Engineering Economic Analysis

208 RATEOF RETURN ANALYSIS

Using a net present worth of 0, tryi=10%:

NPW =-100 + 20(P/F,10%, 1) + 30(P/F,10%,2) +20(P/F, 10%,3)

• 40(P/F,10%,4) +40(P/F,10%,5)

= -100 + 20(0.9091) + 30(0.8264) + 20(0.7513) + 40(0.6830)

• 40(0.6209)

=-100 + 18.18 + 24.79 + 15.03 + 27.32 + 24.84

=-100 + 110.16=+10.16

The trial interest rateiis too low. Select a second trial,i=15%:

NPW = -100 + 20(0.8696) + 30(0.7561) + 20(0.6575) + 40(0.5718)

• 40(0.4972)

=-100 + 17.39 + 22.68 + 13.15 + 22.87 + 19.89

=-100 + 95.98

=-4.02

FIGURE 7-1 Plot of NPW versus

interest ratei.

15

5%

These 10 and 15% points areplotted in Figure 7-1. By linear interpolation we compute the rate

of return as follows:.

(

10.16

)

IRR=10% + (15% - 10%) .. - 13.5%

10.16 + 4.02

We can prove that the rate of return is very close to 131/2%by showing that the

unrecovered investment is very close to zero at the end of the life of the investment.f'