The internal rate of return (IRR) and the corresponding criterion has well-known difficulties of applicability and reliability. Among other problems, a project may have no real-valued IRR. The latter problem has been recently solved by Magni (2010a), who shows that, for any project, a unique return function exists which maps aggregate capitals into rates of return, each of which is a weighted average of one-period (internal) rates of return, so it is called Average Internal Rate of Return (AIRR). Given the extent to which the IRR notion is rooted in real-life applications as well as in academia, this paper aims to supply a genuine IRR even for a project which has no IRR. This seemingly paradoxical result is achieved by introducing 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 genuinely expresses a rate of return (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.
