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# PEH:Valuation of Oil and Gas Reserves

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Chapter 19 – Valuation of Oil and Gas Reserves

D. R. Long, Long Consultants, Inc.

Pgs. 1517-1589

ISBN 978-1-55563-120-8
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This chapter describes the use of a reserves estimate to prepare an economic evaluation and perhaps then place a value on the reserves. This chapter often refers to a document titled Perspectives on the Fair Market Value of Oil and Gas Interests[1] published by the Society of Petroleum Evaluation Engineers (SPEE) in the spring of 2002. In this chapter, that document is referred to as the SPEE FMV document. To value reserves, the nature of the ownership must be considered. Reserves ownership is usually derived from contractual agreements that specify the obligations of the parties to those agreements for the payment of costs and the sharing of revenues. These agreements often include specific commitment obligations such as the drilling of wells. A common arrangement for such contracts is the oil and gas lease. Another common contractual structure is the production-sharing arrangement. Appendix A, which describes common types of oil and gas property interests, is from the SPEE FMV document.[1]

Sec. 19.8 discusses fair market value (FMV). While an FMV estimate is often not the main reason an economic evaluation is prepared, it is useful to keep in mind that it may be used for such a purpose. Like the estimation of reserves, the preparation of an economic evaluation has subjective elements. If the evaluation, inclusive of the reserves estimates and production schedules, is prepared in a manner anticipating an FMV estimate as the goal, the objective evaluator will be inclined to use appropriate judgment. One must be cautious, however, and be mindful of the applicable reserves definition. For example, a reserves definition that might be used for property acquisition might not meet the reporting requirements of the U.S. Securities and Exchange Commission (SEC).

The use of the word "valuation" in the title of this chapter is a carryover from the first handbook.[2] J.J. Arps wrote the valuation chapter, and reference to his name in this chapter is generally the same as a reference to the chapter he authored in that handbook. Arps’ use of the term valuation seemed to have a relatively narrow scope. Valuation referred to the processes for the determination of FMV and embraced what he called an "analytical appraisal" method, which involved present worth discounting to address the time value of money. There are numerous references and comparative statements in this chapter about these methods because, despite a few variations that have occurred in the interim, enough is the same that presentation of the historical perspective is useful. Arps also included a section on "different concepts of valuation." Those methods have been discarded.

The analytical valuation methods embraced by Arps[2] are still in use, but today’s business environment is quite different. Arps’ chapter was for use only in the U.S. domestic market, but the marketplace has expanded vastly. Interest and discount rates are considerably higher, and there have been significant changes in the U.S. federal tax code. U.S. federal tax rates are lower now than in 1962, but other aspects of the law also have changed.

In 1962, the primary buyers for oil and gas properties were major oil and gas companies. Sellers were successful wildcatters or mall oil and gas companies called independents. Today, the independents are the buyers and the majors are the sellers. There are many more independents today, and the major oil companies are undergoing consolidation. The marketplace for oil and gas properties involves a much greater number of transactions and is more competitive.

The properties tend to be different from those familiar to Arps in 1962. Today, gas reserves are much more likely to be the major source of projected future income. Ownership is more fractionated. In addition, discussion is much more likely to be about the rate of decline than about how many more years the rate will remain constant. Production rates are much more likely to be governed by the capacity of wells to produce than by artificial restraint imposed by regulation. Constant price projections are unlikely because there are futures markets for both oil and gas. The value offered for properties is more likely to include a significant component for reserves involving higher degrees of uncertainty.

One of the most significant changes in the oil and gas reserves evaluations is the use of the computer. In 1962, most cash flow projections were tabulated by hand on large ledger sheets. After plotting historical production curves by hand, forecasting was done by field to reduce the computational load. Modern petroleum economic evaluation software has eased laborious procedures tremendously. Forecasts are often done on a well-by-well basis, and sensitivity studies are much easier. The most valuable attributes of petroleum economic software are the scheduling tools and the summarization capabilities.

Despite the changes since 1962, some things remain the same. The offering price of the buyer is still very sensitive to the cost of money. The buyer’s intent is to derive some measure of profit. No matter what form that profit takes in the buyer’s figuring of the offering price, it must be of a sufficient magnitude to cover risks inherent in the industry. Another factor that remains the same is that the U.S. still has a federal income tax.

To facilitate meaningful discussion, some basic definitions need to be understood.

• Oil and Gas Reserves Study—A study of geologic and other information for estimating oil and gas reserves within the scope of a specified set of definitions. The definitions will usually include reserves classed as proved and will often categorize unproved reserves. Unproved reserves classes include probable and possible reserves. If reserves are estimated to support an economic evaluation, the reserves estimator will generate or describe associated schedules of future production. For a description of the proved, probable, and possible reserves classification system, see the chapter on estimating oil and gas reserves in this section of the Handbook .
• Oil and Gas Reserves Economic Evaluation—A report, often inclusive of an oil and gas reserves study and usually prepared by or under the direction of a petroleum engineer, that presents schedules of future net cash flow and discounted net cash flow based on the reserves and production schedules from an oil and gas reserves study. The reserves classes of the reserves study can be expected to flow through to the summary levels of the economic evaluation because such classifications are a tool for the assessment of uncertainty.
• Valuation—The process of determining value, whether it be for estimating FMV or for another purpose and whether it be derived with discounted cash flow projection methods or with other methods.

In this chapter, the term "reserves report" refers, sometimes collectively and at other times individually, to both a reserves study and an economic evaluation of reserves. The meaning should be clear from the context of the discussion. Each of the processes has specific obligations for objectivity and disclosure regarding methods. SPEE, an organization sometimes referred to as a sister organization to SPE but with no official relation, recently developed a set of Recommended Evaluation Practices (REPs). [3] These REPs and other information about SPEE, which is a strong promoter of ethical standards, are available at www.spee.org. SPEE also publishes Guidelines for the Application of Petroleum Reserves Definitions. [4] Sec. 19.8 includes excerpts from the SPEE FMV document, [1] which similarly presumes the preparation of an oil and gas reserves economic evaluation as described here.

In the following sections, the term valuation is not limited to use with procedures purporting to represent, or necessarily closely tied to, FMV. For example, the U.S. SEC stipulates the use of a 10% discount rate for certain financial reporting purposes. This must be considered a valuation process, but the result is primarily for comparative purposes and is not represented as FMV. A calculation to determine the collateral value of a property or properties (the loan value) would be considered a valuation but would logically be less than FMV.

The term "appraisal" is not used beyond this introduction. Appraisal was a term used by Arps. [2] It is most commonly used today with real estate. It has specific connotations that may not be consistent with methods used in the valuation of oil and gas reserves. Real estate appraisals are commonly made with comparative sales principles. The principle valuation techniques described in this chapter are based on anticipations of future revenue and conceptually bear little resemblance to the common real estate appraisal processes. The term appraisal is avoided in connection with the valuation of oil and gas reserves. There is a place in oil and gas valuation work for the comparative sale method.

A common application of valuation methods is to determine value for taxation. Jurisdictions will usually specify procedures somewhat differently than those contained in this chapter. Those differences often involve the way the cash flow projections are prepared. For example, it is sometimes specified that the valuation procedure ignore anticipated taxes to be levied by the taxing authority requiring the valuation. The taxing authority might specify a discount rate or method for arriving at the discount rate to be used in determining value. The evaluator should be knowledgeable about local practices.

The valuation procedures discussed in this chapter are classed properly as methods for the valuation of underlying assets, as opposed to methods for the valuation of a company. The value of a company is some combination of a perception of how well the organization’s management will manage its assets for growth (or otherwise) and its debts and other liabilities. Individual property assets are, however, often more valuable when combined than when viewed separately.

In recognition of the international makeup of today’s SPE, it is appropriate to write from an exclusively international perspective. Oil and gas companies around the world with roots in capitalistic societies operate on the basis of an incentive for profit from operation and a share of either the volume of oil and gas sold or some benefit from that sale. In the U.S., fractional interests are usually of a nature described in Appendix A. In other parts of the world, it is more common for the operator of the property to receive revenue on the basis of a more complex sharing arrangement made with a country’s national government or other governmental faction. This chapter does not delve into the complexities of these sharing arrangements. The valuation circumstances described are generally specific to properties located in the U.S. An understanding of the principles should allow portability for universal application.

## The Need for Economic Evaluations

Valuations of oil and gas properties are needed for many of the same reasons appraisals are needed for homes, cars, jewelry, or any other assets. Lenders require some type of valuation when assets are used as collateral for a loan. Taxes are often assessed on the basis of property value. Property values have a bearing on rates for insurance policies and settlements after loss, damage, or foreclosure. Economic evaluations are seldom made simply for curiosity. In most cases, they are needed for some business reason. Here is a listing of reasons economic evaluations are needed in the oil and gas industry:

• Project Evaluation—Proposals to drill wells, set platforms, or otherwise provide for the facilities required to produce or enhance the production of oil and gas require economic justification before implementation.
• Prioritize Opportunities—When presented with a set of investment opportunities, all of which pass certain minimum criteria and assume some restraint on available capital, discussion and theorization are never exhausted during the selection process. Economic analysis is part of the process.
• Acquisition and Divestiture—Buyers and sellers of properties need valuations to prepare for acquisition and divestiture transactions. The buyer’s need for an evaluation is obvious. Sellers with a compulsion to seek the highest compensation usually prepare an economic evaluation to gauge the adequacy of an offer.
• Financing—Loans by banks or other institutions are directly collateralized by a company’s property portfolio or a specified group of properties.
• Taxation—Governmental entities from the Internal Revenue Service (IRS) to local taxing authorities such as school districts want money, and the taxes are often determined on the basis of the value of the reserves.
• Securities Laws—In the U.S., the SEC requires the reporting of reserves information, which mainly comes from oil and gas reserves and economic evaluations.
• Legal Settlements—Some of the most dramatic arguments over property values occur in settlement proceedings involving foreclosure. Foreclosure is often associated with a condemnation case wherein lands are rendered unusable for oil and gas development because of confiscation for a public use that covers a wide area, such as a new water reservoir or recreational lake. Alternatively, a company going through bankruptcy proceedings might convince the court that creditors would be better served under a plan in which the company retained the interest. At one time, there were many court cases involving take-or-pay provisions of contracts between producers and pipeline companies.
• Allocation of Values—Value allocation can be part of legal settlements when issues are fundamentally divisive, but allocation is often an element when parties are trying to work together to promote common interests. Unitization is the process in which groups of small properties are united into a larger unit with interest holders of the smaller properties trading their interests for a smaller fraction of the new unit. Sometimes the process is the reverse and involves the distribution of interests. Either way, economic valuation is usually part of the process.

## Evaluation Methods

### Deterministic Cash Flow

The primary method of evaluation discussed in this chapter is the deterministic cash flow method. Projected schedules of quantities of reserves from a deterministic reserves study projected in selected future time frames (usually calendar years) are displayed in the results, but computations are often made monthly. Schedules of future prices and costs are projected for the same time frames. Volumes are multiplied by prices, and costs are deducted to estimate future net revenue (FNR). Present worth calculations to factor in the time value of money are applied to the projected cash flow stream, and the results are reported. A table presenting a suite of present worth values over a range of discount rates is usually included. Individual projections are usually made by well or ownership entity. Each projection is classed in a reserves category (i.e., proved, probable, or possible) and more specific subclasses are common. The results are summarized at the reserves category level.

This valuation procedure is based on the methods used to estimate reserves in the chapter on the estimation of oil and gas reserves in this section of the Handbook. Within the limits of the reserves category definitions, the parameters used in the estimation of reserves are generally average values. In the case of proved reserves, the results of the calculation are perceived to be best estimates. In the case of probable and possible reserves categories, the best estimate perception is inherently qualified with the perspective of "if they exist at all." Probable and possible reserves quantities have not been adjusted for risk.

### Decision Trees

Decision tree analysis is a very useful tool to value estimated reserves deterministically. The result is a calculation of expected value or a range of discrete values. Sec. 19.6 illustrates this principle simply. The chapter on risk analysis and decision making in the Emerging and Peripheral Technologies section of this Handbook is a must-read chapter in connection with the application of the principles discussed here. Even if the methods are not physically used, the perspectives offered by both decision tree and Monte Carlo simulation must be considered. The chapter on general economics in the General Engineering section of this Handbook also presents a perspective on the use of decision trees for analysis.

### Sensitivity Analysis

In this procedure, variables in a deterministic analysis are modified and results are recalculated to check the effect on the economic calculation. The results might be presented on a chart, or they might be expressed in a manner such as a one-dollar reduction in the projected gas prices reduces the FNR by 20%. The use of this type of procedure with decision trees has been a traditional evaluation tool with deterministic reserves valuation procedures.

### Monte Carlo Simulation

Monte Carlo simulation is a method in which a frequency distribution representing what is perceived to be the full range of possible values for parameters is substituted for the single average values, instead of the use of single-value averages or estimates for parameters, as in a deterministic calculation. The frequency distribution for a parameter, such as porosity, might be shaped in a number of ways. Bell shapes, indicating a normal distribution, or triangular shapes are common. The value at the peak of the distribution’s shape is the most likely value (the mode), and the higher values to the right and lower values to the left are defined as less likely. See the chapter on risk analysis and decision making in the Emerging and Peripheral Technologies section and the chapter on general economics in the General Engineering section of this Handbook.

In the case of oil and gas reserves economic evaluation, all the parameters used in the estimation of reserves quantities (such as porosity and water saturation) and the additional variables introduced in the economics of the evaluation process (such as prices, costs, and sometimes timing) are often represented as probability distributions. If a parameter, such as oil price, is locked into a contract, there might be no reason to assign a distribution to that parameter unless the model is intended to consider the default of a contracting party. The simulator is then allowed to run through what are often thousands of iterations. At each iteration, the simulator selects a value for each parameter from the frequency descriptions and computes and stores results. Because of the way the distributions are defined and the way the simulator takes its samples, the values for the individual parameters from the distributions that are closer to the mode value are selected more often. Occasionally, but not often, the simulator will select values at the extremes of the distributions. The method of sampling the described distributions is a math problem of its own.

A Monte Carlo simulator is not a numerical reservoir simulator. It is not a model of the depletion process of a reservoir. In numerical reservoir simulators, the reservoir is characterized in discrete segments and those segments are assigned values of porosity, permeability, fluid saturation, and pressure. The rocks and fluid properties are characterized, and the model is run most often with the intent of mathematically replicating the physical behavior of pressure and fluid flow within the formation during reservoir depletion or enhanced-recovery process. Input to a Monte Carlo simulation will require distributions for expected production rates and recovery factors. Those distributions might be determined with the aid of a reservoir simulator, but it is not expected (today) that the software be linked or integrated.

All the Monte Carlo generated results of reserves and cash flow projection would be incomprehensible; therefore, summary results, selected by the modeler, are reported. Output distributions often include only reserves quantities in total, FNR, and present worth values at a few discount rates. The results represent calculated distributions of expectations for reserves, FNR, and present worth (discounted FNR) at one or more discount rates. Depending on how the model is constructed, it may or may not be possible to distinguish between reserves and revenues derived from areas of the reservoir categorized (deterministically) as proved, probable, or possible.

Any (deterministic) model built in a spreadsheet can be converted to a Monte Carlo model by replacing some of the input values with probability distributions. Conversely, all the errors and pitfalls that might cause a deterministic model to lead to a false indication of value will similarly affect a Monte Carlo simulation. The construction of a Monte Carlo simulation model requires all the work and care that goes into a deterministic model and more.

### Real Options

As applied to the evaluation of oil and gas reserves and associated opportunities, real options analysis is a new concept. In this Handbook, the use of option theory for the valuation of real options is mentioned in the chapter on risk analysis and decision making in the Emerging and Peripheral Technologies section and in the chapter on petroleum economics in the General Engineering section. Several SPE technical papers have addressed the subject in recent years. [5][6][7][8][9][10][11] Financial analysts use option-pricing models (OPMs) to value puts and calls on stocks. These stock options to sell or purchase at a specified price, at or before some specified time, always have some value of zero or greater. They are never negative because the option may be allowed to expire with no additional consequence to the holder. After the option is obtained, there is no further expectation of the possibility of financial loss. The value of the financial option stems from the opportunity to exercise the option immediately, plus the speculative potential that it can be held and exercised in the future for a greater financial gain. OPMs for valuing financial options consider the current stock price, the strike or exercise price associated with the particular option, the risk-free interest rate, the time to maturity of the option, and the variance in the stock price.

Real options represent investment opportunities outside the stock market that have some resemblance to stock options. The option to buy production from a lease in a future specified month at a specified price is essentially identical to a stock option. Most real options are not so ideal in nature and are often extremely complicated. Real options usually are not structured like the previous example, in which someone has contracted to purchase production. Real options are perhaps better thought of in oil and gas industry terms as anticipated opportunities and/or alternatives. Real options are more like the decisions we make in our everyday lives.

In most circumstances, real options will not have a specific exercise date, and many real options involve liability such that their value has the potential to be negative at a future date. The time frame associated with real options may be very long. Real option valuation (ROV) involves the application of the methods derived for the valuation of stock options to the valuation of real options. Real options that are perceived to be of value often revolve around management’s perceived future opportunity to make an intelligent decision on the basis of the circumstances existing when the decision is made (i.e., an optional course in a future oil and gas property management decision).

In an attempt to acquire an oil and gas property, whether producing or not, many attach an additional value to being the operator. Sometimes that additional value has to do with cash flow projections and the opportunity to receive income from partners as overhead compensation [Council of Petroleum Accountants Socs. (COPAS) charges]. Perhaps more often, the additional value attached to being operator has to do with a greater degree of control. The operator is able to exercise options, and that flexibility has value. The operator has more real options than the nonoperator does.

In attempting an acquisition in a competitive market, incremental value frequently is added in recognition that the acquirer will have specific opportunities, in the future, to deviate from and optimize the exploitation plan on the basis of anticipated future events and new information or technology that will become available. It is unlikely that either the deterministic reserves evaluator or the Monte Carlo modeler has made an exhaustive accounting for all possible opportunities. The details behind all possible future opportunities cannot be fully anticipated. ROV is a tool that might be useful for quantifying such potential incremental value.

When considering an acquisition, future potential opportunities sometimes will not be of any specific nature. A common incentive behind oil and gas properties acquisition is the experience that with ownership there is additional value often attributed to serendipity. Perhaps real option analysis could be of assistance in quantifying such value. The use of option theory to quantify oil and gas industry investment opportunities is not a widely accepted method at this time.

### Rules of Thumb, Yardsticks, and Comparative Sales

A number of "unit value processes" have been referred to as evaluation methods, but they are more properly described as screening tools. As a comparative measure between transactions, the price paid per barrel of reserves is often computed. Because most transactions involve reserves of both oil and gas in inconsistent proportions, a value per equivalent barrel is often computed, which necessitates the application of a relationship of equivalency between a thousand cubic feet of gas and a barrel of oil. The value of a thousand cubic feet of gas can easily vary over a broad range (more than 20%, often much more) only on the basis of quality issues, exclusive of transportation costs related to location or cost of production or processing to make marketable. Oil has its own issues, of which quality is only one, but the equivalency issue is only the beginning of the problem with trying to use unit value methods as a means of valuation. Such methods make no allowance for the timing or cost of recovery, there is no provision for transportation or other cost to market the production, and there is no recognition of what capital might be required to accomplish the recovery.

There is nothing wrong with making these comparisons. They are of interest, and sometimes the questions raised expose errors or facts that have not been, but should be, disclosed. If there is a comparative method that helps you become comfortable with the result of a valuation, use it. If it exposes a weakness in the valuation, fix the valuation.

Sometimes there are attempts to value oil and gas interests on a multiple of current income with the current income rate expressed in dollars per month or dollars per year. The value approximation might be expressed as 3 years or 36 months at current. The number of potential flaws in this type of valuation are so numerous and varied that an attempt to initiate a list seems futile. There are circumstances that require a determination of value in which the time and effort required is not warranted for even a minimum effort to generate a cash flow projection. Given a general knowledge of the character of the reserves and knowledge of valuation results of other properties of somewhat similar character, the multiple of current income approach may be the best of bad alternatives. In such circumstances, the income rate multiple might be selected on the basis of analogy with the valuations of other properties thought to be similar in character but for which a more rigorous valuation procedure has been appropriate.

Another valuation method is the use of the comparative sale. This is often the only practical tool and is particularly useful. Unlike the real estate market, it is usually impossible to locate a suitable basis for the comparison. The comparative sale method relies on the use of analogy to infer value. It is easy for the technique to be flawed, unless the valuation is done with complete understanding and with great care. For instance, it is common for the purchaser of an interest to attach an element of value that is not known to the observer. This attachment of added value occurs with the greatest frequency when small interests are traded but is not uncommon with transactions of any size. SPEE’s FMV document labels these added values "strategic" values. An industrial user, for example, might purchase a fractional interest in a property near one of its facilities to provide an emergency fuel source in the event of a cutoff of its regular supply; therefore, it might pay a premium price for that interest. Given that the industrial user’s needs are satisfied, someone valuing other interests in the same or nearby property could be mistaken in using that transaction as an analog. The SPEE FMV document suggests that the best use of comparative sale methods for oil and gas interests is in the valuation of nonproducing properties, but it points out that even then the process is more complicated than in the real estate business. It is not intended to imply that the use of the comparative sale method in the real estate market is easy, it is just much more difficult (perhaps less certain is a better perspective) when the value of minerals comes into play. Garb[12] discusses a variety of valuation methods, and his article is recommended reading.

## The Nature of Reserves Reports and Discounted Cash Flow Schedules

While seldom listed as the preferred method by agencies requiring valuations (such as the U.S. IRS), the most practical valuation method for oil and gas properties is usually based on the expectations of future income. Reserves estimates and projections of future rates of production are used with expectations for oil and gas prices, items of burden, and costs to compute estimates, usually tabulated by calendar year, of future cash flow. Table 19.1 presents the presentation form of the results of that calculation. Sometimes the form for the presentation is in greater detail, which results in the information being stacked on the page with the lines representing the calendar year period repeated two or three times. For valuation purposes, the projected cash flow stream is then analyzed in a variety of manners. Table 19.1 represents a projection for a single producing property in which the only production stream is oil. In most cases, a valuation is based on a summary level cash flow in which projected economics are derived from the expectation for the sale of produced oil, gas, and other substances such as sulfur. Table 19.1 illustrates certain elements to set the stage for later discussion.

Table 19.1 contains the results of a reserves and cash flow projection. Col. 1 indicates the time intervals associated with the individual lines. The intervals sometimes are indicated by their ending month (with the beginning of each interval being the end of the previous one), but the times are indicated by calendar year in Table 19.1. In Table 19.1, the beginning of the first interval is as of 1 September 2001. Col. 2 presents the full well stream (commonly referred to as the gross or 8/8) production quantity schedule from the reserves report. (It is not production; it is a forecast of production. Terminology and proper expression in the economic evaluation business is a common problem. [13]) Col. 3 gives the production quantity schedules netted to the interest being evaluated by multiplying the gross quantities by the fractional revenue interest. The interest fractions will be displayed, unless the page is a summary. The revenue (income) interest is commonly less than the working (expense) interest because of royalty burdens or other sharing arrangements. Col. 4 presents the projected oil price schedules, which is projected to escalate in this example. Col. 5 is the product of the net oil quantity times the oil price. Col. 6 represents items of deduction for local taxes, and Col. 7 shows deductions for operation costs. Col. 8 presents capital cost (none is scheduled in this example), which is another deduction item. The values in Col. 9 represent the time interval’s summary of revenue less items of deduction and the result of the net cash flow projection, which is computed by subtracting Cols. 6, 7, and 8 from Col. 5. Various items of identification and information are also presented. This identification information should include identification of the well or forecast entity and the reserves category. The present worth suite is also displayed. In Table 19.1, it is in the bottom right corner and is presented with discount rates from zero to 100%. Cols. 11 through 13 are included to facilitate the following discussion of present worth discounting. They usually are not displayed in standard presentations.

Table 19.1 presents values and items that represent the projected cash flow for an existing well producing proved developed reserves. If the cost to drill and equip the well ($800M) were included in the capital costs as an initial outlay before production started, the discount factor would be 1.0 and the cumulative net revenue and discounted values would be reduced by that amount. Further, the indicated rate of return (ROR) for such an investment can be determined from the present worth table to be between 20 and 30%. Discounting is a widely used method for accounting for the time value of money. It is not a method for evaluating risk. Like the loan shark, cash outlays bearing substantial risk of recoupment require the potential of a high ROR. The high ROR should be the apparent result of an analysis of risk, not the method. The method of risk analysis should be based on the element of risk: production rate, reserves, prices, and cost. Elevating the discount rate reduces the value of income in proportion to its distance into the future. If the reserves are correct but the beginning production rate of a new well is off by 25%, sensitivity analysis should be used to assess the risk or lower the forecasted rate so that the projection represents an expected value. Arbitrary discount rate adjustments should not be made. Despite sharing this view, the SPEE FMV document presents some material involving one elevated discount rate risk analysis method. If you are contesting a valuation instead of establishing value, it might be worth review. The discount rate may be thought of as an inverted interest rate. As the discount rate increases, the value of future income is reduced. At a given discount rate, the farther in the future a dollar of income is expected to be received, the less it is computed to be worth. The present worth profile of Table 19.1 shows that as the discount rate increases, the value of the projected cash flow stream decreases. At a discount rate of zero, the present worth is the same as the total of the projected cash flow. Not all discounting methods are the same. Continuous discounting at a rate of 12% and annual midpoint discounting at a rate of 12% do not yield the same results. The standard discounting method historically used in the oil and gas industry is midpoint discounting with either annual or calendar year time frames, as Table 19.1 illustrates. Today, with software that is more sophisticated and with some change in logic, other discounting methods frequently are used. A logical means of discounting is a method that recognizes when the cash from the sale of oil or gas is received by the owner. From that view, middle-of-the-production-month discounting would be too optimistic and so would end-of-month discounting. A retarded discounting method that recognizes that income is often received a month or two after associated quantities are produced is a possibility but is not a method known to be supported by existing software. A common method of discounting computes an annual discount rate factor with the following equation: ....................(19.1) where Df = discount factor for the specific point in time, r = annual rate of discount expressed as a fraction, and t = time in years from the as of date to the point of reference for discounting. The value assigned to t determines if the discounting is midframe or end of frame and as suggested, could be set beyond the end of the frame. Table 19.1 illustrates calendar year midpoint discounting. Example 19.1 Calculate the 12% discount factor for cash received at midyear in the fifth time interval of the projection in Col. 12 of Table 19.1. Solution. The effective date is 1 September of 2001; therefore, there are 4 months following the "as of" date remaining in 2001 at the effective date. Then there are 3 full years of 12 months each (2002, 2003, and 2004). You must go 6 months into 2005 to get to the middle. t = 4 + 12 + 12 + 12 + 6 = 46 months = 3.833 years. ....................(19.1) The value of Df is expressed in Table 19.1 as 0.6476. Therefore, the discount FNR for the fifth year of the Table 19.1 projection is$150,001 × 0.647636 = $97,146. The sum of the discount factor net revenue for all years is referred to as the present worth of the income stream, but this amount should not be confused with the FMV. It is common to compute present worth values at multiple discount rates and to display the computed results as a set of numbers. The term present worth profile probably stems from the shape of the graph when the present worth values are plotted with the discount rates typically represented on the x-axis. Other equations sometimes are used for discounting. Monthly discounting at the annual rate divided by 12 and envisioning monthly compounding is given by ....................(19.2) If the example is recalculated with Eq. 19.2, the discount factor is It is easy to see how the formula could be modified to discount daily or even hourly. Continuous discounting is accomplished with ....................(19.3) where e is the base of the natural logarithm. Calculating the discount factor with Eq. 19.3, The size of the time intervals used for scheduling is independent of the compounding rate envisioned by the discount factor formula. The only logic behind the use of discount rate formulas other than the annual equation is that the factors are more conservative. There is some obvious logic behind end-of-period discounting or even a retarded discounting, but the logic behind compounded discounting with fractional portions of a year is not clear. Whatever use is made of an economic evaluation of reserves, an assessment of uncertainty is usually required. Acceptable reserves reports always include definitions given partially to indicate the estimator’s opinion of certainty. A guide to the level of certainty generally is expressed by the reserves category in which the reserves quantity falls. Even though the confidence in reserves quantity is theoretically the same between proved reserves classes of proved producing and proved undeveloped, there is unquestionably more uncertainty in the timing for recovery for classes of reserves that are not physically on production. Within a reserves class such as proved, there are well-recognized subclasses like proved developed producing, proved developed nonproducing, and proved undeveloped. Many evaluators maintain additional reserves classes added by individual evaluators for distinction. Reserves categories like "proved developed nonproducing shut-in" and "proved developed nonproducing behind pipe" are common in that they give the user of the report additional insight as to the nature of the reserves. SPEE includes a suggested extended classification system in Guidelines for the Application of Petroleum Reserves Definitions[4]. The list is potentially endless. Regardless of the depth of the classification system, if the reserves estimate is made deterministically, which is still the most common method, the classification system cannot describe the uncertainty fully. An inspection of any of the common (deterministic) reserves definitions will reveal that the reserves class system is not based entirely on level of certainty. Even if certainty is the only criterion, the variations within a class may be significant. Probabilistic reserves estimating procedures, which yield values that quantify uncertainty, can be an important valuation tool. This discussion focuses on results from deterministic procedures. The nature of a reserves report is such that a true assessment of value (whether the report is prepared deterministically or probabilistically) can be made only with a thorough understanding of how the report was prepared and with an understanding of the nature of the properties. This assessment also must include judgment regarding the completeness, quality, and suitability of the availability of data, not only in the preparation of the reserves estimates but in the economic data as well. See Sec. 19.6. Assuming that a suitable production schedule has been provided with the reserves report, the key elements in generating the cash flow projections are discussed in the order in which they are encountered in Table 19.1. ### Report Effective Date The effective date is the time at which the elements that generate the cash flow projection start to be used. This is normally time zero for discounting purposes. The cumulative production (normally shown, although it is not included in the Table 19.1 example) will include the cumulative actual production plus estimated production for a stub period if production up to the effective date was not complete. For example, if the effective date of the report is at the end of the year, but production was available only through October when the production projection was made, the cumulative production will include an estimate of production for the last two months of the year. In preparation of the economic projection, the estimated future production will be cropped at the front end and used only from the effective date forward. A distinction is sometimes made between "effective date" and "as of date." Effective date is the time zero for discounting and scheduling, and as of date is the date through which information was available. For example, given a report prepared for estate tax purposes with the date of death and a time zero of 1 January and with that report being published on 1 July of the same year with all the information available at the time of report preparation, the effective date might be considered 1 January but the as of date is 1 July. There is no standard terminology. ### Interest Position This is intertwined with the subject of Appendix A. Generally, the interest position is defined in terms of an entity’s fractional responsibility for costs, with a separate fraction defining its share of the proceeds from sales. There are sometimes financial, accounting, security, and/or business issues relative to whether an entity owns its fractional share of production or is merely the beneficiary of the revenue from sales. Such issues are ignored here, but Guidelines for the Application of Petroleum Reserves Definitions[4] discusses the subject. The displayed interest positions are generally the ones applicable on the effective date of the report, and subsequent changes that might occur may or may not be displayed. Reversionary interest positions, if they exist, are not likely to be clearly identified in the petroleum economics schedules that resemble Table 19.1. ### Prices The prices used in generating the cash flows are often dictated by the report’s intended user. The SEC sets forth its own requirements. Lending institutions generally have pricing guidelines as a part of their collateral valuation procedure. If the report is being prepared for the determination of FMV, the evaluation engineer will likely be the judge as to the view of the market place. For such purposes, it is not the evaluation engineer’s place to be an economist and predict future prices of a global economy. The evaluator is attempting to reflect the view of the market. It is often convenient (and defensible) to rely on the indications by the New York Mercantile Exchange (NYMEX) futures market. One of the nice features of the NYMEX futures market is that it is available every business day. Other useful market indicators become available periodically, such as the State of Texas’ annual budget. It is interesting to compare the numbers. Because of price volatility, the time over which any such comparison is valid might be very short or indeterminable. NYMEX prices reflect benchmark prices for West Texas Intermediate Sweet crude and Henry Hub gas. While care must be used, it is usually possible to use historical prices over a brief period to arrive at suitable differentials to these NYMEX indexes and to then base future price projections appropriately. Hooper and Rutherford[7] is a valuable source for an industry perspective. Like the State of Texas budget, it is sometimes difficult to pin down the time frame to which the perspective applies. It sometimes seems that the NYMEX futures market is out of sync with the mainstream of the industry and with what a property purchaser would use as a guide for a decision on an acquisition. Different segments of the industry are not always synchronized. The evaluator must take care that the prices used in the economic projection reflect certain other sales features. If transportation charges apply, they usually should be reflected in a reduced price, unless care is taken to be sure those transportation fees are reflected in the cost column. Also, while oil production and sales volume difference usually balance out over time (assuming a lack of theft or errors), gas sales quantities are commonly less than produced quantities because of lease use and shrinkage. The reserves engineer commonly forecasts wellhead production by necessity. Net produced and reserves quantities are reported conventionally as the fraction of the wellhead volume indicated by the revenue interest fraction. To get the arithmetic correct, it is often necessary to account for lease use and shrinkage losses (commonly as high as 6% or greater), gas liquids recovered, and the net back of liquids recovered in an off-site gas processing plant in the gas price. To ensure that input variables and/or the economic model will project future cash flow suitably, it is a good idea to determine if historical produced quantities and prices can be used to duplicate historical revenue. In a presentation before the SPEE annual meeting in Park City,[14] Rick Riseden indicated the importance of being able to "follow the cash." His subject was the valuation of royalty interests where not all the operator’s records might be available but the principle is the same. If you try to follow the cash and cannot, how can you predict future revenues with any accuracy? ### Taxes U.S. federal income taxes are not included in this item and the calculation of such taxes is not presented in this chapter, but Sec. 19.7 discusses the characteristic impact on value. This tax element is what is often referred to as local property taxes. In reality, the taxes normally included are all taxes other than federal and state income taxes. The nature of the tax structure varies from state to state. SPEE maintains a document[15] that presents a summary of the structure of these taxes by state. While the summary is quite helpful, caution is necessary. Laws and rates change frequently, and some provisions of the laws might not be fully covered in the SPEE material. It is best to consult evaluators with local experience. ### Operating Costs It is common practice to use historical average costs for a preceding time period as the initial cost for projection purposes. Usually, the historical costs are calculated at a cost per well per month and projected forward in the same manner with future costs at the summary level declining as a direct function of the number of wells projected to be producing. Future costs typically are escalated at a rate commensurate with some perceived inflation rate thought to be consistent with the projection of oil and gas prices. "Nonrecurring" costs are often removed from the historical averages before determining the parameters for projection of future costs. The costs projected in the economic evaluation are generally field-level expenses and exclude general and administrative (overhead) costs. To the extent a working interest owner is billed overhead charges by the operating company (COPAS charges are in that category), those charges are included in the operating costs of the nonoperating working interest owner. There is much room for abuse, deception, and pitfalls concerning value on the operating cost side of the valuation process. [16] In the case of an offshore platform, it is obvious that there is a substantial base level expense that is not proportional to the number of producing wells. On a property producing a lot of water, the operating cost is more likely to be related to the amount of water being produced than the number of wells or amount of oil. Whether or not onshore operating costs can be expected to vary directly with the number of wells is a matter of circumstances and judgment. It is usually a mistake to eliminate costs classed as nonrecurring. It might be appropriate to spread such costs over a number of wells or make a judgment as to expected frequency of occurrence. Some costs of operation are classed as "make marketable" charges. The most common of these is the cost to compress gas to the pressure required to enter the sales line, to reduce the water content, or to extract impurities such as carbon dioxide, nitrogen, and/or hydrogen sulfide to meet pipeline specifications. These charges are not handled in proportion to expense interest but are usually charged to the property owner in proportion to the revenue interests; thus, it is not universally true that royalty owners do not bear any share of the costs of operations. ### Capital Costs These costs are listed separately from operation costs because of the difference in their nature and because, if any after income tax economic calculation projection is to be made, there is a difference in the structure of their deductibility in net income computations. The capital costs most commonly included in petroleum economic projections are for the drilling of new wells and the workover of existing wells. Other common costs are for the addition of compression; installation, expansion, or addition of production collection and separation systems; the addition of artificial lift; and the installation of offshore platforms. Planned improved-recovery projects require additional capital outlays for facilities. There occasionally are repetitive needs for relatively small, but potentially significant, amounts of capital that go unnoticed by the evaluator during reviews of historical expenditures. Such capital items are often associated with large units with consolidated facilities and are not captured in the "operating cost" category of historical expenditures or budgets. Engineers are accustomed to including capital for new wells, recompletions, and workovers, but they are sometimes unaware that the operating costs they are provided include only expensed portions of repetitive historical costs. Reserves reports sometimes include income from sources other than from the sale of produced oil and gas. When the income is from the sale of byproducts such as sulfur, the treatment is relatively straightforward because it is a third sales revenue stream. If the income results from the processing of gas for the recovery of liquids, the economic model is often adjusted to reflect the associated quantities, but at other times, it is considered sufficient to make an adjustment of the gas price to reflect the elevated income level. A different approach might be required if reporting under U.S. SEC guidelines. If the income results from providing a service such as disposing of produced saltwater for a fee paid by neighboring operators, the issue is less clear because the evaluation includes an income stream associated with a business other than the production of oil and gas. Evaluations have been observed that include, as a part of the petroleum economics, the operator’s income (likely treated as a reduction or credit against other expenses) from COPAS payments received from others. The key to knowing the proper means of evaluation is to know the use of the report and any controlling regulations. Conspicuous disclosure of unusual circumstances is recommended. Sometimes there are material exit costs such as well and offshore platform abandonments and site remediation. Future environmental liability also could be a significant cost. Economic evaluation of reserves should include such considerations; however, a report may present a fine perspective on specific underlying values but not be a complete expression of value. The preparers of reserves studies and evaluations usually have limited expertise in such matters. It is a good idea to read carefully the qualifications that are always contained in a thoughtfully prepared report or statement of opinion. This section conveys the message that these projections of production and associated expense and income are constructed to be a model of the future and should include consideration of all parameters that bear on those expectations. A well-constructed model will include a specific value assignment to all the variables that might be included as a distribution should a Monte Carlo simulation be constructed later. As discussed in Sec. 19.4.3, it is a very good idea to be sure you can "follow the cash." ## The Nature of Risk and Uncertainty Forrest A. Garb is the author of the following text taken from the SPEE FMV document. [1] The petroleum industry has written extensively on the risk associated with exploration and development. Very little has been published, however, addressing the uncertainties associated with acquisition and operation of producing properties. The uncertainties associated with estimating the reserves and value of oil and gas producing properties are divided into three classifications. The technical uncertainty that the hydrocarbon volumes estimated do exist in the ground and that the recoverable amounts can be produced within the time frame projected, the economic uncertainty that product prices, operating costs, equipment costs, inflation, and market conditions will be in reasonable agreement with the assumptions used in the economic analysis, and the political uncertainty that world economics, international political stability, taxation, and regulations will not be significantly different than perceived at the time of the evaluation. 1. Technical Uncertainty. Technological uncertainty relates to whether or not the hydrocarbon volumes estimated actually exist in the ground and whether the reserves and recovery rates will be as projected. Technical uncertainty is strongly influenced by the length of time that the property has produced and the quantity and quality of the information available about that property. For example, porosity derived from well logs might truly measure the pore space of a rock, yet the logs may not identify how much of that pore space is interconnected. A Styrofoam™ cup is porous; however, the pores are not interconnected, otherwise the cup would leak. Because reservoirs depend on the pores to transmit oil or gas to the wellbore, pore space makes no contribution to reserves if, like the cup, it is not interconnected. In technical terms, the rock must have permeability. As the reservoir depletes during the production process, it is often possible to analyze its performance and, hopefully, confirm that its effective size is close to that indicated earlier through the use of logs, geological interpretations, and other data. Too often however, there are surprises. When prices for oil and gas are stable and/or expectations for future oil and gas prices fall within a narrow range, technical uncertainties (reservoir fluid content, productive area, porosity, net pay thickness, water saturation, producing mechanism, recovery factor, and producing rate) dominate the concerns. Somewhat stable industry costs and prices cause the estimation of reserves and producing rates to be the most significant inputs in the evaluation of a property. 2. Economic Uncertainty. Instability in oil and gas prices and questions about costs and taxation have, at times, caused economic uncertainty to take precedence over technical uncertainty. Prices at which oil and gas are expected to be sold are not the only variables that can affect the economic uncertainty. Capital, operating, and drilling costs react to increases and reductions in industry activity. Drilling costs during slow periods have been known to decline to as low as 50% of the costs prevalent during boom times. Operating costs do not necessarily follow changes in oil and gas prices as is frequently assumed in projections. Cost reductions, which may reflect the availability of equipment and services when the industry is operating below capacity (possibly due to low oil and gas prices), could disappear as quickly as they appeared and must be considered in the assessment of uncertainty. Inflation and interest rates on borrowed capital also add to uncertainty. 3. Political Uncertainty. Political uncertainty includes uncertainty regarding local and national taxes, environmental regulations, and global concerns. Oil prices have been significantly influenced by artificial supply restraints for almost all of the industry’s life. There is the risk of nationalization, operational restrictions, and social unrest in foreign host countries. Exporting countries could restrict the exportation of crude produced within their boundaries or require the producer to sell that oil domestically at prices significantly below the world price. Revenues generated from local sales might not be easily repatriated by the producing company. In other circumstances, the terms of agreements and contracts might be subject to capricious interpretations or obligations. A balance recognizing the element of romance and the possibility for better results than expected versus the uncertainty of predicted outcomes or the risk of loss is the target of an FMV analysis. The procedures for assessing risk and uncertainty include deterministic and probabilistic methodologies. Deterministic methods can be applied to yield one or a specific set of multiple results. Probabilistic methods target a description of all possible outcomes. The question, "What is the value of a property?" implies that there is a single answer. For most business transactions a single answer is required. The most frequently used procedure to assess the value of a property is deterministic. If only a "most likely" case is developed, the fact that it is highly unlikely that this case will actually occur is ignored. The question, "What is the range of outcome possibilities for this property?" recognizes that there is no single answer and perhaps one should look to a probability theory as an aid in business decisions. Despite the limitations imposed, the thrust of this monograph is to address deterministic procedures. The consideration of alternate outcomes in the assessment of FMV is encouraged, whether it is through the use of multiple deterministic analyses or fully probabilistic procedures. Additional discussion of probabilistic procedures is included in the SPEE Monograph 1, second edition, dated October 1998. [4] ## Methods to Adjust for Risk and Uncertainty ### Application of Adjustment Factors for Risk and Uncertainty For the economics presented in a reserves report to be useful in estimating value (loan value, exchange value, FMV, etc.), some method of adjustment may be needed so that the economics reflect an expected case. Garb[12] indicated "adjustment factors reflecting the uncertainties attributed to the different categories of reserves can be used to index or to equate their FNR stream of the equivalent of proved producing reserves." Table 19.2 presents qualitative observed monetary value risk factors (MVRF). It replicates the table from Guidelines for the Application of Petroleum Reserves Definitions[4] that summarizes part of the results of the SPEE annual parameters surveys and includes a range of factors grouped by deterministic reserves category. Table 19.2 presents value ranges generally greater than those presented by Garb, [12] but the intended application is similar and the ranges in Table 19.2 are more current. The table uses the term uncertainty, but risk would have been a better term. The footnotes state the factors "assume risk factors reported were those applied against monetary values," but it is not precisely clear what the values apply to because of the way the surveys were conducted. They undoubtedly apply to deterministic reserves categories. Consider the proved undeveloped reserves category and the simple cash flow schedule presented in Table 19.3. The discount rate for the present worth calculation in the right column is not shown. Assume that the discount rate used to calculate that column is the discount rate that would represent FMV, if this were a cash flow summary for proved developed producing reserves. Table 19.2 shows a range of factors from 0.50 to 0.90 for the proved undeveloped reserves category. For this illustration, we used a factor of 0.70. Applying the 0.70 factor to the$1,936,000 present worth value results in an adjusted value of $1,355,000. Is this the correct application of the method? The answer depends significantly on precisely when the decision to spend the capital must be made. What if the factor of 0.70 is applicable to reserves risk and all the capital must be committed up front? If the revenues were reduced to 70%, which could be expected to be the implication of a 0.70 factor applied to reserves, the values in Table 19.3 would appear as the values in Table 19.4 and would have no value at the discount rate used. This type of analysis is essentially a decision tree calculation of expected results, given the circumstances described. Another possibility is that the need for adjustment may have nothing to do with uncertainty regarding the reserves quantity. Table 19.5 presents a cash flow example and present worth calculation that is the same as in Table 19.3, except that the receipt of revenues has been delayed by one year. Again, the result is a value considerably less than the$1,355,000 suggested in Table 19.3 after application of the 0.70 factor to the discounted value. There are other possibilities that could cause an evaluator to make value adjustments independent of concerns about the confidence associated with reserves quantities. Another crucial consideration relative to Table 19.5 would be the possibility of overexpenditure of capital cost. There are almost an infinite number of possibilities, which is why probabilistic analysis and Monte Carlo simulation can be useful decision-making tools.

There are many aspects of uncertainty other than those associated with reserves quantities. Risk and uncertainties of all aspects should be addressed. It is unlikely that subjectivity can be eliminated from the evaluation. In making deterministic adjustments for risk, it is often helpful to think about how the distributions for variables might be described in a Monte Carlo simulation and to attempt to estimate what the most likely results would be. This will not help much in determining the breadth of the value range that might be revealed by Monte Carlo simulation, but it should help in coming up with values approximating the mode. If the deterministic method is the sole means of evaluation, it is hoped that the distribution of expected values will be narrow and the mode will be very meaningful.

## The Effect of Federal Income Taxes on U.S. Acquisition Economics

This section shows how federal income taxes can affect the economic evaluation process and gives the reader some understanding of how after federal income tax (AFIT) and before federal income tax (BFIT) relate in the U.S. This section does not delve into the U.S. federal tax code and the mechanics of making after tax cash flow computations, which can be done with petroleum economic software packages. Any evaluator intending to make such an analysis should consult a tax professional.

The marketplace in which oil and gas interests are traded involves transactions in countries with income taxes at the federal and, sometimes, local levels. Cash flow calculations that have been described are BFIT. When a property is purchased, it is assumed that the buyer made the acquisition with the intent of making a profit. If one could determine precisely the nature of the bottom line economic return expectations of the buyer, it would help greatly in making estimates of FMV. If such expectations were known and universal, an FMV estimation formula could be devised that would be reasonably portable around the world. It is generally perceived by observers of the U.S. oil and gas property marketplace that the impact of income taxes is sufficiently small and the variations in other variables influencing perceived value are sufficiently large that it is not normally possible, from the data available on a specific transaction, to discern (back into) the AFIT (bottom line) economic parameters of the purchaser.

If BFIT rates of return that characterized market value are known and one is attempting to transport or compare the observations to another market, can the BFIT results be backed into an AFIT bottom line ROR? For example, when making computations relative to a company’s weighted average cost of capital (WACC), the results are usually first expressed in terms of an AFIT ROR. The following equations are suggested for calculating WACC:

....................(19.4)

or

....................(19.5)

The relationships expressed in Eqs. 19.4 and 19.5 do not work in the evaluation of project economics because the purchase price of the property is, over time, a deductible item as a reduction of income on which tax is paid (i.e., the statutory tax rate is not the effective tax rate). Fig. 19.1 includes three computed present worth profiles that contain many assumptions but were constructed with the intent of illustrating theoretical differences in BFIT and AFIT (U.S.) rates of return. The federal income tax rate used to generate the AFIT profiles is 35%. In preparing the economics for one AFIT case, it was assumed that 70% of the purchase price was loaned to the buyer at an interest rate of 8% and that 90% of the revenue was dedicated to loan repayment. The other AFIT case was run with similar assumptions but without the loan. The economic life of the example is 19 years. The purchase price was deducted in the AFIT calculation with the units of depletion method.

A specific purchase price can be represented by a horizontal line on Fig. 19.1 (ignore the posted lines on the graph that approach being horizontal for now and think about a horizontal line at a y- axis price of approximately $2,700,000). From Fig. 19.1, it appears that such a purchase could be represented by three different discount rates as shown in Table 19.6. The burden imposed by income taxes in terms of the discount rate is shown to vary more than 2 percentage points simply based on one financing option. In the U.S., it is generally perceived that income taxes cause the spread between the BFIT discount rate and the AFIT purchase price to be approximately 4 to 6%. There is a price to pay for leveraging up the purchase price through financing in the manner described. The payment of interest reduces the total future net revenue and absolute profit in terms of total dollars. Another way to compare the BFIT and AFIT calculations is by looking at ratios rather than spreads in discount rates. Fig. 19.1 plots the ratios to show how the benefits of leveraging with a loan improve, from a discount rate point of view, as the ROR increases. In the example, a loan interest rate of 8% and a tax rate of 35% are used. The leveraging effect stems from the deductibility of the interest from otherwise taxable revenues and the fact that the after tax ROR is greater than the interest rate times one minus the tax rate. [8 × (1−0.35) = 5.2%.] From Fig. 19.1, it is clear that below a 5% discount rate, the ratio of AFIT (no leverage) purchase price to the BFIT present worth is greater than the corresponding ratio with leverage, which indicates an undesirable condition for financing. If the financing costs more that the desired after tax ROR times one minus the statutory tax rate, there is no leveraging benefit. The ratios plotted on Fig. 19.1 show that as the ROR increases beyond 5%, so do the benefits of leveraging with a loan. In the example presented by Fig. 19.1, AFIT leveraged case purchase prices bear a relatively constant ratio to the BFIT present worth values at approximately 0.9 over a wide range of values. This flatness isa usual occurrence and if it were to hold true over a wide range of conditions, it would be easy to approximate the AFIT leveraged purchase price by "haircutting" the BFIT present worth by 10%. This is only an observation at this time. Fig. 19.1 includes the 10% discounted present worth parameters that would result from flat future pricing, as set forth by the U.S. SEC filings. This "single point" on Fig. 19.1 is posted on the vertical 10% line approximately half way between the lines connecting the Case 1 BFIT present worth values and the lines connecting the AFIT indicated purchase prices. The SEC data point plots essentially on top of the AFIT ROR at 10% (loan-leveraged case) at a purchase price of$2,900,000.

## Fair Market Value

The FMV definition offered by SPEE[1] is "the price a willing buyer will pay and a willing seller will accept for a property, when the property is exposed to the market for a reasonable period and neither party has any compulsion to buy or to sell, and both have reasonable knowledge of relevant facts." The market for oil and gas properties is not static. Because it can be expected to change in the future, it is helpful to reflect on how valuations or perceptions of value have changed from the past. Perhaps what is most surprising is what little change there has been.

Table 19.7 describes the valuation methods embraced by Arps. [2] Arps’ statements have been slightly modified to conform to today’s terminology. Additional perspective offered by Arps is added in Italics. Each of these methods presumes that ROR is the applicable criterion (or hurdle) for valuation but that is not always the case, as is discussed later. The reason for the reverse order is that it is helpful to present the method that Arps considered "the most sophisticated approach" first so that the latter methods can be related to it. Today it is more common to refer to "present worth" as discounted future cash flow or discounted future net revenue, but there is no difference.

Any adjustments for risk suggested or implied in the parameters of Table 19.7 are management’s judgment of general industry risk (perhaps inclusive of oil and gas price uncertainty) or experience and are not normally project specific unless the project is unusual in terms of a company’s normal business. The risk or uncertainty associated with specific projects must be assessed on the basis of the specific merits of the individual parameters of those projects. Adjustments for project risk are discussed in Sec. 19.6.

There is debate about how overhead or general and administrative (G&A) expenses enter the cash flow projections. Some suggest that all costs and capital expenditures should be inflated to account for G&A; others argue that G&A should be a scheduled expense; and still others conclude it should not be considered at all. Some perceive that the elevation of the AFIT ROR above the cost of capital includes a component to cover G&A in addition to components for profit and industry risk. In practice, cash flow schedules in the majority of reserves reports do not include overhead expenses except for those billed to nonoperating working interest owners by the operator of the property. Such charges are frequently referred to as COPAS charges because of the manner in which the rates are established.

Method 3 is used today essentially unchanged except that the discount rates are higher because of differences in the cost of money and industry risk. Method 3 is used often internally by companies to arrive at a price they might offer to a potential seller, but it is seldom used by outside parties to estimate value. There likely will be several more columns of detail in the economics than shown by Table 19.1. There are many details, and people want to see that detail if it has been judged to be worth that much work. The basic calculations are handled easily by most petroleum economic software packages, but one must take care to model the company’s internal cash flow mechanics. The need for detail is partly because the method is used to investigate the leveraging benefits of financing. The benefits of the use of loan leverage to increase the offering price while maintaining the ROR were illustrated previously. Such leveraging has the disadvantage of reducing the undiscounted projected cash flow because of the payment of interest. If Method 3 were to be used for a purpose other than internal use, it probably would be for estimating FMV while speculating as to complexion of the likely acquirer. Similarly, a third party could be investigating how a recent change in tax rates or structure might affect those in the acquisition market.

There is always interest in the components of the AFIT ROR target discount rate. Generally, the components are expected to include the cost to borrow money and/or acquire capital, a margin to cover overhead and profit, and management’s safety factor (referred to as industry risk component).

Method 2 uses an elevated discount rate to adjust for federal income tax effects. Arps classed this method as "not recommended." [2] The primary reason for Arps’ criticism is that when the discount rate is elevated, the value of cash projected to flow at times more distant into the future is reduced more than warranted in comparison with Method 3. David and Hickman[17] wrote about a market for long-life reserves in 1990; however, others suggest that there is greater uncertainty related to those more distant projections of cash flow and that such reduction is warranted. When Arps wrote the 1962 chapter from a U.S. perspective, production levels were often regulated and projections of production and future cash flow were more often expected to be constant at existing levels for a significant time.

Method 2 is the most popular method today. Its modern popularity seems to stem from at least two sources. In 1982, SPEE began an annual publication that is currently titled Survey of Economic parameters Used in Property Evaluation. [18] The questionnaire for that survey has inherently embraced Method 2 from inception. The publication has gained wide use and acclaim and is a source to those needing quantification of the discount factor required to apply Method 2. Another reason for Method 2’s popularity is that it requires both a discount rate and a factor. Method 2 results in a simpler expression with a single parameter. Additionally, taxing authorities at state and county levels often require an expression of value in terms of the Method 2 discount rate, which might have had some bearing on the original construction of the SPEE questionnaire.

Method 1 uses discounted cash flow to estimate value, but a factor is applied to the discounted future net revenue to account for income taxes. In the Method 1 described by Arps, a "safe" discount rate was selected and value was determined by a factor that had a midrange of 0.71. [2] Arps’ application of Method 1 used a discount rate lower than the rate used in Method 3. The modern application of Method 1 (although it is not used very much) uses the AFIT ROR target rate from Method 3 and a higher factor, the midrange of which is 0.825 from Table 19.1.

Because the modern application is to use a higher discount rate in comparison to the cost of money at the times being considered, a higher factor representing a smaller reduction in the discounted values is perhaps to be expected. Another factor that might bear on the difference in the factor is the U.S. federal income tax rate and structure. When Arps wrote the 1962 chapter, the income tax rate for corporations was 50% but there was a financial arrangement available known as an ABC transaction. Today the tax rate is lower and the ABC transaction was eliminated by Congress in the late 1960s. It is not clear how historical modification of tax rates and laws have affected market values.

FMV estimation has thus far focused on ROR considerations and the present worth of projected cash flow streams. That perspective is always important but is not necessarily the controlling factor. Other economic parameters that measure the nature of a contemplated investment also affect market value. The critical ones are payout, which is the length of time required for recovery of the investment (purchase price) from the projected cash flow stream, and return on investment (ROI), which is the projected future cash flow or FNR divided by the investment (in this case, the purchase price). Payout for oil and gas property acquisition is normally expected to be 5 years or less. Some suggest that this limitation is not a true evaluation parameter but the result of the application of other criteria

ROI is probably, or should be, a controlling parameter in many valuations. Arps, [2] in commenting on one of his own studies of 34 property transactions made during the postwar years in the Mid-Continent, Gulf Coast, and California, indicated "in none of these transactions did the total consideration exceed two-thirds of the undiscounted future net cash income before federal taxes." To be in line with this two-thirds observation by Arps, the ROI must be greater than 1.5. Many[12] set higher limits, as high as 2 or 3, while others find 1.7 to be an acceptable minimum. Sometimes a correlation is perceived between ROI and acceptable minimum ROR. ROI is a good indicator of the susceptibility of an investment to risk. If reserves (or any other parameter factored into the cash flow calculation) are missed by 25% on a project evaluated with an ROI of 2, the economic result will probably be tolerable. If the originally projected ROI was 1.5, the results will be embarrassingly poor. Low ROI acquisition opportunities are usually of quite short life and often seem attractive because of short payout times. Investors willing to take such risks need to have cash because the value of the asset diminishes so rapidly that if any of the purchase is financed (with the properties being acquired put up for collateral), the loan value will be only a small fraction of the purchase price. When ROI is the parameter controlling the purchase price, the ROR will often seem to be abnormally high.

Estimates of FMV are probably best made with the insight derived by observing the characteristics of marketplace transactions. Rather than direct use of comparative sale methods, as might be done in real estate, it is better to use ROR, ROI, and payout as tools in the comparative process. Even then, adjustments must be made that account for differences in circumstances such as tax credits, tax structure, production-sharing contract terms, and risks. The parameter used as a basis for comparison most often is the ROR. Discussions over a property’s value, if the risk components can be dealt with, often are reduced to what ROR represents value. The SPEE FMV document[1] suggests that the applicable BFIT ROR in the U.S. correlates with the 30-year Treasury bond rate according to the following formula:

....................(19.6)

as a percent where Rtb = 30-year U.S. Treasury bond rate expressed as a percent.

This relationship was derived from a 20-year review of SPEE’s annual Survey of Economic parameters Used in Property Evaluation. [18] The average BFIT ROR indicated by survey respondents in the summer of 2001 was 15.4%, and the mean was 15.0%. These survey results included participants outside SPEE. The membership was surveyed through an example problem to solicit opinions with a described set of circumstances to convey high levels of confidence. This survey resulted in a mode ROR of 19.2% in a narrow distribution. The results seem to be inconsistent, but the difference probably lies in perceptions of risk.

## Nomenclature

 Cat = weighted average cost of capital after federal income tax Cbt = weighted average cost of capital before federal income tax Df = discount factor for a specific point in time e = base of the natural logarithm iR = ROR before federal income tax r = annual rate of discount expressed as a fraction or percent Rtb = 30-year U.S. Treasury bond rate, expressed as a percent t = time in years from the as of date to the point of reference for discounting TR = tax rate

## References

1. 1.0 1.1 1.2 1.3 1.4 1.5 Long, D.R. ed. 2002. Perspectives on the Fair Market Value of Oil and Gas Interests, Vol. 1. Houston, Texas: SPEE.
2. 2.0 2.1 2.2 2.3 2.4 2.5 2.6 Arps, J.J. 1962. Valuation of Oil and Gas Reserves. In Petroleum Production Handbook, vol. 2, Ch. 38, T.C. Frick and R.W. Taylor, eds. Richardson, Texas: SPE.
3. SPEE Recommended Evaluation Practice Program, SPEE, www.spee.org/rep-main.htm
4. 4.0 4.1 4.2 4.3 4.4 Guidelines for the Application of Petroleum Reserves Definitions, second edition, Vol. 1. 1998. Houston, Texas: Monograph Series, SPEE.
5. Lohrenz, J. and Dickens, R.N. 1993. Option Theory for Evaluation of Oil and Gas Assets: The Upsides and Downsides. Presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, 29-30 March. SPE-25837-MS. http://dx.doi.org/10.2118/25837-MS
6. Walkup, G.W. Jr. and Chatwin, R.E. 1999. Case Studies of a Real Option Approach to Asset Valuation in the Petroleum Industry. Presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, 20–23 March. SPE-52952-MS
7. 7.0 7.1 Hooper III, H.T. and Rutherford, S.R. 2001. Real Options and Probabilistic Economics: Bridging the Gap. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October 2001. SPE-71408-MS. http://dx.doi.org/10.2118/71408-MS
8. Luehrman, T.A. 2001. Extending the Influence of Real Options: Problems and Opportunities. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September-3 October. SPE 71407. http://dx.doi.org/10.2118/71407-MS
9. Markland, J.T. 1992. Options Theory: A New Way Forward for Exploration and Engineering Economics? Presented at the Oil and Gas Economics, Finance and Management Conference, London, United Kingdom, 28-29 April 1992. SPE-24232-MS. http://dx.doi.org/10.2118/24232-MS
10. Zettl, M. 2000. Extending the Option Pricing Theory for the Valuation of E&P Projects. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 1-4 October. SPE-62968-MS. http://dx.doi.org/10.2118/62968-MS
11. Faiz, S. 2001. Real-Options Application: From Successes in Asset Valuation to Challenges for an Enterprisewide Approach. J Pet Technol 53 (1): 42-47, 74. SPE-68243-MS. http://dx.doi.org/10.2118/68243-MS
12. 12.0 12.1 12.2 12.3 Garb, F.A. 1990. Which Fair-Market-Value Method Should You Use? (includes associated papers 20323 and 20382 and 20392 and 20987 and 21304 and 21305 ). J Pet Technol 42 (1): 8-17. SPE-20276-PA. http://dx.doi.org/10.2118/20276-PA
13. Wright, J.D. and Thompson, R.S. 2001. A Comparative Analysis of 12 Economic Software Programs. Presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, Texas, 2-3 April 2001. SPE-68588-MS. http://dx.doi.org/10.2118/68588-MS
14. Riseden, R. 2002. Valuation of Royalty Interests. Presented at the 2002 SPEE Annual Meeting, Park City, Utah, June.
15. SPEE Oil & Gas Production Taxes, Section 29 and COPAS. SPEE. http://www.spee.org/productiontaxes.htm
16. Doering, M.A. 1993. Acquisition Pitfalls: Operating-Cost Forecasts. J Pet Technol 45 (9): 858-862. SPE-25841-PA. http://dx.doi.org/10.2118/25841-PA
17. David, A. and Hickman, T.S. 1990. What Is the Market Value of Long-Life Reserves? Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 23-26 September 1990. SPE-20508-MS. http://dx.doi.org/10.2118/20508-MS
18. 18.0 18.1 Survey of Economic parameters Used in Property Evaluation. 2001. Presented at the 2001 SPEE Annual Meeting, San Diego, California, June.

## Appendix A—Description of Asset

This appendix is a reproduction of Appendix A from Perspectives on the Fair Market Value of Oil and Gas Interests. It provides a general description of typical contractual arrangements for fractional ownership and/or beneficial rights.

A fundamental step in any property evaluation is a description of the asset. In the determination of FMV, the evaluator must be certain that the mineral interest is correctly described. The lease or production sharing agreement and any other significant issues relevant to ownership need to be reviewed and understood. If the asset is a piece of real estate, the physical dimensions and a complete description of the property are prepared along with a description of any structures that may be present. If the asset is the inventory of a retail business, then the stock must be counted and categorized. In these instances, the assets can be accurately described and quantified with little doubt as to their existence. In the oil and gas industry, however, the situation is somewhat different.

When evaluating oil and gas assets in the form of reserves, the process of describing the asset requires an estimate of the volume and quality of oil, gas, and by-product reserves that may be recovered in the future from subsurface reservoirs. These products are not available at the surface to be examined. One aspect of oil and gas property ownership is that ownership is usually of a fractional nature. Even if the property ownership is in the U.S., taxing authorities will somehow share in the revenue stream.

Types of Oil and Gas Property Ownership. The most common types of oil and gas property interests or ownership are A. Working Interests B. Royalties (landowner’s, overriding, and sliding scale) C. Net Profits Interests D. Production Payments E. Production Sharing Arrangements

The following discussion defines these types of contractual arrangements and, in addition, includes common variations of the basic oil and gas interest types.

In the United States and to a great degree in Canada, the minerals are deeded privately and, at least at the origin of the country’s claim to lands, were transferred and/or deeded in tandem with ownership of the surface of the land. In almost all other parts of the world, the mineral ownership is the property of the government of the country and is separate from the private surface ownership, if any. All the indicated ownership types could be broadly classified as production sharing arrangements because all are strictly contractual in nature.

Today in the United States and Canada it is not uncommon to find that the surface and mineral interests have been severed through contractual agreement. Such severance occasionally (frequently) is the root of disputes when the mineral owners require access to the minerals through surface locations.

A. Working Interests. A working interest owner has an obligation to pay a share of costs. That share of costs is sometimes referred to as an expense interest. In some groups within the industry, the term working interest is synonymous with the term expense interest. Working interests receive a "revenue interest," also referred to as a net revenue interest (NRI) or division order interest. An NRI is a fractional interest in the gross revenue from the sales of oil, gas, and sometimes other products from a property. The NRI is normally less than expense interest due to royalty interest burdens.

Types of working interests are

1. Working Interest—This is the lessee’s or operating interest (conventionally equal to the expense interest) under an oil and gas lease, which is also called a leasehold interest. A working interest is created by a lease agreement or a deed. Its primary characteristic is the right to enter the property to explore, drill, and conduct production operations. The working interest can be owned by one entity or partitioned between several entities as in a joint venture or unit operation. If there is more than one entity, one party is usually designated as the "operator." The other working interests, if any, are "nonoperating" working interests. The working interest fractions add up to 100%.
2. Carried Interest—A carried interest is a fraction of the total working interest in an oil and gas property that is not required to pay development and, in some cases, operating costs. The carried interest portion reflects the lack of participation in all or a portion of capital costs. The capital requirement normally attributable to the carried interest’s working interest position is, through agreement, paid by others, normally by one or more of the other working interest owners putting up a disproportionate share. The classic reason for one of the working interest owners to carry the other is a means of buying one’s way into participation. This type of buy-in is sometimes referred to as a "promote." In some provisions for carried interests, the owner of the carried interest does not receive any income until the other working interest owners that put up the disproportionate share receive the return of their capital investment or an otherwise agreed on sum of money, which might be considerably in excess of the disproportionate amount put up to carry the carried interest. A carried interest may apply to one or more wells, the lease, or to the prospect.
3. Reversionary Interest—In some situations, a portion of the working interest (the expense part, the NRI part, or both) reverts to another party when a specified condition occurs. The carried interest described above is a form of a reversionary interest. The condition that triggers the reversion often is occasioned by a "payout" of an investment. There may be a change in the working interest, or an overriding royalty could become a working interest. Multiple reversionary interests with different triggers often apply to a single property.
4. Terminable Interest—A terminable interest is a working interest that terminates on the payment of specified charges from the production revenue. This is another description of a class of reversionary interest.

B. Royalty Interests.

1. Landowner’s Royalty Interest—This is the landowner’s share of production retained in the lease agreement. If the minerals have been severed from the surface, it is the interest retained by the mineral interest owner. This income is free from capital investment and from most operating expenses except for a pro rata share of production and severance taxes. Sometimes the lease requires the royalty to bear its share of power, substitute fuel, marketing costs, and other costs to make the produced oil and gas marketable substances. Other such costs include compression, dehydration, and the removal of impurities.
2. Overriding Royalty Interest (ORRI)—An overriding royalty interest is in addition to the landowner’s royalty interest, and its terms and conditions are similar to the "basic lease" unless otherwise specified. An ORRI is carved out of the working interest. It usually represents a payment to a middleman for services rendered. The ORRI holder’s benefit of ownership generally expires with the expiration of the lease to which it is associated.
3. Drillsite Royalty—A drillsite royalty is paid for the use of a parcel of land for drilling and production operations for directionally drilled wells when the completion interval is not under the drillsite tract.
4. Compensatory Royalty—This is also called an "offset" royalty. This is a payment from the lessee to the lessor in lieu of drilling an offset well. This usually occurs when the lease would require the drilling of an "offset" well, but the lessee does not consider the drilling of the required well to be economic.
5. Shut-in Royalty—A royalty is paid (usually in the form of a periodic fixed amount stipulated by the lease agreement) when a gas well, capable of economic production, is shut-in because of a lack of a market for the gas (e.g., pipeline is not yet installed).
6. Term Royalty—Any royalty on production from a lease that has a fixed duration in time (i.e., 20 years) is a term royalty. Most royalties are associated with leases that are evergreen (i.e., the lease continues as long as production is in paying quantities), and those royalties are not term royalties.
7. Minimum Royalty, Sliding Scale Royalty, Step-Scale Royalty—These royalties reflect minimum or varying royalty rates, which can depend on such variables as (1) total oil (or gas) rate, (2) average daily rate per producing well, and (3) the oil (or gas) price.

C. Net Profits Interests. A net profits interest is a share of the revenue from a well or property that bears a share of expenses and a share of the income, often very similar to a non-operated working interest. The holder of the net profits receives income when the operation to his position is profitable but has no (or a modified) cost burden when the income from the sale of production is insufficient to cover costs from operating a well or property. Net profits interests are carved out of the working interest. The net profits can be on an operating cost basis only or may also reflect the recovery of capital costs. The structure of net profits interests are often such that costs from periods of non-profitable or negative cash flow operations are paid from later periods of operations when the operations are profitable or have positive cash flow. One of the working interest owners, frequently the one from which the net profits interest was carved, administers the funds of the net profits interest account and, on the occasion of negative cash flow, at least temporarily absorbs the loss. Net profits interests may have tax (U.S. federal income tax) consequences that are identical to a working interest with similar associated expense and revenue interest fractions.

D. Production Payment. A production payment describes a financial arrangement wherein the owner of the production payment is entitled to a specified portion of the oil or gas production for a limited period of time or, as in most cases, until a specified condition is satisfied [normally related to when an amount of money (plus interest) has been received]. This income is free of production costs. A production payment is often used in financing an acquisition or a portion of the sales price to the seller with a bank loan. It is sometimes a method of "nonrecourse" financing, wherein the production payment holder can look only to the property to satisfy the loan.

There are two basic types of production payments, the "reserved" and the "carved out" payment. It is "reserved" when the owner of an interest assigns all or part of his interest and obtains an oil payment for a specified sum of money or a specified volume of production (barrels or MCF). A "carved out" payment is one in which a party assigns only a payment of a specified sum of money (usually with interest) out of a certain share of the grantor’s production revenue. However, none of the grantor’s interest in the property has been assigned, only a certain sum of money. A production payment may be "deferred" and not begin until after the operator has realized a certain sum of money, or until a specified period of time has elapsed.

E. Production Sharing Arrangements. Production sharing agreements can have terms similar to production payments. However, production payments are normally structured to satisfy a previous monetary commitment, while a production sharing arrangement is normally structured to compensate and provide incentives for an operator to perform under a contract to produce a government’s minerals.

## SI Metric Conversion Factors

 bbl × 1.589 873 E − 01 = m3 ft3 × 2.831 685 E − 02 = m3