## Analyzing the Rule

When compared to the NPV rule, the payback period rule has some rather severe shortcomings. First of all, the payback period is calculated by simply adding up the future cash flows. There is no discounting involved, so the time value of money is completely ignored. The payback rule also fails to consider any risk differences. The payback would be calculated the same way for both very risky and very safe projects.

Perhaps the biggest problem with the payback period rule is coming up with the right cutoff period, because we don't really have an objective basis for choosing a particular number. Put another way, there is no economic rationale for looking at payback in the first place, so we have no guide as to how to pick the cutoff. As a result, we end up using a number that is arbitrarily chosen.

Suppose we have somehow decided on an appropriate payback period, say, two years or less. As we have seen, the payback period rule ignores the time value of money for the first two years. More seriously, cash flows after the second year are ignored entirely. To see this, consider the two investments, Long and Short, in Table 9.2. Both projects cost \$250. Based on our discussion, the payback on Long is 2 + (\$50/100) = 2.5 years, and the payback on Short is 1 + (\$150/200) = 1.75 years. With a cutoff of two years, Short is acceptable and Long is not.

Is the payback period rule guiding us to the right decisions? Maybe not. Suppose again that we require a 15 percent return on this type of investment. We can calculate the NPV for these two investments as:

NPV(Short) = -\$250 + (100/1.15) + (200/1.152) = -\$11.81 NPV(Long) = -\$250 + (100 X {[1 - (1/1.154)]/.15}) = \$35.50

Ross et al.: Fundamentals I IV. Capital Budgeting I 9. Net Present Value and I I © The McGraw-Hill of Corporate Finance, Sixth Other Investment Criteria Companies, 2002

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