Engineering Economic Analysis

462 INFLATION AND PRICECHANGE

benefitsin the inflationsituation increasedin proportion to the inflation.This exampleshows

that when future benefitsfluctuatewith changesin inflationor deflation, the effectsdo not al-

ter the year-O-baseddollar estimates. Thus, no special calculations are needed in before-tax

calculations when future benefits are expected to respond to inflation or deflation rates.

The after-tax calculations illustrate a different result. The two situations, with equal

before-tax rates of return, do not produce equal after-tax rates of return:

Situation

No inflation

5% inflation

Before-Tax

Rate of Return

12%

12%

Mter- Tax

Rate of Return

6.7%

4.9%

Thus, 5% inflation .results in a smaller after-tax rate of return, even though the benefits

increase at the same rate as the inflation. A review of the cash flow table reveals that while

benefits increase, the depreciation schedule does not. Thus, the inflation results in increased

taxable income and, hence, larger income tax payments; but there are not sufficient increases

in benefits to offset these additional disbursements.

The result is that while the after-tax cash flow in actual dollars increases, the augmented

amount is not high enough to offsetbothinflation and increased income taxes. This effect is

readily apparent when the equivalent year-O-based-dollar after-tax cash flow is examined.

With inflation, the year-O-based-dollar after-tax cash flow is smaller than the year-O-based-

dollar after-tax cash flow without inflation. Of course, inflation might cause equipment to

have a salvage value that was not forecast, or a larger one than had been projected. This effect

would tend to reduce the unfavorable consequences of inflation on the after-tax rate of return.

Using Spreadsheets for Inflation Calculations

Spreadsheets are the perfect tool for incorporating consideration of inflation into analyses

of economic problems. For example, next year's labor costs are likely to be estimated as

equal to this year's costs times (1 + f), wheref is the inflation rate. Thus each year's

value is different, so we can't use factors for uniform flows,A.Also the formulas that link

different years are easy to write. The result is problems that are very tedious to do by hand,

and easy by spreadsheet.

Example 14-10 illustrates two different ways to write the equation for inflating costs~

Example 14-11illustrates that inflation reduces the after-taxrate of return because inflation

makes the depreciation deduction less valuable.

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G9sts f9r construction of a small, remotemi,ne are for labor apd tratispOJ.1ati9n.Jjabor costs

ar~ e5}pectedt~be $350,000 t4e first year,\Vit?inflatiop. of6%annuany.Up.it~~W0rta~on

aCQsts.~e.' e~pected"19 ipJiate at5% annually,bJit th~ gqluII).yllqr1Jiatyrial befug:n]J)Y~Cl~h;lJlges

e~cJi)e.;lt.~ iiiiie:6 amriirs,:tke ffiin~<fuati($tl c~m~ ~tlIn1t1~:tO iJ~-:4b;<)QO~q~;000,~

$R(),Q20, ap.d $30,000 in Yews J thro~gh .4.Theinflatiop~a~e f9rthe val~e 9f~~dol~~ is

,Q~tie~n~.;~ ifi.f't4e JIDJl J!.§e§.l!!liI.Qt. 7- %"'''.. - M< ...»;.~all~;.isth£ egu.ival~nt;lQJ:luaJc()~tfo:rthj$ 4-YeID"i?:roject?.,;j,":: 111I 1;.; ~= ~i lEt' !;; ~~

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