Capital budgeting techniques using discounted fuzzy versus probabilistic cash flows

Risk analysis involves the development of the probability distribution for the measure of effectiveness. The risk associated with an investment alternative is generally either given as the possibility of an unfavorable value of the measure of effectiveness or measured by the variance of the measure of effectiveness. In an uncertain economic decision environment, an expert's knowledge about discounting cash flows consists of a lot of vagueness instead of randomness. Cash amounts and interest rates are usually estimated by using educated guesses based on expected values or other statistical techniques to obtain them. Fuzzy numbers can capture the difficulties in estimating these parameters. In this paper, the formulas for the analyses of fuzzy present value, fuzzy equivalent uniform annual value, fuzzy future value, fuzzy benefit-cost ratio, and fuzzy payback period are developed and given some numeric examples. Then the examined cash flows are expanded to geometric and trigonometric cash flows and using these cash flows fuzzy present value, fuzzy future value, and fuzzy annual value formulas are developed for both discrete compounding and continuous compounding.