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COST CONCEPTS AND DESIGN EcONOMICS

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OBJECTIVE:

The objective (~fChapter 2 is to ana(yze short-term altemotives when the time value olmoney is not alactor. IFe accomplish this "with three types ofproblems: (1.) Economic breakevell analysis; (2.) Cost-driven design (3.) Present economy studies

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The word cost (or expense) has meanings that vary in usage. Cost concepts and other economic principles used in an engineering economy study depend on the situation and on the decision to be made. Many types of cost arise in economy studies of a new existing enterprise whenever any change in operations or policy is made. While an engineer may be cognizant of the various types of cost, it appears that classifying the same and giving the applications of each will make them clearer.

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MANUFACTURING COSTS The several types of manufacturing costs incurred by a typical manufacturer are illustrated in Figure 2.1. In converting raw materials into finished goods, a manufacturer incurs various costs of operating a factory. Most manufacturing companies divide manUfacturing costs into three broad categories: direct materials, direct labor, and manufacturing overhead.

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Figure 2.1 Various types of manufacturing costs

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11 I Chapter 2 . Cost Concepts and Design Economics DIRECT MATERIALS Direct raw materials refer to any materials that are used in the final I

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product and that can be easily traced into it. Some examples are wood in furniture, steel in bridge construction, paper in printing firms, and fabric for clothing manufacturers. It is also important to note that the finished' product of one company can become the raw materials of another company. For example, the computer chips produced by Intel are raw'materials used by Dell C'.-omputer in its personal computers. DIRECT LABOR

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Like the term direct material, direct labor is for those labor costs that go into the production of a product. The labor costs of assembly-line workers, for example, would be direct labor costs, as would the labor costs of welders in metal fabricating industries, carpenters or bricklayers in home building, and machine operators in various manufacturing operations.

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MANUl"~~U1UNGOVERHEAD

Manufacturing overhead include all costs of manufacturing except direct materials and direct labor. In partiCUlar, they include such items as indirect materials, indirect labor, maintenance and repairs on production equipment, heat and light, property taxes, depreciation, insurance of manufacturing facilities, and overtime premium. The most important thing to note about manUfacturing overhead is the fact that unlike direct materials and direct labor, it is not easily traceable to specific units of output. In addition, many manufacturing overhead costs do not change as output changes, as long as the production stays within the capacity. NON-MANUFACTURING COSTS There are two additional costs in supporting any manufacturing operations. They are (II marketing or selling costs and (21 administ:rative costs. Marketing or selling costs include all costs necessary to secure customer orders and get the finished product or service into the hands of the customer. • Overhead: Heat and light, property taxes, depreciation or similar terms, associated with its selling and administrative functions. • Marketing: Advertising, shipping, sales travel, sales commissions, and sales salaries. Administrative costs include all executive, organizational, and clerical costs associated with the general management of an organization. • Administrative functions: Executive compensation, general accounting, public relations, and secretarial support. STANDARD CO.STS Standard costs are planned costs per unit of output that are established in advance of actual production or service delivery. They are developed from anticipated direct labor hours, materials, and overhead categories (with their established cost per unit). Standard costs play an important role in cost control and other management functions. Some typical uses are the following: • Estimating future manufacturing costs • Measuring operating performance by comparing actual cost per unit with the standard unit cost • Preparing bids on products or services requested by customers • Establishing the value of work in process and fmished inventories

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I Chapter 2 . Cost Concepts and Design Economics

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COST CLASSIFICATION FOR PREDICTING COST BEHAVIOR In engineering economic analysis, we need to predict how a certain cost will behave in response to a change in activity. For example, a manager will want to estimate the impact a 5% increase in production will have on the company's total wages, before a decision to alter production is made. Cost behavior describes how a cost item will react or respond to changes in the level of business activity. ' FIXED COSTS

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Fixe,d costs are those unaffected by changes in activity level over a feasible range of operations for the capacity or capability available. Typical fixed costs include insurance and taxes on facilities, general management and administrative salaries, license fees, and interest costs on borrowed capital. VARIABLE COSTS Vadable costs are those associated with an operation that varies in total with the quantity of output or other measures of activity level. Examples of these costs are the costs of materials and labor used in a product or service. INCREMENTAL COSTS An incremental cost (or incremental revenue) is the additional cost (or revenue) that results from increasing the output of a system by on,e (or more) units. This cost is often associated with "go-no go· decisions that involve a limited change in output or activity level. COST CONCEPTS RELEVANT TO DECISION MAKING Costs are important feature of many business decisions. In making decisions, it is essential to have a firm grasp of the concepts of differential cost, opportunity cost, and sunk cost. OPPORTUNITY COST Opportunity cost may be defined as the potential benefit that is given up as you seek an alternative course of action. It 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. Thus, it is the cost of the best rejected (foregone) opportunity and is often hidden or implied. In economic sense, opportunity cost could mean the contribution to income that is foregone by not using a limited resource in its best use. Or, we may view opportunity costs as cash flows that could be generated. from an asset the frrm already owns, provided they are not used for the alternative in question. In general, accountants do not post opportunity cost in the accounting records of an organization. However, this opportunity cost must be e,,-,plicitly considered in every decision. SUNK COST

Sunk cost is one that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative course of action. We need to be able to recognize sunk costs and then handle them properly in an analysis. Specifically, we need to be alert for the possible existence of sunk costs in any situation that involves a past expenditure that cannot be recovered, or capital that has already been invested and cannot be retrieved.

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141 Chapter 2 -Cost Concepts and Design Ecanomics 'i

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Utility is the power to satisfY human wants and needs. It is most commonly measured in terms of value, expressed in some medium of exchange as the price that must be paid to obtain the particular item.

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Goods ·and services may be divided into two types: necessities and luxuries. Obviously, these terms are relative, because, for most goods and services, what one person considers a necessity may be considered a luxury by another. For all goods and services, there is a relationship between the price that must be paid and the quantity that will be demanded or purchased. p

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Units of Demand

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Figu... 2.2 - General Price-Demand Relationship

From Figure 2.2, as the selling price per unit (P) is increased, there will be less dewand (D) for the product, and as the selling price is decreased, the demand will increase. The relationship between price and demand can be ..., -pressed as the linear function for 0:5. D :5. a, and a > 0, b > 0,

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where a is the intercept on the price axis and -b is the slope. Thus, b is the amount by which demand increases for each unit decrease in p. Both a and b are constants. It follows, of course, that

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(2-1)

(2-2)

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15 I Chaptel' 2 . Cost Concepts and Design Economics BREAK-EVEN ANALYSIS

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Break-even analysis involves investments of capital wherein at a certain level of production, the total income of the company would just be equal to the total expenses, thus resulting in no loss nor profit-

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TOTAL REVENUE FUNCTION

The total revenue, TR, that will result from a business venture during a given period is the product of the selling price per unit p and the number of units sold D. Thus, I

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TR = price x demand = pD

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(2-3)

if the relationship between price and demand as given in Eq. 2-1 is used,

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TR = {a-bD)D =a-bD2 for O:5D:5~, aM a>O, b>O,

(2-4)

The relationship betweerl total revenue and demand for the condition expressed in Eq. 2-4 m8J7 be represented by the curve shown in Figure 2.3. From calculus, the demand 15 that will produce maximum total revenue can be obtained by solving

d1R --=a-2bD=O dD

(2-5) a2

a2 4b

a2 4b

MaximumTR = a15 -b15 2 = - - - = 2b

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Demand

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Price = a - bD

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Figur" 2.3 - Total R"v"nu" Function"" a Function of n"mand

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17 I Chapter 2 . Cost Concepts and Design Economics

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Obviously, the conditions for which breakeven and maximum profit occur are our primary interest, First, at any volume (demand), D, Profit (Loss) n

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= Total Revenue -·Total Costs = (aD - bD4) - (Cp + cvD) = -bD 4 + (a - cv)D - CF for 0 :s; D :s; ~ and

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> b, b > O.

(2-9)

In order for a profit to occur, based on equation 2-9, and to achieve the typical results depicted in Figure 2.4, two conditions must be met:

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> 0; that is, the price per unit that will result in no demand has to be greater than the variable cost per unit. (This avoids negative demand.) 2. Total revenue must exceed total cost for the periods involved. 1. (a - cv)

If these conditions are met, we can find the optimal demand at which maximum profit will occur by taking the first derivative of equation 2-9 with respect to D and

setting it equal to zero:

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The optimal volume D that maximizes profit is a-Co D""=-2b

(2-10)

To ensure that we have maximized profit (rather than minimized it), the sign of the second derivative must be negative. Checking this, we find that

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d 4 (profit) dD2

= -2b,

which will be negative for b > O. An economic breakeven point for an operation occurs when total revenue equals total cost. Then for total revenue and total cost, as used in the development of equation 2-9 and 2-10 and at any demand D,

Total revenue = Total cost

(breakeven point)

aD - bD2 = CF + cvD -bD 2 + (a - cv)D - CF'= O.

(2-11)

Because equation 2-11 is a quadratic equation with one unknown (D), we can solve for the breakeven points D{alld D; (the roots of the equation]: D' = -(a - cv)

± ;I (a - cv)2 2(-b)

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4(-b) (-CF )

(2-12)

With the conditions for a profit satisfied, the quantity in the brackets of the numerator (the discriminant) in equation 2-12 will be greater than zero. This will ensure that Di and D; have real positive, unequal values.

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18 I Chapter 2 - Cost COllcepts and Design Economics

l ; Example 2.1

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A company prDduces an electrollic timing switch that is used in consumer and commercial products. The fixed cost is Php730,OOO per month, and the variable cost is Php830 per unit. TI,e selling price per unit isp=1800 - O.2D. For this situation, a. Determine the optimal volume for this product and confinn that a profit occurs (illStead of a loss) at this demand. b. Find the volume at which breake1Jen occurs; that is, what is the range of profitable demand? .16 SOLUTION:

a. Profit

= Total Revenue - Total Cost

= pD - (CF + cuD) = (1800 - 0.2D)D Profit •

+ 830D)

Takulg the first delivative of the equation and equating it to zero: d(Profit) dD

= -0.4D + 970 = 0

-0.4D =-970

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~ 1800D - 0.2D 2 - 730,000 - 830D ~ -0.2D 2 + 970D - 730,GOO

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D=

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-970 -004

= 2,425 units

To confirm that a profit occurs, instead of a

loss~

we take the second

de~ivative

of the profit equation: d'