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Non-Linear Cash-Flow Functions in Mining Project Valuations

Neil Winkelmann
Tuesday, January 27, 2015
First presented: 
Vancouver Mining Seminar II
Non-linear cash-flow functions are common in mining projects. Examples include those caused by grade-recovery functions, dynamic cut-off policies, sliding scale royalties, and excess profits taxes. They are problematic for valuations as simply using averages or expected values typically leads to estimation errors. Characterization of the non-linear cash-flows may be achieved by the use of Monte-Carlo simulation. Simulation is straightforward in theory, but extremely difficult to do well in practice. Stochastic models of the independent variables (price, grades, costs, recoveries, etc.) are difficult to construct and correlations between these variables are hard to estimate. Results of simulations are often either mistrusted or ascribed more significance or precision than is warranted.
This presentation illustrates the principles of using simulation for valuing non-linear cash-flows with built-in Excel functionality, but with a focus on the limitations of the simulation approach. The example presented is a hypothetical gold mine subjected to severe excess profits tax. A single stochastic variable, gold price, is used to demonstrate the principles.
SRK North America