Academic journal article Economic Inquiry

Valuing Petroleum Reserves Using Current Net Price

Academic journal article Economic Inquiry

Valuing Petroleum Reserves Using Current Net Price

Article excerpt


The Hotelling Valuation Principle (HVP) states that, when valuing any depleting mineral reserve, one can simply multiply the current net price (price less unit extraction cost) associated with those reserves by the quantity of reserves:

(1) [V.sub.S] = [[Lambda].sub.S][R.sub.S],

where [[Lambda].sub.S] = ([p.sub.S] - [c.sub.S]) is the current (time s) net price and [R.sub.S] is current recoverable reserves in place (Miller and Upton [1985a]). The derivation combines Discounted Cash Flow (DCF) analysis with Hotelling's [1931] result that in equilibrium the net price of a non-renewable resource must rise at the rate of interest. With net cash flows being inflated and discounted at the same rate, the result is intuitive, and its simplicity has drawn the attention of mineral appraisers and national income accounting agencies.(1) The U.S. Department of Commerce, for instance, uses equation (1) as one method of valuing the stock and depletion of the nation's mineral assets (Carson [1994]).

Miller and Upton [1985a, 24] empirically test the principle against oil and gas reserve values imputed from firm balance sheets, and conclude that it "provides not only reasonably good descriptions of the structure of actual market values of a sample of U.S. petroleum-producing companies, but substantially better descriptions than the publicly available alternative appraisals based on much the same underlying raw data." They claim that the abstractions of the HVP - constant marginal cost, perfect information and perfect competition - do not appear to invalidate the empirical performance, and so Miller and Upton propose that equation (1) remains theoretically intact even when these abstractions are relaxed.

Further investigation, however, has found the HVP to severely overvalue oil and gas reserves. For example, Watkins [1992] finds that the formula overvalues oil and gas reserve transactions by an average of 85%.(2) Indeed, in Miller and Upton's original work, the imputed reserve values are less than the HVP values in 81 of 94 valuations in the first data set, and in 95 of 98 in a second data set, in many cases by 50% or more.(3) Several empirical studies have found that the coefficient on [[Lambda].sub.S][R.sub.S] in equation (1) is in the order of one half. This tendency of the HVP to overstate the value of petroleum reserves is recognized by users of the principle such as Bartelmus et al. [1994], who nevertheless continue to rely on it for reserve valuation.

Several economists have attempted to explain the overvaluation. Magliolo [1986] investigates data sources and tax effects. Cairns and Davis [1998] and Davis and Moore [1998] show that, for the case of hard-rock mining, capacity constraints on production produce a coefficient on [[Lambda].sub.S][R.sub.S] that is less than one. Others have instead rejected not only the HVP as a valuation tool, but also the entire Hotelling theory underlying the principle. For example, Adelman [1993] and Watkins [1992] argue that (i) for practical purposes there is no binding resource stock constraint for oil and gas, as explicitly assumed by Hotelling [1931], and (ii) oil and gas net price data do not reveal Hotelling's r% rule. McDonald [1994] adds that regulation of well spacing and extraction rates is another important facet of oil production that is not modeled by Hotelling, and that this could be a cause of the empirical failure of the principle.

Still others propose that oil reserves cannot be valued accurately using a discounted cash flow framework. Rather, the analyst must also incorporate an "option value" which arises whenever producers can adjust production through time in response to realizations of stochastic events such as price fluctuations (Brennan and Schwartz [1985]; Paddock, Siegel and Smith [1988]; and Smit [1997]). This position is valid, but it does not explain the empirical failures of equation (1). …

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