Real Option Valuation of Mineral Exploration/Mining Projects using Decision Trees - Differentiating Market Risk from Private Risk

摘要

Only a few complex real options can be valued using closed-form equations, such as the Black and Scholes formula, because these algorithms are restrictive and prevent the construction of practical project evaluation models. Although a binomial lattice method paired with the 'risk-neutral probability' provides an easier and flexible modelling of exploration and mining projects, it has limitations when projects are complex, long-lived and influenced by the interplay of various market and private uncertainties. In order to overcome these limitations, modern decision tree software using dynamic programming capability can be used for real option valuations. This is a powerful computational tool in which the impact of various sources of uncertainties can be differentiated, so that the optimal decision path can be explicitly displayed visually. There has been significant academic controversy surrounding whether different real option (RO) valuation methods would lead to different real option values (ROV). This paper, using a realistic copper mining example, demonstrates that as long as the same degree of subjectivity and consistency are used in different real option valuation methods, they yield the same result. This conclusion is valid irrespective of whether the cash flow volatility generated by various sources of uncertainties is handled in an aggregated or in an explicit and differentiated manner. This paper compares two choices for an investor either to 'buy now and develop' a project or to enter into a 'two-year option to purchase' after the proponents have developed it. It also shows how significantly different net after-tax operating cash flows may be generated by these different choices on the same underlying asset represented by the project. This is due to the difference in the amount and timing of the relevant capital investments affecting the depreciation and amortisation charges and as a consequence, the income tax paid.