Sensitivity, Risk, And Probabilistic Analyses

INTRODUCTION In the preceding chapters we have discussed the various elements of mineral economic analysis, their interrelationships, and the most accepted and advanced techniques by which these elements are manipulated to provide the decision maker quantitative measurements for judging alternate investment opportunities. Regardless of how carefully the economic evaluation is made, and how comprehensive the study of economic parameters has been, uncertainty still remains a significant factor in the outcome of the analysis. The investor or money manager is acutely aware of the uncertainty factor. Many of the economic parameters are functions of economic forecasts and value estimates that can- not be known with any degree of certainty. The postulated DCF-ROR is based upon certain estimates representing "best guess" values, and a single point parameter DCF-ROR analysis represents a combination of "best guesses." The wise decision maker looks at such an analysis and asks the "what if" questions. What if the production cost is 10% higher than the estimate? What if there is an overrun in construction costs? What if the mineral price falls lower than expected? What will be the effect of a higher royalty rate? Many more such questions may arise in trying to assess the total risk involved in funding a mineral project. Prior to the advent of the computer it was difficult to answer all such anticipated questions because of the many laborious calculations involved. Now, with the aid of the computer, most of these questions can be answered by the analyst at the same time the original computations are made by using the process of sensitivity analysis. Sensitivity analysis shows the effect of critical parameter changes upon the DCF-ROR or other profitability measure. When probability of occurrence can be associated with the various parameter value levels, sensitivity analysis becomes probabilistic analysis, and the risk factor can be quantitized in terms of total probability. SENSITIVITY ANALYSIS The determination of the sensitivity of the profitability index (usually the DCF-ROR) to changes in the various economic parameters, taking them one at a time, is called sensitivity analysis. The analysis may be performed for any number of parameters involved in the DCF-ROR computation. Generally, in mineral evaluations the most sensitive and most tested parameters are: the metal or mineral price, the operating cost, the annual production grade, and the initial capital invest-