Engineering Economic Analysis

204 RATEOF RETURNANALYSIS

In this chapter we will examine three aspects of rate of return, the third of the three major

analysis methods. First, we describe the meaning of "rate of return"; then, the calculation

of rate of return is illustrated; finally, rate of return analysis problems are presented. In an

appendix to this chapter, we describe difficulties sometimes encountered in attempting to

compute an interest rate for cash flows of certain kinds.

INTERNAL RATEOFRETURN

In Chapter 3 we examined four plans to repay $5000 in 5 years with interest at 8%

(Table 3-1). In each of the four plans the amount loaned ($5000) and the loan duration

(5 years) were the same. Yet the total interest paid to the lender varied from $1200 to

$2347, depending on the loan repayment plan. We saw, however, that the lender received

8% interest each year on the amount of money actually owed. And, at the end of 5 years,

the principal and interest payments exactly repaid the $5000 debt with interest at 8%. We

say the lender received an "8% rate of return."

Internal rate of return is defined as the interest rate paid on the unpaid balance of

aloansuch that the payment schedule makes the unpaid loan balance equal to zero

when the final payment is made.

;

Insteadof lendingmoney,we might invest$5000in a machinetool wit;ha 5-yearuse-.
fullife and an equivalent uniform annual benefit of $1252. An apprqpriate question is,
What rate of return would we receive on this investment? The cash flow would be as
,, follows:

Year

o 1 2 3 4 5

Cash Flow

-$5000

+1252

+1252

+1252

+1252

+1252

We recognize the cash flow as Plan 3 of Table 3-1. We know that five payments of

$1252 are equivalentto a present sum of $5000 when interest is 8%. Therefore, the rate of

return on this investment is 8%. Stated in terms of an investment, we may define internal

Significance of the Cutoff Rate of Return

Internal rate of return is the interest rate eamed on the unrecoveredinvestmentsuch

that the payment schedule makes the unrecovered investment equal to zero at the end

of the life of the investment.

It must be understood that the 8% rate of return does not mean an annual return of 8% on the

$5000 investment, or $400 in each of the 5 years with $5000 returned at the end of Year 5.

Instead, each $1252 payment represents an 8% return on the unrecovered investmentplus