Engineering Economic Analysis

216 RATEOF RETURNANALYSIS

Thus,

. 20

(PjF, 1,1)= - = 0.7143 28

From the compound interest tables: rate of return=40%.

One may be tempted to select Alt. 1, based on these rate of return computations. We

have already seen, however, that this is not the correct solution. Solve the problem again,

this time using present worth analysis.

Present Worth Analysis

Alternative 1

NPW= -10+ 15(PjF,6%, 1) = -10+ 15(0.9434)=+$4.15

Alternative 2

NPW=-20 +28(P j F,6%, 1)=-20 + 28(0.9434)=+$6.42

Alternative 1 has a 50% rate of return and an NPW (at the 6% MARR) of +$4.15. Alter-

native 2 has a 40% rate of return on a larger investment, with the result that its NPW (at the

6% MARR) is +$6.42. Our economic criterion is to maximize the return, rather than the

rate of return. To maximize NPW, select Alt. 2. This agrees with the rate of return analysis

on the differences between the alternatives.

i.

If the computations for Example 7-6 do not convince you, and you still think Alternative 1 would

be preferable, try this problem.

You have $20 in your wallet and two alternative ways of lending Bill some money.

(a) Lend Bill $10 with his promise of a 50% return. That is, he will pay you back $15 at the

agreed time.

(b) Lend Bill $20 with his promise of a 40% return. He will pay you back $28 at the same

agreed time.

You can select whether to lend Bill $10 or $20. This is a one-time situation, and any money not

lent to Bill will remain in your wallet. Which alternative do you choose?

SOLUTION

So you see that a 50% return on the smaller sum is less rewardingfo you tnan 40% on th"elarger ;,

sum? Since you would prefer to have $28 than $25 ($15 from Bill plus $10 remaining in your

wallet) after the loan is paid, lend Bill $20.