Some Alternative Investment Rules


Before examining competitors of the NPV approach, we should ask: Why consider usingNPV in the first place? Answering this question will put the rest of this chapter in a properperspective. There are actually a number of arguments justifying the use of NPV, and youmay have already seen the detailed one of Chapter 3. We now present one of the simplestjustifications through an example.


The Alpha Corporation is considering investing in a riskless project costing $100.The project pays $107 at date 1 and has no other cash flows. The managers of thefirm might contemplate one of two strategies:
1. Use $100 of corporate cash to invest in the project. The $107 will be paid as adividend in one period.
2. Forgo the project and pay the $100 of corporate cash as a dividend today.If strategy 2 is employed, the stockholder might deposit the dividend in the bankfor one period. Because the project is riskless and lasts for one period, the stock-holder would prefer strategy 1 if the bank interest rate was below 7 percent. Inother words, the stockholder would prefer strategy 1 if strategy 2 produced lessthan $107 by the end of the year.

The comparison can easily be handled by NPV analysis. If the interest rate is 6 percent,the NPV of the project is Because the NPV is positive, the project should be accepted. Of course, a bank interest rateabove 7 percent would cause the project’s NPV to be negative, implying that the projectshould be rejected.

Thus, our basic point is:
Accepting positive NPV projects benefits the stockholders.

Although we used the simplest possible example, the results could easily be applied tomore plausible situations. If the project lasted for many periods, we would calculate theNPV of the project by discounting all the cash flows. If the project were risky, we could de-termine the expected return on a stock whose risk is comparable to that of the project. Thisexpected return would serve as the discount rate.

Having shown that NPV is a sensible approach, how can we tell whether alternative ap-proaches are as good as NPV? The key to NPV is its three attributes:

1. NPV Uses Cash Flows Cash flows from a project can be used for other corporate pur-poses (e.g., dividend payments, other capital-budgeting projects, or payments of corporateinterest). By contrast, earnings are an artificial construct. While earnings are useful to ac-countants, they should not be used in capital budgeting because they do not represent cash.
2. NPV Uses All the Cash Flows of the Project Other approaches ignore cash flows be-yond a particular date; beware of these approaches.
3. NPV Discounts the Cash Flows Properly Other approaches may ignore the time valueof money when handling cash flows. Beware of these approaches as well.


Defining the Rule
One of the most popular alternatives to NPV is the payback period rule. Here is how thepayback period rule works.

Consider a project with an initial investment of $50,000. Cash flows are $30,000,$20,000, and $10,000 in the first three years, respectively. These flows are illustrated inFigure 6.1. A useful way of writing down investments like the preceding is with the notation:
(-$50,000, $30,000, $20,000, $10,000)

The minus sign in front of the $50,000 reminds us that this is a cash outflow for the investor,and the commas between the different numbers indicate that they are received—or if theyare cash outflows, that they are paid out—at different times. In this example we are assum-ing that the cash flows occur one year apart, with the first one occurring the moment we de-cide to take on the investment.

The firm receives cash flows of $30,000 and $20,000 in the first two years, which addup to the $50,000 original investment. This means that the firm has recovered its investmenwithin two years. In this case two years is the payback period of the investment.

The payback period rule for making investment decisions is simple. A particular cut-off time, say two years, is selected. All investment projects that have payback periods oftwo years or less are accepted and all of those that pay off in more than two years—if atall—are rejected.

Problems with the Payback Method

There are at least three problems with the payback method. To illustrate the first two prob-lems, we consider the three projects in Table 6.1. All three projects have the same three-year payback period, so they should all be equally attractive—right?

Actually, they are not equally attractive, as can be seen by a comparison of differentpairs of projects.

Problem 1: Timing of Cash Flows within the Payback Period Let us compare projectA with project B. In years 1 through 3, the cash flows of project A rise from $20 to $50 whilethe cash flows of project B fall from $50 to $20. Because the large cash flow of $50 comesearlier with project B, its net present value must be higher. Nevertheless, we saw above thatthe payback periods of the two projects are identical. Thus, a problem with the payback pe-riod is that it does not consider the timing of the cash flows within the payback period. Thisshows that the payback method is inferior to NPV because, as we pointed out earlier, theNPV approach discounts the cash flows properly.

Problem 2: Payments after the Payback Period Now consider projects B and C, whichhave identical cash flows within the payback period. However, project C is clearly preferredbecause it has the cash flow of $60,000 in the fourth year. Thus, another problem with thepayback method is that it ignores all cash flows occurring after the payback period. Thisflaw is not present with the NPV approach because, as we pointed out earlier, the NPV ap-proach uses all the cash flows of the project. The payback method forces managers to havean artificially short-term orientation, which may lead to decisions not in the shareholders’best interests.

Problem 3: Arbitrary Standard for Payback Period We do not need to refer to Table6.1 when considering a third problem with the payback approach. When a firm uses theNPV approach, it can go to the capital market to get the discount rate. There is no compa-rable guide for choosing the payback period, so the choice is arbitrary to some extent.

Managerial Perspective
The payback rule is often used by large and sophisticated companies when making rela-tively small decisions. The decision to build a small warehouse, for example, or to pay fora tune-up for a truck is the sort of decision that is often made by lower-level management.Typically a manager might reason that a tune-up would cost, say, $200, and if it saved $120each year in reduced fuel costs, it would pay for itself in less than two years. On such a ba-sis the decision would be made.

Although the treasurer of the company might not have made the decision in the sameway, the company endorses such decision making. Why would upper management condoneor even encourage such retrograde activity in its employees? One answer would be that itis easy to make decisions using the payback rule. Multiply the tune-up decision into 50 suchdecisions a month, and the appeal of this simple rule becomes clearer.

Perhaps most important though, the payback rule also has some desirable features formanagerial control. Just as important as the investment decision itself is the company’s abil-ity to evaluate the manager’s decision-making ability. Under the NPV rule, a long time maypass before one decides whether or not a decision was correct. With the payback rule weknow in two years whether the manager’s assessment of the cash flows was correct.

It has also been suggested that firms with very good investment opportunities but no avail-able cash may justifiably use the payback method. For example, the payback method could beused by small, privately held firms with good growth prospects but limited access to the capi-tal markets. Quick cash recovery may enhance the reinvestment possibilities for such firms.

Notwithstanding all of the preceding rationale, it is not surprising to discover that asthe decision grows in importance, which is to say when firms look at bigger projects, theNPV becomes the order of the day. When questions of controlling and evaluating the man-ager become less important than making the right investment decision, the payback periodis used less frequently. For the big-ticket decisions, such as whether or not to buy a machine,build a factory, or acquire a company, the payback rule is seldom used.

Summary of the Payback Period Rule

To summarize, the payback period is not the same as the NPV rule and is therefore con-ceptually wrong. With its arbitrary cutoff date and its blindness to cash flows after that date,it can lead to some flagrantly foolish decisions if it is used too literally. Nevertheless, be-cause it is so simple, companies often use it as a screen for making the myriad of minor in-vestment decisions they continually face.

Although this means that you should be wary of trying to change rules like the paybackperiod when you encounter them in companies, you should probably be careful not to fall intothe sloppy financial thinking they represent. After this course you would do your company adisservice if you ever used the payback period instead of the NPV when you had a choice.


Aware of the pitfalls of the payback approach, some decision makers use a variant called thediscounted payback period rule.Under this approach,we first discount the cash flows. Thenwe ask how long it takes for the discounted cash flows to equal the initial investment.

For example, suppose that the discount rate is 10 percent and the cash flows on a proj-ect are given by
(-$100, $50, $50, $20)

This investment has a payback period of two years, because the investment is paid back inthat time.
To compute the project’s discounted payback period, we first discount each of the casflows at the 10-percent rate. In discounted terms, then, the cash flows look like
[-$100, $50/1.1, $50/(1.1)]=(-$100, $45.45, $41.32, $15.03)

The discounted payback period of the original investment is simply the payback period forthese discounted cash flows. The payback period for the discounted cash flows is slightly lessthan three years since the discounted cash flows over the three years are $101.80 ($45.45 $41.32  $15.03). As long as the cash flows are positive, the discounted payback period willnever be smaller than the payback period, because discounting will lower the cash flows.

At first glance the discounted payback may seem like an attractive alternative, but oncloser inspection we see that it has some of the same major flaws as the payback. Like pay-back, discounted payback first requires us to make a somewhat magical choice of an arbi-trary cutoff period, and then it ignores all of the cash flows after that date.

If we have already gone to the trouble of discounting the cash flows, any small appealto simplicity or to managerial control that payback may have, has been lost. We might justas well add up the discounted cash flows and use the NPV to make the decision. Althoughdiscounted payback looks a bit like the NPV, it is just a poor compromise between the pay-back method and the NPV.

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