The IRR formula is simply the NPV formula solved for the particular rate that sets the NPV to 0. The same equation is used for both methods.
The NPV method assumes that cash flows will be reinvested at the firm's cost of capital, while the IRR method assumes reinvestment at the project's IRR. Reinvestment at the cost of capital is a better assumption in that it is closer to reality.
For independent projects, the NPV and IRR methods indicate the same accept or reject decisions. Assuming that Project A and B are independent, consider their NPV profiles.
However, for mutually exclusive projects, ranking conflicts can arise. Assuming that Project A and B are mutually exclusive, consider their NPV profiles.
For mutually exclusive projects, the NPV and MIRR methods will lead to the same accept or reject decision when:
However, the projects can generate conflicting results if the NPV profiles of two projects cross (and there is a crossover rate):
Two conditions cause the NPV profiles to cross:
The root cause of the conflict between NPV and IRR is the rate of return at which differential cash flows can be reinvested. Both the NPV and IRR methods assume that the firm will reinvest all early cash flows. The NPV method implicitly assumes that early cash flows can be reinvested at the cost of capital. The IRR method assumes that the firm can reinvest at the IRR.
Whenever a conflict exists, the NPV method should be used. It can be demonstrated that the better assumption is the cost of capital for the reinvestment rate (Hint: don't focus too much on this topic, as it is beyond the scope of the CFA exam).
Multiple IRRs is a situation where a project has two or more IRRs. This problem is caused by the non-conventional cash flows of a project.
In fact, non-conventional cash flows can cause other problems, such as negative IRR or an IRR that leads to an incorrect accept or reject decision. However, a project can have only one NPV, regardless of its cash flow patterns, so the NPV method is preferable when evaluating projects with non-normal cash flows.
|Cynthialixu: Good hint. =)|
|bidisha: i had the same thought... need more of these kinds of hints.|
| fanDango: Even though it was at the end of the section...|
|MathLoser: NPV is the only acceptable criterion when ranking projects.|