A Quasi-IRR for a Project Without IRR

Abstract

Discounted cash flows methods such as Net Present Value and Internal Rate of Return are often used interchangeably or even together for assessing value creation in industrial and engineering projects. Notwithstanding its difficulties of applicability and reliability, the internal rate of return (IRR) is commonly used in real-life applications. Among other problems, a project may have no real-valued IRR, a circumstance that may occur in projects which require shutting costs or imply an initial positive cash flow such as a down payment made by a client. This paper supplies a genuine IRR for a project which has no IRR. This seemingly paradoxical result is achieved by making use of a new approach to rate of return (Magni, 2010), whereby any project is associated with a unique return function which maps aggregate capitals into rates of return. Each rate of return is a weighted average of one-period (internal) rates of return, so it is called Average Internal Rate of Return (AIRR). We introduce a twin project which has a unique IRR and the same NPV as the original project's, and which is obtained through an appropriate minimization of the distance between the original project's cash flow stream and the twin project's. Given that the latter's IRR lies on the original project's return function, it represents an AIRR of the original project. And while it is not the IRR of the project, the measure presented is 'almost' the IRR of the project, so it is actually the "quasi-IRR" of the project.

The Internal Rate of Return Approach and the AIRR Paradigm: A Refutation and a Corroboration

“…If a project has no IRR, a quasi-IRR can nonetheless be computed, which is quasi an IRR of the project in the sense that it is the IRR of the (twin) project which most closely resembles the original project. Such a quasi-IRR represents an AIRR of the original project, associated with the IRR-implied capital of the twin project (see Pressacco et al 2011).…”