On the Fuzzy Internal Rate of Return

Abstract

In a capital investment we usually deal with projects taking a long time - as a rule some years - for its realization. In such cases, a description of uncertainty within a framework of traditional probability methods usually is impossible due to the absence of objective information about the probabilities of future events. This is the reason for the growing interest in the application of interval and fuzzy methods in budgeting, which has been observed for the last two decades. There are many financial parameters proposed in literature for the project quality assessment, but the two primary among them — net present value, NPV, and internal rate of return, IRR - are necessarily used in a financial analysis. Whereas the problem of NPV fuzzy estimation is now well studied and many authors have contributed to its solution, obtaining of fuzzy IRR seems to be rather an open problem. This problem is a consequence of inherent properties of fuzzy and interval mathematics, but it seems unnatural to have crisp IRR in a fuzzy environment when all other financial parameters are fuzzy. In this paper, the problem of IRR estimation in fuzzy setting is considered in the framework of more general problem of fuzzy equations solving. Finally, the concept of restricted fuzzy IRR as the solution of the corresponding non-linear fuzzy equation is proposed and analyzed.