Abstract
Multiple-interest-rate analysis is employed to derive a new, dual equation for NPV. The analytical device of a quantum of value enables the new equation to demonstrate that the fourth IRR pitfall concerning non-flat yield curves is irrelevant. The equation supplies an alternative reason to the IRR pitfalls for preferring NPV to IRR as an investment criterion, and suggests that textbooks citing the IRR pitfalls as reasons to prefer NPV require revision.
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Notes
Hazen (2003) extends Lohmann(1988) to produce a similar equation to (5.5a). The IRR is employed to extract from a project’s cash flows another set of cash fl ows labeled the investment stream. The NPV of the investment stream is calculated using the cost of capital as discount rate and labeled the net investment (NI), giving (in current notation) the equation similar to (5.5a): NPV = NI.m1. The decision criterion advocated by Hazen is that the original project is judged profitable if NI is profitable. Hazen demonstrates that this procedure works no matter which project IRR is employed to produce the NI. Each IRR has an associated net investment, and any ‘IRR-NI’ pair produces invest/ not-invest decisions for single projects consistent with decisions made using the NPV criterion. If the Hazen equation is divided throughout by the size of the investment (I0) then equation (5.5a) implies NI/I0 is the product of the unorthodox mark-ups from the cost of capital to the IRRs. Hazen does not make this connection and stays with the notion of using each IRR singly (compared with using all interest rates together). The Hazen methodology has the inevitable drawback of any single interest rate methodology, namely, when comparing mutually exclusive projects, its ranking can still conflict with the NPV ranking. Another drawback is that while making explicit use of complex IRRs the methodology considers only their real parts, not their imaginary parts. Finally, the methodology fails to give meaning to the complex rates.
At no point in the a ? nalysis is it suggested that a dual equation for NPV is actually calculated. Th e calculation of a conventional equation like (5.1) suffices. The point of the analysis is to deconstruct NPV and give fresh insight into its relationship with IRR.
The first pitfall is that, by itself, a value for IRR does not convey whether a project involves lending or borrowing. This pitfall is not substantive. First, nobody takes an investment decision on the basis of a single statistic; any business manager requests supplaiementary information. Second, supplementary information is always available because a value for IRR is not produced out of the air; the cash flows I0) and ci are necessary to calculate IRR, and therefore the nature of the project must always be apparent
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© 2014 Michael J. Osborne
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Osborne, M. (2014). Multiple-Interest-Rate Analysis Demonstrates Why the IRR Pitfalls Are Irrelevant and Provides a Better Reason to Prefer NPV as an Investment Criterion. In: Multiple Interest Rate Analysis: Theory and Applications. Palgrave Pivot, London. https://doi.org/10.1057/9781137372772_5
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DOI: https://doi.org/10.1057/9781137372772_5
Publisher Name: Palgrave Pivot, London
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