Multiple internal rates of return

A potential problem with the internal rate of return method that we have yet to mention is that multiple internal rates of return are possible. A necessary, but not sufficient, condition for this occurrence is that the cash-flow stream changes sign more than once. For example the pattern -,+,+,- reveals two changes in sign from minus to plus and from plus to minus. In conventional cash flow patterns, where cash outflow was followed by one or more cash inflows. In other words, there was but one change in sign (from minus to plus), which ensured a unique internal rate of return.

However, some projects which we could label as non-conventional, involve multiple changes in sign. For example, at the end of a project there may be a requirement to restore the environment. This often happens in an extractive industry like strip mining where land must be reclaimed at the end of the project. Additionally, with a chemical plant there are often sizable dismantling costs. Whatever the cause, these costs result in a cash outflow at the end of the project and, hence, in more than one change in sign in the cash-flow stream.

Whether these changes in sign cause more than one internal rate of return also depends on the magnitudes of the cash flows. Most projects have only one change in sign in the cash-flow stream, but some have more. When this occurs, the financial manager must be alert to the possibility of multiple internal rates of return. No one internal rate of return makes sense economically when there are multiple internal rates of return. Therefore, an alternative method of analysis must be used.

When multiple IRR situations are analyzed, calculators and computer programs are often fooled and produce only one IRR. Perhaps the best way to determine if a problem exists is to calculate the net present value of a project at various discount rates.

Summary of shortcomings of IRR method

We have seen that the net present value method always provides correct rankings of mutually exclusive investment projects,

whereas the internal rate of return method sometimes does not. With the IRR method, the implicit reinvestment rate will differ depending on the cash-flow stream for each investment proposal under consideration. With the net present value method, however, the implicit reinvestment rate namely, the required rate of return is the same for each investment.