 5 years, determine the salvage value of this equipment at the end of 5 years

Sinking Fund Method • A plant erected to manufacture socks has a first cost of P10,000,000 with an estimated salvage value of P100,000 at the end of 25 years. Find the appraised value using sinking fund method assuming an interest of 6% at the end of 10 years and 20 years

Sum of Years Digit Method • A company purchases an asset for P10,000 and plans to keep it for 20 years. If the salvage value is zero at the end of 20th year. What is the depreciation in the third year? Use SYD method

Sum of Years Digit Method • ABC Corporation makes its policy that for every new equipment purchased, the annual depreciation cost should not exceed 20% of the first cost at any time without salvage value. Determine the length of service if the depreciation used is the SYD method

Declining Balance Method • A machine cost P7350 has a life of 8 years and has a salvage value of P350 at the end of 8 years. Determine its book value at the end of 4 years using Declining balance method

Declining Balanced Method • The original cost of a certain machine is P150,000 has a life of 8 years with a salvage value of P9,000. how much is the depreciation on the 5th year, using declining balanced method

Declining Balanced Method • A machine costing P720,000 is estimated to have a book value of P40,545.73 when retired at the end of 10 years. Depreciation cost is computed using a constant percentage of the declining book value. What is the annual rate of depreciation in %?

Double Declining Balanced Method • Erectors Co. owns earth moving equipment that cost P90,000. After 8 years it will have estimated salvage value of P18,000. compute the depreciation charge using double declining balanced method for 1st two years and book value at the of 5 years.

Working Hours Method • A lathe machine costs P300,000 (brand new) with a salvage value of P15,000 is expected to last for 28500 hours in a period of 5 ears. In the first year of service it was used for 8000 hrs. compute the depreciation for the 1st year and book value at the end of the first year.

Service Output Method • A certain machine cost P40,000 and has a life of 4 years and salvage value of P5,000. the production output of this machine in units per year for first year, 1800 units, second year 2200 units, third year 3,000 units, fourth year 4,000 units. If the units produced are of uniform quality, what are the annual depreciation charges?