The Relationship between NPV and Irr in the Presence of a Non-Flat Yield Curve

A new relationship is derived for net present value (NPV) per dollar invested that is composed entirely of interest rates. The rates are mark-ups to the cost of capital, each mark-up being an internal rate of return (IRR) embedded in the complex plane. The result has been shown before, but only in the context of a flat yield curve. In this paper, the derivation is done in the context of a non-flat yield curve. Despite the extra complications introduced by the structure in the yield curve, the analysis results in a simple and elegant equation. The interpretation of the equation supports the preference for NPV held by academics because it is shown to contain all relevant information. The traditional IRR, often preferred by practitioners, is shown to be but one component of the NPV and therefore an incomplete measure of return. The general concept of IRR is still important, however, because the core equation shows that all the IRRs are the building blocks, in fact the only building blocks, of NPV per dollar. The new result is also shown to provide yet another expression for the modified internal rate of return