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What is the Correct Risk-Adjusted Discount Rate (radr) to Use?

 

The discount rate for mineral asset valuation performs the same function as with the valuation of any asset – it accounts for the time value of money and project risk.  As such, one would think that standard financial theory, such as the Capital Asset Pricing Model (CAPM), could be used to determine the appropriate discount rate for a given discounted cash flow approach.  However, it is increasingly difficult to answer this discount rate question.  For example, gold is often thought to be a “zero beta” asset, and as such, according to the CAPM, producing gold projects with proven reserves should be discounted at the after tax risk-free rate.  Yet gold projects with Proven Reserves are typically evaluated at a radr of 14% on a nominal, after-tax basis.  Other producing mineral projects are discounted at up to 19% (Bhappu and Guzman, 1995).  Oil is also a zero beta asset, yet producing proven reserves here, too, are evaluated at a nominal radr of 15% (before tax) (SPEE 1999).  The firms then either increase the radr for reserve uncertainty, or apply the above market factors to the NPV calculated using the aforementioned radrs.

Whenever I see a disconnect between theory and practice, I tend to question the theory rather than those whose careers rest on their decision making.  Finance theory, in my mind, fails to take into account the lack of diversification of many mineral extracting companies, whose managers and employees are exposed to mineral price risk.  Any one bad project outcome can force the company into bankruptcy.  Decision makers in these companies therefore add a significant insurance premium to their discount rate to ensure that they only take on projects that carry substantial chance of success.  Even with this cushion, though, the extractive industries have not managed more than a modest return to their shareholders: mining has returned only 5% to investors between 1973 and 1999 after adjusting for inflation (Humphreys 2000).  Oil has done slightly better, at 8%.  I have a hunch that this may be related to real options analysis, which I will comment on below.

What about discount rates for projects with less certain reserves?  Finance theory says that reserve uncertainty is unsystematic, and so, as long as reserve estimates are unbiased, no addition discounting for this risk should take place.  This is clearly not what happens in practice.  Reserve risk is penalized highly by decision makers in these firms.  The approach, which seems reasonable to me, is to value each class of reserves separately, first calculating the NPV of the class as if the reserves were Proven and producing, and then applying the above market factors specific to each class.  Another way to get the same impact of reserve risk is to use a higher radr for risky or non-producing reserves, with the premium reflecting the undesirable unsystematic risk that is not supposed to concern decision makers.  However, since finance theory gives us no advice as to the appropriate increment to the radr, there is no way of knowing what radr should be used.  I, therefore, prefer to value uncertain reserves (Probable Reserves, and Measured, Indicated, and Inferred Resources) at the typical 14% - 19% nominal radr for proven and producing properties and then adjust the resulting NPV downwards for resource risk using the market factors that we see industry applying.

Since individual mineral assets have finite lives, it is inappropriate to use a capitalization rate as a radr when valuing these assets.  Capitalization rates are rates that convert a perpetual income stream to a present value (or convert an investment into a perpetual income stream). 

 

Typically, if one observes a perpetual firm annually generating $1 million in after tax cash flows to all providers every year, and observes that its market value is, say, $5 million, one would calculate the firm’s capitalization rate as 1/5 = 20%/yr.  If a firm of comparable risk were being valued, and if that firm was expected to generate a perpetual annual stream of $3 million, an NPV analysis would value that firm at 3/.2 = $15 million.  This capitalization rate approach cannot be used for mineral property valuation because of the finite life of reserves; to use a capitalization rate would be to overestimate value, as it presumes that production continues indefinitely.  Mineral firms, on the other hand, who have an intellectual capital that produces perpetual income by identifying new projects to replace old, may be valued using a capitalization rate.