A New Approach to Studying Net Present Value and the Internal Rate of Return of Engineering Projects under Uncertainty with Three-Dimensional Graphs

Cost-benefit analysis (CBA) is very useful when appraising engineering projects and examining their long-term financial and social sustainability. However, the inherent uncertainty in the estimation of completion time, final costs, and the realization of benefits often act as an impediment to its application. Since the emergence of fuzzy set theory, there have been significant developments in uncertainty modelling in project evaluation and investment analysis, primarily in the area of formulating a fuzzy version of CBA. In this context, in studying the key indicators of CBA, whereas fuzzy net present value (fNPV) has been investigated quite extensively, there are significant issues in the calculation of fuzzy internal rate of return (fIRR) that have not been addressed. Hence, this paper presents a new conceptual model for studying and calculating fNPV and fIRR. Three-dimensional fNPV and fIRR graphs are introduced as a means of visualizing uncertainty. A new approach is presented for the precise calculation of fIRR. To facilitate practical application, a computerization process is also presented. Additionally, the proposed methodology is exemplified in a sample motorway project whereby its advantages over traditional stochastic uncertainty modelling techniques such as Monte Carlo analysis are discussed. Overall, it is concluded that the new approach is very promising for modelling uncertainty during project evaluation for both project managers and project stakeholders.