Relevant and Irrelevant Internal Rates of Return

Abstract

One problem with internal race of return is the possibility that given cash flows may result in more than one internal rate of return. The purpose of this paper is to develop a method for determining relevance of an internal rate of return. An Internal rate of return is considered relevant if its derivatives with respect to each of the cash flows are positive. It is determined that the necessary and sufficient conditions for relevance are: (1) the net future value function has a negative derivative at a relevant root; and (2) a relevant Internal rate of return must be greater than -1. Our method of analysis identifies a single relevant rate for the dual race problem and for a special case when there are three rates, However, when more than one Internal rate of return meets the conditions for relevance, our analysis cannot be extended to choose among the relevant rates.

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