An interval-valued extension of the internal rate of return

Annals of Finance. 2025. Vol. 21. No. 4. P. 415–433.

Mikhail V. Sokolov, Polyakova E.

This paper introduces an interval-valued extension of the internal rate of return (IRR). This extension is motivated by the inability to assign to an investment project a particular rate of return satisfying a set of reasonable axioms. We demonstrate that there exists an essentially unique extension consistent with a natural set of axioms. Notably, in the most significant case, the extension maps a project to an interval with the lower and upper bounds defined by the minimal and maximal roots of the IRR polynomial, respectively. This result effectively reconciles several existing generalizations of the IRR, all of which yield values within this interval. The interval-valued IRR preserves the essential properties of the conventional IRR, thereby enhancing the ranking of investment projects by their rate of return. Furthermore, it serves as a robust extension of the IRR for measuring portfolio performance and making accept/reject investment decisions.

Keywords: internal rate of return, cash flow, investment project, portfolio performance, interval-valued metric

Publication based on the results of: Economic and mathematical analysis of markets, games, and decision-making (2025)