Characterizing the Real Roots for P, A, and F with Applications to Environmental Remediation and Home Buying Problems

Abstract

Historically, work on multiple roots for the internal rate of return (PW = 0) equation focuses on tests for the root's uniqueness and interpreting the meaningfulness of computed roots. Instead, this article starts with problems that consist of P, A, and F cash flows. Then for all possible values of these cash flows, this article develops the boundary conditions for no, single, and multiple real roots of either positive or negative sign. The results of characterizing these roots are applied to two examples as a foundation for conclusions about those multiple root problems and hypotheses about other problems with multiple roots. The first example is an important class of resource development projects that may require significant expenditures for environmental remediation at the conclusion of operation. The second example of buying versus leasing a home is often used to demonstrate the value of economic analysis to students.