Valuation of projects with minimum revenue guarantees: A Gaussian copula–based simulation approach

This technical note presents a numerical simulation technique to perform valuations of infrastructure projects with minimum revenue guarantees (MRG). It is assumed that the project cash flows—in the absence of the MRG—can be described in a probabilistic fashion by means of a very general multivariate distribution function. Then, the Gaussian copula (a numerical algorithm to generate vectors according to a prespecified probabilistic characterization) is used in combination with the MRG condition to generate a set of plausible cash flow vectors. These vectors form the basis of a Monte Carlo simulation that offers two important advantages: it is easy to implement and it makes no restrictive assumptions regarding the evolution of the cash flows over time. Thus, one can estimate the distribution of a broad set of metrics (net present value, internal rate of return, payback periods, etc.). Additionally, the method does not have any of the typical limitations of real options–based approaches, namely, cash flows that follow a Brownian motion or some specific diffusion process or whose volatility needs to be constant. The usefulness of the proposed approach is demonstrated with a simple example.