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OTHER PITFALLS OF THE IRR RULE

The IRR rule is subject to problems beyond those associated with mutually exclusive investments. Here are a few more pitfalls to avoid. Pitfall 2: Lending or Borrowing? Remember our condition for the IRR rule to work: the project s NPV must fall as the discount rate increases. Now consider the following projects:

Each project has an IRR of 50 percent. In other words, if you discount the cash flows at 50 percent, both of them would have zero NPV. Does this mean that the two projects are equally attractive? Clearly not. In the case of J we are paying out $100 now and getting $150 back at the end of the year. That is better than any bank account. But what about K? Here we are getting paid $100 now but we have to pay out $150 at the end of the year. That is equivalent to borrowing money at 50 percent.

If someone asked you whether 50 percent was a good rate of interest, you could not answer unless you also knew whether that person was proposing to lend or borrow at that rate. Lending money at 50 percent is great (as long as the borrower does not flee the country), but borrowing at 50 percent is not usually a good deal (unless of course you plan to flee the country). When you lend money, you want a high rate of return; when you borrow, you want a low rate of return. If you plot a graph like Figure 4.2 for project K, you will find the NPV increases as the discount rate increases. (Try it!) Obviously, the rate of return rule will not work in this case.

Project K is a fairly obvious trap, but if you want to make sure you don t fall into it, calculate the project s NPV. For example, suppose that the cost of capital is 10 percent. Then the NPV of project J is + $36.4 and the NPV of project K is $36.4. The NPV rule correctly warns us away from a project that is equivalent to borrowing money at 50 percent. When NPV rises as the interest rate rises, the rate of return rule is reversed:

When NPV is higher as the discount rate increases, a project is acceptable only if its internal rate of return is less than the opportunity cost of capital.

Pitfall 3: Multiple Rates of Return. Here is a trickier problem. King Coal Corporation is considering a project to strip mine coal. The project requires an investment of $22 million and is expected to produce a cash inflow of $15 million in each of Years 1 through 4. However, the company is obliged in Year 5 to reclaim the land at a cost of $40 million. At a 10 percent opportunity cost of capital the project has an NPV of $.7 million. To find the IRR, we have calculated the NPV for various discount rates and plotted the results in Figure 4.5. You can see that there are two discount rates at which NPV = 0. That is, each of the following statements holds:

In other words, the investment has an IRR of both 6 and 28 percent. The reason for this is the double change in the sign of the cash flows. There can be as many different internal rates of return as there are changes in the sign of the cash-flow stream.8 Is the coal mine worth developing? The simple IRR rule accept if the IRR is greater than the cost of capital won t help. For example, you can see from Figure 4.5 that with a low cost of capital (less than 6 percent) the project has a negative NPV. It has a positive NPV only if the cost of capital is between 6 percent and 28 percent.

When there are multiple changes in the sign of the cash flows, the IRR rule does not work. But the NPV rule always does.