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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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