Example 1016 Multiple Hurdle Rates

The following time line describes the cash flows of a bad project developed by a team at Idiots, Inc. The appropriate discount rates for riskless cash flows of various maturities are given below the cash flows.

Cash Flows and Discount Rates for Date

Compute the IRR and the two hurdle rates for the project.

Answer: The unique IRR is -19.81 percent. The hurdle rates are found by first discounting the cash flows from years 1 -3, which gives a present value of -\$.882. The cash flows of the (zero NPV) bond portfolio that tracks the future cash flows of the project are therefore

Tracking Portfolio Cash Flows at Date

Note that, in contrast to the cash flows of the project, the cash flows of the tracking portfolio have two sign changes and thus may have more than one IRR. The two hurdle rates of the four cash flows of the tracking portfolio are 6.86 percent and 976.04 percent. Both hurdle rates exceed the IRR, implying the project should be rejected.

These considerations suggest the following IRR adoption rule for projects with later and early cash flow streams:

Result 10.6 (The appropriate internal rate of return rule.) In the absence of constraints, a project with a later cash flow stream should be adopted only if its internal rate of return exceeds the hurdle rate(s). A project with an early cash flow stream should only be adopted if the hurdle rate(s) exceed the internal rate of return of the project.

16A similar problem arises with an early cash flow stream when the present value of its future cash flows is positive. In this case, the project has a positive NPV. If the project has two hurdle rates because of this, both will exceed the IRR and indicate that the project should be adopted. Since a project has a positive NPV when it has an early cash flow stream with future cash flows that have a positive present value, the internal rate of return rule in this case makes the correct decision, regardless of which of the two hurdle rates is used.

Sign Reversals and Multiple Internal Rates of Return

The last subsection noted that multiple internal rates of return for the bond portfolio that tracks the project, and thus determines the hurdle rates, do not prevent us from using the IRR to determine whether projects with later or early cash flow streams should be adopted. By contrast, the existence of multiple internal rates of return for the project's cash flows has a major impact on one's ability to use the IRR for evaluating invest-

ments.

A project could have more than one internal rate of return if its cash flows exhibit more than one sign reversal. These multiple sign reversals can arise for many reasons. For example, environmental regulations may require the owner of a strip mine to restore the land to a pristine state after the mine is exhausted. Or the tax authorities may not require a firm to pay the corporate income tax on the sale of a profitable product until one year after the profit is earned. In this case, the last cash flow for the project is merely the tax paid on the last year the project earned profits. The next section illustrates how mutually exclusive projects can create sign reversals, even when the cash flows of the projects per se do not exhibit multiple sign reversals.

In the event of multiple sign reversals, many practitioners employ very complicated and often ad hoc adjustments to the internal rate of return calculation. In principle (although rarely in practice), these adjustments can ensure that the IRR rule yields the same decisions as the net present value rule. However, it makes little sense to bother with these troublesome procedures when the net present value rule gives the correct answer and is easier to implement.

Mutually Exclusive Projects and the Internal Rate of Return

When selecting one project from a group of alternatives, the net present value rule indicates that the project with the largest positive net present value is the best project.

Do Not Select the Project with the Largest IRR. It is easy, but foolhardy, to think that one should extend this idea to the internal rate of return criterion and adopt the project with the largest IRR. Even if all the projects under consideration are riskless and have the later cash flow stream pattern, each project might have different hurdle rates if the term structure of interest rates is not flat. If the project with a large IRR also has a larger hurdle rate than the other projects, how does one decide? Is it then more appropriate to look at the difference between the internal rate of return and the cost of capital or the ratio? Fortunately, it is unnecessary to answer this question because even if all the projects have the same hurdle rate, the largest internal rate of return project is not the best, as Example 10.17 illustrates.