Replica Analysis for Maximization of Net Present Value

In this paper, we use replica analysis to determine the investment strategy that can maximize the net present value for portfolios containing multiple development projects. Replica analysis was developed in statistical mechanical informatics and econophysics to evaluate disordered systems, and here we use it to formulate the maximization of the net present value as an optimization problem under budget and investment concentration constraints. Furthermore, we confirm that a common approach from operations research underestimates the true maximal net present value as the maximal expected net present value by comparing our results with the maximal expected net present value as derived in operations research. Moreover, it is shown that the conventional method for estimating the net present value does not consider variance in the cash flow.