Comparing different real option valuation approaches as applied to a copper mine

One of the main challenges in valuing an option where the underlying is an infrequently traded ‘real’ asset, such as a mining project, is the complexity and potential bias inherent in determining the volatility of its operating cash flows. This, of course, is not the case for frequently traded assets (e.g. shares of a mining company), where the volatility, i.e. the annualised standard deviation of daily price changes, captures the effects of both market risks (i.e. commodity prices and exchange rates) and private/project risks (i.e. reserves and grades, metal recoveries, variability of capital and recurrent costs etc.). In addition, most real option analysis papers feature simplified and to some degree unrealistic examples. This is particularly unhelpful where alternative investment options inevitably lead to different levels and timing of significant depreciation and amortisation charges against revenue, often the main or even the only source of cash flows, and to different tax liabilities, resulting in very different cash flow patterns and therefore project values. These issues have contributed to the low level of adoption of real option analysis by the mining industry. This paper makes empirical use of a realistic discounted cash flow model of a copper mine to compare the results obtained by various real option analysis approaches. It concludes that both the positive bias inherent in using an estimate of volatility aggregating the effect of all sources of uncertainty and, to a degree, modelling complexity can be circumvented by using real option analysis approaches, such as decision trees or Monte Carlo simulation, that rely on the probability distributions of individual uncertain variables rather than aggregated forms of cash flow volatility, producing more accurate and generally more conservative real option values.