ME 443

1. ME 443 COST CONCEPTS Prof. Dr. Mustafa Gökler

2. COST CONCEPTS • Engineering economic analysis is primarily concerned with comparing alternative projects on the basis of an economic measure of effectiveness. • This comparison process utilizes a variety of cost terminologies and cost concepts.

3. COST TERMINOLOGY • (1) life-cycle costs • (2) past costs • (3) sunk costs • (4) future costs • (5) opportunity costs • (6) direct, indirect, and overhead costs • (7) fixed and variable costs • (8) average costs • (9) marginal costs.

4. LIFE-CYCLE COSTS The life-cycle cost for an itemis the sum of all expenditures associated with the item during its entire service life. Life-cycle costs may also be expressed as the summation of acquisition (including first cost, initial investment) ,operation, maintenance, and disposal costs.

5. FIRST COST The first cost of an item normally involves many more cost elements than just the basic purchase price

6. MARKET VALUE The monetary value of the item at the time of disposal is defined as the market or trade-in value (i.e., the actual dollar(TL) worth for which the item may be sold at the time of disposal).

7. SALVAGE VALUE after deducting the cost of disposal, the net dollar (TL) worth at the time of disposal is termed the salvage value Salvage Value = Market Value – Cost of Disposal

8. BOOK VALUE The value of the capital asset at the end of a given accounting period during the asset's life is termed the book value

9. BOOK VALUE There are various depreciation methods that can serve to estimate the rate of deterioration and consequent decrease in value of the asset. These methods will be discussed in Chapter 6. BOOK VALUE = INITIAL VALUE - DEPRECIATION

10. SCRAP VALUE Scrap valuerefers only to the value of the material of which the item is made

11. ECONOMIC LIFE The economic life of an item is generally shorter than the functional life. In this course, the end of life for an item will mean the end of its economic life, rather than its functional life.

12. PAST and SUNK COSTS Past costs are historical costs that have occurred for the item under consideration. Sunk costs are past costs that are unrecoverable. (Capital loss)

13. FUTURE and OPPORTUNITY COSTS All costs that may occur in the future are termed future costs The cost of forgoing the opportunity to earn interest, or a return, on investment funds is termed an opportunity cost

14. DIRECT COSTS Direct material and labor costs are the costs of material and labor that are easily measured and can be conveniently allocated to a specific operation, product, or project.

15. INDIRECT COSTS Indirect costs for both labor and material are either very difficult or impossible to assign directly to a specific operation, product, or project.

16. OVERHEAD COSTS Overhead costs consist of all costs of manufacturing other than direct material and direct labor. A given firm may identify different overhead categories such as factory overhead, general and administrative overhead, and marketing expenses. Overhead amounts may be allocated to a total plant, departments within a plant, or even to a given item of equipment.

18. FIXED COSTS Fixed costs (FC) do not vary in proportion to the quantity of output. General administrative expenses, taxes and insurance, rent, building and equipment depreciation, and utilities are examples of cost items that are usually invariant with production volume and hence are termed fixed costs. Such costs may be fixed only over a given range of production; they may then change and be fixed for another range of production.

19. VARIABLE COSTS Variable costs(VC) vary in proportion to quantity of output. These costs areusually for direct material and direct labor.

20. TOTAL COST TC(x) = FC + VC(x)

21. TOTAL COST-TOTAL REVENUE

22. BREAK-EVEN POINT TR(x) = px p :selling price TC(x) = FC + VC(x) VC= vx v: unit cost At BEP TR(x) = TC(x) = FC + VC(x) px = FC + vx x = FC /( p-v) at BEP

23. BREAK-EVEN POINT

24. AVERAGE COSTS The average cost of one unit of output (unit cost) is the ratio of total cost and quantity of output (miles traveled, production volume, etc.). That is, AC(x)= TC(x)/x where AC(x) = average cost per unit of x TC(x) = total cost for x units of output x = output quantity

25. MARGINAL COSTS For a total cost function that is continuous in the output variable x, marginal cost is defined as the derivative of the total cost function with respect to x, dTC(x)/dx This is true for continuous functions thatarelinear or nonlinear in the output variable x

26. MARGINAL COST If the total cost function is discontinuous and defined only for discrete values of x (for example, x = 1, 2, 3, . then difference equations must be used to determine marginal costs. For example, TC(6) - TC(5) is the marginal cost of increasing the output quantity from x = 5 to x = 6. Thus, in the discrete case, marginal cost is always the cost required to increase the output quantity x by one unit at a specified level of output.

27. MARGINAL REVENUE/PROFIT The concept of marginalism is general and applies to other mathematical functions as well. For example, marginal revenues can be determined from total revenue functions, marginal profit values can be determined from total profit functions, and so forth

28. EXAMPLE (2.3) A small firm blends and bags chemicals, primarily for home gardening purposes. The market area for the firm is local, and all sales are to wholesaledistributors. For one pesticide dust product, sales and production cost records over the past 10 seasons have been reviewed and analyzed.

29. EXAMPLE (2.3cont.) The following equations approximate the relationships among selling price, sales volume, production costs, and profit before income taxes. Let t = number of tons per season SP(t) = selling price in order to sell t tons = $(800 - 0.8t)

30. EXAMPLE (2.3cont.) TR(t) = total revenue when t tons are sold at a particular selling price = Selling price x Demand = $(800 - 0.8t)t = $(800t - 0.8t2) MR(t) = the marginal revenue at a sales volume of t tons = dTR(t)/dt = $(800 - 1.6t)  TC(t) = the total production cost for t tons = $(10,000 + 400t)

31. EXAMPLE (2.3cont.) TP(t) = total profit when t tons are sold = TR(t)— TC(t) = $(800t - 0.8t2) - $(10,000 + 400t) = $(-0.8t2 + 400t - 10,000) AP(t) = average profit per ton when t tons are sold = TP(t)/t= $(-0.8t + 400 - 10,000/t)  The equations will be applied for the range, 0 < t < 1000

32. EXAMPLE (2.3cont.) MAXIMIZE TOTAL REVENUE (TR(t)= 800t - 0.8t2) dTR(t)/dt = 800 - 2(0.8)t = 0 t = 500 tons TR(500) = $800(500)—$0.8(500)2= $200,000 Marginal Revenue at t = 500 tons   MR(500) = $800—$1.6(500) = 0 IMAXIMIZE PROFIT (TP (t)= -0.8t2 + 400t - 10,000) dTP(t)/dt) = 2(-0.8)t + 400 = 0 t = 250 tons  TP(250) = -0.8(250)2 + 400(250) - 10,000= $40.000

33. EXAMPLE (2.3cont.) The average profit per ton for t = 250 tons AP(250) = -0.8(250) + 400 - 10,000/250 = $160/ton To obtain the break-even point (BEP) TR(t) = TC(t)  800t - 0.8t2 = 10,000 + 400t

34. EXAMPLE (2.3cont.) -0.8t2 + 400t - 10,000 = 0 Solving for the positive roots of this quadratic equation yields t = 26.39, 473.61 26.39 < t < 473.61,firm will make profit. t < 26.39 or t > 473.61 firm will lose.

35. EXAMPLE (2.3cont.)