Average Internal Rate of Return and Investment Decisions : A New Perspective

The internal rate of return (IRR) is often used by managers and practitioners for investment decisions. Unfortunately, it has serious flaws: among others, (i) multiple real-valued IRRs may arise, (ii) complex-valued IRRs may arise, (iii) the IRR is, in general, incompatible with the net present value (NPV) in accept/reject decisions (iv) the IRR ranking is, in general, different from the NPV ranking, (v) the IRR criterion is not applicable with variable costs of capital (vi) it does not measure the return on initial investment, (vii) it does not signal the loss of the entire capital, (viii) it is not capable of measuring the rate of return of an arbitrage strategy. The efforts of economists and management scientists in providing a reliable project rate of return have generated over the decades an immense bulk of contributions aiming to solve these shortcomings. This paper offers a complete solution to this long-standing unsolved issue by changing the usual perspective: the IRR equation is dismissed and a new theory of rate of return is advanced, endorsing a radical conceptual shift: the rate of return does not depend on cash flows, but on the invested capital: only as long as the capital is determined, a rate of return exists and is univocally individuated, by computing the ratio of income to capital. In particular, it is shown that any arithmetic mean of the one-period return rates implicit in a project reliably informs about a project's profitability and correctly ranks competing projects. With such a measure, which we name ”Average Internal Rate of Return”, complex-valued numbers disappear and all the above mentioned problems are wiped out. The traditional IRR notion may be found back as a particular case