Handbook of Industrial Automationedited - Chapter 10 doc

Although eachcash ¯ow occurs at distinct points in time and has adi€erent magnitude, both cash ¯ows would be equiva-lent at the interest rate of 6% compounded annually.1.3.2 Simple and C

Engineering is the profession that is devoted to the

application of scienti®c knowledge for practical

purposes Through the application of scienti®c

knowl-edge, engineers are continually developing products,

processes, and services for the bene®t of society

Engineers have been instrumental in many of the

advances of society For example, the state of modern

transportation can be linked to the e€orts of engineers

While undertaking such pursuits, the engineer is

typically faced with a variety of alternatives These

alternatives may include material selections, the degree

of computer automation, the selection of an applicable

safety system, and the means of manufacturing Each

alternative will have inherent technical advantages and

disadvantages that the engineer must evaluate The

evaluation of any alternative will also have to consider

the constraints of the particular problem or project

The engineer will typically be well informed about

the technical aspects of various alternatives However,

the engineer must also have a sound understanding of

the economic feasibility of the various alternatives

Indeed, money is a scarce resource that must be

allo-cated in a prudent fashion

This chapter provides a foundation in the basic

principles of engineering economics Through the

application of these basic principles, the engineer will

be able to address economic issues One such issue is

the economic feasibility of alternatives Engineering

economics o€ers a means to assess any receipts and

disbursements associated with an alternative Such anassessment will consider the magnitude and timing ofthe receipts and disbursements In¯ation and taxesmay also be factors that enter into the economicevaluation of an alternative The basic principles ofengineering economics also provide methods for thecomparison of alternatives and the subsequent selec-tion of an optimal alternative For example, an engi-neer may be confronted with the selection ofmachinery from a variety of sources As another exam-ple, the engineer may face the economic decision ofmanufacturing a part versus purchasing a part

It should also be recognized that there are tions to engineering economics Certain problems maynot have the potential to be evaluated properly in eco-nomic terms Some problems may be highly complexwherein economics is a minor consideration Still otherproblems may not be of sucient importance towarrant engineering economic analysis

limita-1.2 ELEMENTARY CONCEPTS OFENGINEERING ECONOMICSThere are several fundamental concepts that form afoundation for the application of the methods of engi-neering economics One fundamental concept is therecognition that money has a time value The value

of a given amount of money will depend upon when

it is received or disbursed Money possessed in the

829

present will have a greater value than the same amount

of money at some point in the future

It would be preferable to receive $1000 in the

pre-sent rather than receiving $1000 ®ve years hence Due

to the earning power of money, the economic value of

$1000 received at the present will exceed the value of

$1000 received ®ve years in the future The $1000

received today could be deposited into an interest

bear-ing savbear-ings account Durbear-ing the intervenbear-ing period of

®ve years, the $1000 would earn additional money

from the interest payments and its accumulated

amount would exceed $1000

The time value of money is also related to the

purchasing power of money The amount of goods

and services that a quantity of money will purchase

is usually not static In¯ation corresponds to a loss in

the purchasing power of money over time Under the

pressures of in¯ation, the cost of a good or service

will increase As an example, during the period of

1967 to 1997 the cost of a U.S ®rst-class postage

stamp rose to 32 cents from 5 cents De¯ation is

the opposite condition of in¯ation Historically,

in¯a-tionary periods have been far more common than

periods of de¯ation

A fundamental concept that is related to the time

value of money is interest Money is a valuable

com-modity, so businesses and individuals will pay a fee for

the use of money over a period of time Interest is

de®ned as the rental fee paid for the use of such a

sum of money Interest is usually quanti®ed by the

interest rate where the interest rate represents a

percen-tage of the original sum of money that is periodically

applied For instance, a ®nancial institution may

charge 1% per month for a borrowed sum of money

This means that at the end of a month, a fee of 1% of

the amount borrowed would have to be paid to the

®nancial institution

The periodic payment of interest on a loan

repre-sents a cash transaction During such a transaction, a

borrower would view the associated interest as a

dis-bursement while the interest would be a receipt for the

lender In engineering economics analysis, a point of

view must be selected for reference All analysis should

proceed from a sole viewpoint

Engineering economic analysis should also only

consider and assess feasible alternatives Alternatives

that ordinarily would be feasible may be infeasible due

to the particular constraints of a problem or project A

frequently overlooked alternative is the do-nothing

alternative Under the do-nothing alternative, the

option of doing nothing is preferable to any of the

other feasible alternatives

It is the inherent di€erences between alternativesthat must be evaluated Indeed it is the di€erences inalternatives that will lead to the selection of an optimalalternative Such an evaluation will utilize money as acommon unit of measurement to discern the di€er-ences between alternatives The evaluation of alterna-tives should also utilize a uniform time horizon toreveal the di€erences in alternatives

It is essential to recognize that any decisions aboutalternatives will only a€ect the present and the future.Therefore, past decisions and any associated costsshould be ignored in engineering economic analysis.The associated costs from past decisions are known

as sunk costs Sunk costs are irrelevant in engineeringeconomic analysis

1.3 ECONOMIC EQUIVALENCE ANDCASH FLOWFORMULAS

1.3.1 Economic Equivalence

In engineering, two conditions are said to be equivalentwhen each condition produces the same e€ect orimpact The concept of equivalence also pertains toengineering economics Two separate alternatives willhave economic equivalence whenever each alternativepossesses the same economic value Any prospectiveeconomic equivalence between two alternatives will

be dependent upon several factors One factor is therespective magnitudes of the cash ¯ow for each alter-native Another factor is the timing of the receipts anddisbursements for each alternative A third factor is theinterest rate that accounts for the time value of money.Through a combination of these factors, two cash

¯ows that di€er in magnitude may possess the sameinherent economic value The concept of economicequivalence is revealed through the cash ¯ows asso-ciated with a routine loan Suppose an individualborrowed $10,000 at 6% compounded annually to berepaid in annual instalments of $2374 over ®ve years.One cash ¯ow would be the sum of $10,000 at thepresent The other cash ¯ow would entail ®ve annualpayments of $2374 that totaled $11,870 Although eachcash ¯ow occurs at distinct points in time and has adi€erent magnitude, both cash ¯ows would be equiva-lent at the interest rate of 6% compounded annually.1.3.2 Simple and Compound Interest

There are di€erent ways in determining the amount ofinterest that a sum of money will produce One way issimple interest Under simple interest, the amount of

interest accrued, I, on a given sum of money, P, is

calculated by

where P is the principal amount, n the number of

inter-est periods, and i the interinter-est rate Hence with simple

interest, a sum of money would increase to

With simple interest, any interest earned during an

interest period does not earn additional interest in

forthcoming interest periods

In contrast, with compound interest, the interest is

determined by the principal sum of money and on any

interest that has accumulated to date So any previous

interest will earn interest in the future For example, if a

sum of money, P, is deposited into an interest-bearing

account at an interest rate, i, after one period the

amount of money available, F, would be determined

by

If the sum of money were deposited for two periods,

the amount of money available, F, would be

deter-mined by

F ˆ …P…1 ‡ i††…1 ‡ i† ˆ P…1 ‡ i†2 …4†

In general, the amount of money, F, that would

accu-mulate with n additional periods would be

Compound interest is more prevalent in ®nancial

transactions than simple interest, although simple

interest is often encountered in bonds

1.3.3 Cash Flow Diagrams and End-of-Period

Convention

In engineering, diagrams are frequently drawn to help

the individual understand a particular engineering

issue A cash ¯ow diagram is often used to depict the

magnitude and the timing of cash ¯ows in an

engineer-ing economics issue A cash ¯ow diagram presumes a

particular point of view A horizontal line is used to

represent the time horizon, while vertical lines from the

horizontal line depict cash ¯ows An upward arrow

indicates a receipt of money, while a downward

arrow is a disbursement (see Fig 1)

In this chapter, there is an assumption that cash

¯ows will be discrete and will occur at the end of a

period Continuous ¯ows of cash over a period will

not be considered An extensive discussion of uous cash ¯ows is o€ered in the references

contin-1.3.4 Cash Flow Patterns

In ®nancial transactions, a cash ¯ow may undertake avariety of patterns The simplest pattern is the singlecash ¯ow Under this cash ¯ow pattern, a single pre-sent amount is transformed into a single future amount(see Fig 2)

The uniform series is another cash ¯ow pattern.With this pattern, all of the cash ¯ows are of thesame magnitude and the cash ¯ows occur at equallyspaced time intervals (seeFig 3)

A cash ¯ow that increases or decreases by the sameamount in each succeeding period would be a uniformgradient cash ¯ow pattern (seeFig 4) Whereas, a cash

¯ow that increases or decreases by the same percentage

in each succeeding period would be a geometricalgradient cash ¯ow pattern (seeFig 5)

Figure 1 Cash ¯ow diagram

Figure 2 Present amount and future amount

An irregular cash ¯ow pattern would occur ever the cash ¯ow did not maintain one of the afore-mentioned regular patterns Occasionally, a portion of

when-an irregular cash ¯ow pattern may exhibit a regularpattern (see Fig 6) In Fig 6, the overall cash ¯owpattern would be classi®ed as irregular but in the

®nal three years there is a uniform series pattern.Equivalent relationships between the various cash

¯ow patterns may be developed mathematically Due

to the time value of money, such relationships will bedependent upon the prevailing interest rates and theduration of the associated cash ¯ows

1.3.5 Single-Payment Compound Amount FactorDue to the time value of money, a single cash ¯ow, P,will increase over time to an equivalent future value, F.The future value, F, will depend upon the length oftime, the prevailing interest rate, and the type of inter-est If the single cash ¯ow, P, is invested at a constantcompound interest rate, i, for a given number of inter-est periods, n, then the future value, F, will be deter-mined by Eq (5) Eq (5) may be rewritten to introducethe following notation:

The conversion factor, …FjP; i; n†, is referred to as thesingle-payment compound amount factor It is inter-preted as ``to ®nd the equivalent future amount, F,given the present amount, P, at the interest rate, i,for n periods.'' The single-payment compound amountfactor, …FjP; i; n†, is simply the quantity (1 ‡ i†n Theevaluation of the single-payment compound amountfactor is an easy calculation Tabulated values of thesingle-payment compound amount factor for interestrates of 1%, 8%, and 10% may be found inTables 1to

Figure 3 Uniform series

Figure 4 Uniform gradient

3 Note, other economic equivalence factors can also

be found inTables 1to 3

Example 1 A sum of $5000 is deposited into an

account that pays 10% interest compounded annually

To determine the future value of the sum of money 20

years hence, utilize Eq (6):

F ˆ $5000…1 ‡ 0:10†20ˆ $33,637

1.3.6 Single Payment Present-Worth Amount

Factor

Through simple algebra, Eq (6) can be solved for P,

wherein the resulting factor, …PjF; i; n†, is designated as

the single-payment present worth factor:

Example 2 In the settlement of a litigation action, a

boy is to receive a lump sum of $250,000 10 years in the

future What is the present worth of such a payment

presuming an annual compound interest rate of 8%?

P ˆ $250,000…1 ‡ 0:08† 10ˆ $115,798

Example 3 What annual rate of interest was earned if

an investment of $11,000 produced a value of $21,000

1.3.7 Compound Amount Factor

Formulas can be derived that relate a single future

cash ¯ow pattern, F, to a uniform series of cash ¯ow

patterns, A The equivalent future amount, F, that a

uniform cash ¯ow pattern, A, will produce is

F ˆ A …1 ‡ i†in 1

Example 4 A design engineer expects to collect $5000

per year on patent royalties The patent remains in e€ect

for the next 10 years What is the future value of this

series of patent royalties if it is deposited into a fund thatearns 10% compounded annually?

F ˆ A…FjA; i; n† ˆ $5,000…FjA; 10%; 10†

ˆ $5000…15:937†

ˆ $79,6851.3.8 Sinking Fund FactorSimilarly, an equivalent uniform series cash ¯owpattern, A, can be obtained from a single future cash

P ˆ A …1 ‡ i†i…1 ‡ i†n n1

1.3.10 Capital Recovery FactorThe capital recovery factor is the reciprocal of the pre-sent-worth factor This conversion factor transforms asingle present amount, P, to a uniform series of cash

manu-of the loan is 8% compounded annually, what is theperiodic payment that the manufacturer must pay?

A ˆ P…AjP; I; n† ˆ $50,000…AjP; 8%; 5†

ˆ $50,000…0:2505†

ˆ $12,525

N FjP PjF FjA AjF PjA AjP AjG

N FjP PjF FjA AjF PjA AjP AjG

N FjP PjF FjA AjF PjA AjP AjG

1.3.11 Uniform Gradient Series Factor

As previously discussed, a cash ¯ow series is not

always uniform Gradient series are frequently

encoun-tered in engineering economics Formulas for

conver-sion factors of gradient series have likewise been

developed Speci®cally, a uniform gradient series can

be expressed as a uniform series of cash ¯ows by

A ˆ G …1 ‡ i†i…1 ‡ i†n nin 1i

1.3.12 Geometrical Gradient Present-Worth

Factor

Cash ¯ow series that increase or decrease by a constant

percentage, g, with each succeeding period can be

con-verted to a present amount by the geometric gradient

present worth factor

Example 6 A manufacturer has established a new

pro-duction line at an existing facility It has been estimated

that the additional energy costs for the new production

line are $5,000 for the ®rst year and will increase 3% for

each subsequent year The production line is expected to

have a life span of 10 years Given an annual compound

interest rate of 5% what is the present worth of the

energy costs for the new production line?

First calculate the value of g* given that g ˆ 3% and

P ˆ A1

1 ‡ g

…1 ‡ g*†n 1g*…1 ‡ g*†n

Hence, there are three conditions that can occur,concerning the frequency of the compounding periodsand the frequency of the periods for the cash ¯ow.First, the frequency of the compounding periods andthat of the cash ¯ow are synchronized Secondly, thecompounding periods are shorter than the periods forthe cash ¯ow Third, the compounding periods arelonger than the corresponding periods of the cash ¯ow

If the periods of the compounding and the ¯ow offunds are synchronized, the aforementioned conver-sion factors can be utilized to determine any equivalentcash ¯ow When the compounding periods and theperiods of the cash lows are not synchronized, thenintermediate steps to synchronize the periods must beundertaken prior to utilizing the aforementioned con-version factors

Example 7 What is the present value of a series ofannual payments of $90,000 over 10 years at the rate

1.3.14 Amortized Loans

The capital needed to ®nance engineering projects will

not always be available through retained earnings

Indeed, money will often have to be borrowed There

are many types of loans that exist, but this chapter will

focus upon the standard amortized loan With an

amortized loan, the loan is repaid through installments

over time

The most prevalent amortized loan has monthly

installments with interest that is compounded monthly

Also, the monthly installments are ®xed Each

install-ment consists of a portion that pays the interest on the

loan and a portion that repays the outstanding

bal-ance With each succeeding installment, the interest

portion will diminish, while the portion devoted to

the repayment of the outstanding balance will increase

The magnitude of an installment payment is

deter-mined through the use of the capital recovery

conver-sion factor In short, the payment, A, is found by

Noting that each installment payment consists of an

interest portion and a remaining balance portion, the

following notation is introduced:

Ij ˆ interest payment in period j

Prj ˆ principal payment in period j

Bj ˆ outstanding balance at end of period j

The interest portion of any installment payment is

simply the product of the outstanding balance times

the prevailing interest rate:

The portion of the installment that may be applied to

the outstanding balance:

Example 8 A consulting ®rm obtains a $10,000 loan to

purchase a computer workstation The terms of the loan

are 12 months at a nominal rate of 12% compounded

monthly What is the monthly installment payment?

How does the interest portion of the installment payment

vary monthly?

The installment payment is calculated by merely

applying the capital recovery conversion factor,

(AjP; i; n†:

A ˆ $10,000…AjP; 1%; 12† ˆ $10,000…0:08885†

from Eq: …14†

ˆ $888:50The interest portion of the ®rst installment would be

I1ˆ …B1 1†i ˆ …$10,000†…0:01† from Eq: …15†

ˆ $100:00Hence, the portion of the ®rst installment applied to theprinciple would be the di€erence between A and I1:

Pr1ˆ A I1ˆ $888:50 100:00 from …16†

ˆ $788:50The new outstanding balance would be

B1ˆ $10; 000 788:50

ˆ $9211:50Through an iterative process, the values for Ijand Bjcan

be found for the remaining 11 months Obviously, theiterative nature of this problem is ideal for a computerapplication

Installment Payment Principal Interest Balance

Ijˆ …Bj 1†i ‡ A…PjA; i; n j ‡ 1†i …17†The corresponding remaining balance after n j pay-ments may also be found via the following formula:

Likewise, the principal payment for a particular ment would be obtained by subtracting the interest

install-paid for a particular installment from the periodic

payment:

Returning to Example 8, the interest portion of the

sixth payment may be found as follows:

Often an engineer will be faced with the responsibility

of determining the economic feasibility of various

pro-jects and propositions known as alternatives In short,

the engineer will have to make a decision on whether to

proceed with an alternative With a thorough

under-standing of cash ¯ow patterns and the compounding of

interest, one may apply a variety of techniques to

eval-uate various alternatives

The application of these techniques requires that

one be able to classify alternatives Alternatives are

classi®ed as independent whenever the decision to

pro-ceed with the alternative or to reject the alternative has

no bearing on other prospective alternatives For

example, the decision for a consulting ®rm to purchase

a new computer system would ordinarily be unrelated

to the ®rm's decision as to whether the ®rm should

utilize a particular long-distance carrier for its

telecom-munication system

Alternatives may also be classi®ed as mutually

exclusive Such a condition exists when there are a

series of alternatives from which only one alternative

may be selected If an engineer had to select a

machine for a workstation from three distinct

machines each having unique ®rst costs,

mainte-nance costs, and salvages, then this would be a

con-dition where the alternatives were mutually exclusive

With mutually exclusive alternatives, the selection of

an alternative prevents the selection of another

alternative

Often when identifying alternatives, an individual

must include the do-nothing alternative The

do-noth-ing alternative simply represents the opportunity to

maintain the existing conditions In many instances,

after the careful evaluation of a series of alternatives,

the optimal decision will be to do-nothing or to tain the existing conditions The selection of the do-nothing alternative will preserve the scarce resource ofcapital

main-The comparison of various alternatives involves theestimation of cash ¯ows for each alternative Theseestimated cash ¯ows also extend over several time per-iods A decision will have to made as to the duration ofthe planning horizon The planning horizon representsthe time period over which the alternatives will beevaluated The selection of the planning horizon isimportant If the planning horizon is too short, oneruns the risk of rejecting alternatives that are initiallyexpensive but generate large returns in the future.Conversely, a planning horizon that is too long canresult in an entity collapsing before it reaps any bene-

®ts from accepted alternatives

Further, the basic concept of time value of moneymust be incorporated into the evaluation of alterna-tives This is accomplished through the selection of

an interest rate that will be used to adjust the variouscash ¯ows in the panning horizon This interest ratehas been identi®ed with a variety of names: minimumattractive rate of return (MARR), discount rate, return

on capital, and cost of money In this chapter, the termMARR will be used

The determination of the value of the MARR isimportant The value of the MARR should not bearbitrarily assigned The MARR should recognizethe cost of capital and should compensate for therisk associated in adopting an alternative If theMARR is set unnecessarily high, an entity may need-lessly reject worthwhile projects Similarly, if theMARR is set too low, an entity can be exposed tothe potential of investing in projects that are expensiveand wasteful

1.4.1 Present-Worth MethodThis technique for evaluating economic alternativesentails the conversion of any pertinent estimated cash

¯ows to the present The cash ¯ows are converted bythe methods previously discussed in this chapter Inshort, all cash ¯ows are converted to an equivalent Ppattern that is referred to as the present worth (PW).The conversions utilize a chosen MARR and a speci-

®ed planning horizon Each alternative must be ated over the same planning horizon If the economicalternative is an independent alternative, then the alter-native is accepted by entity whenever the present worthhas a value greater than zero

evalu-Example 9 A consulting company is considering

undertaking a project The initial cash outlay for the

10 year project would be $50,000 The project is

esti-mated to yield $8000 per year for 10 years If the

MARR is 10%, should the project be undertaken?

When faced with mutually exclusive alternatives,

the optimal alternative is the alternative with the

high-est present worth Indeed, the present worth of each

alternative can be used to rank the alternatives It

should also be noted that on occasion each of the

mutually exclusive alternatives may have a negative

present worth In such a situation, one would select

the alternative that was the least costly by choosing

the alternative that had the highest present worth

Example 10 Two different machines are being

consid-ered by a manufacturing company Due to constraints,

the manufacturing company must select one of the two

machines Machine A has an initial cost of $75,000 and

an estimated salvage of $25,000 after ®ve years The

annual operating costs for Machine A are assessed at

$7500 Machine Bhas an initial cost of $50,000 and

its salvage is negligible after ®ve years Its operating

costs are $9000 per year Given a MARR of 10%,

which machine should the company select?

of the estimated cash ¯ows into a uniform annual cash

¯ow that is known as the annual worth (AW) Theconversion of the cash ¯ows is based on an identi®edMARR and a speci®ed time horizon Each alternativemust be evaluated over the same planning horizon Anindependent alternative will be accepted, if its annualworth exceeds zero

For mutually exclusive alternatives, the annualworth of each alternative provides a ranking Thealternative with the greatest annual worth is the opti-mal alternative It is also possible, that each of thealternatives may have a negative annual worth Thebest alternative still would be the alternative that hadthe greatest annual worth This would be the leastcostly alternative

Example 11 Two different machines are being ered by a manufacturing company Due to constraints,the manufacturing company must select one of the twomachines Machine A has an initial cost of $75,000 and

consid-an estimated salvage of $25,000 after ®ve years Theannual operating costs for Machine A are assessed at

$7500 Machine Bhas an initial cost of $50,000 andits salvage is negligible after ®ve years Its operatingcosts are $9000 per year Given a MARR of 10%,which machine should the company select? Utilize theannual worth approach

AW ˆ $50,000…AjP; 10%; 5† $9000

AW ˆ $50,000…0:2638† $9000

AW ˆ $22,190Hence, Machine Bis preferred to Machine A Also notethe consistency between the annual worth and present-worth methods See Example 10

1.4.3 Rate of Return Method

For independent alternatives, this technique relies on

the concept of determining the interest rate where an

alternative's receipts will be equivalent to its

disburse-ments The interest rate is known as the rate of return

(ROR) The rate of return is then compared to the

MARR If the rate of return exceeds the MARR,

then the alternative is viewed favorably and funds are

expended for it

Example 12 A consulting company is considering

undertaking a project The initial cash outlay for the

project would be $50,000 The project is estimated to

yield $8000 per year for 10 years If the MARR is

10%, should the project be undertaken? Solve using the

Thus ROR is between 9 and 10% Using interpolation

the ROR is found to be 9.6% The project is rejected

because the ROR (9.6%) is less than the MARR

(10%) Note the consistency between methods of

eval-uating alternatives See Example 9

For mutually exclusive alternatives, the optimal

alternative is not decided from the individual rates of

return of each alternative Rather, an incremental

ana-lysis is employed The incremental anaana-lysis compares

pairs of alternatives First, the alternatives are ranked

according to the initial investments Then for the

alter-native that has the smallest initial investment, its rate

of return is calculated Provided that its rate of return

is greater than the MARR, then it is accepted as viable

alternative The viable alternative is then compared to

next most expensive alternative The comparison is

based on the incremental additional investment and

the incremental additional cash ¯ows If the

incremen-tal investment yields a rate of return greater than the

MARR, then the more expensive alternative is

selected Conversely, if the incremental investment

does not have a rate of return greater than the

MARR, then the more expensive alternative is

rejected This pairwise comparison continues until all

of the alternatives have been examined

Example 13 Consider four mutually exclusive tives, each of which has an eight-year useful life:

Alternative D vs Do-nothing:

PW ˆ $250 ‡ $61…PjA; 8%; 8†

ˆ $250 ‡ $61…55:7466† ˆ $100:54Conclude that the incremental ROR > MARR;hence accept Alternative D and reject do-nothing.Alternative C vs Alternative D:

PW ˆ … $300 $250† ‡ …$50 $61†…PjA; 8%; 8†

ˆ $50 ‡ … $11†…5:7466† ˆ $21:86Conclude that the incremental ROR > MARR;hence accept Alternative C and reject AlternativeD

Alternative Bvs Alternative C:

PW ˆ … $400 $300†

‡ …$60 $50†…PjA; 8%; 8†

ˆ … $100† ‡ $10…5:7466† ˆ $42:53Conclude that the incremental ROR < MARR;hence reject Alternative Band keep Alternative C.Alternative A vs Alternative C:

PW ˆ … $500 $300† ‡ …$61 $50†…PjA; 8%; 8†

ˆ … $200† ‡ $11…5:7466† ˆ $136:78Conclude that the incremental ROR < MARR;hence reject Alternative A and keep Alternative C.Through the pairwise comparison of the incrementalROR, Alternative C is accepted as the optimal alterna-tive

1.4.4 Bene®t±Cost Ratio

This technique operates on the simple concept that in

order for an alternative to be deemed worthwhile it

bene®ts must outweigh its costs To make such a

com-parison requires that the bene®ts and costs be

pre-sented in equivalent economic terms Ordinarily, the

bene®ts and costs are expressed as either equivalent

P patterns or equivalent A patterns These equivalent

P patterns or A patterns are determined using a given

MARR and a stated planning horizon

For independent alternatives, the bene®ts are then

compared to the costs by means of a ratio If the ratio

of bene®ts to costs exceeds unity, then the alternative

should be accepted

Example 14 A local government is evaluating a

con-struction proposal for a roadway The initial cost of the

roadway is $1,650,000 It is estimated that the annual

maintenance costs on the roadway will be $75,000 The

estimated annual bene®ts to be derived from the roadway

are $310,000 The useful life of the roadway is 20 years

without a salvage Using the bene®t±cost approach,

should the road be constructed with a 10% MARR?

Annual projected bene®ts: $310,000

Annual project costs:

roadway should be constructed

Mutually exclusive alternatives require an

incremen-tal analysis One cannot select the optimal alternative

by merely examining individual bene®t±cost ratios

Initially, the alternatives are ranked in ascending

order of equivalent ®rst costs The ®rst viable

alterna-tive is then found by selecting the alternaalterna-tive with the

smallest initial costs that has an individual bene®t±cost

ratio greater than 1 Once a viable alternative is found,

then any remaining alternatives are evaluated on a

pairwise basis to analyze whether additional costs are

justi®ed by the additional bene®ts Throughout this

procedure, once a viable alternative is found, it

remains the alternative of choice unless the incremental

pairwise analysis yields a superior alternative Then the

superior alternative becomes the alternative of choice

This incremental pairwise comparison continues untilall alternatives have been examined

1.4.5 Payback MethodThis is a technique that is often used due to its simpli-city and its ease of application In short, the paybackmethod determines the length of time for an alternative

to pay for itself Under the most common form of thepayback method, any relevant cash ¯ows are notadjusted for their inherent time value For mutuallyexclusive alternatives, the optimal alternative would

be the one with the shortest payback

There are inherent disadvantages to this commonform of the payback method It ignores the timevalue of money Also, the common form of the pay-back method ignores the duration of the alternatives.Example 15 Examine the following four alternatives.Note that each alternative has a payback period of twoyears However, the alternatives are obviously notequivalent

Alt I Alt II Alt III Alt IV

Both payback methods provide estimates that may

be useful in explaining economic alternatives.However, due to the inherent ¯aws with these methods,

it is recommended that the payback methods only beused as an ancillary technique

1.5 AFTER-TAX ANALYSISThe consideration of taxes must often be included inthe evaluation of economic alternatives In such an

evaluation, taxes are simply another expenditure.

Indeed, an alternative that may initially appear to be

viable may lose its viability with the inclusion of taxes

The magnitude of this taxation depends upon the

prevailing federal, state, and local tax laws These tax

laws have been passed by legislatures so that these

governments can operate Taxation occurs in many

di€erent forms A partial listing of various forms of

taxation includes federal income tax, state income

tax, local income tax, local property tax, state and

local sales tax, federal excise tax, and federal and

state gasoline tax

The topic of taxes is complex Tax laws are

conti-nually changing due to political forces and underlying

economic conditions In this chapter, the

concentra-tion will be upon federal income taxes The techniques

introduced will be applicable notwithstanding the

inconstant nature of taxes

1.5.1 Depreciation

The term depreciation has several meanings In one

sense, depreciation refers to the deterioration of an

asset For example, as a machine ages, its downtime

will often increase and its overall productivity will

diminish Similarly, depreciation can be equated with

obsolescence A desktop computer from the mid-1980s

is obsolete in the late 1990s

However, in engineering economics, the concept of

depreciation that is utilized by accountants is adopted

Depreciation is simply the accounting procedure that

amortizes the cost of an asset over the estimated life of

the asset In short, the cost of an asset is not expensed

at the time of purchase but rather is rationally spread

throughout the useful life of the asset Such a concept

is adopted because this concept of depreciation is

utilized in the calculation of federal income taxes

It should be noted that depreciation does not

repre-sent a cash ¯ow Rather it is an accounting procedure

Heretofore, all of the economic analysis has

concen-trated upon cash ¯ows Depreciation must be included

in any after-tax economic analysis because

deprecia-tion will a€ect the amount of taxes owed

There are some basic terms associated with

depre-ciation Book value, BVj, denotes the undepreciated

value of an asset The cost basis of an asset is usually

the acquisition cost Hence, the book value is the

dif-ference between the cost basis and the accumulated

depreciation costs The book value is given in the

fol-lowing formula:

BVjˆ CB …D1‡ D2‡


‡ Dt† …20†

where BVj is the book value, CB is the cost basis, and

Dt is the depreciation charge for year t

The salvage value of an asset is the estimated value

of an asset at the end of its estimated life

Over the years, a variety of methods have been used

to calculate depreciation charges These methods areprescribed by the Internal Revenue Service (IRS).Prior to 1981, the permissible depreciation methodswere straight-line, declining balance, and sum-ofyears digits The Economic Recovery Tax Act of

1981 introduced the accelerated cost recovery system(ACRS) In 1986, the Tax Reform Act again modi®edallowable depreciation methods with the introduction

of the modi®ed accelerated cost recovery system(MACRS) This chapter will examine the MACRSmethod of depreciation The MACRS applies to assetsplaced in service after December 31, 1986 The refer-ences o€er rigorous examinations of the other depre-ciation methods for assets placed in service prior toDecember 31, 1986

The MACRS categorizes assets into eight tions known as the recovery period: 3-year, 5-year, 7-year, 10-year, 15-year, 20-year, 27.5-year, and 39-year.The IRS has guidelines that determine into which clas-si®cation an asset should be placed These guidelinesare found in the IRS Publication 946 How toDepreciate Property [1] Table 4 gives examples ofsome common assets and their pertinent recoveryperiods

classi®ca-For each MACRS classi®cation, the IRS has

speci-®c depreciation rates The depreciation rates are therecovery allowance percentages The MACRS methodalso uses a half year convention so that all property istreated as if it were placed into service at the midyear.Hence, depreciation charges exist for an additional taxyear beyond the class designation For instance, 3-yearproperty will be allocated over four tax years.Table 5sets forth the recovery allowance percentages for thevarious classi®cations

The depreciation charges then for any given yeardepend upon the acquisition cost and the appropriaterecovery allowance percentage The depreciationcharge is then simply the product of the acquisitioncost and the appropriate recovery allowance per-centage

Example 16 A computer system with an initial cost of

$20,000 is purchased in 1997 by an engineering ing company Compute the allowable annual deprecia-tion charges and the corresponding book values.Computers are classi®ed as having a 5-year recoveryperiod

consult-Table 4 MACRS Classi®cations of Depreciable Property

3-year Fabricated metal products; special handling devices for food and

beverage manufacture; tractor units for over-the-road use;

certain livestock5-year Automobiles; light and heavy trucks; computers and copiers;

equipment used in research and experimentation; equipmentused in oil wells

7-year All other property not assigned to another classi®cation; of®ce

furniture and equipment; single-purpose agricultural structures;

railroad track; telephone station equipment10-year Assets used in petroleum re®ning; assets used in manufacture of

castings, forgings, tobacco, and certain food products; vesselsand water transportation equipment

15-year Waste-water plants; telephone distribution equipment; industrial

steam and electrical generation equipment; railroad wharvesand docks; storage tanks

20-year Municipal sewers; barges and tugs; electrical power plant27.5-year Residential rental property

Table 5 MACRS Recovery Allowance Percentages

1.5.2 Income Tax Rates

Federal income tax rates for both corporations and

individuals have varied over the years Note, the top

federal income tax rate for an individual in 1970 was

70%, while in 1995 it was 39.6% The income tax rates

are also graduated so that the rate depends upon the

taxable income In 1997, a corporation with a taxable

income of $40,000 was taxed at the rate of 15%,

whereas the corporation with a taxable income of

$1,000,000 would be taxed at the 34% level for all

taxable income over $335,000

In engineering economic analysis an e€ective

income tax rate is usually used The e€ective

income-tax rate is simply a percentage The product of the

e€ective income tax rate and the taxable income then

yields the tax owed The concept of an e€ective income

tax rate often combines the federal, state, and local

income tax rates

1.5.3 Factors Affecting Taxable Income

The taxable income re¯ects the quantity from which

income taxes are determined Therefore, the taxable

income includes before-tax cash ¯ows such as income

and expenses Also, included in the taxable income are

any applicable depreciation charges Recall, these

depreciation charges are not cash ¯ows Depreciation

charges will further reduce the taxable income and in

turn reduce the tax liability

Loans are commonly used to ®nance businessoperations The interest paid on such loans is ordina-rily viewed as an expense by the federal government.Hence, any interest paid on a loan by a corporationwould be deductible from the taxable income Note,only the interest payments on a loan and not the prin-cipal portion is deductible In essence, this reduces thee€ective cost of borrowing through the alleviation oftax liability

1.5.4 After-Tax Analysis

In order to proceed with an after-tax analysis on analternative there are several preliminary considera-tions The MARR must be established The MARRused for after-tax analysis should not be the sameMARR used for before-tax analysis The e€ectiveincome tax rate must be identi®ed Remember thatthe e€ective income tax rate is often based upon theprevailing federal, state, and local income tax rates Ifnecessary, the appropriate depreciation method andassociated depreciation charges must be calculated.Similarly, any relevant interest on loans must be deter-mined Also, the length of the time horizon needs to beset

The underlying concept is to try to calculate anafter-tax cash ¯ow for each period within the timehorizon After securing these after-tax cash ¯ows,then one can proceed to utilize any of the previouslymentioned means of evaluating alternatives For exam-ple, an after-tax present-worth analysis is simply wherethe present-worth technique is applied to the after-taxcash ¯ows Similarly, an after-tax rate of return utilizesthe rate-of return technique on after-tax cash ¯ows.The following example illustrates the procedures forcompleting an after-tax cash ¯ow analysis

Example 17 With the purchase of a $100,000 ter system, a consulting ®rm estimated that it couldreceive an additional $40,000 in before-tax income.The ®rm is in the 30% income tax bracket and expects

compu-an after-tax MARR of 10% If the funds for the puter are borrowed on a 4-year direct 8% reduction loanwith equal annual payments, what is the present worth ofthe after-tax cash ¯ow?

com-First ®nd the annual loan payment:

A ˆ P…AjP; 8%; 4† ˆ $100,000…0:3019† ˆ $30,190Then determine the interest paid each year on the loan:

Ij ˆ A…PjA; j; n j ‡ 1†i from Eq: …17†

Note that computers are classi®ed as having a 5-year

recovery period Hence, the annual depreciation

1.6 INFLATIONThe purchasing power of money is not static over time.Prices for goods and services are rarely constant fromone year to the next With in¯ationary pressures, thecost of goods and services increases with time.Whereas, decreasing prices would signify the condition

of de¯ation

Recall that the time value of money is based uponthe earning power of money and also the purchasingpower of the money When evaluating alternatives orcomputing economic equivalence, it is often desirable

to separate the earning power of money from its chasing power In short, an ``in¯ation-free'' analysis isfrequently preferred

1.6.1 Measures of In¯ation

Indexes of in¯ation are frequently used to monitor

changes in prices The Consumer Price Index (CPI) is

perhaps the most widely referenced index of in¯ation

Indexes of in¯ation are merely weighted averages of a

series of goods and services The index then tracks how

the prices of the goods and services vary from period to

period

Care should be undertaken in the selection of an

in¯ation index One should verify that a particular

in¯ation index is tracking the factors that are needed

for a particular analysis For example, rises in the cost

of groceries may not be a signi®cant factor to an

equip-ment manufacturer

An in¯ation index will have a base year or time

period Subsequent changes in price are measured

against the base year or period For example, the

CPI has a base year of 1967 with a value of 100.00

In 1990, the CPI index had a value of 391.4 This

indicates that comparable goods and services that

cost $100 in 1967 would have cost $391.40 in 1990

With the selection of an appropriate in¯ation index,

it is possible to analyze economic alternatives on an

in¯ation-free basis Such an approach requires that

one convert all of the cash ¯ows to a particular year

or time period based on the in¯ation index Once the

conversion has been made, then an alternative can be

evaluated using any of the previously mentioned

tech-niques for the evaluation of alternatives However, one

must still include a means to account for the time value

of money based upon the earning power of money

This interest rate is generally called the in¯ation-free

interest rate and is denoted as i0

Example 18 In 1985, a manufacturing company

invested in a new process that cost $4,500,000 In the

subsequent four years, the net pro®t after taxes made by

the facility, along with the price index was:

Year Net pro®t (actual $) Price index (1967 ˆ 100)

If the in¯ation-free rate of return, i0, was 3%, determine

the present worth of the investment in 1985 dollars Was

the investment a sound one?

First express net pro®t in terms of 1985 dollars:

1.6.2 Average In¯ation Rate

A diculty associated with an in¯ation index is thatthe index tracks past in¯ationary patterns It will notnecessarily give reliable estimates of future in¯ationarytrends Also, from the examination of an in¯ationindex, it is obvious that in¯ation is rarely constant.Hence, an average in¯ation rate is often used toaccount for the variation in the in¯ation rates over

a number of years An average in¯ation rate can becalculated from an in¯ation index by the followingequation:

…Index†t…1 ‡ f†nˆ …Index†t‡n …21†1.6.3 Actual and Constant Dollars

In any analysis where in¯ation is taken into account,there are a few fundamental terms and relationshipsthat must be understood Constant dollars representmoney where the money has been adjusted for in¯a-tionary e€ects Cash ¯ow patterns may be expressed inconstant dollars A notation with a prime superscriptoften denotes a constant dollar cash ¯ow pattern For

instance, an F0 would denote a constant dollar future

cash ¯ow

Actual or current dollars represent a monetary

value that incorporates both in¯ation and the earning

power of money Estimates in actual dollars represent

the true sums of money that one could anticipate to

receive or disburse

The in¯ation-free interest rate, i0, is an estimate of

the earning power of money without in¯ation, whereas

the market interest rate, i, combines the earning power

of money and the e€ects of in¯ation The market

inter-est rate is what one will encounter in common

every-day experiences The interest rate on a standard

mortgage is an example of a market interest rate

The in¯ation-free interest rate, the market interest

rate, and the average in¯ation rate are related by the

following equation:

Therefore, a series of cash ¯ows can then be expressed

either in constant dollars or in actual dollars The

con-version from actual dollars to constant dollars in any

given period would be accomplished by multiplying by

the following factor:

…Constant dollar†nˆ …Actual dollar†n…1 ‡ f † n

…23†

Similarly, the conversion from constant dollars to

actual dollar utilizes this factor:

…Actual dollar†n ˆ …Constant dollar†n…1 ‡ f †n …24†

For after-tax analysis where the average in¯ation rate

is estimated, it is recommended that the subject cash

¯ows be converted to actual dollars Such a conversion

will enable one to readily assess the pertinent tax

liabil-ities

There are two approaches for a before-tax analysis

with in¯ation One approach calls for all of the cash

¯ows to be expressed in terms of actual dollars with the

subsequent analysis to use the market interest rate, i

Under the second approach, all of the cash ¯ows are

expressed in terms of constant dollars with the

sub-sequent analysis utilizing the in¯ation-free interest

rate, i0

Example 19 A manufacturing corporation is

con-structing a new production line The associated

produc-tion costs for the new line are estimated at $2.5 million

Over the ensuing years, the production costs areexpected to increase $100,000 per year in actual dollars.The yearly in¯ation rate is presumed to be 4% and themarket interest rate is 8% Given a life span of 10 years,

®nd the annual worth of the production costs in terms

A ˆ A1‡ G…AjG; 8%; 10†

A ˆ $2,500,000 ‡ 100,000…3:8713†

A ˆ $2,887,130Convert to present worth:

P ˆ $2,887,130…PjA; 8%; 10†

P ˆ $2,887,130…6:7101†

P ˆ $19,372,931Convert to constant annual worth using i0ˆ 3:846%:

IRS Publication 946 How to Depreciate Property.Washington DC: United States Government PrintingOf®ce, 1997

DG Newnan, B Johnson Engineering Economic Analysis.San Jose, CA: Engineering Press, 1995

GJ Thuesen, WJ Fabrycky Engineering Economy.Englewood Cliffs, NJ: Prentice Hall

CS Park Contemporary Engineering Economics MenloPark, CA: Addison-Wesley, 1997

Chapter 10.2

Manufacturing-Cost Recovery and Estimating Systems

Eric M Malstromy and Terry R Collins

University of Arkansas, Fayetteville, Arkansas

2.1 INTRODUCTION

This chapter overviews cost recovery and estimating

systems typically used by manufacturing

organiza-tions The chapter begins by overviewing conventional

manufacturing-cost estimating systems Cost centers

are described, as are types of costs and use of

perfor-mance standards in making cost estimates Process

design and its e€ect on manufacturing costs is

addressed, as is the integration of learning curves

into estimating procedures Contingency allowances

are addressed, as is the concept of making cost reviews

or re-estimates based on the progress of a

manufactur-ing project

Conventional cost recovery systems are next

described In these systems direct labor is used as a

recovery basis variable Concepts of capital budgeting

are introduced as are subsequent adjustments of

obtained labor/overhead rates

Quick-response estimating is next described with an

emphasis on cost variable identi®cation and

construc-tion of estimating relaconstruc-tionships The relaconstruc-tionship to

group technology and production mix/volume

scenar-ios is addressed as well Cost estimating software

devel-opment concepts are introduced The merits of

purchasing commercially available software versus

in-house software development are described

Activity based costing is described in some detail

Topics include mechanics of the recovery procedure,

and the identi®cation and selection of cost drivers

The chapter concludes by discussing how high levels

of manufacturing automation impact the processes ofmanufacturing cost estimating and recovery

2.2 CONVENTIONAL COST ESTIMATINGPROCEDURES

Manufacturing-cost estimating is a topic that has notenjoyed high visibility in university curricula In 1981,only three books existed that addressed this subject insucient depth to permit them to be used is textbooksfor university courses on this subject [1±3] In 1981,almost no university faculty specialized in the ®eld ofcost estimating This continues to be true at present.The result has been limited availability of suitabletexts on this subject To be an e€ective cost estimatorrequires prior industrial experience Comparatively fewuniversity faculty members have signi®cant workexperience outside academia Consequently, scantacademic research on this subject has, or is beingaccomplished

2.2.1 Cost Estimating De®nedCost estimating may be described as the process bywhich a forecast of costs required to manufacture aproduct or complete a speci®ed task can be made.The estimate consists of the costs of people, materials,methods, and management The accuracy of a cost

849yDeceased

estimate is a function of the degree of design or project

de®nition available at the time the estimate is made

The more ®nalized and ®rm the design and de®nition,

the more accurate the estimate is likely to be Estimate

accuracy is also a function of the time and resources

that the estimator has available to compile a bid

Accuracy may also be a€ected by the quantity of

units that are to be fabricated or produced

2.2.2 Role of Engineers in Cost Estimating

Engineers have had historically a limited role in the

cost estimating process Few engineering curricula

have formal courses on this subject Good estimating

skills require detailed knowledge of an organization's

product line, production facilities, and manufacturing

processes In many cases nondegreed personnel who

have formal shop ¯oor experience have better

back-grounds with which to perform cost estimating tasks

Engineers have a professional need to be

knowl-edgeable about estimating procedures [11] They need

this knowledge to specify cost-e€ective designs Often

engineers assume managerial positions which

encom-pass or oversee the estimating function

2.2.3 Basic Steps in the Estimating Process

The steps in compiling a cost estimating include

deter-mining whether each part in the bill of materials of an

end item should be made in-house or purchased This

is followed by preliminary process sequence planning

and the subsequent tallying of labor and material

costs Dependent costs must also be determined and

tallied These include the costs of indirect labor and

overhead, manufacturing engineering, and inspection/

quality control Finally, an appropriate contingency

allowance must be determined and included

2.2.4 Types of Manufacturing Costs

Two of the most basic types of manufacturing costs are

direct labor and direct material [1, 4] Direct labor is the

cost of all ``hands-on'' e€ort to manufacture a product

Typical direct labor activities include machining,

assembly, inspection, testing, and troubleshooting

Direct material is the cost of all components and raw

materials included in the end product that is be

pro-duced The sum of direct labor and direct material is

often referred to as prime cost

Factory expenses may be de®ned as the total costs

for rent, heat, electricity, water, expendable factory

supplies, and indirect labor Factory cost is often

de®ned as the sum of prime cost plus factory expenses.General expenses are the costs of design engineering,purchasing, oce sta€ salaries, and depreciation.Manufacturing cost is the sum of general expensesplus factory cost

Sales expenses are all costs incurred in selling anddelivering the end product These include the cost ofadvertising, sales commission, and shipping costs.Total costs may be de®ned as the sum of sales expenseplus manufacturing cost

Finally, the selling price of the end product is thesum of the total costs plus the organization's desiredpro®t margin

2.2.5 Performance StandardsPerformance standards are the best prior estimate ofthe length of time a labor task is likely to require Suchstandards can therefore be applied to determine thelabor content of a manufacturing cost estimate.Principal data sources for work standards are fromtime study analyses and predetermined time systems.The role of and use of performance standards inmaking cost estimates is described in more detail inRefs 1 and 4

2.2.6 Cost Centers and Shop OrdersCost estimating requires the use of both cost centersand shop orders Often organizational divisions anddepartments are de®ned by numerical codes Forexample, if a three-digit code is used, the hundredsdigit might be used to indicate a department Thetens digit can be used to designate a division within

an department Finally, the units digit may denote abranch within a division within a department Somesample organization codes indicating both depart-ments and divisions are illustrated inTable 1

Cost estimating requires establishing an audit trailfor charge tracability An account number is used todetermine where in the organization a labor chargehas occurred The cost center is often a numerical sub-set of the account number and re¯ects all or part of theorganization code of the department, division, orbranch in which the labor charge has occurred

A job order is basically a project number re¯ectingwhich manufacturing project has been or should be

``billed'' for labor or material charges A shop order

is an authorization to perform work on a given costcenter A shop order code is usually alphanumeric informat The alpha pre®x of the shop order code re¯ectsthe type of manufacturing e€ort on a given cost center

that is being performed A labor charge on a

manufac-turing project is thus made in conjunction with a cost

center, a job order, and a shop order The cost center

speci®es where in the organization the work was

per-formed The job order speci®es which manufacturing

project was or should be billed for the charge Finally,

the shop order indicates what type of manufacturing

e€ort is being performed on the project

Example cost centers and shop orders are illustrated

in Table 2 Readers desiring more detailed information

on cost centers, job orders, and shop orders shouldconsult Refs 1 and 4

2.2.7 Making the Initial Cost EstimateInitial cost estimates are those made prior to the start

of production They are important as their accuracysets the pro®t/loss position of the ®rm The processbegins by reviewing the bill of materials or part explo-sion structure of the end item to be manufactured Adetermination must initially be made on an item-by-item basis as to whether each individual componentshould be purchased or fabricated in-house Usuallythese determinations are made on the basis of whichalternative is less expensive The cost estimator mustanticipate the process sequence for each part in the bill

of materials which is to be fabricated Prior shopexperience of the estimator is vital in accurately antici-pating the process sequence that will be used to actu-ally make each part

The preliminary sequence is speci®ed by generating

a sketch process routing for each ``make'' part Thisrouting contains:

Table 1 Sample Organization Codes

Standards and Calibration Division 430

Product Design Engineering Division 710

Research and Development Engineering

Table 2 Example Cost Centers and Shop Orders

43 Standards and Calibration Mechanical and electronic calibration O-XXXXX

The anticipated sequence of manufacturing

opera-tions

The departmental location for each operation

The required machines and equipment for each

routing operation

A brief description of each production operation

The applicable shop order and cost center

Estimated setup and ``per piece'' run times for each

operation

The estimated times are obtained from performance

standards or time study analyses Alternately, some

machine cycle times are often estimated from

formulae

2.2.8 The Contingency Allowance

The contingency allowance is an estimate supplement

used to account for work content and materials that

are expected to occur, but cannot be accurately

antici-pated or accounted for at the time the initial cost

esti-mate is made The contingency allowance varies with

both the degree of initial design de®nition and the time

available to make the estimate Vernon [3] has de®ned

seven separate estimate classes as a function of the type

and quantity of information available at the time the

estimate is made These classes are illustrated in Table

3 Malstrom [1, 4] has described typical contingency

allowance percentages as a function of estimate

con®-dence and design de®nition These percentages are

summarized inTable 4

2.2.9 Aggregating Labor and Material CostsMalstrom [1, 4] has discussed how labor and materialcosts are aggregated for compilation of initial estimatetotals Labor hours are tallied by shop order withincost centers Each cost center has a separate andoften di€erent labor overhead rate determined by thecapital budgeting process (described later) The labor/overhead (LOH) rate for each cost center convertslabor hours into labor dollars and overhead dollars.Material costs are aggregated and totaled by individualcost centers as well

The labor, overhead, and material cost dollars aretotaled for each cost center The sum of these costtotals over all cost centers is the estimated productioncost (EPC) The contingency allowance is expressed as a

®xed percentage of the EPC The EPC plus the dollarmagnitude of the contingency allowance is theestimated total cost (ETC) Adding pro®t to the ETCresults in the total bid cost that can be submitted to aprospective customer Malstrom has illustrated how tosummarize these costs on an estimate grid This grid isillustrated in Fig 1

2.3 COST REVIEWS

A cost review is a follow-on cost estimate of a facturing task that has already begun and is in process

manu-at the time the cost review is made The time required

to complete a cost review is signi®cant and

approxi-Table 3 Information De®ning Numerical Estimate Classes

Detailed tool, machine, gage and equipment lists X X

Source: Ref 3.

mates the level of e€ort required to compile an initial

cost estimate Consequently, cost reviews are generally

performed only on those jobs where ®scal de®cits or

surplus are expected to occur

The procedure begins by selecting a review date

This date is a ``snapshot'' of the project's ®scal status

at a given point in time Prior to the review date are

actual expenditures on the project which have

occurred After the review date are those expenditures

expected to occur up until the project being reviewed is

expected to be completed

The mechanics of the cost review procedure are

illu-strated in the cost review grid illuillu-strated inFig 2 This

grid lists all cost centers on which direct labor

expen-ditures are expected to occur The procedure begins by

recording all labor hour charges that have occurred, by

shop order, prior to the review date Each cost center

has four distinct rows The Estimated row contains

estimated labor hours and costs from the most recent

prior cost estimate or review for each of the cost

cen-ters The Expended row contains dollar expenditures

for labor and material by cost centers The labor dollar

expenditures correspond to the labor hours expended

by shop order for each cost center These hourly

entries are entered, by shop order in the Used column

for each cost center

The cost analyst next estimates the required hours

to complete the project for each cost center by shoporder These hour entries are placed in the To Comp.column for each cost center and shop order Materialdollar expenditures required for project completion areestimated for each cost center as well The materialdollar expenditures are entered in the To Completerow for each cost center in the Material column ofthe grid

Next, labor and overhead rates are entered in the ToComplete row for each cost center These rates may behigher than those used in the most recent prior costestimate or review The To Comp hours are thentotaled by shop order and entered in the Hrs column

of the To Complete row for each cost center The totals

in the Hrs column of the To Complete row are plied by the labor and overhead rates for each costcenter These dollar totals are entered Labor andOverhead columns of the To Complete row for eachcost center

multi-The next step is to add the entries of the Expendedand To Complete rows The resultant sums are placed

in the Total row of each cost center as illustrated inFig 2 The information is next transferred to the costestimate grid illustrated in Fig 3 The hour entriesfrom the Used column of Fig 2 are transcribed tothe Hrs Exp to Date column of Fig 3 by both shoporder and cost center The hour entries from the ToComp column of Fig 2 are transferred to the Hrs toCompl column of Fig 3 by shop order and cost center.Hour and dollar entries from the Total row of Fig 2are next transcribed to the Direct Labor Hours, Labor,Overhead, Material, and Total Cost columns of Fig 3

by cost center The entries in the Total Cost column ofFig 3 are summed The contingency allowance andpro®t margin are adjusted as necessary depending onwhether a cost de®cit or surplus is projected to occur.Readers desiring a more detailed description of thecost review process are urged to consult Refs 1 and 4.2.4 LEARNING CURVES

Learning or product improvement curves re¯ectdecreasing labor costs as the production quantity com-pleted increases These decreases re¯ect the e€ects ofboth human learning and process improvements asso-ciated with the startup of production

2.4.1 Learning Curves De®nedLearning curves may be described by

Table 4 Estimate Classes

A Excellent con®denceÐrepeat job, excellent

de®nition, no major changes anticipated

B Good con®denceÐnew design, ®rst build, good

de®nition, some design changes anticipated

Contingency 10±20%

C Average con®denceÐpreliminary or partial design,

verbal information, changes anticipated

Contingency 20±30%

D ``Ball park'' estimatesÐde®nition very sketchy and

preliminary, many unknowns several designchanges anticipated Contingency 30±40%

F BudgetingÐan estimate prepared only for the

purpose of budgeting funds Contingencyallowance levels vary depending on designde®nition

X Directed estimateÐa modi®cation of any previous

cost estimate to conform to budget cuts andrestrictions which are not based on scopedecisions Adjustments may be increases orreductions in the allowance or in any cost element

as directed by top management decisions

Y ˆ KXn …1†

where

K ˆ Time in hours required to produce the first

unit:

X ˆ Total units manufactured

n ˆ A negative exponent which determines the

percent by which Y decreases each time X is

doubled

Y ˆ The cumulative average time per unit to

build a quantity of X units

The de®nitions above are for cumulative average

learn-ing curves Unit learnlearn-ing curves also exist and may be

used for cost analysis purposes With unit curves, Y is

de®ned as the time in hours required to build the Xth

unit The remaining variables described above are the

same for both types of curves Readers desiring moredetailed descriptions of learning curves are urged toconsult Refs 1, 4, 5, 6, and 13

2.4.2 Learning-Curve Considerations inEstimating Procedures

Cost estimates are dependent on labor hours derivedfrom work or labor standards Without exception,work or time standards are derived from constant

``time per unit'' values The e€ects of process ment and human learning are usually not directly con-sidered in labor standard development To e€ectivelyintegrate the e€ects of learning into estimating proce-dures, it is necessary to determine at what quantitylevel on the learning curve the standard time isreached Construction of actual learning curvesrequires the determination of both K and n in Eq.Figure 1 Cost estimate grid

improve-(1) The nature of labor standard development makes

this determination dicult in practice

An alternate approach is to compile historical ratios

of actual to standard hours after manufacturing tasks

are complete These ratios can be compiled and

aggre-gated by both shop order type, production quantity,

and product type or family Multivariate linear

regres-sion can be used to determine mathematical functions

which specify predicted ratios of actual to standard

hours by shop order as functions of both production

quantity and product type or family These ratios may

be used as multipliers for hourly totals by shop order

compiled by the estimating methods previously

described The e€ects of learning curves will be

embedded in these multipliers

2.5 CAPITAL BUDGETING

Capital budgeting may be de®ned as the way in which

individual labor/overhead rates are determined for each

cost center Most capital budgeting procedures utilize

direct labor as a recovery basis variable The procedure

is to estimate the required overhead that must becharged in addition to the direct labor for each costcenter, to recover the cost of both indirect labor andburden associated with the operation of a manufactur-ing facility The capital budgeting procedure has beendescribed in some detail by Malstrom [5] and is repro-duced in some detail in the sections that follow.2.5.1 Components of LOH Rates

The labor/overhead rate for any cost center has fourdistinct components [12] The ®rst of these is the directlabor rate The direct labor rate is the composite aver-age of all direct labor wages (including bene®ts) on thecost center being analyzed The second component isthe expense rate The expense rate is the sum of allindirect labor dollars estimated to be expended in abudgetary quarter divided by the total number ofdirect labor hours estimated to be expended duringthat same quarter

Burden is the cost, in dollars, of rent, utilities, ing/equipment depreciation, and expendable suppliesFigure 2 Cost review grid

build-for any budgetary quarter Finally, general and

admin-istrative costs are the cost of top executives' salaries

and centralized plant computing facilities The labor/

overhead rate for any cost center may be described by

LOHCCˆ LD‡ ER‡ B ‡ G&A …2†

where

LOHCCˆ The labor=overhead rate for a specific

cost center in dollars=hr

LDˆ The direct labor rate; dollars=hr

ERˆ The expense rate; dollars=hr

B ˆ Burden in dollars=hr

G&A ˆ General and administrative cost rate

in dollars=hrThe dollar amounts for burden and general adminis-

trative costs expected to be expended during any

quarter are divided by the total number of direct

labor hours to be expended to determine the burden

and G&A cost rates in Eq (2)

The mechanics of the capital budgeting process arebest illustrated with an example This example is thesubject of the following section and has been adaptedfrom Ref 5

2.5.2 A Capital Budgeting ExampleConsider a manufacturing plant with a total of 1000employees Suppose it is desired to determine thelabor/overhead rate for the machining cost center 22.For example purposes we will assume that cost center

22 has a total of 200 employees Of this total we willfurther assume that 150 are involved with direct laboractivities

To begin our analysis, we need to know the rest ofthe cost centers that exist and the respective number ofemployees in the plant that are associated with them.These stang levels are illustrated inTable 5 In Table

5, there are a total of four cost centers on which directlabor is performed These include cost centers 21, 22,

23, and 42 which are Manufacturing Engineering,Machining, Assembly, and Inspection respectively.Figure 3 Revised cost estimate grid

Each of these four cost centers contain some indirect

labor employees as well Some examples of this indirect

labor would be supervisory and secretarial personnel

The remaining cost centers in Table 5 support directly

labor activities and contain only indirect labor

employees

We wish to determine the labor/overhead rate

asso-ciated with cost center 22 Let us assume that 40 hours

exist in each work week Assume further that there are

exactly four weeks in each month and that a budgetary

quarter consists of three months Then the number of

direct labor hours worked each quarter on cost center

22 is

40 hr=week  4 weeks=month  3 months

ˆ 4780 hr

Total number of work hours per quarter

ˆ 488 hr=employee  150 direct labor employees

ˆ 72,000 hr

2.5.3 Direct Labor Determination

Our ®rst step is to determine the direct labor rate, LD,

in Eq (2) This term is merely a composite average of

all of the direct labor hourly wage rates, including

bene®ts, on this cost center For example purposes

we will assume that this average is $10.00 per hour

2.5.4 Expense Rate Determination

The expense rate in Eq (2) recovers the cost of indirect

labor employees There are two types of indirect labor

costs that need to be recovered The ®rst is the cost ofindirect labor on cost center 22 itself The second isthe cost of indirect labor on pure indirect labor costscenters that support the manufacturing activities ofcost center 22

The average salary levels of indirect labor ees, by cost center, are summarized in Table 6 Theaverage indirect salary on cost center 22 is $28,000per year We need to recover one-fourth of this amountfor the next quarter for the 50 indirect employees whowork in cost center 22 This amount is

employ-$7000=employee  50 employees ˆ $350,000The indirect labor cost centers in Table 5 are costcenters 30, 41, 43, 50, 60, 71, and 72 Direct labor costcenters 21, 23, and 42 also have indirect costs.However, these costs are recovered through thelabor/overhead rates that will be determined and asso-ciated with these cost centers

The indirect labor cost centers support all four ofthe direct labor cost centers A common way to amor-tize these costs over the direct labor cost centers is onthe basis of the total number of employees (direct andindirect) on each of the direct labor cost centers FromTable 5, cost centers 21, 22, 23, and 42 have employeetotals of 100, 200, 200, and 50, respectively According

to the proration logic, pure indirect labor cost centerssupport the direct labor cost centers proportionately

on the basis of people Therefore, the percentage forcost center 22 would be determined as

200=…100 ‡ 200 ‡ 200 ‡ 50† ˆ 200=550The total number of employees on each of the four costcenters are used since the other pure indirect labor costcenters support all of cost center 22, not just the direct

Table 5 Employee Staf®ng Levels by Cost Center