Multiple IRRs


In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values. In this case a discount rate may be used for the borrowing cash flow and the IRR calculated for the investment cash flow. This applies for example when a customer makes a deposit before a specific machine is built.

In a series of cash flows like (−10, 21, −11), one initially invests money, so a high rate of return is best, but then receives more than one possesses, so then one owes money, so now a low rate of return is best. In this case, it is unclear whether a high or a low IRR is better. There may even be multiple IRRs for a single project, such as in the above example, 0% and 10%. Examples of this type of project are strip mines and nuclear power plants, where there is usually a large cash outflow at the end of the project.

Multiple internal rates of return As cash flows of a project change sign more than once, there will be multiple IRRs. NPV i

Multiple internal rates of return: As a project's cash flows change more than once, there will be multiple IRRs. NPV is a preferable metric in these cases.


When a project has multiple IRRs, it may be more convenient to compute the project's IRR with the benefits reinvested. Accordingly, a Modified Internal Rate of Return (MIRR) is used, which has an assumed reinvestment rate, usually equal to the project's cost of capital.

It has been shown that with multiple internal rates of return, the IRR approach can still be interpreted in a way consistent with the present value approach, provided that the underlying investment stream is correctly identified as net investment or net borrowing.

Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV. Managers find it easier to compare investments of different sizes in terms of percentage rates of return than by dollars of NPV. However, NPV remains the "more accurate" reflection of value to the business. IRR, as a measure of investment efficiency may give better insights in capital constrained situations. However, when comparing mutually exclusive projects, NPV is the appropriate measure.

Key Points

  • In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values.

  • It has been shown that with multiple internal rates of return, the IRR approach can still be interpreted in a way that is consistent with the present value approach provided that the underlying investment stream is correctly identified as net investment or net borrowing.

  • NPV remains the "more accurate" reflection of value to the business. IRR, as a measure of investment efficiency may give better insights in capital constrained situations. However, when comparing mutually exclusive projects, NPV is the appropriate measure.

Terms

  • Modified Internal Rate of Return – the modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and, as such, aims to resolve some problems with the IRR.

  • Mutually Exclusive – describing multiple events or states of being such that the occurrence of any one implies the non-occurrence of all the others.

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