Valuing the Stock and Flow of Mineral and Renewable Assets in National Income Accounting
This project will advance the field of environmental asset valuation so that additions to and depletion of natural resources may be accurately included in national economic accounts. The project specifically focuses on the valuation of mineral and energy resources. The broad objectives of the project are to assess and critique the existing methods of valuing commercial mineral resources and to improve upon and supplement these methods by producing valuation methodologies that take into account price, stock, and development timing uncertainty. The new valuation methods will be applied to both proved/produced and unproved/nonproduced commercial mineral and energy resources.
The methods to be employed consist of modifications to existing valuation formulations, such as the Hotelling Valuation Principle, and the application of a new valuation technique known as multinomial option pricing of real assets. The valuation tools that are developed will be both more accurate and cover a more comprehensive list of assets than previous valuations.
|Colorado School of Mines|
|October 1, 1995 - September 30, 1997|
Cost to Funding Agency:
|Project Status Reports:|
The purpose of this project is to advance methods of environmental asset valuation in order to accurately include additions to, and depletion of, mineral resources in national economic satellite accounts. Current income accounting does not debit the accounts for depletion of natural assets and is thus thought to misrepresent the wealth of the nation. This project focuses specifically on the valuation of mineral and energy resources, which are among the first natural resource assets to be included in the United States Department of Commerce’s "Green Accounting" efforts. The broad objectives of the project are to assess and critique the existing methods of valuing the stock and depletion of commercial mineral resources, and to improve upon and supplement these methods by producing valuation methodologies that take into account price, stock, and development timing uncertainty. The goal of the project is to produce valuation methods that are not only accurate and theoretically sound, but are parsimonious and require a relatively limited amount of data such that they can be feasibly included in national income accounting exercises at a reasonable cost.
Because mineral assets do not transact on open markets, their value or "price" must be estimated via financial and economic theory. To date, valuation has been performed only on proven
reserves via various discounted cash flow methods. These methods are flawed, being based on rather simplistic formulations and yielding wide ranges of values (see Table 1 below). The approach that we take in this project is to modify these valuation formulations to correct for their weaknesses. This includes reformulating the financial theorems used to generate the valuation formulas such that they produce values that more closely match the few observed market transaction prices.
To date, we have had some success in developing improved valuation formulas for valuing the stock and depletion of proven assets where the quantity of mineral stock is known with relative certainty. These formulas remain parsimonious, requiring little more than current prices and extraction costs, yet are in close agreement with selected empirical observations of value based on market transactions. The formulas we have developed all have the basic form:
Table 1. Asset Account for the United States of America, 1987, Showing Bounds on Current
Estimates of Mineral Resource Stock and Depletion, Billions of Dollars
(Source: Bureau of Economic Analysis)
valuation parameters that we provide to the valuer. This looks remarkably like the net price formula V _ (P-C)R that is so popular in green accounting exercises, and yet through the a and K terms we incorporate many of the subtleties of mineral asset pricing left out of the net price result.
Valuing unproven reserves is more difficult, as not only do we need to estimate the unit price of the reserve, but the quantity of the mineral reserve is also uncertain. The first step has been to characterize the nature of this reserve uncertainty. Based on data for proven reserves, we find that there seems to be both a time trend in estimated reserve quantity as well as jumps, both positive and negative, as new information about the
reserve is discovered. Having characterized the stochastic nature of reserve changes, we are now proceeding to use this information in a multinomial option pricing framework, where the unproven reserve is valued as an option on proven reserves.
The new valuation methods can be applied to both proven/produced and unproven/nonproduced commercial mineral and energy resources. Time permitting, we will provide examples of these calculations. Our results will enable green accounting efforts to move forward, especially with regard to including an estimate of the stock and depletion of unproven mineral assets in satellite accounts.
Graham A. Davis and David J. Moore, "Valuing Mineral Stocks When Capacity Constrains Production," September, 1997, 11 pp.
Robert Cairns and Graham A. Davis, "On Using Current Information to Value Hard-rock Mineral Properties," June, 1997, 17 pp.
Robert Cairns and Graham A. Davis, "Valuing Petroleum Reserves using Current Net Price," September, 1997, 44 pp.
Imad A. Elhaj, "An Option-Based Procedure for Valuing Unproved Natural Resource Reserves," no date, 41 pp.