NPV, IRR, PI, PP, and DPP: a unified view

TL;DR

This paper presents a unified axiomatic framework for common investment profitability metrics, revealing their limitations and conditions for optimal use across different economic scenarios.

Contribution

It introduces a unified interpretation of profitability metrics and characterizes their applicability and limitations for various investment projects.

Findings

Provides a unified interpretation of profitability metrics.

Shows that IRR and others are undefined for some projects.

Identifies conditions for choosing the most appropriate metric.

Abstract

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.