## Table

Ordinary and Discounted Payback years (look for the highlighted figure in Year 3). The discounted cash flows total $300 only after four years, however, so the discounted payback is four years, as shown.1

How do we interpret the discounted payback? Recall that the ordinary payback is the time it takes to break even in an accounting sense. Because it includes the time value of money, the discounted payback is the time it takes to break even in an economic or financial sense. Loosely speaking, in our example, we get our money back, along with the interest we could have earned elsewhere, in four years.

Figure 9.3 illustrates this idea by comparing the future value at 12.5 percent of the $300 investment to the future value of the $100 annual cash flows at 12.5 percent. Notice that the two lines cross at exactly four years. This tells us that the value of the project's cash flows catches up and then passes the original investment in four years.

Table 9.3 and Figure 9.3 illustrate another interesting feature of the discounted payback period. If a project ever pays back on a discounted basis, then it must have a positive NPV.2 This is true because, by definition, the NPV is zero when the sum of the discounted cash flows equals the initial investment. For example, the present value of all the cash flows in Table 9.3 is $355. The cost of the project was $300, so the NPV is obviously $55. This $55 is the value of the cash flow that occurs after the discounted payback (see the last line in Table 9.3). In general, if we use a discounted payback rule, we won't accidentally take any projects with a negative estimated NPV.

Based on our example, the discounted payback would seem to have much to recommend it. You may be surprised to find out that it is rarely used in practice. Why? Probably because it really isn't any simpler to use than NPV. To calculate a discounted payback, you have to discount cash flows, add them up, and compare them to the cost, just as you do with NPV. So, unlike an ordinary payback, the discounted payback is not especially simple to calculate.

A discounted payback period rule has a couple of other significant drawbacks. The biggest one is that the cutoff still has to be arbitrarily set and cash flows beyond that point are ignored.3 As a result, a project with a positive NPV may be found unacceptable

'In this case, the discounted payback is an even number of years. This won't ordinarily happen, of course. However, calculating a fractional year for the discounted payback period is more involved than it is for the ordinary payback, and it is not commonly done.

2This argument assumes the cash flows, other than the first, are all positive. If they are not, then these statements are not necessarily correct. Also, there may be more than one discounted payback.

3If the cutoff were forever, then the discounted payback rule would be the same as the NPV rule. It would also be the same as the profitability index rule considered in a later section.

Ross et al.: Fundamentals IV. Capital Budgeting of Corporate Finance, Sixth Edition, Alternate Edition

9. Net Present Value and Other Investment Criteria

© The McGraw-Hill Companies, 2002

PART FOUR Capital Budgeting

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