Engineering Economic Analysis

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418 REPLACEMENTANALYSIS

Looking at this second case from anopportunity costperspective, we use an annual

cost comparison to calculate capital recovery effect of the first cost as follows:

Annualized first COStSK-30=$200(Aj P, 10%,3) =$80

Annualized first costEL-40=$1050(AjP,10%,5)=$277

Thedifferencein annualized first cost between the SK-30 and EL-40 is:

AFCEL-40 - AFCSK-30=$277- $80=$197

Now using acashjlowperspective to look at the first costs of the defender and challenger,

we can calculate thedifferencedue to first cost between the SK-30 and EL-40.

Annualized first costSK-30=$O(Aj P,10%, 3)=$0

Annualized first costEL-40=($1050 - 200)(Aj P,10%,5)=$224

AFCEL-40 - AFCSK-30= $224 - $0=$224

When the remaining life of the defender (3 years) differs from that of the useful life of

the challenger (5 years), analyses of the annualized first costs yield different results. The

correct differenceof$197 is shownby using theopportunitycostapproach,.and an inaccurate

difference of $224 is obtained if thecashjlowperspective is used. In the opportunity cost

case the $200 is spread out over 3 years as a cost to the defender, yet in the cash flow case

the opportunity cost is spread out over 5 years as a benefit to the challenger. Spreading the

$200over 3 years in one case and 5 years in the othercase does not produceequivalent

annualized amounts. Because of the differencein the livesof the assets, the annualized$200

opportunity cost for the defender cannot be called an equivalentbenefit to the challenger.

In the case of unequal lives, the correct method is to assign the current market value of

the defender as its time zero opportunity costs, rather than subtracting this amount from the

first cost of the challenger. Because the cash flow approach yields an incorrect value when

challenger and defender have unequal lives, theopportunity costapproach for assigning a

first cost to the challenger and defender assets shouldalwaysbe used.

Repeatability Assumptions Not Acceptable

Under certain circumstances, the repeatability assumptionsdescribed earlier may not apply

for a replacement analysis. In these cases replacement analysis techniques 1,2, and 3 may

not be valid methods for comparison.For instance,a decisionmaker may set the studyperiod

instead of assuming that there is an indefinite need for the asset. For example, co~r the

case of phasing out production after a certain number of years-perhaps a person who is

about to retire is closing down a business and selling all the assets. Other examples include

production equipment such'as molds and dies that are no longer needed when a new model

with new shapes is introduced.

The study period could potentially be set at any number of years relative to the lives of

the defender and the challenger, such as equal to the life of the defender, equal to the life

of the challenger, less than the life of the defender, greater than the life of the challenger,

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