Economic AnalysisTaking Income Taxes into Account 383SOlW..:TlO....~(t.O.' ~. ...EXAMPlE12=6(a)..,..'.
Use the following equation to calculate the before-tax rate of return:
20,000 =1000(P/A, i,4) +500(P/ G,i,4) +20,OOO(Pj F, i, 4)
Tryi=8%:
20,000 #=1000(3.312) + 500(4.650) + 20,000(0.7350)
#=3312 + 2325 + 14,700 = 20,337
Sinceiis too low, tryi=10%:
20,000 #=1000(3.170) + 500(4.378) + 20,000(0.6830)
#=3170 + 2189 + 13,660 = 19,019
(
20,337- 20,000
Before-tax rate of return =8% + 2% 20,337 - 19,019.' )=8.5%For a before-tax cash flow gradie!lt of $500, the resulting after-tax cash flow gradient is
(1 - 0.39)(500)=$305..20,000=61O(Pj A, i,4) +305(P jG, i,4)+.20,000(P/F, i, 4)
Tryi=5%:
20,000 *610(3.546) + 305(5.103) + 20,000(0.8227) #=20, 173
Sinceiis too low, tryi=6%:
20;000 $olO(3~465r+ 3ot>(4:4945)+ 20,000(0.7921) i: 19,304
(
20, 173~ 20,000
)After-tax. rate ofietnrn :::;.5%,+. J
-,~~ r:!t. ..'%'h 20,173 _ 19,3"^04 ~ 5.2% I
... iii II d\TABLE12-4 Cash Flow Table for Example 12-6
(c) (d) (e)
(a) A(Taxable 39% Income After-Tax
Before-Tax (b) Income) Taxes CashFlowYear CashFlow Depreciation (a)-(b) (c) x-0.39 (a)+(d)
(^0) -$20,000 -$20,000
(^1) 1,000 - $1000 -$390 610
(^2) 1,500 - 1500 -585 915
(^3) 2,000 - 2000 -780 1,220
4
{ 2,500
2500 -975
20,000 { 1,525
-
20,000