Valuing Multi-Zone Deposits with Modern Asset Pricing (Real Options) Techniques


Michael Samis

Conventional project valuation techniques, such as discounted cash flow (DCF) method, are more frequently being criticised for the manner in which they consider the interacting effects of uncertainty and project structure (including management flexibility) on project value. Modern asset pricing (MAP; often called “real options valuation” when applied to the analysis of flexibility) is a more general valuation framework that corrects many of the shortcomings of common valuation methods. Previous mining applications of MAP have tended to treat the ore deposit as a homogenous entity. While useful for demonstration purposes, this is inadequate for practical application in industry. This paper presents a MAP valuation example that allows for the heterogeneous nature of an ore deposit. It shows that deposit structure may increase the complexity of the mine planner’s decision so that results of a standard DCF analysis, or a simple MAP analysis that ignores the details of deposit structure, are misleading. In the example, a management is considering the development of an adjacent low-grade zone while mining operations in a high-grade zone are ongoing. If the low-grade zone is developed before high-grade reserves are exhausted, the proposed development will include both low-grade zone development and a capacity expansion to handle additional low-grade reserve production. If development of these reserves is delayed until the high-grade reserves are depleted, then the low-grade reserves can be developed without a capacity expansion. A typical DCF analysis would reduce the management’s decision problem to three alternatives: 1) continue mining only in the highgrade reserves, 2) immediately develop the low-grade reserves and expand capacity, and 3) delay low-grade zone development until the high-grade reserves are exhausted. The model presented here allows the management to reconsider the development and capacity expansion decision on a discrete half-year basis. It delineates price regions, for given levels of high-grade zone reserves, in which it is optimal to develop the low-grade zone, defer low-grade zone development and abandon the mine irrevocably. The model presented here extends the ability of mine planners to describe actual project structure while using the MAP valuation framework that is already noted for its capacity to combine project uncertainty and risk insights with a dynamic project description.
Keywords: valuation, discounted cash flow, DCF, modern asset pricing, MAP, MAP valuation, MAP analysis, DCF analysis, low-grade zone, high-grade zone