Engineering Economic Analysis

Calculating Rate of Return 211

950

40J t t 0-1-2

1 1000

Since $40 is received each 6 months, we will solve the problem using a 6-month interest period. Let PW of cost=PW of benefits, and.write

1000 =40(P/A, i,2) +950(P/F, i, 2)

Tryi= 11/2%:

1000 ~ 40(1.956) + 950(0.9707)=78.24 + 922.17 ~ 1000.41

Theinterestrate per 6 months,~ mon,is veryclosetoI1h%.Thismeansthenominal(annual)

interest rate is 2 x 1.5%=3%. The effective (annual) interest rate=IRR=(1 + 0.015)2-

1 =3.02%.

SOUhION'TO b

1000

J t t t t t t t t t t t t. t t t t t t

I-l-2-3-4-5 6--7-8--:-:::-IO~II-12-\3~14-15~16-17~18

A =40

950

Given the same $40 semiannual interest payments, for 6-month interest periods we write

950 =40(P/A, i,18) +IOOO(P/F, i, 18)

Tryi =5%:

950 ~ 40(11.690) + 1000(0.4155)=467.60+415.50 ~883.10

The PW of benefits is too low. Try a lower interest rate, say,i=4%:

.". '950 ~40(12.659) 4- 1000(0.4936)~'''506.3<1+~93.60~ == ~

~ 999.96

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1000 =40(P/A, i,2) +950(P/F, i, 2)