A Companion For NPV: The Generalized Relative Rate of Return

Abstract

We show how to determine a unique rate, for a particular cash flow stream, that is used only whenever a project demands outside resources to compound the rates of the existing term structure precisely at those times. The net present value of the cash flow stream when discounted with the thus-modified term structure becomes zero. We therefore determine a vector of rates that belongs to the induced space of internal rates of return for that cash flow stream. The rate is applicable under discrete stochastic interest rate representations and provides maximum loan rates that may be contracted only when needed thus keeping a project financially autonomous. (Any investments required may be fully repaid by the project's own cash outflows).

Notes

See also Hartman and Schafrick (2004).

For a historical development of MIRR, see Biondi (2006).

This is a direct consequence of the relationship between NPV and b_n (the future value) and b_n a strictly decreasing function of ϕ.