Solving the Paradox of Multiple IRR\'s in Engineering Economic Problems by Choosing an Optimal -cut

Until now single values of IRR are traditionally used to estimate the time value of cash flows. Since uncertainty exists in estimating cost data, the resulting decision may not be reliable. The most commonly cited drawbacks to using the internal rate of return in evaluatton of deterministic cash flow streams is the possibility of multiple conflicting internal rates of return. In this paper we present a fuzzy methodology for solving problems of multiple IRR in any type of streams. Utilization of fuzzy cash flow allows modeling of uncertainty in estimating cost data. The approach of -cut is to decrease the range of the final fuzzy set by increasing the degree of membership. For each fuzzy IRR in an optimum -cut, and an obtained present value of each stream, it is possible to decide on acceptance or rejection of a project according to the type of each stream (borrowing or investing). The upper bound of -cut is the worst case for borrowing and the lower bound of -cut is the worst case for investing. It is shown that both the internal rate of return and the present value are important in decision making and by analyzing the sensitivity of these values relative to the -cut variation, one can see the behavior of the project and choose a narrower fuzzy range.