Engineering Economic Analysis

Inflation Effect on After-Tax Calculations 461

After- Tax R~te of Return, No Inflation

Year

o

1-6

Before-Tax

Cash Flow

-$12,000

+2,918

Straight-Line

Depreciation

Taxable

Income

46% Income

Taxes

$2000 $918

Actual Dollars, and

Year-O-BasedDollars,

After-Tax CaSh Flow

-$12,000

-$422 +2,496

From compound interest tables: after-tax rate of return equals 6.7%.

PW of cost=PW of benefit

12,000 =2496(P/A, i, 6) (P/A, i,6) = 12,000

2496 = 4.81

Converting to Year-O-BasedDollars and Solving for Rate of Return

Actual Dollars, Year-O-Based

After-Tax Conversion Dollars, After-Tax

,Cash Flow Factor Cash Flow

-$12,000 -$12,000

+2,575 x(1.05)-1 = +2,452

+2,657 x (1.05)-2 = +2,410

+2,744 X (1.05)-3 = +2,370

+2,835 X(1.05)-4 = +2,332

+2,931 x(1.05)-5:;::: +2,297

+3,031 X(1.05)-6 = +2,262

Year

o 1 2 3 4 5 6

Linear interpolation between 4 and 5%:

--

Present

Wodhat5%

-$12,000

+2,335

+2,186

+2,047

+1,919

+ 1.800

+ 1,688

-25

Present

Wodhat.4%

-$12,000

+2,358

+2,228

+2,107

+ 1,993

+1,888

+1,788

+362

--

From Example 14-9, we see that the before-tax rate of return for both situations (no infla-

tion and 5% inflation) is the same. Equal before-tax rates of return are expected because the

After- Tax Rate of Return, 5 % Inflation II

Before- Tax Straight-Line Taxable 46% Income Actual Dollars, ,II

Year Cash Flow Depreciation Income Taxes After-Tax Cash Flow

(^0) -$12,000 -$12'000.'
(^1) + 3,064 $2000 $1064 -$489 +2,575
(^2) +3,217 2000 1217 -560 + 2,657
(^3) +3,378 2000 1378 ,.-634 +2,744
(^4) +3,547 2000 1547 -712 + 2,835
(^5) +3,724 2000 1724 -793 +2,931
(^6) +3,910 2000 1910 -879 +3,031 I II:,