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Other Investment Criteria

Use of the net present value rule as a criterion for accepting or rejecting investment projects will maximize the value of the firm s shares. However, other criteria are sometimes also considered by firms when evaluating investment opportunities. Some of these rules are liable to give wrong answers; others simply need to be used with care. In this section, we introduce three of these alternative investment criteria: internal rate of return, payback period, and book rate of return.

INTERNAL RATE OF RETURN

Instead of calculating a project s net present value, companies often prefer to ask whether the project s return is higher or lower than the opportunity cost of capital. For example, think back to the original proposal to build the office block. You planned to invest $350,000 to get back a cash flow of C1 = $400,000 in 1 year. Therefore, you forecasted a profit on the venture of $400,000 $350,000 = $50,000, and a rate of

return of Rate of return = profit = C1 investment = $400,000 $350,000 investment investment $350,000 = .1429, or about 14.3%

The alternative of investing in a U.S. Treasury bill would provide a return of only 7 percent. Thus the return on your office building is higher than the opportunity cost of capital.1

This suggests two rules for deciding whether to go ahead with an investment project:

1. The NPV rule. Invest in any project that has a positive NPV when its cash flows are discounted at the opportunity cost of capital.

2. The rate of return rule. Invest in any project offering a rate of return that is higher than the opportunity cost of capital.

Both rules set the same cutoff point. An investment that is on the knife edge with an NPV of zero will also have a rate of return that is just equal to the cost of capital. Suppose that the rate of interest on Treasury bills is not 7 percent but 14.3 percent. Since your office project also offers a return of 14.3 percent, the rate of return rule suggests that there is now nothing to choose between taking the project and leaving your money in Treasury bills. The NPV rule also tells you that if the interest rate is 14.3 percent, the project is evenly balanced with an NPV of zero:2

The project would make you neither richer nor poorer; it is worth what it costs. Thus the NPV rule and the rate of return rule both give the same decision on accepting the project.

A CLOSER LOOK AT THE RATE OF RETURN RULE

We know that if the office project s cash flows are discounted at a rate of 7 percent the project has a net present value of $23,832. If they are discounted at a rate of 14.3 percent, it has an NPV of zero. In Figure 6.2 the project s NPV for a variety of discount rates is plotted. This is often called the NPV profile of the project. Notice two important things about Figure 4.2:

1. The project rate of return (in our example, 14.3 percent) is also the discount rate which would give the project a zero NPV. This gives us a useful definition: the rate of return is the discount rate at which NPV equals zero.3

2. If the opportunity cost of capital is less than the project rate of return, then the NPV of your project is positive. If the cost of capital is greater than the project rate of return, then NPV is negative. Thus the rate of return rule and the NPV rule are equivalent.

CALCULATING THE RATE OF RETURN FOR LONG-LIVED PROJECTS

There is no ambiguity in calculating the rate of return for an investment that generates a single payoff after one period. Remember that C0, the time 0 cash flow corresponding to the initial investment, is negative. Thus Rate of return = profit = C1 investment = C1 + C0 investment investment C0

But how do we calculate return when the project generates cash flows in several periods? Go back to the definition that we just introduced the project rate of return is also the discount rate which gives the project a zero NPV. Managers usually refer to this figure as the project s internal rate of return, or IRR.4 It is also known as the discounted cash flow (DCF) rate of return.

Let s calculate the IRR for the revised office project. If you rent out the office block for 3 years, the cash flows are as follows:

There is no simple general method for solving this equation. You have to rely on a little trial and error. Let us arbitrarily try a zero discount rate. This gives an NPV of $148,000:

With a zero discount rate the NPV is positive. So the IRR must be greater than zero. The next step might be to try a discount rate of 50 percent. In this case NPV is $194,000:

NPV is now negative. So the IRR must lie somewhere between zero and 50 percent. In Figure 4.3 we have plotted the net present values for a range of discount rates. You can see that a discount rate of 12.96 percent gives an NPV of zero. Therefore, the IRR is 12.96 percent. You can always find the IRR by plotting an NPV profile, as in Figure 4.3, but it is quicker and more accurate to let a computer or specially programmed financial calculator do the trial and error for you. The nearby box illustrates how to do so. The rate of return rule tells you to accept a project if the rate of return exceeds the opportunity cost of capital. You can see from Figure 4.3 why this makes sense. Because the NPV profile is downward sloping, the project has a positive NPV as long as the opportunity cost of capital is less than the project s 12.96 percent IRR. If the opportunity cost of capital is higher than the 12.96 percent IRR, NPV is negative. Therefore, when we compare the project IRR with the opportunity cost of capital, we are effectively asking whether the project has a positive NPV. This was true for our one-period office project. It is also true for our three-period office project. We conclude that

The rate of return rule will give the same answer as the NPV rule as long as the NPV of a project declines smoothly as the discount rate increases.

The usual agreement between the net present value and internal rate of return rules should not be a surprise. Both are discounted cash flow methods of choosing between projects. Both are concerned with identifying those projects that make shareholders better off and both recognize that companies always have a choice: they can invest in a project or, if the project is not sufficiently attractive, they can give the money back to shareholders and let them invest it for themselves in the capital market.

INTERNAL RATE OF RETURN (IRR) Discount rate at which project NPV = 0.