Use of criteria NPV and IRR for choosing among investment projects

Abstract

Two of the most important criteria are the net present value (NPV) and the internal rate of return (IRR) for choosing among investment projects. In many circumstances, investment projects are ranked in the same order by both criteria. In some situations, however, the two criteria provide different rankings. The debate is an old one (e.g. going back to Böhm-Bawerk, 1884). Let us explain the essence of the NPV and IRR indicators. The basis of economic calculations in the field of investment is the idea that a cash euro today is more valuable than a euro promised in a year. If a bank lends N euros to an entrepreneur today, then in a year the bank demands to return N(1 + E) euros, where E is the bank interest. Another type of calculation is carried out by the entrepreneur. If he invests N euros in some project today, then in a year he hopes to receive N(1 + IRR) euros, where IRR is the internal rate of return of the project implemented by the entrepreneur. Naturally, the value of IRR is only an assumed, indicative, and the entrepreneur is expecting IRR more than E. The present work arose from discussions of the results of the French economist Pierre Masse “Le Choix des investissements, critères et méthodes” published in 1959. The main goal of the paper is to give the proof of both IRR and NPV formulas (in a particular simplified case) and a geometric interpretation of these very complex equations (useful for the training purpose, at least). The analysis of IRR and NPV indicates an unequivocal choice among the criteria NPV and IRR. This confirms a simple numerical example on the fallacy of Masse’s IRR reasoning. No unambiguous solution has been found yet. It can be explained if we allow that the bank interest relates to Macroeconomics, largely concerned with nation scale projects but the entrepreneur interest relates to Microeconomics, to internal rate of return. The world continues to search for a single consistent criterion for evaluating investments.