Average Internal Rate of Return for Risky Projects

Abstract

The average internal rate of return (AIRR), introduced by Magni (2010), fixes many deficiencies associated with the traditional internal rate of return (IRR), including apparent inconsistency with net present value (NPV). The AIRR approach breaks down project NPV into scale (the capital invested) and economic efficiency (the AIRR), and maintains NPV consistency for accept/reject decisions.

Here we examine extensions of the AIRR to risky capital asset projects, a domain where the IRR appears intractable. We show that one can uniquely break down a risky NPV into a risk-sensitive project scale and a risk-sensitive extended AIRR, representing risky project efficiency, so that consistency with NPV for accept/reject decisions is maintained in the certainty-equivalent sense, in direct analogy to the deterministic case. This novel breakdown gives managerial insight by helping determine a risky project’s locus of uncertainty, be it the project scale, or economic efficiency, or both. In this way, risky features of competing projects can be explored in more detail, leading to insights substantiating the NPV ranking. We also show that under risk neutrality, the expected AIRR is equal to the AIRR of the expected cash flow, a property that notoriously fails for the stochastic IRR.

Keywords: Decision analysis, risk, finance, investment criteria, capital budgeting; utility-Preference, theory, rate of return, ROI

JEL Classification: G31, C60, G30, M41, C02