On the long-standing issue of the internal rate of return: a complete resolution

The IRR problem. As widely known, the IRR has serious flaws: (i)multiple real-valued IRRs may arise, (ii) the meaning of each IRR may be ambiguous (rate of return or rate of cost?), (iii)complex-valued IRRs may arise, (iv) the IRR is, in general, incompatible with the net present value (NPV) in accept/reject decisions and the IRR ranking is, in general, different from the NPV ranking, (v)the IRR decision criterion is not applicable with variable costs of capital. Since the origins of the notions (Boulding 1935, 1936; Keynes 1936), the IRR drawbacks have stimulated an immense bulk of contributions over the decades investigating this issue and searching for some solution (see references in Gronchi 1987 and in Magni 2010a). We here present two autonomous solutions which solve the IRR problems completely by dismissing the traditional the IRR equation and considering a simple mean of period rates. As a pleasant byproduct, we find that accounting rates of return are meaningful economic rates of return, whereas the IRR is just a particular case of the mean of period rates.