310 Planning and Forecasting
maybe 30% this time. At 30%, the NPV is −$13.35. Apparently, 30% is too
high. The next guess should be lower. Following this algorithm, the IRR of
21.9% will eventually be located.
The IRR rule stipulates that a project should be accepted if its IRR is
greater than some agreed-on threshold, and rejected other wise. That is, to be ac-
cepted a project must produce percentage returns higher than some company-
mandated minimum. Often the minimum threshold is set equal to the firm’s cost
of capital. If the IRR beats the WACC, then the project is accepted. If the IRR
is less than the WACC, the project is rejected.
For example, suppose a project costs $1,000 to set up, and then produces
a one-time cash inf low of $1,100 one year later. The IRR of this project is 10%.
If the company imposes a minimum threshold of 20%, this project will be re-
jected. If the company’s threshold is 8%, this project will be accepted. We saw
previously that the brewery project IRR was 21.7%. If the agreed threshold is
the brewery’s 20% WACC, then the IRR rule would indicate that the project
should be accepted.
The IRR rule is appealing in that it usuallygives 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 adding wealth for the investors. Un-
fortunately, the IRR rule frequently breaks down and gives misleading advice.
The IRR rule suffers from two f laws. 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
manager ial resources.
The second f law in the IRR rule stems from the fact that a given project
may have multiple IRRs. 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 f lows gives an NPV of zero. Notice, how-
ever, that 100% is another correct value for the IRR: Discounting all cash
f lows 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