Engineering Economic Analysis

This cash flow represents a $5000 investment with benefitsthat produce an 8% rate of

returnon the unrecoveredinvestment...

Althoughthetwodefinitionsof internalrateofreturnarestateddifferently,oneinterms.

of a loan and the other in terms of an investment, there is only one fundamental concept

being described. It is that the int~rnal rate of return is the interest rate at which the

benefits are equivalent to the costs or the present worth (PW)is O.Since we are describing

situations of funds that remain within the investment throughout its life, the resulting rate

of return is described as the internal rate of return,i.

Calculating Rate of Return

To calculate a rate of return on an investment, we must convert the various consequences

of the investment into a cash flow. Then we will solve the cash flow for the unknown

value of the internal rate of return (IRR). Five forms of the cash flow equation are as

follows:

PW of benefits - PW of costs= 0

PW of costs=PW of benefits

PW of benefits= 1

PW of costs

Net present worth= 0

EUAB- EUAC= 0

The five equations represent the same concept in different forms. They can relate costs and

benefits with the IRR as the only unknown. The calculation of rate of return is illustrated

by the following examples.

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CalculatingRateof Return^205

the partial return of the investment. This may be tabulated as follows:

Unrecovered 8 % Return on Investment Unrecovered

Investment at Unrecovered Repayment at Investment at

Year Cash Flow Beginning of Year Investment End of Year End of Year

(^0) -$5000
(^1) +1252 $5000 $ 400 $ 852 $4148
2 +1252 4148 331 921 3227
(^3) +1252 3227 258 994 2233
(^4) +1252 2233 178 1074 1159
(^5) +1252 (^1159) - (^93) - 1159 0
$1260 $5000
(7-1)
(7-2)
(7-3)
(7-4)
(7-5)
t