Abstract
The internal rate of return (IRR) is often used by managers and practitioners for investment decisions. Unfortunately, it has serious flaws: (1) multiple real-valued IRRs may arise; (2) complex-valued IRRs may arise; (3) the IRR is, in general, incompatible with the net present value (NPV) in accept/reject decisions; (4) the IRR ranking is, in general, different from the NPV ranking; (5) the IRR criterion is not applicable with variable costs of capital. 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 article offers a complete solution to this long-standing unresolved issue by changing the usual perspective: the IRR equation is dismissed and the evaluator is allowed to describe the project as an investment or a borrowing at his discretion. This permits showing 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 call average internal rate of return, complex-valued numbers disappear and all the above-mentioned problems are wiped out. The economic meaning is compelling: it is the project return rate implicitly determined by the market. The traditional IRR notion may be found as a particular case.
Highlights
The inception of the internal rate of return (IRR) traces back to Keynes (1936) and Boulding (1935, 1936a,b)
We show that the IRR is just an Average Internal Rate of Return’ (AIRR) associated with a specific class of investment streams
Managers, practitioners have long since recognized that the net present value (NPV) criterion is a theoretically sound decision criterion for capital budgeting in most circumstances (e.g. Fisher 1930; Weston and Copeland 1988; Brealey and Myers 2000; MacMinn 2005), and even real options may be framed in terms of an ‘expanded’ NPV.4
Summary
The inception of the internal rate of return (IRR) traces back to Keynes (1936) and Boulding (1935, 1936a,b). The author makes use of the notion of ‘investment stream’, which is the sequence of capitals periodically invested in the project He shows that the problems of uniqueness and nonexistence of the IRR are overcome by considering that any IRR is univocally associated with its corresponding investment stream. The corresponding arithmetic mean is shown to represent an unfailing economic yield, here named ‘Average Internal Rate of Return’ (AIRR) This return rate correctly signals desirability of a project and correctly ranks any bundle of competing projects. The approach purported in this work is computationally very simple and gets rid of complex-valued roots of polynomials; it admits of a straightforward economic interpretation as the project is reduced to its basic ingredients: (i) capital invested, (ii) average internal rate of return, (iii) cost of capital.
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