A numerical study for a mining project using real options valuation under commodity price uncertainty

Commodity price is an important factor for mining companies, as price volatility is a key parameter for mining project evaluation and investment decision making. The conventional discounted cash flow (DCF) methods are broadly used for mining project valuations, however, based on commodity price uncertainty and operational flexibilities, it is difficult and often inappropriate to determine mining project values through traditional DCF methods alone. In order to more accurately evaluate the economic viability of a mining project, the commodity price and its inherent volatility should be modelled appropriately and incorporated into the evaluation process. As a consequence, researchers and practitioners continue to develop and introduce real options valuation (ROV) methods for mining project evaluations under commodity price uncertainty, incorporating continuous time stochastic models. Although the concept of ROV arose a few decades ago, most of the models that have been developed to-date are generally limited to theoretical research and academia and consequently, the application of ROV methods remains poorly understood and often not used in mining project valuations. Analytical and numerical solutions derived through the application of ROV methods are rarely found in practice due to the complexity associated with solving the partial differential equations (PDE), which are dependent on several conditions and parameters. As a consequence, it may not generally be applicable to evaluate mining projects under all project-specific circumstances. Therefore, the greatest challenge to ROV modelling is in finding numerically explicit project values. This paper contributes towards the further development of known theoretical work and enhances an approach to approximating explicit numerical project values. Based on this work, it is possible to formulate more complex PDEs under additional uncertainties attached to the project and to approximate its numerical value or value ranges. To ensure the project is profitable and to reduce commodity price uncertainty, delta hedging and futures contracts have been used as options for deriving the PDE. Moreover, a new parameter for taxes has been incorporated within the PDE. This new PDE has been utilised to approximate the numerical values of a mining project considering a hypothetical gold mine as a case study. The explicit finite difference method (FDM) and MatLab software have been used and implemented to solve this PDE and to determine the numerical project values considering the available options associated with a mining project. In addition, commodity price volatility has been determined from historical data, and has again revealed price volatility as having a significant impact on mining project values.