UDC 519.862.6
Authors
V. B. Gisin
Professor, Dept. of data analysis, decision making and financial technologies,
Financial University under the Government of the Russian Federation, Moscow, Russia
E. S. Volkova
PhD, Associate Professor, Dept. of data analysis, decision making and financial technologies,
Financial University under the Government of the Russian Federation, Moscow, Russia
Abstract
The paper considers the net present value (NPV) and the internal rate of return (IRR) of cash flows with fuzzy payments. A characteristic feature of the present paper is the study of cash flows with interactive fuzzy payments. The interaction is modeled using triangular norms. A concept of IRR is introduced using the extension principle. Explicit formulas are given for calculating IRR. It is shown that if the cash flow is typical and the payments are presented by triangular fuzzy numbers then IRR is a fuzzy number. Conditions are studied providing that the uncertainty of NPV does not increase with an increase in the number of payments and depends only on the uncertainty of the payments (in this case we say that the addition of fuzzy payments is quasi-crisp). It is shown that considering fuzzy payments it is natural to assume that the corresponding fuzzy numbers are shaped by distribution functions. For common families of triangular norms and distribution functions, the combinations of parameters are described that provide quasi-crisp addition of fuzzy payments. The concept of the price of information is introduced in the case, where the decision to undertake a project is made on the basis of NPV. The higher is the price of information, the more reasonable is refining the input data. In this paper, the concept of the price of information is applied to decision making with respect to fuzzy cash flows. It can be used in other problems with fuzzy input data and fuzzy financial results.
Keywords
Investment project, Fuzzy cash flow, Triangular norm, Measure of uncertainty, Price of information
