We consider the problem of multiple mathematical solutions of the IRR equation, which is a mathematical base for numerous applications in the financial industry, such as investment performance measurement, all yields related valuations for bonds, spot interest rates, forward rates, and lots of other applications. Previously, this problem has been studied mostly from the mathematical perspective, and no satisfactory resolution has been found. Our research takes into account both mathematical and business aspects of the problem. We discovered and convincingly proved that the largest root of the IRR equation, which accordingly produces the largest rate of return, is the most adequate solution of the IRR equation, both from mathematical and business perspectives, which should be used in practical computations of rate of return based on the IRR equation. Based on our study, we introduced the “Rule of the largest root” for choosing the right solution of the IRR equation, which effectively solves the problem of multiple roots of the IRR equation. Solving this long-standing problem, which is of very high practical and theoretical importance in finance, opens lots of new opportunities for developing new robust financial instruments and advanced analytical methods.

Yuri Shestopaloff, Ph.D., SegmentSoft Inc.
Alexander Shestopaloff, University of Toronto