Abstract
Discounted cash flows methods such as Net Present Value and Internal Rate of 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 massively 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.
Highlights
The net present value (NPV) and the internal rate of return (IRR), both conceived in the 1930s (Fisher, 1930; Boulding, 1935), are arguably the most widely used investment criteria in real-life applications (Remer and Nyeto, 1995a, 1995b; Graham and Harvey, 2001)
Magni (2010) introduces a new approach to rate of return, based on the finding that any project is not associated with a rate of return but with a return function, which exists and is unique, and which maps aggregate capitals to rates of return, each of which is called Average Internal Rate of Return (AIRR), being a weighted average of one-period internal rates of return
He shows that any IRR and its associated capital lies on such a return function
Summary
The net present value (NPV) and the internal rate of return (IRR), both conceived in the 1930s (Fisher, 1930; Boulding, 1935), are arguably the most widely used investment criteria in real-life applications (Remer and Nyeto, 1995a, 1995b; Graham and Harvey, 2001). Hazen (2003) supplies an NPV-compatible decision criterion for both real-valued and complex-valued IRRs by associating their real parts with the real parts of the capital streams, so shedding new lights on the multiple-IRR problem. This problem is tackled by Hartman and Schafrick (2004) as well, who partition the graph of the NPV function in loaning part and borrowing part, so singling out the "relevant rate of return". This problem is tackled by Hartman and Schafrick (2004) as well, who partition the graph of the NPV function in loaning part and borrowing part, so singling out the "relevant rate of return". Bosch, Montllor-Serrats and Tarrazon (2007) use payback coefficients to derive a normalized index compatible with the NPV, while Kierulff (2008) endorses the use of the Modified Internal Rate of Return. Osborne (2010) explicitly links all the IRRs (complex and real) to the NPV and Pierru (2010) gives complex rates a significant economic meaning. Percoco and Borgonovo (2012), using sensitivity analysis, focus on the key drivers of value creation and show that IRR and NPV provide different results. Ben-Horin and Kroll (2012) suggest that the multiple-IRR problem has limited relevance in practice
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