Revealing the True Meaning of the IRR via Profiling the IRR and Defining the ERR

Since the late 1950s, most textbooks and many professors have been inadvertently defining the internal rate of return (IRR) of an investment incorrectly vis--vis the reinvestment of an investment's cash flows. The genesis of this unfortunate error can be traced to an article by Renshaw (1957). Most textbooks and many professors have since paraphrased a quotation taken from the Renshaw article that attempted to paraphrase (out of context) the words of Solomon (1956). Both the Renshaw and the Solomon quotations, in their entireties, go on to properly explain the issue of reinvestment vis--vis the IRR. However, the paraphrasing of the partial quotation of Renshaw has perpetuated what some now call the "reinvestment rate controversy." The Renshaw (1957:193) quotation states: "...the (net) present value (NPV) approach assumes reinvestment of intermediate cash receipts at the discounting rate, while the internal rate-of-return (IRR) approach assumes reinvestment at the internal rate..."

The fact is that neither approach makes any assumption whatsoever about either the reinvestment of cash flows or the rate of return to be earned if reinvestment were to be considered. The discounted cash flow (DCF) equations for the IRR and the NPV are just that: formal statements of equivalence. Equations do not make assumptions; people make assumptions. A calculation cannot assume; people assume. Hence, reinvestment has nothing to do with the calculation of the IRR. However, reinvestment may be critical to the application of the IRR as an investment decision-making tool. What follows infra, hopefully, will clarify the confusion and settle the controversy regarding the issue of reinvestment vis--vis the IRR.