Calculation of the profitability of fuzzy investment cash flows using the reliable economic rate of return measure

Today, due to the breadth, diversity and multiplicity of investment projects, decision makers and investors are faced with the issue of choosing the most profitable project. The economic rate of return (ERR) index is one of the proper indices that has been presented to determine the profitability of the projects. However, the ERR index has important shortcomings that have led to serious limitations in its use. In this regard, this paper introduces a new measure called the reliable economic rate of return (RERR), which has originated from ERR measure, but it has resolved the drawbacks of ERR index. On the other hand, this paper proposes a new solution by considering the values of the cash flow in terms of fuzzy numbers. After calculating the fuzzy economic rate of return, the profitability potentiality degree of the investment projects can be determined as well as their reliability based on the net present value (NPV) method.

  This paper proves that if we equate the initial cash flow of investment projects with the sum of the negative values ​​of the relevant cash flow stream, then the RERR value would be greater than ‘-1’. In this regard, this paper proposes a solution to modify the initial and final values ​​of the investment cash flow stream, merely without changing middle values. Thereby, the NPV of the modified cash flow does not change. On the other hand, it is sometimes difficult to estimate the values of cash flows as a crisp number, which may lead to a wrong decision in accepting or rejecting projects. For this purpose, this paper considers the values of cash flow stream as fuzzy numbers and describes a solution for calculating the fuzzy RERR using the α-cut method and the RERR index. The proposed solution is compatible with the NPV method and also has fewer calculations than the other methods. This paper also proposes a method that calculates the profitability potentiality degree of projects and provides more comprehensive information to the decision makers by examining the intervals obtained from cutting the fuzzy values of the projects and presenting a new and reliable solution.

Using the @RISK software, it was found that the estimation of fuzzy return rate using RERR index and α-cut method is very close to the simulation result. It confirms the appropriate accuracy of the proposed solution. Also, the results obtained from the software in determining the profitability of projects indicated that the proposed solution is more accurate than the methods of ‘comparison of the expected intervals’ and ‘strict exceedance possibility’. It is also fully compatible with the NPV method.

In this research the market rate is assumed constant, while, in practice it can vary over the periods. Defining the market rate as an inconstant parameter, using the robust optimization approach and investigating the subject of this paper under other uncertainty environments are future study suggestions to both researchers and practitioners.

One of the most important applications of this study is in risky projects wherein estimating the values of cash flow stream as a crisp number is difficult. The results of this paper help decision makers in reducing risk and determining the project profitability. It is worth mentioning that the solution proposed in this paper can be used for all projects with any cash flow stream value.

 Failure to make the correct decision regarding the acceptance or rejection of the projects could have major negative consequences for the companies, organizations and even society. This paper helps decision makers, investors and organizations to determine the projects profitability that could benefit organizations and society.

This paper proposes the RERR measure as a profitability index such with several favorable properties: (ⅰ) it exists and is unique, (ⅱ) it is NPV-consistent in accepting/rejecting decisions, (ⅲ) it provides values greater than ‘-1’, (ⅳ) it takes into account all of the project’s outflows which may be regarded by some practitioners as an appropriate indicator of the overall investment. Furthermore, this paper proposes an appropriate method for calculating the fuzzy RERR and a new method for determining the profitability potentiality degree of the investment projects based on the NPV method.