Engineering Economic Analysis

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After-Tax ReplacementAnalysis 427

Since these lives are the same, a present or future worth analysis also could have been used.

, However,far more commonly the lives of the defender and the challenger are different. In

such cases, if we are willing to make the assumption of a continuing requirement for the

asset, then the comparison method to use is the annual cash flow method.As in our previous

discussion, this method allows a direct comparison of the annual cash flow of the defender

asset over its life against the annual cash flow of the challenger over its minimum cost life.

The annual cash flow method is also appropriate for comparison when the lives are equal

(as in Example 13-12),but more importantly,it is appropriate for the case of lives that are

different, under thereplacement repeatabilityassumptions.

. Minimum Cost Life Problems
In this section we illustrate the effect that tax considerations can have on the calculation
of the minimum cost life of the defender and the challenger. The c~culation of minimum
EUAC on an after-tax basis can be affected by both the depreciation method used and by
changes in the asset's market value over time, for either defender or challenger.Using an
accelerated depreciation method (like MACRS) tends to reduce the after-tax costs early
in the life of an asset. This effect alters the shape of the total EUAC curve-the concave
shape can be shifted and the minimum EUAC changed. Example 13-14 illustrates the
effect that taxes can have when either the straight-line or MACRS depreciation method is
used.

Some.new production machinery has a first cost of $100,000 and a useful °lifeof 10 years. Its

estimated operating and maintenance (O&M) costs are $10,000 the first year, which will increase

annually by $4000. The asset's before-tax market value will be $50,000 at the end of the first

year and then will-decreaseby $5000 annually.Calculate the after-tax cash flows using MACRS

depreciation. This property is a 7-yearMACRSproperty.The company uses a 6% after tax MARR

and is.;'subjectto a combined federal/state tax ~ateof 40%.

SOLUTION

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To fin~ the minimum cost life of this new production machinery we first.find the after-tax cash

flow effect of the O&M costs and depreciation (Table 13-2). Then, we find the ATCFs of dis-

posalifthe equipment is sold in each of the 10 years (Table 13-3). Finally in the closing sec-

tion od spreadsheets, we combine these two ATQFs (in FiguI"e1~-7) and choose.the minimum

cost lif~.

. In,I'Ta1;l1~~3-2, th~ O&M expense simply starts at $10,00~ ~d increases .at $~OOOpet; year. I
Thed~preclatlOn entrIes equal the 7-yearrt .MACRS depreclat.10n values gIVen ill Table 11-3 -
~lUl!i~ned b)' t.qe:$1OO,OPQfirq~.tgIJlphts.sim~~..&Mcostsminus: =~ ==
the depreciation values, is then multiplied 1;Iymn;lUsthe tax rate to detenn,iqe the impact of
this taX,ableincome on taxes. The O&M expense plus taxes is the. Table 13-2 portion of t!Ie
'" tpta1,A'tCF. 'II ~F .. II '= = II'

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