Engineering Economic Analysis

EconomicAnalysisTaking Income Taxes into Account 381

For a before-tax rate of return, we must first compute the before-tax cash flow.

Year Before-Tax Cash Flow

o -$3000

1 +800

2 +WO

3 +800

4 +800

5

{

+800

+750

• Solve for the before-tax rate of return,IRRBT:

3000 =800(P/A, i,5) +750(P/F, i, 5)

Tryi=15%:

3000 ~ 800(3.352) + 750(0.4972) ~ 2682 + 373= 3055

Sinceiis slightlylow,tryi=18%:

3000 ~ 800(3.127) + 750(0.4371) :fl=2502 + 328 = 2830

(

3055 - 3000

)

IRRBT =15%+ 3% =15%+ 3%(0.15)=15.7%

3055 - 2830

..
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For an after-tax rate of return,we must set up the cash flow table (Table 12-3). The starting point

is the before-tax cash flow. Then we will need the depreciation schedule for the truck:

.. .. B- S 3000 - 750

Stnnght-ltne depreCIatIOn= ;;;- = ~ =$450 peryear

Taxableincome is the before-tax cash flowminusdepreciation. For this medium-sizedpro:(itable
corporation, let's assume an incremental federal income tax rate of 34%. Therefore income taxes
are 34% oftaxableincome. Finally, the after-tax cash flow equals the before-tax cash flowminus
income taxes. These data are used to compute Table 12-3.
The after-tax cash flow may be solved to find the after-tax rate of return, IRRAT.Tryi= 10%:

3000 :fl=681(P /A,10%,5) +750(P/F,10%,5)

~ 681(3.791) + 750(0.6209) :- 3047

Sinceiisslightlylow, tryi= 12%:

3000 ~ 681(3:605)+150(0.5674)= 2881 .,

(

3047 - 3000

IRRAT= 10% + 2% 3047 - 2~81.. .. .' ~1O.6%)

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