TY - JOUR

T1 - NPV, IRR, PI, PP, and DPP: A unified view

AU - Sokolov, M.V.

N1 - Export Date: 19 October 2024 CODEN: JMECD Адрес для корреспонденции: Sokolov, M.V.; European University at St. Petersburg, 6/1A Gagarinskaya st., Russian Federation; эл. почта: mvsokolov@eu.spb.ru Сведения о финансировании: National Research University Higher School of Economics, ВШЭ Текст о финансировании 1: I am grateful to Alexander Alekseev, Maxim Bouev, Liudmila Galliulina, Alexander Nesterov, Ekaterina Polyakova, and Evgeny Zalyubovsky for helpful comments that greatly improved the paper. This work was supported by HSE University (Basic Research Program).

PY - 2024/10/1

Y1 - 2024/10/1

N2 - This paper introduces a class of investment project's profitability metrics that includes the net present value (NPV) criterion (which labels a project as weakly profitable if its NPV is nonnegative), internal rate of return (IRR), profitability index (PI), payback period (PP), and discounted payback period (DPP) as special cases. We develop an axiomatic characterization of this class, as well as of the mentioned conventional metrics within the class. The proposed approach offers several key contributions. First, it provides a unified interpretation of profitability metrics as indicators of a project's financial stability across various economic scenarios. Second, it reveals that, except for the NPV criterion, a profitability metric is inherently undefined for some projects. In particular, this implies that any extension of IRR to the space of all projects does not meet a set of reasonable conditions. A similar conclusion is valid for the other mentioned conventional metrics. For each of these metrics, we offer a characterization of the pairs of comparable projects and identify the largest set of projects to which the metric can be unequivocally extended. Third, our study identifies conditions under which the application of one metric is superior to others, helping to guide decision-makers in selecting the most appropriate metric for specific investment contexts. © 2024 Elsevier B.V.

AB - This paper introduces a class of investment project's profitability metrics that includes the net present value (NPV) criterion (which labels a project as weakly profitable if its NPV is nonnegative), internal rate of return (IRR), profitability index (PI), payback period (PP), and discounted payback period (DPP) as special cases. We develop an axiomatic characterization of this class, as well as of the mentioned conventional metrics within the class. The proposed approach offers several key contributions. First, it provides a unified interpretation of profitability metrics as indicators of a project's financial stability across various economic scenarios. Second, it reveals that, except for the NPV criterion, a profitability metric is inherently undefined for some projects. In particular, this implies that any extension of IRR to the space of all projects does not meet a set of reasonable conditions. A similar conclusion is valid for the other mentioned conventional metrics. For each of these metrics, we offer a characterization of the pairs of comparable projects and identify the largest set of projects to which the metric can be unequivocally extended. Third, our study identifies conditions under which the application of one metric is superior to others, helping to guide decision-makers in selecting the most appropriate metric for specific investment contexts. © 2024 Elsevier B.V.

KW - (Discounted) Payback period

KW - Capital budgeting

KW - Internal rate of return

KW - Net present value criterion

KW - Profitability index

UR - https://www.mendeley.com/catalogue/148e9748-4a65-36c9-830b-86763465c01c/

U2 - 10.1016/j.jmateco.2024.102992

DO - 10.1016/j.jmateco.2024.102992

M3 - статья

VL - 114

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -