Engineering Economic Analysis

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280 OTHERANALYSISTECHNIQUES

costs and benefits. This may represent a lot of calculations to locate points through which

the line passes.

Figure9-2b showshow the incrementalbenefit-costratio(L\.Bj L\.C)changesas one

moves along the line of feasible alternatives.Figure 9-2b also plots the ratio of incremental

net present worthto incremental cost (L\.NPWjL\.C). As expected, we are adding increments

of NPW as long asL\.BjL\.C> 1. Finally, in Figure 9-2c, we see the plot of (total) NPW

versus the size of the project.

This three-part figure demonstrates that present worth analysis and benefit-cost ratio

analysis lead to the same optimal decision. We saw in Chapter 8 that rate of return and

present worth analysis led to identical decisions. Any of the exact analysis methods-

present worth, annual cash flow,rate of return, or benefit-cost ratio-will lead to the same

decision. Benefit-cost ratio analysis is extensively used in economic analysis at all levels

of government.

PAYBACK PERIOD

Payback period is the period of time required for the profit or other benefits from an

investment to equal the cost of the investment. This is the general definition for payback

period, but there are other definitions. Others consider depreciation of the investment,

interest, and income taxes; they, too, are simply called "payback period." For now, we will

limit our discussion to the simplest form.

Payback period is the period of time required for the profit or other benefits of an

investment to equal the cost of the investment.

The criterionin all situations is to minimize the paybackperiod. The computationof payback

period is illustrated in Examples 9-6 and 9-7.

The cash flows for two alternatives are as follows:

Year

o 1 2 3 4 5

A

-$1000

+200

+200

+1200

+1200

+1200

B

-$2783

+1200

+1200

+ 1200

+ 1200

+1200

You may assume the benefits occur throughout the year rather than just at the end of the year.

Based ong~.!>a~kperiod, ,,;:hichaltern~tiveshould be selected?

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