Assessing the Probabilistic Fuzzy Net Present Value for a Capital Investment Choice Using Fuzzy Arithmetic

Abstract

This work applies fuzzy theory to capital budgeting and combines with a probability method in developing the fuzzy net present value algorithms for evaluating the investment projects. The estimation of cash flows in fuzzy numbers catches the vague characteristics of estimation, and the forecast of probabilities of economic prospects describes the randomness of outcomes. Using α-cuts and the interval of confidence of fuzzy numbers, this study defines the fuzzy net present value (FNPV), expected FNPV, and deviation, and derives their membership functions. The fuzzy performance index (FPI), the fuzzy expected value to standard deviation, is them proposed to be the decision indicator. After a ranking procedure, the higher-FPT project is a better choice. The situations of unequal durations and unequal costs of capital for mutually exclusive projects, which are seldom discussed in previous studies, are considered by estimating the fuzzy equivalent annuity (FEA) and fuzzy equivalent annuity to infinity (FEAI). The ranking of their FPIs is also derived. The proposed step-by-step operational algorithms of the membership functions hopefully conduce to more convenient practical implementation. Finally, a numerical example demonstrates the feasibility of the proposed algorithms.