This cash flow represents a $5000 investment with benefits that produce an 8% rate of
returnon the unrecoveredinvestment..
Althoughthetwodefinitionsofinternalrateofreturnarestateddifferently,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) (7-1)
PW of benefits
=1
PW of costs
(7-2)
Net present worth= 0 (7-3)
EUAB - EUAC= (^0) (7-4)
PW of costs=PW of benefits (7-5)
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.
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