A new decision-making method for the assessment of investments and companies based on fuzzy mid-points

Abstract

[eng] In decision-making, we face a situation where we have to decide whether it is worth performing an investment or not, based on a multitude of variables. The Net Present Value (NPV) indicates the profit that our investment will produce over a series of time periods within a fixed time horizon. Its computation begins with certain data or variables from which we can obtain a cash-flow for each time period under consideration. Some of these variables involved in the aforementioned computation can take values within an interval of possibilities whose end-points are their pessimistic forecast (PF) and their optimistic one (OF). From these values, the expert subjectively generates two distinct cash-flow projections: the Optimistic Cash Flow (OCF) and the Pessimistic Cash Flow (PCF). The Net Present Value (NPV) is then computed using a cash-flow obtained as the arithmetic mean of both projections. However, there are infinite possible intermediate cash-flows that could be considere to obtain the NPV. Given the lack of an analytical reason to select the arithmetic mean cash-flow as the most appropriate one, and considering that such a choice could be derived from an appropriate aggregation function, in this paper we introduce a new decision-making method for the assessment of investments and companies. This method is based on the use of fuzzy mid-points and aggregation functions. Moreover, the new methodology incorporates a penalization, fixed following an analytical procedure and thus reducing subjectivity, for the elapsed time and for the discrepancy between OCF and PCF in order to generate the NPV. Finally, all methodologies are tested by applying them to a paradigmatic example where real data is considered and the NPV of a five-year hotel assessment is computed. Here, it is illustrated that the proposed methodologies could be appropriate for the assessment of investments and companies, particularly when operating under uncertainty.