Valuation of projects withminimum 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.