Reserve asset values and the Hotelling Valuation Principle: further evidence.

• Author: Adelman, M.A.

1. Introduction

   An economics classic [14] was restated by Dasgupta and Heal [6]: the net price of a mineral must rise at the rate of discount. But econometric analysis failed to verify this, according to Miller and Upton [15].

   The Hotelling Principle is often couched in terms of flow equilibria in output markets. The Rule can also be derived [27] as a condition of stock equilibrium in asset markets. Miller and Upton followed the asset framework in defining the Hotelling Rule, a formulation they called the Hotelling Valuation Principle (HVP): the market value of a mineral in the ground is equal to its current net price. This follows from the fact that if the net price rose at the rate of interest, the present value of the net price would be the same whenever the resource is extracted, given asset value maximization.

   The HVP expresses the Hotelling Rule in a form which lends itself easily to empirical testing. Miller and Upton compared a sample of companies' estimated oil and gas reserve values directly with net prices, and concluded that they were indeed equal. But estimates they made later [16] showed the in-situ value as only about half the net price; they ascribed this to unsatisfactory data.

   Later papers by Adelman [1] and Watkins [30] rejected the HVP for reasons both of theory and data. The issue is important because long run changes in the prices of minerals are important to the world economy and to many governments. For example, Boskin et al. [4] estimated the value of the U.S. government's mineral holdings at nearly 20 times what they would be worth if the 1989 price were assumed constant, and revenues discounted at the conventional industry rate [1].

   We show the Hotelling Valuation Principle to be a special case, which can be tested for, of a more general formula. The estimated in-situ values then give useful insights into expected oil and gas prices.

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2. The Data

   The data consist of amounts paid for 34 developed oil and gas reserves in Alberta over the period February 1989 to March 1991. Only six observations were for single properties; three were for three to four properties. The remaining 25 observations were for corporate reserve assets (12) or for transactions relating to 20 or more properties. An absence of price and cost data for individual reservoirs precludes analysis on a property basis. But since the bulk of the transactions are for multiple properties, reliance on average cost and price data is not distortive.

   [ILLUSTRATION OMITTED]

   Miller and Upton inferred in-situ reserve values from stock market values, after adjusting for liabilities and the value of non-reserve properties. They would avowedly have preferred to use the kind of data we employ here [15, 15]. The transaction values relate solely to the purchase of reserves and thus are uncontaminated by other property values.

3. Analysis of the Reserve Transaction Data

   The data in Table I immediately suggest regressing the transaction values on the respective volumes of oil and gas reserves to estimate unit reserve prices. What is the appropriate specification of the function to be estimated?

   Conventional cash-flow capital budgeting methods for valuing mineral properties suggest a valuation expression ([V.sub.T]) of the form:

   [V.sub.T] = [integral of] ([p.sub.ot] - [c.sub.ot])[f.sub.ot][e.sup.-it] dt between limits [n.sub.o] and t=0 + [integral of] ([p.sub.gt] - [c.sub.gt])[f.sub.gt][e.sup.-it] dt between limits [n.sub.g] and t=0 (1)

   where

   [p.sub.ot], [c.sub.ot] are prices and costs of oil, respectively, times t

   [p.sub.gt], [c.sub.gt] are prices and costs of gas, respectively, times t

   [f.sub.ot], [f.sub.gt] are quantities of oil and gas production, respectively, times t

   t is (continuous) time

   [n.sub.o] is remaining reservoir life for oil

   [n.sub.g] is remaining reservoir life for gas.

   Costs represent all costs, i.e., extraction, future development (if any), income taxes, royalties, etc. If future development costs were anticipated, unit costs could be quite lumpy. All RHS variables are of course expected values.

   The linear separation inherent in (1) implies no interaction between oil and gas production and costs. This would certainly hold if the transaction related to an oil reservoir and a non-associated gas reservoir.

   However, it is more likely that the transactions relate to oil reservoirs with some associated gas, or to natural gas reserves containing some liquids. If so, there could be some interaction between oil and gas production, individual costs, and joint costs. This would not matter if such relationships were linear, as they would be if production gas-oil ratios (GORs) were constant. But if there were strong non-linear relations between, say, associated gas production and oil production, then a "reduced form" of expression (1) might thwart a linear regression of asset values on reserve volumes and prevent interpretation of the reserve coefficients in a straightforward way.

   It is doubtful that any non-linearities among the oil and gas production and cost data would be sufficient to violate the essentially additive nature of the conventional reserves evaluation procedure: estimate the net present value of expected flows of oil production plus the net present value of expected natural gas production from each property under review.

   Thus the basic regression expression can be written as:

   [V.sub.T] = [b.sub.o] + [b.sub.1][R.sub.o] + [b.sub.2][R.sub.g] (2)

   where

   [R.sub.o] = [integral of] [f.sub.ot]dt between limits [n.sub.o] and 0

   and

   [R.sub.g] = [integral of] [f.sub.gt]dt between limits [n.sub.g] and 0

   If reserves were zero, [V.sub.T] would be zero and the intercept term should be constrained as zero. Then the regression equation becomes

   [V.sub.T] = [b.sub.1][R.sub.0] + [b.sub.2][R.sub.g]. (3)

   Note that the expression (2) can still be useful since the statistical significance of the intercept can indicate the degree of "cleanliness" of the data.

4. Regression Results

   When the constant term was suppressed, the data in Table I yielded:

   [Mathematical Expression Omitted].

   These results suggest an in-situ value for oil reserves of $5.37/barrel and $0.44/Mcf for natural gas reserves over a two year period (February 1989 to March 1991).

   The degree of (linear) fit is reasonable, both coefficients are highly significant and there is no evidence of autocorrelation. The Goldfeld-Quandt test (and visual inspection of...