Optical Illusion in the Comparison of NPV Profiles of Mutually Exclusive Projects

Abstract

In the comparison of NPV profiles of a pair of mutually exclusive projects, it is customary overlay the two NPV Profiles in a two dimensional graph with NPV on the vertical axis and discount rate horizontal axis. The project NPVs are then compared at each feasible discount rate. By having the horizontal axis represent one discount rate, the two potentially different project discount rates are effectively forced to be equal to each other. This leads to the identification of a crossover discount rate, below which one of the projects dominates, and above which the other project dominates. As a corollary, it is observed that, when the discount rate is below the crossover rate, project ranking in terms of the NPV is inconsistent with ranking in terms of IRR, but consistent with each other when the discount rate is higher than the crossover rate. However, such a characterization hinges crucially on the implicit assumption that the same discount rate is applied to both projects. This characterization falls apart when projects are allowed to have different discount rates. A series of examples is presented which demonstrates that much of the incorrect conjectures about dominance by one project over another can be avoided simply by explicitly incorporating the missing independent variables, a separate discount rate for each project, in the comparative analysis of the two NPV profiles.

Keywords: Capital Budgeting, NPV Profile, IRR, Corporate Finance

JEL Classification: G11, G31, G30