The Relevant Internal Rate of Return

In this article we present a method for determining project acceptability in the presence of multiple internal rates of return. An internal rate of return is an interest rate that equates the present worth of a cash flow stream to zero. When unique, it provides valuable information about the return on the investment and is often viewed as a measure of efficiency. Unfortunately, this analysis is clouded when there are multiple internal rates of return, which can occur when a project is defined by a mixture of positive and negative cash flows. While many methods have been presented in the literature to deal with this problem, we believe ours to be unique in that it does not rely on the computation of another measure of worth, but rather, the identification of the relevant rate of return from the set of internal rates of return. We show that this rate always produces decisions consistent with present worth under the assumption that at least one real internal rate of return exists. In doing so, we provide new definitions of when a project is borrowing from, or loaning to, the firm. These definitions help in understanding the meaning of multiple internal rates of return, which is also discussed.