Chapter 41

Valuation of Oil and Gas ReservesForrest A. Garb, H.J. GJII~& Timothy A. Larson, Ernst&Ass,ocs * Whitney

Types of Oil and Gas Property OwnershipThe most common types of oil and gas property ownership in the U.S. are mineral interests, working interests, royalties, overriding royalties. net-profits interests. and production payments. A mineral interest in a property is a part of the fee simple interest. In most states, the mineral interest can be severed from the surface interest and transferred by a mineral deed (in Louisiana, the mineral and surface interest cannot be severed in perpetuity). The owner of the minerals, either through fee simple title or by a mineral deed, can exccutc a lease of the oil and gas rights. Consideration paid for a lease is called a lease bonus. During the primary term of the lease, it can be held by paying rentals. production, or drilling activities. The rentals, usually called delay rentals, are paid in lieu of drilling or production. From an income-tax standpoint, these rentals are ordinary income to the lessor and arc deductible by the lessee. For tax purposes, a bonus must be capitalized as a part of the cost of the lease by the lessee. This bonus is income that is subject to depletion for the mineralinterest owner; although if the lease is not eventually productive, the depletion taken must be restored to income in the year the lcase is proved worthless. A royalty or royalty interest is the mineral owner share of production free of the cxpcnse of producs tion. It is distinguished from a mineral interest by the absence of operating rights. The basic royalty interest usually is expressed as a fraction of the total production, such as g of %. !&of %. Royalty has historically been subject to production taxes. federal excise taxes [Windfall Profits Tax (WPT)], and in some states, old ~~lore~t taxes. An overriding royalty interest is an interest in oil and gas produced free of the expense of production and in addition to the usual landowner royalty. It continues s for the life of the lease and is sub,ject to production taxes. taxes. An WPT taxes, and in some states. ud ~~7lowr77 Author of the arlglnal chapter was Jan J Arps (deceased)

overriding royalty interest is commonly expressed as a fraction of the revenue accruing to the working interest; for example, of 7/, of the total oil and gas produced. /8 In some areas, such as the Rocky Mountains, overriding royalties are often expressed as a percentage of % of the total oil and gas produced. A *net-profits interest is a share of the gross production measured by the lessee net profits from the operas tion of a specific tract of land. It is normally carved out of the working interest. A carried interest is a fractional interest in an oil and gas property that gives the owner no personal obligation for operating or development costs. The operaing or development costs attributable to such fractional interest are borne and paid by the owners of the remaining fractional working interest, who recoup such expenditures or an agreed sum out of production from the property. A production payment is a share of the oil, gas, and other minerals produced from a tract of land, free of the cost of production, that terminates when a specific sum from the sale of the oil, gas, and other minerals has been realized by the owner of the interest. There is no personal liability to pay the sum specified in the instrument creating the production payment: the owner looks only to production from the tract of land for the sum specified. A production payment is usually expressed in dollars and may carry an incremental payment computed in the manner of interest. A production payment is said to be carved out when it is transferred out of another oil and gas interest. It is reserved when the interest is retained by the seller upon the sale of another oil and gas interest. Production payments limited to oil or gas only are called oil payment or gas payment, respectively. A reversionary interest is usually a portion of the working interest that reverts to another party on the occurrence of some defined event. This event is often the payout of the investment or some multiple of the investment or may bc the passing of some defined time period.

41-2

PETROLEUM

ENGINEERING

HANDBOOK

TABLE

41.1--REVENUE

INTERESTS

A owns: l/s B/eless /aof I/* Ve less /a J/s a/8, or s/s4 */8) of of of of (of or R/=0.07812 ~OWnS:/40f1/gOf8/or1,&(of8/g)or ,..,, ,...... R/=0.03125 _... R/=0.01562 DOwnS:1/gOf1/80f8/g0r1/6~(Of8/g)Or

All or any part of each of these oil and gas interests may be purchased, sold, or mortgaged at the owner s election. Each economic interest in a property represents the right to a certain fraction of the gross income from the sales of oil and gas [revenue-interest fraction (RI)], and an obligation to pay a certain fraction of the cost of production [workinginterest fraction (WI)]. In the case of royalty interests, overriding royalty interests, carried interests, and production payments. the WI is zero because these interests are free of the cost of production. s A working interest is the lessee or operating interest under an oil and gas lease. The typical oil and gas lease provides for a royalty to be paid to the lessor or other royalty owners, free of the expenses of production; the balance of the production represents the working interest of the lessee, and this part of the production bears the entire expense of production. The working interest created by an oil and gas lease may be further divided by the creation of overriding royalties, production payments, netprofits interests. and carried working interests. When there is one lessee under an oil and gas lease, he must pay the entire cost of production and his WI is 100%. Where two or more lessees jointly own a lease, the WI of each lessee when totaled should add up to 100% of the working interest under such lease. The various co-owners of such a lease normally enter into an operating agreement and designate an operator of the property. For example, for a joint-interest owner who owns a quarter of the working interest, the WI equals 0.25. The WI is in effect equal to the fraction of the cost of production that a lessee has to pay. An RI, also referred to as net interest or division-order interest, is a fractional interest in the total gross revenue from a tract of land that represents the actual quantity of total oil and gas produced from such land attributable to an oil and gas interest in such land. An RI is commonly expressed as a decimal fraction of % of the gross revenue from such production. An example may clarify the system. Landowner A leases his land for oil and gas purposes to D, retaining the usual royalty interest. In order to hedge against non/

productive development, A sells 5/4of his x royalty to B and l/8of his )/8to C. A, B, and C thus become the royalty owners under the land mentioned above. Their RI are computed in Table 4 1.1. s D, the original lessee, then conveys the lease to E, retaining x6 of overriding-royalty interest. The lease is /s now said to be burdened with a x6 override. D now owns l/j6 of or x2s, or RI=0.05469. /8 To support him with his development and operating costs, E now sells one-fourth of his interest in the lease to F. E now owns W of (7/sof % less x6 of 7/sof %) or 31s / 512, or RI=0.61524, while paying U of the costs or WI=O.75. F now owns i/4 of ( of % less x6 of x of /B or %I or 10%121 RI=0.20508 while paying i/4 of the costs or WI=O.25. The working- and revenue-interest fractions pertaining to the various economic interests in this example should now each add up to unity, as shown in Table 4 1.2.

Valuation2-13Determination of Fair Market Value Fair market value of an oil- or gas-productive property, as commonly understood, is the price at which the property would be sold after exposure to the market for a reasonable period of time by a willing seller to a willing buyer, neither being under compulsion to buy or to sell, and both being competent and having reasonable knowledge of the facts. Fiske,3 presenting the viewpoint of the Internal Revenue Service in 1956, listed six methods used to determine the fair market value in order of preferential weight: (1) an actual sale of the property near the valuatton date: (2) a bona tide offer to sell or purchase the property near the valuation date; (3) actual sales of similar properties in the same or nearby oil and gas fields near the valuation date; (4) valuations made for purposes other than federal taxation near the valuation date; (5) analytical appraisals; and (6) opinions of qualified oil or gas operators. This section deals with the determination of the fair market value of oil and gas properties by the analytical- or engineering-appraisal method, enumerated by Fiske as

TABLE

41.2-WORKING

AND

REVENUE

INTEREST

FRACTIONS RevenueInterest Fraction (decimal fraction of revenue) 0.07812 0.03125 0.01562 0.05469 0.61524 0.20508 1 .ooooo

Fractionof Working Interest (decimal fraction of costs) Landowner (Lessor) Royalty Owner Royalty Owner Overridtng-Royalty Owner Operator Nonoperator Total 0 0 0 0 0.75 0.25 1.00

VALUATION

OF OIL AND

GAS

RESERVES

41-3

Item 5. With this method, the appraiser estimates the recoverable hydrocarbon reserves from the property and appraises the probable future net income or cash flow to be realized from the production and sale of these reserves. While fair market value for a hydrocarbon-producing property is not a precise number, it can be approximated within rather close limits by use of the engineeringappraisal method. 3 Preparing a Cash-Flow Projection For the purpose of determining future net income or cash flow, oil and gas production should be forecast on information about future demand for petroleum or on the basis of purchase contracts if these govern but should not exceed the physical ability of the well or wells to produce. Where proration or market curtailment is in force, trends in oil and gas allowables or market should be considered. Usually, the gross income from oil and gas sales to be obtained from such production is based by the appraiser on current posted prices for crude oil and on predicted economic conditions. The constant price projections are required for financing and Securities Exchange Commission filings, while the predicted prices that are based on economic studies are used for business decisions. Gas prices should be based on gas-purchase contracts in force on the properties being appraised. The effect of escalation clauses in such gas-purchase contracts. which are subject to future approval by regulatory agencies, are usually set out separately. In most states, oil and gas production is subject to state, county. and local taxes payable by the producer. The producer customarily charges the appropriate part of these taxes to the various interests in a given property. Tax rates on oil and gas production in the various states have historically varied and may be obtained from the state regulatory agency. The taxes are usually collected by the pipeline company by deduction from the runs. Corporation or private income taxes are normally considered outside the scope of an oil and gas property valuation, but some valuation formulas make indirect allowance for them. Tax ramifications can totally change the economics of a proposed transaction and related cvaluation. For certain purposes, such as bank evaluations, income taxes, as an inherent part of the future income, are sometimes specifically included in the forecast. Operating or production costs comprise the expenses required to produce the oil and gas and to maintain the leases. These costs, usually called direct lifting costs, include the cost of labor, field supervision, power, fuel, repairs, stimulation and/or recompletion of wells, plant repairs, transportation, insurance, and other such items. As the age of the wells increases, additional expenditures may have to be made to keep the wells in operating condition and possibly for disposal of produced salt water. Capital expenditures include the cost of construction of gasoline plants, repressuring systems. additional development wells, artificial lifting equipment, engines. tanks, and other durable items required to produce all the economically recoverable oil. An owner of a working interest in oil or gas properties pays the full amount of his working-interest share of direct costs and capital expenditures, but he pays production and federal excise taxes only on the production to his net

revenue interest. Royalty or overriding royalty interests, however, ordinarily bear none of the normal lifting costs or capital expenditures but do bear production and federal excise taxes on their revenue-interest portion of the oil or gas produced. The gross income to be realized from the production of the revenue-interest portion of the oil and gas reserves, when reduced by the amounts necessary for production and federal excise taxes, the working-interest share of operating expenses, repairs, recompletions, and additional capital expenditures, is the future net income or the net cash flow generated from the production of the estimated oil and gas reserves. Salvage value of equipment at the time of abandonment is ordinarily not included in the cashflow projection because such income is usually offset by the cost of properly plugging and abandoning the property in compliance with state regulations. An exception is sometimes made where the life of the property is short and such salvageable equipment minus abandonment costs constitutes a major part of the value. After the technical analysis of the properties has been made, which results in a determination of the volume and rate of production of oil and gas, and these data have been reduced to a projection of future operating net income or cash flow, it becomes necessary to establish the appraisal value. Analytical Methods for Computation of Appraisal Value Although there are many methods for computing appraisal value, only the most popular will be discussed. All these compute the appraisal value of a property by the discounted-cash-flow procedure and give proper weight to the time pattern of future income. Appraisal values that are based on a given fraction of the undiscounted future cash income or on payout in a given number of years do not meet this requirement and are not included. The examples provided are from the original edition of this handbook and reflect the economic conditions current at that time. The methodology remains valid, however, and any values in the examples would be subject to change with time. Appraisal value equal to a fraction of the present worth of the net cash flow before federal taxes computed at a safe rate of interest. Method 1 is relatively simple, easy to understand, and widely used. It is based on the premise that future income should only be discounted at an interest rate that reflects the current-time value of money and that such interest rate-which fluctuates with the prevailing cost of money-is not used as a vehicle for the risk factor. In its application, the combined present worth of the future operating net income or cash flow is calculated by discounting the future annual cash-flow increments at prevailing or projected compound interest rates. An example of such a present-worth computation at an interest rate of lO%/yr is shown in Table41.3. While Table41.3 is a hand calculation, most calculations are made with electronic data processing equipment, as shown in Table 41.4. The total present worth of the future net operating income, which in this example is $1,499,941, is not to be construed as the market value of the oil or gas property. The purchaser of such a property logically is entitled to

41-4

PETROLEUM

ENGINEERING

HANDBOOK

TABLE 41.3-CASH-FLOW PROJECTION AND PRESENT-WORTH CALCULATION FOR XYZ OIL COMPANYS INTEREST IN PRODUCING OIL PROPERTYOperakx Revenue Working XYZ Interest, co. RI = 0 375 011 Sales Price = $29 OO/bbl Productron Taxes =~.WO Estimated Operatlnq plus $0 0019/bbl = 5800 OO/well-month Expenses Lease Mary Jones Creek Freld Rock State: Texas Acres, 100 No of Wells Operation 111185 50.301 Rlx Step 1 Step 3 x Price (0 046 x step 3]+ [O 0019 x step Z] well-months wells x months 18.863 547.023 25,199 12 9.600 1II186 42,570 15,964 462,949 21,326 12 9.600 l/1/87 30,738 11,527 334,276 15,399 12 9,600 111188 24,180 9,068 262,957 12,113 12 9.600 111189 19.490 7.309 211.954 9,764 12 9,600 l/1/90 13.847 5,193 150.586 6,937 12 9.600 l/l/91 4,506 1.690 49.003 2,258 12 9,600 1 Total 185,632 69,614 2.018.748 92,996 84 67,200

Interest:WI = 0.500

Date of Evaluation l-l-85 Step 1 2 3 4 5 6 7 8 Estimated Gross Future

lease

productron. bbl Net productron to XYZ. bbl 011 revenue. dollars Production taxes, dollars Producing

Operating costs. dollars Step 5 x $800 Capital expendttures, dollars XYZ share of operating WI x [Step 6+ Step 71 plus capital costs, dollars

4.800 14,336 4.800 7,982 428,841 08668 371,713 4,800 4,957 309.120 0.7880 243.582 4.800 3,174 242,870 0.7164 173,980 4,800 1,973 195,417 06512 127,261 4.800 987 137.862 0.5920 81.618 4,800 152 41.793 0.5382 22,493 1,499.941 33.600 33,561 1.858.591

9 10 11 12

Net federal excise* (WPT). dollars Future net revenue. dollars 10% annual deferment F,, =(Step 1 +i) - 09535 479,294 factor (Table 41 11) Present worth of XYZs cash flow Step 3 - Step 4 -Step 8 - Step 9 502,688

TABLEXYZ 011 co

41.4-PROJECTION

OF ESTIMATED

PRODUCTION011

AND

REVENUE

AS OF JAN. 1, 1985XYZ Mary Rock Texas 011 co Jones Creek Freld

Working Net Gas

Interest Interest

0.500000 0.375000 0.375000 Future Production 011 or Condensate Gas Gross (Mscf) ~ Net (Mscf)

Proved Pnmary Producing

lmtlalWells 1

Net Oil lnteresl

Future Gross 011 Revenue 547.023 462,949 334,276 262,957 211,954 150.586 49.003 2.018.748 0

Revenue

Before Production Taxes Total Revenue 547.023 462,949 334,276 262,957 211,954 150.586 49,003 2.018.748 0 2.018.748 ProductIon Taxes 25,199 21.326 15,399 12,113 9,764 6,937 2,258 92.996 0 92,996 WFPTX($) 14,336 7.982 4,957 3,174 1.973 987 152

(dollars) Costs 19,136 12,782 9.757 7.974 6.773 5.787 4.952 67.161 0 67.161

Future Net Revenue ~ 502.688 428.841 309,120 242,870 195,417 137,862 41,793 1.858.591 0 1.858.591

Discounted Value at 10 00% 479,294 371.713 243,582 173,980 127,261 81.618 22,493 1.499.941 0 1.499.941 ($)

Number Year 1985 1986 i987 1988 1989 1990 1991 Sub Total Remainlna Total The Wells 1 1 1 1 1 1 1 0

of

Gross WI) 50,301 42,570 30,738 24,180 19,490 I 3,847 4,506 185.632 0 185,632

Net (bbl) 18.863 15,964 11,527 9,068 7.309 5,193 1,690 69,614 0 69,614

Gas Revenue

~

~

2.018.748 Prices and Windfall Profit Taxes Year 1985 1986 1987 1988 1989 1990 1991 $/bbl 29 00 29 00 29 00 29 00 29 00 29 00 29 00

asof-date gross oil pnce = $29 OO/bbl. tax tier3.

$/Mscf

Year $/bbl $/Mscf WFPTX

Total WFP

Tax

=$33.561

VALUATION

OF OIL AND

GAS

RESERVES

41-5

TABLE

41 S-DISCOUNTED

FUTURE

NET CASH

INCOME

VS. PROPERTY

LIFE

Average 5% Deferment Factor on Cash-Flow Protection 0.82 through 0.70 through 0.52 through 0.40 through 0.70 0.52 0.40 0.32

Equivalent Constant-Rate Production (wars) 8 15 30 45 through through through through 15 30 45 60

Percentage of 5% Discounted Value of Future Number of Net Cash Income Transactions Paid 11 13 6 4 60 50 58 68 through through through through 84 89 89 98

Average Percentage of 5% Dtscounted Value of Future Net Cash Income Paid 71 70 75 78

a profit above the bank interest rate. Also, when cash flow is computed by this method, the federal income taxes on the operating net income usually are not deducted, and allowance must be made for them. In addition, a risk-ofdoing-business factor is usually included. Depending on whether cost-depletion or percentagedepletion allowance is applicable and depending on the amounts of future intangible development expenditures and equipment depreciation, thih federal income tax liability will vary on the basis of the tax rate applicable to the interest owner. The profit margin required in the transaction may also vary widely because of risks inherent in the operation of the property and the respective trading ability of the parties to the transaction. In addition, in the opinion of many operators, the longterm inflationary trend may put a premium on future income from sales of a basic raw material, such as crude oil or natural gas. Prospective purchasers should. therefore, weigh all these factors with the federal taxes payable and the risks of the operations as negative factors and the inflationary effects and possible additional romance in the transaction as plus factors. Thus they can arrive at the proper fraction of the present worth at some safe interest rate that they are willing to pay. In a speech presented at the Petroleum Engineers Club of Dallas, Oct. 17, 1952, H.J. Gruy considered as fair market value two-thirds of future net cash income before amortization and federal taxes, discounted at 5 %/yr. This methodology is still in use. However, the discount rate at the time of the evaluation is substituted for the 5 %/yr rate. A study by Garb et al. in 1981 indicated that, in spite of varying tax and economic conditions, one classic yardstick for estimating the value of oil in the ground had remained reasonably constant through the years. An analysis of IO major transactions during the period 1979-8 I, a volatile oil-price period, indicated that oil reserves in the ground demonstrated a market value of approximately one-third of their posted wellhead price. Dodson listed in 1959, among some seven different methods that may be used to determine the fair market value of oil and gas reserves, percentages of the present worth, which may vary from 50 to 100% but which recently have been from 75 to 80 % A study by Arpsh of 34 actual property transactions made during the postwar years in the mid-continent, gulf coast, and California showed that the percentage of the 5% discounted value of future net cash income (before amortization and federal taxes) paid for these properties varied with their future lives. as shown in Table 41.5.

These data show a tendency for the average percentages of the last column to increase when the estimated life of the properties becomes longer. In none of these transactions did the total consideration exceed two-thirds of the updiscounted future net cash income before federal taxes. Fagin introduced an empirical market-value yardstick that is based on the trend in actual prices paid for producing properties during the postwar years in longlife fields such as East Texas (see Table 41.6). To find the market value by this yardstick for constant-rate production of a similar character, the percentage shown in Co]. 3 of the market-value-yardstick table for the applicable number of years of constant-rate production of Col. 2 of this table is determined. This percentage is then multiplied with the average 5% deferment factor of Col. I and with the undiscounted future net cash flow to yield the estimated market value. Example Problem 1. A property with an estimated future net cash flow of $1 ,OOO.OOO a IO-year constantand value of rate life would have a market 0.73x0.79x$1,000,000=$577,000. Solution. When the given cash-flow projection does not show a constant rate, the appropriate percentage is found in Co]. 3, which corresponds to the applicable average 5% deferment factor from Col. I of Table 41.6. This percentage is then multiplied by the average 5%deferment factor of Col. I and by the undiscounted future net cash flow to yield the estimated market value. Example Problem 2. A property with an estimated future net cash flow of $500,000. which has a 5 % discounted value of $375,000 (average deferment factor 0.75). would have a market value of 0.72 x0.75 x $SOO,OOO= $270,000.

TABLE

41.6-FAGINS

MARKET-VALUE

YARDSTICK Market Value as Percentage of 5% Discounted Value of Future Net Cash Flow 79 73 71 68 66 70 71

Average 5% Deferment Factor on Cash Flow Projection 0.88 0.79 0.70 0.63 0.52 0.44 0.32

Equivalent Constant-Rate Projection Wars) 5 10 15 20 30 40 60

41-6

PETROLEUM

ENGINEERING

HANDBOOK

TABLE Year 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 2% 0.9901 0.9708 0.9517 0.9330 0.9147 0.8968 0.8792 0.8620 0.8451 0.8285 0.8123 0.7964 0.7807 0.7654 0.7504 0.7357 0.7213 0.7071 0.6932 0.6797 0.6664 0.6533 0.6405 0.6279 0.6156 0.6035 0.5917 0.5801 0.5687 0.5576 0.5466 0.5359 0.5254 0.5151 0.5050 0.4951 0.4854 0.4759 0.4665 0.4574 0.4484 0.4396 0.4310 0.4226 0.4143 0.4062 0.3982 0.3904 0.3827 0.3752 3% 0.9853 0.9566 0.9288 0.9017 0.8754 0.8500 0.8252 0.8012 0.7778 0.7552 0.7332 0.7118 0.6911 0.6710 0.6514 0.6324 0.6140 0.5961 0.5788 0.5619 0.5456 0.5297 0.5142 0.4993 0.4847 0.4706 0.4569 0.4436 0.4307 0.4181 0.4059 0.3941 0.3826 0.3715 0.3607 0.3502 0.3400 0.3301 0.3205 0.3111 0.3021 0.2933 0.2847 0.2764 0.2684 0.2606 0.2530 0.2456 0.2384 0.2315

41.7-MIDYEAR 4% ~ 0.9806 0.9429 0.9066 0.8717 0.8382 0.8060 0.7750 0.7452 0.7165 0.6889 0.6624 0.6370 0.6125 0.5889 0.5663 0.5445 0.5235 0.5034 0.4841 0.4654 0.4475 0.4303 0.4138 0.397s 0.3825 0.3678 0.3537 0.3401 0.3270 0.3144 0.3023 0.2907 0.2795 0.2688 0.2584 0.2485 0.2389 0.2297 0.2209 0.2124 0.2042 0.1964 0.1888 0.1816 0.1746 0.1679 0.1614 0.1552 0.1492 0.1435

LUMP-SUM 4'12% ~ 0.9782 0.9361 0.8958 0.8572 0.8203 0.7850 0.7512 0.7188 0.6879 0.6583 0.6299 0.6028 0.5768 0.5520 0.5282 0.5055 0.4837 0.4629 0.4429 0.4239 0.4056 0.3882 0.3714 0.3554 0.3401 0.3255 0.3115 0.2981 0.2852 0.2729 0.2612 0.2499 0.2392 0.2289 0.2190 0.2096 0.2006 0.1919 0.1837 0.1758 0.1682 0.1609 0.1540 0.1474 0.1410 0.1350 0.1291 0.1236 0.1183 0.1132 5% 0.9759 0.9295 0.8852 0.8430 0.8029 0.7646 0.7282 0.6936 0.6605 0.6291 0.5991 0.5706 0.5434 0.5175 0.4929 0.4694 0.4471 0.4258 0.4055 0.3862 0.3678 0.3503 0.3336 0.3177 0.3026 0.2882 0.2745 0.2614 0.2489 0.2371 0.2258 0.2150 0.2048 0.1951 0.1858 0.1769 0.1685 0.1605 0.1528 0.1456 0.1386 0.1320 0.1257 0.1197 0.1140 0.1086 0.1034 0.0985 0.0938 0.0894

DEFERMENT

FACTORS 6% 6%% 0.9690 0.9099 0.8543 0.8022 0.7532 0.7073 0.6641 0.6236 0.5855 0.5498 0.5162 0.4847 0.4551 0.4273 0.4013 0.3768 0.3538 0.3322 0.3119 0.2929 0.2750 0.2582 0.2425 0.2277 0.2138

FLs=(l+~J'h-' 7% 0.9667 0.9035 0.8444 0.7891 0.7375 0.6893 0.6442 0.6020 0.5626 0.5258 0.4914 0.4593 0.4292 0.4012 0.3749 0.3504 0.3275 0.3060 0.2860 0.2673 0.2498 0.2335 0.2182 0.2039 0.1906 0.1781 0.1665 0.1556 0.1454 0.1359 0.1270 0.1187 0.1109 0.1037 0.0969 0.0905 0.0846 0.0791 0.0739 0.0691 0.0646 0.0603 0.0564 0.0527 0.0493 0.0460 0.0430 0.0402 0.0376 0.0351

3'/2% 0.9829 0.9497 0.9176 0.8866 0.8566 0.8276 0.7996 0.7726 0.7465 0.7212 0.6968 0.6733 0.6505 0.6285 0.6072 0.5867 0.5669 0.5477 0.5292 0.5113 0.4940 0.4773 04612 0.4456 0.4305 0.4159 0.4019 0.3883 0.3751 0.3625 0.3502 0.3384 0.3269 0.3159 0.3052 0.294s 0.2849 0.2753 0.2659 0.2570 0.2483 0.2399 0.2318 0.2239 0.2163 0.2090 0.2020 0.1951 0.1885 0.1822

5 % 120.9736 0.9228 0.8747 0.8291 0.7859 0.7449 0.7061 0.6693 0.6344 0.6013 0.5700 0.5403 0.5121 0.4854 0.4601 0.4361 0.4134 0.3918 0.3714 0.3520 0.3337 0.3163 0.2998 0.2842 0.2693 0.2553 0.2420 0.2294 0.2174 0.2061 0.1953 0.1852 0.1755 0.1664 0.1577 0.1495 0.1417 0.1343 0.1273 0.1207 0.1144 0.1084 0.1027 0.0974 0.0923 0.0875 0.0829 0.0786 0.0745 0.0706

i % h0.9645 0.8972 0.8346 0.7764 0.7222 0.6718 0.6249 0.5813 0.5408 0.5031 0.4680 0.4353 0.4049 0.3767 0.3504 0.3260 0.3032 0.2821 0.2624 0.2441 0.2271 0.2112 0.1965 0.1828 0.1700 0.1582 0.1471 0.1369 0.1273 0.1184 0.1102 0.1025 0.0953 0.0887 0.0825 0.0767 0.0714 0.0664 0.0618 0.0575 0.0535 0.0497 0.0463 0.0430 0.0400 0.0372 0.0346 0.0322 0.0300 0.0279

8% 0.9623 0.8909 0.8249 0.7639 0.7073 0.6549 0.6064 0.5615 0.5199 0.4814 0.4457 0.4127 0.3821 0.3538 0.3276 0.3033 0.2809 0.2601 0.2408 0.2230 0.2064 0.1912 0.1770 0.1639 0.1517 0.1405 0.1301 0.1205 0.1115 0.1033 0.0956 0.0885 0.0820 0.0759 0.0703 0.0651 0.0603 0.0558 0.0517 0.0478 0.0443 0.0410 0.0380 0.0352 0.0326 0.0301 0.0279 0.0258 0.0239 0.0222

8 % /2 0.9600 0.8848 0.8155 0.7516 0.6927 0.6385 0.5884 0.5423 0.4999 0.4607 0.4246 0.3913 0.3607 0.3324 0.3064 0.2824 0.2603 0.2399 0.2211 0.2038 0.1878 0.1731 0.1595 0.1470 0.1355 0.1249 0.1151 0.1061 0.0978 0.0901 0.0831 0.0766 0.0706 0.0650 0.0599 0.0552 0.0509 0.0469 0.0432 0.0399 0.0367 0.0339 0.0312 0.0288 0.0265 0.0244 0.0225 0.0208 0.0191 0.0176

0.9713 0.9163 0.8645 0.8155 0.7693 0.7258 0.6847 0.6460 0.6094 0.5749 0.5424 0.5117 0.4827 0.4554 0.4296 0.4053 0.3823 0.3607 0.3403 0.3210 0.302s 0.2857 0.2695 0.2543 0.239s 0.2263 0.2135 0.2014 0.1900 0.1793 0.1691 0.1595 0.1505 0.1420 0.1340 0.1264 0.1192 0.1125 0.1061 0.1001 0.0944 0.0891 0.0840 0.0793 0.0748 0.0706 0.0666 0.0628 0.0592 0.0559

0.2007 0.1885 0.1770 0.1662 0.1560 0.1465 0.1376 0.1292 0.1213 0.1139 0.1069 0.1004 0.0943 0.0885 0.0831 0.0780 0.0733 0.0688 0.0646 0.0607 0.0570 0.0535 0.0502 0.0472 0.0443

While the examples use a 5 % discount factor that is no longer valid, the methodology remains valid. Users of this technique should use discount rates appropriate for the time of the evaluation. Appraisal value equal to the present value of the net cash flow before federal taxes computed at a speculative rate of interest. Unlike Method 1, the profit margin over and above bank interest rates to take care of inherent risks and federal income tax liabilities is incorporated in Method 2 the higher discount rate. The possible range of such speculative rates of return is reflected by various quotations from the literature. This method is, again, fairly

simple in its application, because federal income taxes are not included in the computation. Use of Method 2 leads to comparatively high market values for properties of very short life. Because experience shows that very few transactions are made where the total consideration exceeds two-thirds of the future net cash income, experienced engineers in such cases usually limit their appraisal value to this maximum. This formula also tends to discriminate against long-life transactions because high speculative rates of return compound rapidly and reduce the value of cash-flow increments 20 to 30 years, hence to very small amounts. For example, Table 41.7 shows that the midyear lump-sum deferment

VALUATION

OFOILANDGASRESERVES

41-7

TABLE Year 1 2 3 4 5 6 7 8 9 IO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 46 49 50 9% 0.9578 0.8787 0.6062 0.7396 0.6785 0.6225 0.5711 0.5240 0.4807 0.4410 0.4046 0.3712 0.3405 0.3124 0.2866 0.2630 0.2412 0.2213 0.2031 0.1863 0.1709 0.1568 0.1438 0.1320 0.1211 0.1111 0.1019 0.0935 0.0858 0.0787 0.0722 0.0662 0.0608 0.0557 0.0511 0.0469 0.0430 0.0395 0.0362 0.0332 0.0305 0.0280 0.0257 0.0235 0.0216 0.0198 0.0182 0.0167 0.0153 0.0140 9% % 0.9556 0.8727 0.7970 0.7279 0.6647 0.6070 0.5544 0.5063 0.4624 0.4222 0.3856 0.3522 0.3216 0.2937 0.2682 0.2450 0.2237 0.2043 0.1866 0.1704 0.1556 0.1421 0.1298 0.1185 0.1082 0.0988 0.0903 0.0824 0.0753 0.0688 0.0628 0.0573 0.0524 0.0478 0.0437 0.0399 0.0364 0.0333 0.0304 0.0277 0.0253 0.0231 0.0211 0.0193 0.0176 0.0161 0.0147 0.0134 0.0123 0.0112

41.7-MIDYEAR 10% 0.9535 0.8688 0.7880 0.7163 0.6512 0.5920 0.5382 0.4893 0.4448 0.4044 0.3676 0.3342 0.3038 0.2762 0.2511 0.2283 0.2075 0.1886 0.1715 0.1559 0.1417 0.1288 0.1171 0.1065 0.0968 0.0880 0.0800 0.0727 0.0661 0.0601 0.0546 0.0497 0.0452 0.0411 0.0373 0.0339 0.0308 0.0280 0.0255 0.0232 0.0211 0.0192 0.0174 0.0158 0.0144 0.0131 0.0119 0.0108 0.0098 0.0089 12% 0.9449 0.8437 0.7533 0.6726 0.6005 0.5362 0.4787 0.4274 0.3816 0.3407 0.3042 0.2716 0.2425 0.2165 0.1933 0.1726 0.1541 0.1376 0.1229 0.1097 0.0980 0.0875 0.0781 0.0697 0.0623 0.0556 0.0496 0.0443 0.0396 0.0353 0.0315 0.0282 0.0251 0.0224 0.0200 0.0179 0.0160 0.0143 0.0127 0.0114 0.0102 0.0091 0.0081 0.0072 0.0065 0.0058 0.0051 0.0046 0.0041 0.0037

LUMP-SUM 15% 0.9321 0.8105 0.7046 0.6129 0.5329 0.4634 0.4030 0.3504 0.3047 0.2650 0.2304 0.2003 0.1742 0.1515 0.1317 0.1146 0.0996 0.0866 0.0753 0.0655 0.0570 0.0495 0.0431 0.0374 0 0326 0.0283 0.0246 0.0214 0.0186 00162 0.0141 0.0122 0.0106 0.0093 0 0080 0.0070 0.0061 0.0053 0.0046 0.0040 00035 0.0030 0.0026 0.0023 00020 0 0017 0.0015 0.0013 0.0011 0.0010 20%

DEFERMENT 25% 0.8945 0.7156 0.5724 0.4579 0.3664 0.2931 0.2345 0.1876 0.1501 0.1200 0.0960 0.0768 0.0615 0.0492 0.0393 0.0315 0.0252 0.0201 0.0161 0.0129 0.0103 0.0082 0.0066 0.0053 0.0042 0.0034 0.0027 0.0022 0.0017 0.0014 0.0011 0.0009 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001

FACTORS 30% 0.8770 0.6747 0.5190 0.3992 0.3071 0.2362 0.1817 0.1398 0.1075 0.0827 0.0636 0.0489 0.0376 0.0290 0.0223 0.0171 0.0132 0.0101 0.0076 0.0060 0.0046 0.0035 00027 0.0021 0.0016 0.0012 0.0010 0.0007 0.0006 00004 0 0003 0.0003 00002 0.0002 0 0001 35%

f Ls =(I + i)/- (continued) 40% 0.8452 0.6037 0.4312 0.3080 0.2200 0.1571 0.1122 0.0802 0.0573 0.0409 0.0292 0.0209 0.0149 0.0106 0.0076 0.0054 0.0039 0.0028 0.0020 0.0014 0.0010 0.0007 0.0005 0.0004 0.0003 0.0002 0.0001 45% 0.8304 0.5727 0.3950 0.2724 0.1879 0.1296 0.0894 0.0616 0.0425 0.0293 0.0202 0.0139 0.0096 0.0066 0.0046 0.0032 0.0022 0.0015 0.0010 0.0007 0.0005 0.0003 0.0002 0.0002 0.0001 50% 0.8165 0.5443 0.3629 0.2419 0.1613 0.1075 0.0717 0.0478 0.0319 0.0212 0.0142 0.0094 0.0063 0.0042 0.0028 0.0019 0.0012 0.0008 0.0006 0.0004 0.0002 0.0002 0.0001 60% 0.7906 0.4941 0.3088 0.1930 0.1206 0.0754 0.0471 0.0295 0.0184 0.0115 0.0072 0.0045 0.0028 0.0018 0.0011 0.0007 0.0004 0.0002 0.0001 70% 0.7670 0.4512 0.2654 0.1561 0.0918 0.0540 0.0318 0.0187 0.0110 0.0065 0.0038 0.0022 0.0013 0.0008 0.0005 0.0003 0.0002

0.9129 0.7607 0.6340 0.5283 0.4402 0.3669 0.3057 0.2548 0.2123 0.1769 0.1474 0.1229 0.1024 0.0853 0.0711 0.0593 0.0494 0.0411 0.0343 0.0286 0.0238 0.0198 0.0165 0.0138 0.0115 0.0096 0.0080 0.0066 0.0055 0.0046 0.0038 0.0032 0.0027 0.0022 0.0019 0.0015 0.0013 0.0011 0.0009 0.0007 0.0006 0.0005 0.0004 0.0004 0.0003 0.0002 0.0002 0.0002 0.0001 0.0001

0.8607 0.6375 0.4722 0.3498 0.2591 0.1919 0.1422 0.1053 0.0780 0.0578 0.0428 0.0317 0.0235 0.0174 0.0129 0.0095 0.0071 0.0052 0.0039 0.0029 0.0021 0.0016 0.0012 0.0009 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0.0001

factor for income received in Year 30 amounts to 0.2371 for 5% interest, 0.0601 for 10% interest, and 0.0046 for 20% interest. Because of these shortcomings, the use of Method 2 is not recommended, particularly when longlife properties are involved with a high profit-toinvestment ratio. In a speech presented at the Oil and Gas Inst. in Dallas, March 26, 1949, E.L. DeGolyer commented, It is rather surprising that more often than not the latter method, i.e. one-half of a 4% discounted future net revenue, is very close to the future net revenue (before amortization and federal taxes) discounted at 10 % per /z year. Dodson listed in 1959 among some seven different methods that may be used to determine the fair market

value of oil and gas reserves, rate of return on investment of apparently 14% or more. From a study of five actual and representative valuations that have served as a basis for settlement for gift or ad valorem taxes, Reynolds concluded in 1959 that: The range of from 13% to 21% annual rate of return before tax adjustments provides limits on which the engineer can operate. He also observed that the data from these appraisals indicate that the project with a short life will demand a higher rate of return than one with a long life and low risk. This is probably caused by the investors long-range faith in the oil industry, the belief that higher prices per unit are in the offing, and the fact that less money management is necessary for reinvesting earnings.

41-8

PETROLEUM

ENGINEERING

HANDBOOK

TABLE Year 1 2 3 4 5 6 7 8 9 IO 11 12 13 14 15 16 80% 0.7454 0.4141 0.2300 0.1278 0 0710 0.0394 0.0219 0.0122 0.0068 0.0038 0 0021 0 0012 0.0006 0.0004 0.0002 0.0001 90%

41.7-MIDYEAR 100% 0.7071 0.3536 0.1768 0.0884 0.0442 0.0221 0.0110 0.0055 0.0028 0.0014 0.0007 0.0003 0.0002 1 10%

LUMP-SUM 120% 0.6742 0.3065 0.1393 0.0633 0.0288 0.0131 0.0059 0.0027 0.0012 0.0006 0.0003 0.0001

DEFERMENT 130% 0.6594 0.2867 0.1246 0.0542 0.0236 0.0102 0.0045 0.0019 0.0008 0.0004 0.0002 140%

FACTORS 150% 0.6325 0.2530 0.1012 0.0405 0.0162 0.0065 0.0026 0.0010 0.0004 0.0002

F,, =(7 +i)- (continued) 160% 0.6202 0.2385 0.0917 0.0353 0.0136 0.0052 0.0020 0.0008 0.0003 0.0001 170% 0.6086 0.2254 0.0835 0.0309 0.0115 0.0042 0.0016 0.0006 0.0002 180% 0.5976 0.2134 0.0762 0.0272 0.0097 0.0035 0.0012 0.0004 0.0002 190% 0.5872 0.2025 0.0698 0.0241 0.0083 0.0029 0.0010 0.0003 0.0001 200% 0.5773 0.1924 0.0641 0.0214 0.0071 0.0024 0.0008 0.0003

0.7255 0.3818 0.2010 0.1058 0.0557 0.0293 0.0154 0.0081 0.0043 0.0022 0.0012 0.0006 0.0003 0.0002

0.6901 0.3286 0.1565 0.0745 0.0355 0.0169 0.0080 0.0038 0.0018 0.0009 0.0004 0.0002

0.6455 0.2690 0.1121 0.0467 0.0195 0.0081 0.0034 0.0014 0.0006 0.0002 0.0001

The aforementioned rates of return were applied to the entire transaction. including the reserved production payment. Because of leverage afforded by the thenpermitted ABC method of purchasing properties. the actual rate of return on the equity capital was higher than the rate of return for the transaction as a whole. The calculated pretax internal rate of return remains a useful yardstick for establishing a fair market value. The acceptable rate of return at any time will be a function of comparative investment opportunities and the subjective assessment of the risk. At the time of this writing, pretax rate of return must fall between 20 and 30% to be compctitivc with other investment options. Appraisal value equal to the present value of the net cash flow after federal income taxes computed at an intermediate rate of interest. Method 3 is the most sophisticated approach to the fair-market-value problem. It requires an actual computation of the federal tax liability for each year and is rather laborious. The method also requires tax and accounting information that may not be readily available to the evaluating engineer. Those favoring this method generally use electronic-data-processing facilities that reduce the actual work by the valuation engineer to the preparation of the basic input data. The rate of return in this type of computation comes close to the actual rate of return that, aside from price fluctuations and errors in estimating, may be realized on the purchase. If this method is followed, the fair market value may be defined as the cash value that, if paid for the property. would yield a satisfactory rate of return on the purchase price. A satisfactory rate of return or yield is one that is sufficient to induce the buyer to risk his funds in the particular project rather than in safer investments offering a lower yield. This rate must be commensurate with the physical hazards of producing and the economic hazards of future production. In principle, it is the same incentive recognized in the regulation of public utilities, where the reasonable rate of return upon the fair value of the property (the rate base) is held to be that sufficient to induce the investment of capital in establishing, mainraining. and expanding the property. Check List of Data Required for Evaluation of Oil- and Gas-Producing Properties Bccausc the prcviouxly discuhscd evaluation procedures

are reflections of the pattern of future revenues, most evaluation methods are based on the predicted projections of oil and gas production. These projections are prepared either by extrapolating established trends in producing capacity or by academically estimating anticipated production on the basis of geologic interpretations and/or analogy (see Chap. 40). To make a sound valuation of a given producing property, the appraiser requires certain basic data. The following check list may serve as a reminder when collecting such data. Maps and Cross Sections. These include ownership maps, geological-structure maps. isopach maps, geological cross sections, etc. Lease-Location Data. List leases to be included and show for each lease the lease name, number of producing wells, number of temporarily abandoned wells, total number of acres, field name, county, state, and legal description of lease. Well Logs. These logs include all electrical, acoustic, and radioactivity logs that have been run in each well. Also, if available, geological-sample logs and directional well-survey reports should be included. Core-Analysis Data. All core-analysis reports for the zones that have been cored and analyzed should be included. Ruid-Sample-Analysis Data. This includes all bottomhole fluid-sample-analysis reports and. for gas wells, gasanalysis, specific-gravity, or recombined-sample-analysis reports. Well History. Chronological history of all well operations including original drilling and completion, recompletions, and remedial work to date should be included. If not otherwise included in a complete chronological well history. provide the following data for each well: conservation commission completion, potential test, and GOR reports: completion (and/or recompletion) date; elevation: kelly bushing, derrick floor, and ground level; total depth* and plugged-back depth; casing size and setting depth; tubing size and setting depth; drillstem test data including intervals tested. time open, fluid recovered. and bottomhole pressure (BHP) data: coring data. including intervals cored. footage recovered. and core description:

VALUATION

OF OIL AND

GAS

RESERVES

41-9

geological tops of all major formations encountered; welllocation plats or location description: producing formation name, interval perforated, initial production and potential test data; depths to top. bottom. oil/water contact, and gas/oil contact: and pay thickness (gross feet and net feet). Past-Production History. This history includes tabulation of oil. water, and gas production by months, by leases, by wells, and by pay zones since original complction. Also, include other past history reports, such as production methods (type and size of equipment and dates installed); BHP and wellhead pressure reports; open-flow potential test reports (gas wells); conservation comniission (or USGS) production. allowable, and MER reports: pipeline run statements: water-disposal and (mating reports: fluid-injection records; and production history of offset operations. Current Production Data. Tabulate for each well the most current actual test of oil. water. and gas produced and include test date. choke size [or stroke length and strokes per minute (spm)], producing tubing pressure, and producing casing pressure. For gas wells, indicate latest shut-in tubing and casing pressures. including date well was shut in and duration of shut-in time. Current-Allowable Data. Summarize allowable formula and current daily allowable rates for each well, per producing day, and per calendar day. Gross Crude Price. For each lease. give the name of the crude purchaser, the average gravity of the oil, and the gross price paid. If the crude is trucked. show the trucking cost per barrel (may be obtained from pipeline run statements). Gross Gas Price. For each lease, give the name of the gas purchaser and summarize the provisions of the gas contract such as the gross gas price per 1,000 cu ft. the contract pressure base. the minimum delivery pressure. the effective date and term ofthe contract. and escalation clauses (may be obtained from gas contracts and FPC approval certificates). Severance and Local Taxes. Indicate the total value of both severance and local (state, county, school. etc.) taxes in terms of a percentage of the total gross income or as an amount per barrel of oil or Mcf of gas produced. Federal Excise Tax (WPT) information. This should include. where applicable. tier. company or entity classification for tax. natural gas classification. and price controls. if any. Operating Expenses. Tabulate actual gross operating expenses per well per month for each lease during the past year. State whether such expenses include. in addition to all direct costs. such items as well-stimulation expenses, wjorkover or recompletion expenses. a portion of district or division overhead expenses. or severance and (xi 1~1/ore777 taxes. Completion and Recompletion Costs. In case of undeveloped or nonproducing reserves. provide an estimate of completed well costs or recompletion costs for reserves behind the casing. Division of Interests. Tabulate the working interest (fraction of /x ofthe costs) and the revenue interest (fraction of /H the income) for each interest owner so that of for each lease 100% of the working interest and 100% of the revenue interest lease is accounted for. Indicate the lease operator (copy of division orders for oil and gas).

Existing Production Payments or Liens. Tabulate the balance due on all production payments or liens as of a recent date and indicate provisions for the rate of payment. Lease andAssignment Provisions. Summarize special provisions of all leases and assignments that may adversely affect the value of the leases. In particular. show special provisions concerning shallower or deeper rights and commitments or obligations for the drilling of wells (may be obtained from lease and assignment agreements). Lease Facilities. Provide complete information concerning lease-facility wells, such as water wells, disposal wells, and injection wells. Provide specifications (size, capacity, etc.) for major lease-facility equipment, such as gas compressors, oil-treating plants, and water-injection plants. OperatingAgreements. In case ofjoint interest or unitized properties, provide a list of the basic provisions of the operating agreement, such as preferential rights to purchase other interests, obligations for development. basis of overhead allocation, and call on the oil (may be obtained from operating agreements and/or letter agreements). Unitization Agreements. In case of unitized properties, provide a list of the basic provisions of the unitization agreement concerning the basis for calculation of participation percentages and future revisions of same owing to possible future adjustments in operating methods, unitized area. etc. (may be obtained from unitization agreements). Special Reports. Provide a copy of all special geological and engineering reports that contain data pertinent to a current evaluation of the property. In particular, special engineering reports concerning plans for future development and secondary recovery operations may be helpful in projecting future production rates and future net operating income. Income Tax Information. Include if applicable.

Forecast of Future Rate of ProductionlZDeclining Production When a property has a well-established performance history and the production rate shows a persistent decline. the appraiser should first make sure that this decline is not caused by either decreasing effectiveness of the lifting equipment or adverse wellbore conditions. If he finds that the lifting equipment is operating properly and that the wellbore is clean, the past decline may be used as a guide for the projection of future production. First the type and rate of decline must be established. Constant-Percentage Decline

When the drop in production rate per unit of time is a constant percentage of the production rate. the production curve is of the constant-percentage-decline type. This can best be demonstrated by plotting the production rate vs. time on semilogarithmic paper, with the production rate on the log scale. which should then show a straightline trend. The production rate may also be plotted vs. cumulative production on regular coordinate paper. which should again show a straight-line trend for this type of decline (Fig. 40. I, Curve I). In either case, the slope of the curve represents the nominal decline fraction or percentage. The decline may also be found by observing the

41-10

PETROLEUM

ENGINEERING

HANDBOOK

Fig. 41.1-Graphical extrapolation hyperbolicand harmonic of rate/time curves on semilog paper. Step 1: Smooth out the given production curve, and select three equidistant pointson it (A, B, and C). Step 2: Draw a vertical midway between A and C through Point line B. Step 3: ProjectA and C horizontally thismidon dle lineand findPointsA and C. Step 4: Draw AD and CE parallel BC. Step 5: Project D back to horizontally the curve and find Point F. Step 6: on draw DX parallel FE, and findthe unknown extrapto olated PointX at the intersection with the horizontal linethrough E.

computing a few points of the curve by means of Eq. 60 of Chap. 40 or by using the graphical extrapolation method on semilog paper shown in Fig. 41.1, which is based on the three-point rule : For any two points * on a hyperbolic rate-time curve, for which the production rates are in a given ratio, the point midway in between will have a production rate which is a fixed number of times the rate of either the first or the last point, regardless of where the first two points are chosen. For example, when the three equidistant points on the past-performance portion of the curve show production rates of 2,000, 1,300, and 1,000 bblimonth, then the future time interval between the ordinates of 1,000 and 650 bblimonth must be equal to the time interval between the ordinates of 650 and 500 bbllmonth. The future projection is then obtained by reading the production rates from the graphically extrapolated curve. Hyperbolic decline is the most common form of production-decline trend found with nonprorated or capacity production. The fractional power n is usually between 0 and 0.50, with the latter value applicable to gravity-drainage-type production under certain conditions. Harmonic Decline When the drop in production rate per unit of time expressed as a fraction of the production rate is proportional to the production rate itself, the production curve is of the harmonic-decline type. Such a curve, plotted as a rate/time graph on semilog paper, does not follow a straight line but shows a rather persistent, pronounced curvature. The rate-cumulative graph on regular coordinate paper shows the same strong curvature (see Fig. 40.21, Curve III). Harmonic decline may be identified graphically by plotting the inverse of the production rate vs. time on regular coordinate paper, which should then show a straight line. It may also be demonstrated by plotting the ratecumulative relationship on semilog paper, which should also follow a straight line. Harmonic decline for production-decline curves does not occur very often, and extrapolation on this basis usually provides a projection that is too optimistic. It is occasionally applicable to capacity production from depletion-type gas wells or to nonprorated production from reservoirs with a bottomwater drive where it is economically feasible to lift and to dispose of large volumes of water. Extrapolation of the rate/time graph may best be carried out by plotting the inverse of the production rate vs. time on regular coordinate paper and extending the straight line obtained. A rate/time graph on semilog paper may also be extended by the same construction on the basis of the threepoint rule for hyperbolic decline illustrated in Fig. 41.1. Part Constant Rate-Part Declining Production

ratio between the production at the end of a given period and at the beginning of that period and obtaining the effective decline by interpolation from Table 40.16 or 40.17. For example, if the production rate from a well or lease declined from 4,286 to 3,000 bbllmonth in 10 months, the ratio between these two production rates is 0.70, and one may read from Table 40.16 that such a drop in rate in 10 months corresponds to an effective decline of 3X %/month. The forecast may then be made on that basis either by reading the future rates from an extrapolation of the straight-line trend on the semilog decline chart or by computing the future rates by means of Table 40.16 or 40.17. Such extrapolation is then continued until the economiclimit rate of production is reached. Hyperbolic Decline When the drop in production rate per unit of time expressed as a fraction of the production rate is proportional to a fractional power n of the production rate (0 vDE>DC

and

&SN, fs

xcd,,

(6)

and v,,=(o.15xV) VDE > DC and the allowable depletion is therefore DA = VDE =$7,700. Alternative Minimum Tax. The Internal Revenue Code of 1954 has been amended at various times to include provisions requiring that a taxpayer pay a specified rate of tax on certain defined tax preference items. These preference items currently include two oil- and gas-related expenses: percentage depletion deductions in excess of the depletable basis in a specific property and certain intangible drilling and development costs. The latter item is not applicable to corporate taxpayers. While the percentage depletion preference item is fairly self-explanatory, the determination of the intangibles that must be included as a preference item requires computation:CIP =c/x-1,'

or cost depletion, DC, when DA =Dc>

VTI>D,>VDE.

VALUATION

OF OIL AND

GAS

RESERVES

41-15

TABLE

41.9-TIER

AND

RATE

STRUCTURE.

WPT Other than Independent Producer W) 70 50 30 15

Independent Producer w Tier 1 Tier 2 Tier 3 Tier 3 (oil other than Tier 2 or 3) (stripper and certainU.S. government interests) oil (newly discovered, heavy and incrementaltertiary oil) (newly discovered oilsubsequent to May 31, 1979) 50 30 30 15

where CIp = preference intangible drilling costs, dollars, and CIX = intangible costs minus CrA, dollars.

I,, is the net income from productive oil and gas properties, defined as the aggregate amount of gross income from all such properties, less deductions allocable to the properties reduced by CIX as set forth above. This preference item can be reduced if the taxpayer chooses to capitalize all or any portion of the intangibles paid or incurred during the year. Windfall Profit Tax. In April 1980, Congress passed the Windfall Profit Tax Act that was designed to tax the oil and gas interest owner on the windfall profit that was to be received as a result of the deregulation of domestic crude-oil prices. The taxable profit is the excess of the selling price over what the price would have been were it sold before decontrol, adjusted by an inflation factor. An additional adjustment is allowed for severance taxes imposed on the difference between the controlled and decontrolled price. The tax base is also limited to 90% of the net income from the property. Once the tax base is determined, the appropriate tax rate must then be applied. Three tiers have been specifically defined into which all taxable crude oil falls. The rates applicable to each tier depend on the classification of the interest owner and the nature of the oil produced. Exemptions for certain interest owners and oil types are also provided. The current tier and rate structure is given in Table 41.9. Newly discovered oil. which falls within Tier 3, is subject to a tax rate schedule that declines from 22.5% in 1984 to 15% in 1986 and thereafter. Tax Consequences Related to Conveyances. Oil and gas taxation of property conveyances has evolved into a complex set of rules that are necessary because of the many variations of transactions that involve oil and gas interests. Any appraiser who is valuing an interest that includes tax consequences should be aware of the types of various transactions. There are four primary methods of disposing of oil and gas interests: sale. sublease, special sharing arrangements in a partnership, and production payments. The acquisition of interests may involve the reciprocal of these methods as well as the receipt of an interest for services. The sale/purchase of an interest provides the easiest forum within which to determine the tax consequences. The

seller will recognize gain that will be characterized as capital or ordinary, depending on various factors that involve the classification of the seller and the tax history of the property. The buyer will merely have basis in the property that should be allocated between the mineral interest and lease and well equipment. Note that an interest owner will often look to the appraiser for guidance regarding the amount that should be allocated to lease and well equipment. A sublease commonly arises where the transfer of a working interest is burdened with a nonoperating interest retained by the assignor. Consideration received by the assignor is ordinary income because it is characterized as a lease bonus. Any basis in the property is attributed to the nonoperating interest that is depletable; it is not allowed as an offset to the income. The assignee purchase s price will be allocated between leasehold cost and lease and well equipment, if applicable. Special sharing arrangements are frequently used in a partnership context to allow special allocation of certain items of income and deduction. The partnership allocation rules explained in the Internal Revenue Code and the regulations published by the Dept. of the Treasury should be used as a guide to confirm the tax treatment of such allocations. A problem exists in the standard third for a quarter transaction outside the partnership context: the expenses paid by the assignee attributable to the seller s retained interest are considered leasehold cost. They are not deductible even if they are in the nature of intangibles. A production payment is the right to a specific share of production from an oil and gas property. Where the production payment is used to finance a project, it is treated as a loan by the lender and the interest owner who carved it out of production. Where a working-interest owner retains a production payment and conveys his working interest, he is treated as having sold his interest and should report the proceeds as income realized from the sale of the property. In certain instances, the holder of the production payment may be treated as owning an economic interest. As indicated previously, this would allow the possible deduction of depletion, subject to the restrictions discussed. The acquisition of an interest in an oil and gas property is frequently made through the performance of services. At one time, it was generally believed that. at the date of transfer, the party receiving the interest was notinvolved in a taxable event. He, along with the other vendors,

dealers, and professionals involved in the propercapital to enable its ty> was merely contributing development. This position, while originally accepted by the Internal Revenue Service, has recently come under

PETROLEUM

ENGINEERING

HANDBOOK

c Fig. 41.2-Discounted-cash-flow method. Rate of return j= I;P/I;C, = P/C, = constant. At abandonment time, C, = Tm, (no interest).

Fig.

41.4-Morkill method. Rate of return I= YZPn;(C, -S) = P/C, -S=constant. At abandonment time t,,C, =S (including interest).

NET PROFIT P=, C 0

attack and is being severely restricted. The government s current position is that in most instances, at the date of transfer, the taxpayer performing services recognizes taxable income. The issue is far from settled, and additional activity is expected to clarify the tax consequences of such transactions.

Different Concepts of ValuationThe literature includes many different methods that may be used to evaluate the known or estimated future projection of net income from a given venture. 7-20 One of them, the discounted-cash-flow method, illustrated in Fig. 41.2. simply reduces these future income payments to present worth or present value by a chosen rate of compound interest or rate of return. It represents the banker s approach to a stream of future income payments and is widely used in industrial work. The Hoskold method, illustrated Fig. 41.3, was spein cifically designed for ventures with a limited life, such as mines or oil or gas wells, and was first used in mineevaluation work. The Morkill method, illustrated in Fig. 4 1.4. is actually a refinement of the Hoskold method and is also mainly applicable to ventures with a limited life, such as mines and oil or gas wells. The accounting method. illustrated in Fig. 41.5, represents the accounting approach to the valuation problem and takes into account the actual depletion pattern applicable to the given venture. It is particularly suited for those ventures where a specified total number of units of production is involved and where. as is the case in most extractive industries. the depletion applied to the original capital investment is on a unit-of-production basis.

Fig. 41.3~Hoskold method. Rate of return = P/C, = constant. j At abandonment time t,,C, = S (including interest.)

VALUATION

OF OIL AND

GAS

RESERVES

41-17

Fig. 41.5-Accounting method. Rate of returnj= Z/XC,. At abandonment time t,, C, = ED, (no interest).

Fig. 41.6-Average-annual-rate-of-return method. Rate of return j present worth of W/present worth of XC, = Area = ABCDElArea FGHK. At abandonment time t,, C, =ZD, (no interest).

The average-annual-rate-of-return method, illustrated in Fig. 41.6, is essentially a refinement of the accounting method and, by applying the present-worth concept to both the net annual profits and the net remaining investment balances, simplifies the computations and properly weighs the time pattern of the income. A complete summary of the basic equations for these different methods and their appraisal and rate-of-return equations will be found in Table 41.10. The top part of this table shows the equations for continuous compounding and the solution for the constant-rate case. The bottom part shows the appraisal equations and the rate-of-return equations for the general case where the cash flow, I, varies from year to year. Discounted-Cash-Flow Method

jetted cash flow to present value by means of the desired rate of interest. The appraisal value is then Cj=I,(l+i )-+I2(l+i I~+. )- fl=r, C;= C I,(l+i )-, n=l .. . ... .. (7) .+Z,(l+i , )-

This method, also referred to as the investors method * or internal-rate-of-return method, , is the one most * often used in appraisal work. It is based on the principle that, in making an investment outlay, the investor is actually buying a series of future annual operating-income payments. The rate of return (with this method) is the maximum interest rate that one could pay on the capital tied up over the life of the investment and still break even. The time pattern of these future income payments is, therefore, given proper weight. No fixed amortization pattern needs to be adopted with this method because the annual amounts available for amortization are equal to the difference between the net income and the fixed profit percentage on the unreturned balance of the investment. The computations necessary for a property evaluation are, therefore, relatively simple. They usually involve only the discounting of the pro-

in which I,, I2 . . . I, represents the projection of the cash income in successive years and the compound-interest factor for the speculative effective interest rate iis computed for the assumption that the entire income for each year is received at mid-year. Appropriate midyear compoundinterest factors (1 +i )- will be found in Table 4 1.11 for speculative effective interest rates from 2 to 200%. In the case of oil-producing properties, the computed earning power by this method is not necessarily the same as the average rate of return later shown on a company s books for the net investment in the property. Most oil companies amortize their investments in producing properties in proportion to the depletion of the reserves or on a unit-of-production basis. However, no provision for such amortization pattern is made in the discounted-cashflow method. When the production rate and the income both follow constant-percentage decline and the ratio between initial and final production rates is substantial, no serious difference will result. However, when the rate of production and the income are constant for a long period of time, a substantial difference may develop and the average rate of return, as shown later on the company books, s may be appreciably higher than the rate of return used in the evaluation by the discounted-cash-flow method.

41-18

PETROLEUM

ENGINEERING

HANDBOOK

TABLE

41.10-SUMMARY

OF EQUATIONS

APPLICABLE

TO DIFFERENT

VALUATION

METHODS

Discounted Cash Flow For continuous compounding, basic equation I df=jC, dl-dC, where f=O C, =C, t=t, c,=o (8)

Hoskold I dl+jS dt=jC, dt+dS where t=O S=O t=t, s=c, (14)

Appraisal equation for constant annual income of I dollars per year

(15)

Rate-of-return equation for constant annual income of I dollars per year General case: Appraisal equation

Solutionforjwhich will satisfy Eq. 9

,

je -I,

i= C, l-e-. = 1,

=ta

c, =

c /,(l+I)- n=,

(7)

5

/(I+/)a-

c,=1 + r[(l +,)a-] or

(10)

c,ii = FPE/ --c JiT-l (1 +i)- 8 Rate-of-return equation Solutionfor ithat will satisfy Eq. 7

(11)

(12)

or

i

j =

L

---(l+i)ys C, 1 -(1 +i)- a

FPE

1

(13)

The method may be illustrated with the diagram of Fig. 41.2, which shows the application of the discounted-cashflow method to a venture that is expected to yield an income of $1 OO,OOO/yrevenly over a period of 10 years and where a speculative nominal rate of return j of lSX/yr is desired. Time in years is plotted on the horizontal axis, while the constant income is represented by the horizontal line for $lOO,OOO/yr in the upper part of the diagram. The top portion of the diagram shows how the portion of the total income, I, allocated to amortization, mk, increases, while the net-profit portion (P) decreases with time. The bottom portion of the chart illustrates the manner in which the cumulative Cmk gradually reduces the unreturned balance of the investment, CB =C; -Cmk, from its initial value, C;, to zero at abandonment of the venture. The computation of the curves for this constant-rate case is based on the basic differential equation for discounted cash flow, Idt=j CBdr-dCB, (8)

where I = yearly net income, dollars, j = nominal annual speculative interest rate, fraction, and Cs = balance of unreturned portion of investment, dollars. Integration of this equation for constant-rate income between the limits r=O, CB = C; and t =t,, , Cs =0 leads to the appraisal value C, for a nominal rate of return j =O. 15:

c;=(l-a-J