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The IRR rule is appealing in that it usually gives the same guidance as the NPV rule when the
threshold equals the company‟s cost of capital. If a project‟s IRR exceeds the firm‟s cost of capital,
the project must be creating wealth for the firm. The project would produce returns greater than the
firm‟s financing costs, and the spread would be added wealth for the investors. Unfortunately, the IRR
rule frequently breaks down and gives misleading advice.
The IRR rule suffers from two flaws. First, it ignores the relative sizes of alternative projects. For
example, suppose a firm had to choose between two projects, each of which lasts one year. The first
project costs $10,000 to set up but then pays back $16,000 one year later. The second project costs
$100,000 to set up but pays back $120,000 one year later. Clearly, the IRR of the first project is 60%,
and the IRR of the second project is 20%. On the basis of IRR, the first project seems to be superior.
However, if the firm‟s cost of capital is 10%, the first project has an NPV of $4,454, whereas the
second project has an NPV of $9,091. Clearly the second project creates more wealth. The first project
has a higher rate of return but on a smaller investment. The second project‟s lower return on a larger
scale is a better use of the firm‟s scarce managerial resources.
The second flaw in the IRR rule stems from the fact that a given project may have multiple IRRs.
The IRR is not always a single, unique value. Consider a two-year project. Initially the project costs
$1,000 to set up. In the first year it returns $3,000. In the second year there is a cleanup costing
$2,000. It is easy to verify that 0% is one correct value for the firm‟s IRR: Discounting at 0% and
adding up all the discounted cash flows gives an NPV of zero. Notice, however, that 100% is another
correct value for the IRR: Discounting all cash flows at 100% per year also gives an NPV of zero. If
the firm‟s cost of capital is 10%, should this project be accepted or rejected? Ten percent is greater
than 0%, but less than 100%. Only by computing the NPV at the discount rate of 10% do we find out
that this project has a positive NPV of $74 and so should be accepted. When a project has two or more
IRRs, the analyst would have no way of knowing which was the correct one to use if he or she did not
also compute the NPV and apply the NPV rule. If the analyst computed only the IRR of 100%, she or
he would reject this valuable project.
It turns out that a project will have one IRR for every change in sign in its cash flows. If a project
has an initial outlay and then subsequently all cash flows are positive inflows, there will be one unique
IRR. If a project has an initial outlay, a string of positive inflows, and then a cleanup cost at the end,
there will be two IRRs since the direction of cash flow changed twice. If there is an initial outlay, a
positive inflow, another net outflow during a retooling year, followed by a positive inflow, the three
sign changes would produce three different IRRs. The IRR rule would provide little guidance in such
a scenario and could possibly lead to an incorrect judgment of the project‟s worth.
In situations where its two fatal flaws are not at issue, the IRR rule gives the same result as the NPV
rule. If the project‟s cash flows change sign only once, there is no problem of multiple IRRs. If all
competing projects are of the same magnitude or if there is only one project under consideration, the
size issue will not be a problem, either. In such a situation, the firm would be justified in selecting the
project on the basis of IRR.
One circumstance in which alternative projects are of equal size and cash flows change direction
only once is in the analysis of alternative mortgage plans. These days, a person financing a home may
choose from a multitude of mortgage plans. A variety of payment schedules are available, and some
plans charge points in exchange for lower monthly payments. Since all mortgages considered by the