KEY CONCEPTS ON ECONOMIC EVALUATION AND DECISION ANALYSIS OF EXPLORATION - PRODUCTION PROJECTS
Centro Superior de Formación Repsol
Exploration & Production
ACKNOWLEDGEMENTS Special thanks to: Marco Antonio Guimarães Dias, professor of Industrial Engineering Departament of “Pontifícia Universidade Católica do Rio de Janeiro”, because his opinion has been key in the bibliography selection. Amparo Cervera, professor of Market Research and Techniques of the Business Administration Department of the Valencia University, because she gave me the access to the Library of Harvard Business School, in Boston. Clara Cardone, Director of the Master of Business Administration Program at the Carlos III University of Madrid, for her advice and guidance.
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CONTENTS Introduction. Exploration economics. Exploration success chance. Exploration considerations. Economic factors influencing evaluations. Energy and the Economy. Oil and Economy. A Relationship of Diminishing Importance. The US example. Measures of profitability: Those, which do not consider the time-value of money. Payout. Profit - to - investment ratio (ROI). Time - value considerations. Measures of profitability: Those, which consider the time -value of money Internal rate of return. Net present value. Net present value gives better decisions. Discounted profit - to - investment ratio (DPR). Risk analysis and oil exploration. statistics: sample space, event, relative frequence probability, Basic principles of statistics: objective probability, subjective probability, conditional probability, etc Probability theory. Operation rules: addition, multiplication and Bayes’ theorems. Analysis based on the condition of dependent events
(sampling with
replacement) Analysis based on the condition condition of independent events events (sampling without replacement)
Risk, uncertainty and estimating. Decision analysis. The expected value concept. Meaning and interpretation of expected values. Decision tree analysis. Solving a decision tree.
Probability distributions. Discrete, continous and cumulative frequency distributions Measures of central tendency: mean, median and mode Measures of variability: standard deviation Distributions of interest in exploration risk analysis: normal and lognormal distributions Preference theory concepts. The mathematical basis for preference theory. Glosary of economic evaluation nomenclature
INTRODUCTION Exploring for new reserves of oil and gas natural is a long-term economic priority for mankind. New reserves must be located to provide economically viable and politically secure petroleum sources essential to an expanding global economy in the future. Millions and millions are spent every year in this search. Oil and gas exploration is, however, a complex and risky business. Most exploration wells are dry holes and are abandoned when drilling is completed, with only a fraction of them leading to commercial developments of new oil and gas reserves. The volatility of oil prices has raised major questions regarding the economic sense of exploration program. The financial and regulatory environments for petroleum exploration have become increasingly complex in recent years. Political risk may also be an important consideration in many foreign countries. Concerted evaluation of new exploration opportunities will not remove many of the difficult to predict risks and uncertainties, but it can improve the economic efficiency of exploration investments, resulting in annual savings of billions of dollars for the industry as a whole. This course has been designed to provide a practical approach to assessing the economic merit of investments made in exploring for new reserves of oil and gas in environments of technical uncertainty. It strives to embrace the spectrum of business disciplines and technological and financial considerations involved and weave them into cohesive format, which facilitates simple yet comprehensive analysis. The course has been organized in the general sequence in which business, operational and financial factors are considered in the normal evolution of petroleum exploration. It is a practitioner’s treatment, concentrating on the assembly and analysis of the best available
information and showing how to communicate to senior management the information used, the way in which the analysis was done, the results which were obtained and the implications these results may have for decisions a corporation may take. While economics is one of the vital tools in decision making, economic analysis is not the only criterion used; unquantifiable factors sometimes underlie major strategic moves.
EXPLORATION ECONOMICS Is defined as quantifying our expectations, in financial terms, with respect to exploring for and developing new oil and gas prospects. Includes consideration of numerous technical and financial factors: exploration costs, success chance, reserve size, well productivities, well spacing, facilities design, development costs, transportation systems, oil/gas prices, contract terms, discount factors, capital cost, etc. According to official exploration drilling statistics, such as those reported by national petroleum agencies, the conventional definition of success means simply that a well was completed and did produce some hydrocarbons. But, geological success is not necessarily the same as commercial success or even economic success. It is well-known the phrase “geological success but economic failure”. The standard definitions of successs contain
some possible outcomes: Geological success, meaning that a reservoired accumulation was found that was at
least large enough to support a flowing test. In onshore any well that flows is likely to be completed, but many such small reservoirs encountered offshore are often reported as shows. Commercial success or completion success. The exploratory well was completed
because anticipated future production revenues will return a profit on the cost of completing and operating it, but not on the costs of exploratory drilling, leasing, and seismic, which are thus viewed as sunk cost and not recoverable. This is an economic success on half-cycle basis, defined as the incremental economics of developing an oil/gas prospect once a discovery has been made. Economic success. The well was completed as the discovery well for a field in which
average wells generate sufficient production revenues to recover the cost to drill, complete, and operate them, as well as the sunk cost to find the field, plus a reasonable profit. Some authors said this is an economic success on full-cycle basis, defined as the economics of discovering and developing an oil/gas prospect including the risk cost of dry holes. The motive for being in the petroleum exploration business is to make a financial profit. It is clear the necessity of to find ideas, methods or criteria to measure the venture’s
attractiveness. The decision maker needs tools to distinguish those investment proposals that are not just a geological success, but large enough to produce the necessary revenues to recover all the expenditure, plus a certain level of profit to attract investors and, at the same time, generate sufficient economic resources to continuing exploring.
EXPLORATION SUCCES CHANCE . Petroleum geologist generally agree that for a subsurface accumulation of hydrocarbons to exist, there must be porous and permeable reservoir rock, hydrocarbons that have moved from a petroleum source rock to the reservoir rock, and a sealed closure or trap capable of containing hydrocarbons. All three of these requirements must be met for a hydrocarbons accumulation will be present. This paradigm becomes the fundamental basis for employing geologic chance factors in estimating probability of geologic success. Serial multiplication of all factors produces a decimal serial fraction equivalent to the probability that a hydrocarbons accumulation is present, which is the probability of geological success. The chance factors should be thought of as a links chain: if any link breaks, the chain fails. If any one of the geologic factors is zero, the prospect will be dry. Chance of hydrocarbon source Chance of prospect structure Chance of permeable reservoir Chance of trapping seal Composite chance of hydrocarbon discovery
= = = = =
0.72 0.60 0.50 0.40 0.0864
Chance that hydrocarbons will be oil Chance of oil discovery
= 0.75 = 0.0648 or 6,48%
This link chain determine the shape of the probability distribution. The Central Limit Theorem provides that distributions resulting from natural multiplication of independent random variables will be lognormal. The lognormal distribution in petroleum science has gained wide acceptance recently (see pag 42). Dry hole risk broken in two major categories. Primary risk is defined as the perceived level of exploration risk before the initial discovery is made in an exploration play or area, i.e.: rank wildcat risk before a play has been demonstrated to be productive. Secondary risk. Is defined as the perceived level of exploration risk after the initial discovery has been made in an exploration play or area. Secondary risk is dependent upon success at the primary risk stage and relates only to whether or not an individual prospect will be a discovery within an already successful exploration play. Independent prospects are defined as secondary risk exploration targets where a discovery in any prospect does not materially change expectations regarding the chance of making a discovery in exploring follow-up prospects. Dependent prospects are defined as primary risk in any one of the prospects significantly enhances the perceived chances for making follow-up discoveries. In some cases, failure to make a discovery in a proximity risk prospect can result in a downgrading of discovery expectations for follow-up prospects.
EXPLORATION CONSIDERATIONS Exploration lands provide the necessary physical base for natural resource companies to develop and undertake exploration programs to find new reserves of crude oil and natural gas. Consequently, oil companies place a heavy emphasis on accumulating large inventories of petroleum lands in attractive geological areas, which are considered to have a good potential for yielding new petroleum discoveries. Attempts are usually made to distribute the land holdings over a number of areas having differing types of petroleum prospects and sometimes contained in a variety of political and administrative settings. Exploration lands are usually made available by host governments to oil companies through different ways. There are a number of key considerations linking land holdings with economic viability of exploration programs including: Acquisition. Oil and gas lands are made available to exploration companies by host
governments through a variety of means and systems. In most countries they are granted by government discretion through negotiations and are based on the programs the companies commit to carry out in exploring them. Often the up-front costs to acquire such land are relatively low, and the companies are required to carry out extensive work programs in order to maintain control of a significant portion of the granted lands for an extended period of time. In other countries oil companies must bid considerable funds up-front and in competition with one another to obtain land rights for oil and gas exploration, absorbing considerable funds, which could otherwise be utilized in undertaking exploration, work. Oil companies also sell and/or trade interests in lands to other oil companies for considerations of cash or for work which one company commits to undertake on another company’s behalf. Farmins and farmouts are particularly important land allocation mechanism because of large land holdings and work commitments of some companies and the benefits often gained in broadening the number of participants to bring fresh exploration ideas to an area to share the burden and opportunity of the extensive and costly work programs. The cost of acquiring land interest, whether by direct purchase or by farmin, plays an important role in the economic viability of many exploration opportunities. In some cases the acquisition costs can be quite high in relation to the potential economic returns from the land acquired, and because these costs represent expenditures at very outset of a long program, they can weigh heavily against the ultimate program value when the time value of those expenditures is considered. Areal extent. Petroleum exploration companies generally seek large tracts of land on
which to carry out explorations activities. On average, only small fractions of initially sough exploration land remain attractive after early exploration surveys are completed. Because land selection often has to be made before the general geological potential of an area is known, oil companies seek large tracts to increase the probability that at least a portion of their lands will ultimately turn out to be geologically attractive and worth drilling.
Large land holdings in an active exploration area also mean that if a discovery is made in the general area, the company will have a reasonable good chance of having a ground floor interest in some of the follow-up exploration potential stemming from the initial discovery. A large land spread is an oil company’s insurance that it will have its fair share
of exploration and production activity in the future. Permit term. The term of an exploration permit or license relates to the amount of time an
oil company has to explore a concession or contract area before it either converts its exploration rights to a production permit or relinquishes them to the host government. Terms for exploration concessions normally range from 3 to 7 years, but in some cases are considerably longer. During the exploration permit stage, an oil company normally conducts a series of jobs in order to evaluate the lands and determine whether they are to be dropped or retained in the form of a production lease. These front-end exploration costs have an extremely important impact on economic viability of a project. Work obligations. A company, which is awarded an exploration concession or contract
area normally, is required to undertake a pre-specified amount of exploration work in order to retain longer term rights to at least part of the territory awarded. This requirements usually takes the form of a work commitment which may be specified in terms of total investment (budget) or total exploration effort, including geophysical surveys and drilling number of wells (work program), which a company must achieve on a specified exploration block in a specified period of time. These work commitments are the host government’s return for awarding the blocks for exploration, and play a very important economic role in the overall outcome of investments made on these lands. Predetermining an appropriate work program for a relatively unexplored block is difficult to do effectively, and frequently the commitments turn out to be either insufficient to test the true potential of a block or to be too onerous (too much work too fast) to be justified based on a block’s true economic potential.
The important difference between discretionary work programs and mandatory work programs has a fundamental impact on exploration economics, and is often not given sufficient attention in assessing exploration program economics. Relinquishments. Exploration permit lands awarded to oil companies usually have time-
specified requirements to relinquish certain percentages of each awarded block at prespecified time points. This forces a company to assess the value of the lands, from a regional perspective, as early as possible in order to retain the most promising portions for future exploration work. From a host government viewpoint, this encourages early exploration activity and keeps a large portion of lands in circulation allowing other companies with different exploration ideas to lease and explore them. Working and carried interests . Working interests refers to the percentage participation a
company has in a petroleum concession or contract area. Normally, a company pays its full working interest portion of the costs of exploration, development and production and receives a pro-rata working interest share of revenues, which relates directly to its working interests in the lands.
In certain cases where a company, the farmee, is farming in on the interest of another company, the farmor, the farmee may spend all of certain exploration expenditure obligations of the farmor in order to earn a portion of the farmor’s interest in certain lands. In such cases the farmor is “carried” through the exploration expense by the far mee. Once
the farmee has earned its interest by fully meeting its expenditure obligations, it will be a working interest partner alongside the farmor, and both companies will share future expenditure on the lands in accordance with their respective working interests. Operating environment considerations . The physical environment and surroundings, in
which oil exploration, development and production activities take place, play an important role in the economic outcome or results of those activities. If an exploration prospect is located onshore, it may be important to know whether or not it is in a remote area, if the terrain is inhospitable, such a mountainous or desert, and whether or not these activities will be exceptionally costly and take a long time to complete. If an exploration prospect is located offshore, it is necessary to know what depth of water it is in, and what range of weather and oceanographic conditions can be expected over time on the proposed location. These factors will bear heavily on the type and cost of facilities required to drill the exploration well and particularly to develop a discovery, and will significantly affect time requirements, capital and ultimately the potential economic attractiveness of the prospect. In both cases, onshore and offshore, when costs or investments are high, sometimes resulting in fields reaching their economic limit at relatively high rates of production. In such cases, fields may either have to be fairly large or to be developed in groups in order to reduce the unit operating and transportation costs. Finally, discovery of natural gas instead of oil can result in more difficult logistical problem in gathering and transporting the production. Consequently, it is imperative that the nature of the operating environment is fully appreciated and considered in the evaluation of petroleum exploration prospect.
ECONOMIC FACTORS INFLUENCING EVALUATIONS Following are some of the factors that influence an evaluation: General Economics. Affect supply and demand. Marketing Factors. Local factors, for example: avaibility of pipeline, refining facilities, etc. Role of the Project in the Company’s overall organization. What is the relationship of
the project to the overall company, facilities available, nature of company, expertise, etc. Availability of capital. There are occasions that projects have to be postponed because it is not possible to find funds, at reasonable price, or there is no room in the company’s
budget. Drilling, Development and Production Costs. Should be obtained from experience.
Look at costs in neighbouring areas, similar circumstances. Value of Money. Varies with:
Time necessary for return. Cost of obtaining it. Opportunity cost of capital. Availibility, equity/loan financing. Reserves. Requires largest geological and engineering effort. Magnitude of reserves is a
serious area of disagreement because of interpretation. Rate of Production. Governs flow of profit. Depends on reservoir characteristics. Historical Trends. Give an idea of values to use. In the case of oil and gas we have to
consider the following: Oil and gas prices. Inflation. Historical finding rates for oil and gas. Capital trends of similar projects and past projects. Opex or operating expenses. Linked to the production as: transport, fuel consumption,
salaries, maintenance, ancillary services, etc. Capex or capital expenses. They are necessary but not related with the production:
acreage, buildings, facilities, machinery, etc. Oil and gas prices. The economic reward for oil and gas exploration must finally come
from the sale of oil and gas production from the discoveries made and developed. Consequently, expectations for the prices to be realized for the products over their production life is an extremely important factor affecting the potential viability of exploration programs.
The oil price is notoriously difficult to forecast. Oil supply and demand curves are not typical of most comodities and the supply of oil is influenced by OPEC policy, who currently produce about 40% of the world’s oil supply. Economists would say that oil demand is inelastic, meaning that demand is not very sensitive to price changes. This is because there are very few immediate substitutes for oil in the short term. On the other hand, oil price fluctuations are beyond the control of oil companies, and most companies no longer use past oil trends for forecasting. Gas prices differ from oil prices in that they are often contractually agreed with the buyer at the outset of a project. The price per unit may have a fixed and variable componet, with the variable componet being linked to the oil price, thus partly indexing the gas sales price to the crude oil price. Energy and the Economy
At least since the time of the first oil shock in October 1973, economists have struggled to understand the ways that disturbances to the supply and demand balance in energy markets influence economic growth and inflation. At the most basic level, oil and natural gas are just primary commodities, like tin, rubber, or iron ore. Yet energy commodities are special, in part because they are critical inputs to a very wide variety of production processes of modern economies. They provide the fuel that drives our transportation system, heats our homes and offices, and powers our factories. Moreover, energy has an influence that is disproportionate to its share in real gross domestic product (GDP) largely because of our limited ability to adjust the amount of energy we use per unit of output over short periods of time. Over longer periods, energy consumption can be altered more easily by, for example, adjusting the types of vehicles that we drive, the kind of homes that we build, and the variety of machines that we buy. Those decisions, in turn, influence the growth and composition of the stock of capital and the productive capacity of the economy. Beginning around 2003, futures prices began moving up roughly in line with the rise in spot prices. Thus, unlike in earlier episodes, the significantly higher relative price of energy that we are now experiencing is expected to be relatively long lasting and thus will likely prompt more-significant adjustments by households and businesses over time. In the long run, higher energy prices are likely to reduce somewhat the productive capacity of the economy. That outcome would occur, for example, if high energy costs make businesses less willing to invest in new capital or cause some existing capital to become economically obsolete. All else being equal, these effects tend to restrain the growth of labor productivity, which in turn implies that real wages and profits will be lower than they otherwise would have been. Under the assumption that energy prices do not move sharply higher from their already high levels, these long-run effects, though clearly negative, appear to be manageable. The developed countries economy is flexible, and it seems to have absorbed the cost shocks of the past few years with only a few dislocations.
In the short run, sharply higher energy prices create a rather different and, in some ways, a more difficult set of economic challenges. Indeed, a significant increase in energy prices can simultaneously slow economic growth while raising inflation. An increase in oil prices slows economic growth in the short run primarily through its effects on consumer spending. At the same time that higher oil prices slow economic growth, they also create inflationary pressures. Higher prices for crude oil are passed through to increased prices for the refined products used by consumers, such as gasoline and heating oil. When oil prices rise, people may try to substitute other forms of energy, such as natural gas, leading to price increases in those alternatives as well. The rise in prices paid by households for energy--for example for gasoline, heating oil, and natural gas--represent, of course, an increase in the cost of living and in price inflation. A jump in energy costs could also increase the public's longer-term inflation expectations, a factor that would put additional upward pressure on inflation. Since about 1980 most Central Banks have worked hard to bring inflation and expectations of inflation down. They attempted to contain the inflationary effects of the oilprice shocks by engineering sharp increases in interest rates, actions which had the consequence of sharply slowing growth and raising unemployment, as in the recessions that began in 1973 and 1981. To the extent that households and business owners expect that the Central Banks will keep inflation low, firms have both less incentive and less ability to pass on increased energy costs in the form of higher prices, and likewise workers have less incentive to demand compensating increases in their nominal wages. Oil and Economy. A Relationship of Diminishing Importance. The US example.
In the long run, the higher relative prices of energy will create incentives for businesses to create new, energy-saving technologies and for energy consumers to adopt them. The market for alternative fuels is growing rapidly and will help to shift consumption away from petroleum-based fuels. Governments can contribute to these conservation efforts by working to create a regulatory environment that encourages the growth in energy supplies in a manner that is consistent with our nation's environmental and other objectives. It has become increasingly apparent that high energy prices have had far less of an impact on the U.S. and global economy that previously believed. The reason is that the petroleum consumption to gross domestic product and energy to gross domestic product ratios have fallen sufficiently in the past few years to make the economy far less sensitive to price increases than anytime in history. To say it another way, energy prices could go much higher before having a significant impact. Or, energy could cost consumers more, potentially a lot more, and not affect the overall economy In U.S. Economy, the petroleum consumption—GDP ratio in the United States will fall to nearly half the current level by 2025 in the base case. This implies that by 2025, the economy will be even less sensitive to energy prices than it is today. Probably in the future U.S. and global economy will continue to be less energy intensive over time.
MEASURES OF PROFITABILITY This chapter considers the meaning and uses of measures of profitability, the parameters used by decision maker to order, accept, reject, or compare investments proposals. These parameters are also frequently called profit indicators, decision criteria or measures of investment worth. There is probably no single measure of profitability that considers all the factors or dimensions of investment projects that are pertinent to the decision maker .
A good measure of profitability must be suitable for comparing and ranking investment opportunities. And it should provide means of telling whether profitability exceeds some minimum, such as the cost of capital or the firm’s average earnings rate.
The measures of profitability could be classified in two main groups: Those, which do not consider the time-value of money. They judge the cash flows as they were received at the same period of time. These indicators are not accurate but, often, are very useful. And those which consider the time-value of money and use the compound and discount factors to homogenize the current of cash flows, which are received at different periods of time. Cash flows are defined as movements of money into or out the treasury. A good understanding of cash flows in and out of the treasury is essential to the proper use and interpretation of profitability measures. Expenditures for drilling costs, lease equipment, and revenues from the sale of oil are examples of cash flows. PAYOUT. It is defined as the length of time required to receive accumulated net revenues
equal to the investment or the length of time it takes to get the invested capital back. Payout time is an approximate measure of the rate at which cash flows are generated early in the project and can be expressed in terms of “before tax” or “after tax”. All the factors equal, the decision maker would like to invest in projects having the shortest payout. One weakness of payout is it tells the decision maker nothing about of earnings after payout time and does not consider the total profitability of the investment opportunity. Consequently, it is not a sufficient criterion in itself to judge the worth of an investment. Payout time has been in wide use for many years as an integral part of the economic analysis of exploration opportunities. It is a useful parameter to compare the relative rates of receipt of revenues early in the projects, but it is not a parameter that reflects or measures all the dimensions of profitability, which are relevant in capital expenditure decisions. When cash flows are constant, the payout period will be equal to the quotient between the initial investment C and the cash flow S; P = C/S.
PROFIT-TO-INVESTMENT RATIO. It is a measure that does reflect total profitability. It is
defined as the ratio of total undiscounted net profit to investment. It is a dimensionless number relating the amount of new money generated from a project per monetary unit invested. It is sometimes called the return-on-investment, or ROI. Total sales – Costs – Investment (Capex) = Net Cash flow
Profit-to-investment ratio ( ROI ) =
Net Cash flow Investment
The denominator of the ratio is usually the drilling cost of a well for a single well prospect. If expenditures extend over a period of time before any revenues are received, the ratio is sometimes computed using the maximum amount of cash invested in, but not yet recovered from the project as the term in the denominator. This investment term is called the maximum out of pocket cash and represents the lowest negative value on a cumulative cash position curve. The major weakness of these ratios is that they do not reflect the time rate patterns of income from the project. Example, consider Prospects A and B. Each has the same profit-to-investment and payout ratios. Prospect A Producing rate at early project’s life
150 Bbl/d
Costs: $/month Investment Payout: months Recoverable Reserves Producing Life Total Revenues (2,92 $/Bbl, 12,5 % royalty and 5% tax) Total Costs Revenues - Costs Net Profit Profit-to-Investment Ratio
575 $ 150.000 $ 14,3 200.000 Bbls 15 years 2,4 M$ 103.500 $ 382.000 $ 212.000 $ 1,41
Prospect B
Same
Same
150 Bbl/d 575 $ 150.000 $ 14,3 243.000 Bbls 30 years 2,9 M$ 207.000 $ 382.000 $ 212.000 $ 1,41
Most decision makers, if given a choice would prefer A over B because prospect A returns total income in one-half time. Thus it should obvious that a missing dimension in these parameters is the time-rate patterns of cash flows. To stress this point in a different way, suppose you invest 1$ today to receive 3$ in three years or 4$ in 10 years. Which would you prefer?
TIME – VALUE OF MONEY CONSIDERATIONS The usual method of relating the time-rate patterns of future cash flows to some measure of profit is by use of “time-value of money” concepts: compounding and discounting. C = Value of a principal sum, as of a specified time, time zero. S = Value of the principal sum plus interest at a future point in time, “n” years away.
i = Effective annual interest rate. n = Number of years separating C and S The time-value of money considerations are based on the following relation: C ( 1 + i )n = S
(1)
This equation is called the compound interest equation and relates the future value, S, to a principal amount of money today, C. The term (1 + i)n is called a compound interest factor. By dividing both sides of the equation by (1 + i)n we get a modified form of the equation, called the present value equation: C = S/( 1 + i )n
(2)
The term, 1/(1 + i)n , is usually called the discount rate factor, when used in the context of above equation. It is very important to recognize that C and S are equivalent in value, even though separated in time by n years. Thus, 100$ invested at 10% compound interest will appreciate in 146.4$ at the end of 4 years. If 10% represents the inflation rate, receiving 100$ today has no greater, or lesser, value than receiving 146.4$ in 4 years. To say that 100$ today will become 146.4$ in 4 years is the same as saying that receiving 146.4$ in 4 years has a present value of 100$. In most petroleum evaluations the common point time for comparing values of monetary sums is the present time, or time zero. Consequently, equation (2) will be used more frequently. We normally speak of compound or discount rates in terms of the nominal interest rate per year. If the investment earns interest once a year the nominal and effective interest are the same. If interest is credited to the investment at periods less than a year, such a quarterly, the effective interest rate is slightly greater than the nominal It is necessary to avoid the common weakness of the first two indicators and introduce those that measure or reflect the time-rate patterns of cash flows and the time-value of money, providing a better quality analysis.
RATE OF RETURN. One of the more widely used profit indicators in recent years. It has
been given many different names, including discounted rate of return, internal rate of return (IRR), marginal efficiency of capital. It is the interest rate, which equates the value of all cash inflows to the cash out- lays when these cash flows are discounted or compounded to a common point in time. Stated differently, it is the interest rate, which makes the present value of net receipts equal to the present value of investments. The rate of return calculation is made after the series of anticipate future cash flows to be received from the investment has been defined. Mathematically is equivalent to solving the following rate of return equation: - C + S1 /( 1 + i )1 + S2 /( 1+ i )2 + … + Sn /( 1 + i )n = 0
(3)
C = initial investment at time zero (wildcat well) S1 = net cash flow at year 1. S2 = net cash flow at year 2. . . .
n = number of years ( project’s life ).
Sn = net cash flow at year n. i = rate of return. If cash flows are equal: S1 = S2 = ... = Sn = S the equation would be: - C + S(( 1+i )n- 1/ i( 1 + i )n) = 0
S(( 1+i )n- 1/ i( 1 + i )n) = C
In addition, if the length of investment life is unlimited, the internal rate of return will be defined by the equation: - C + S/i = 0
i = S/C
If we compare the last equation with we specified in the payout, in case all cash flows are equal, P = C/S, we can infer that the internal rate of return is equal to the reciprocal of payout. IRR i = S/C = 1/P
P = C/S = 1/r = Payout
Specific characteristics of the rate of return concept include:
Computation of rate of return requires a series of trial-and-error computations.
Introduces the “time-value” of money into the criterion.
It is a profit indicator that is independent of the magnitude of the cash flows.
There are certain types of cash flows in which there is more than one discount rate, which satisfies the definition of rate of return. In cash flows having multiple rates of return there is no way to establish which (if any) it is the correct. In situations like this the analysis should be made using other criteria such as net present value.
Cash flows received early in the project are weighted more heavily than later.
It is a convenient measure of profitability to compare with a “minimum”.
It includes the implicit assumption that all cash flows will be reinvested at the computed rate of return when received. This is extremely important characteristic, which is often misunderstood or ignored by those who assume the criterion. To illustrate this point consider the following investment project: C = initial investment = 8.000 S1 = net cash flow at year 1 = 1.000 S2 = net cash flow at year 2 = 3.000 S3 = net cash flow at year 2 = 5.000 - 8.000 +
1.000
3.000
+
(1+r)
+
(1+r)
5.000
r = 4.54% = IRR
(1+r)3
If we suppose that the first cash flow is reinvested at 20% and the second at 10% the IRR would be - 8.000 +
1.000 1.2
+
3.000 1.1 + 5.000 (1+r)3
=0
r = 6.75% = IRR
But if cash flow were reinvested at 3%, the IRR would be 1.000 1.03 - 8.000 +
2
+
3.000 1.03 + 5.000 =0
(1+r)
r = 4.5% = IRR
If cash flows remain in the security box of the company, the IRR would be - 8.000 +
1.000 + 3.000 + 5.000 3
(1+r)
=0
r = 4.0% = IRR
Rate of return is not a completely realistic parameter to rank competing investments. Suppose we had two investment opportunities available with internal rates of return 10% and 30% respectively. The discount factor in a common period of time will be higher for the investment opportunity with lower internal rate of return, and apparently a monetary unit received from the project with lower internal rate of return has more value than a monetary unit received from the other. But, in reality, the value of a monetary unit in certain future period will have a certain value regardless of its source.
Rate of return is very sensitive to errors in estimating initial investment and early cash revenues.
A rate of return cannot be calculated for the following situations:
Cash flows are all negative. Cash flows are all positive. Total undiscounted revenues are less than investment.
In summary, rate of return is certainly a more realistic measure of value than payout and profit to investment ratio, primarily because it includes the time value of money concept. It is a useful measure of the relative profitability of investments having approximately the same total life and cash flow patterns. Its primary weaknesses as a measure of true profitability are the frequent problems of not satisfying the reinvestment assumption. NET PRESENT VALUE (NPV). It is similar to rate of return except that a single, previously
specified discount rate is used for all economic analysis. It is usually called the average opportunity rate, and presumably represents the average earnings rate at which future revenues can be reinvested. One of the advantages of net present value over rate of return is that is computed using a more realistic appraisal of future investment opportunities. - C + S1 /( 1 + i0 )1 + S2 /( 1+ i0 )2 + … + Sn /( 1 + i0 )n = A (npv)
(4)
A is, by definition, the net present value discounted at the average opportunity rate. One of the advantages of npv over rate of return is that it is computed using a more realistic
appraisal of future investment opportunities. If it is positive it means that the investment will earn a rate of return equal to i0 plus an additional amount of cash money equal to the npv. If the average opportunity rate used is realistic of the firm’s ability to invest capital, then it follows those investment opportunities, which have a negative npv, should be rejected. Characteristics of npv as a measure of profitability include the following:
Computation is no longer a trial-and-error solution. There is only a solution.
It has all the features of rate of return regarding time-value of money, plus the added fact that the reinvestment assumption is satisfied because the discount rate presumably reflects future investment opportunities.
If npv=0, then the investment is yielding an internal rate of return (IRR) equal to discount rate used i0. If it is negative it means that the investment will yield a rate of return less than i0. If positive, the sum represents present value cash worth in excess of making a rate of return equal to i0.
The npv is independent of size of cash flows.
The npv concept can be used to evaluate investment alternatives in which all of the cash flow terms are negative. In this instance the preferred decision option will have the least negative present value.
Specifying the rate to use for npv computations is sometimes not an easy procedure. The usual first reaction is to check the overall corporate annual earning rate in past years. But, it may not be realistic because the desired rate is what future invested capital will earn. Predictions of the rate at which future revenues can be reinvested involve an element of uncertainty. The discount rate for npv calculations is usually set by top management after consideration of at least some of the following factors:
If the firm is operating on borrowed capital the rate should at least exceed the interest rate being paid on the loan. If the capital comes from several sources (internally generated funds, debt and equity), the average cost of capital is sometimes used as minimum value of i0. Corporate growth objectives. The risk of oil exploration as compared to less risky investments such as refining, marketing, etc. Future investment opportunities. Are they limited or unlimited?
Npv became very popular and widely used, because the reinvestment assumption is
completely satisfied and based on time-value money system. It is meaningful for all types of cash flows (including those having all negative terms) and compatible with risk factors. NET PRESENT VALUE GIVE BETTER DECISIONS.
Consider the following investment projects and that the opportunity cost is 10% Project
A B
C0
C1
C2
-2.000 -2.000
+2.000 +1.000
+1.000
C3
Payout
+5.000
1 year 2 years
NPV @ 10%
- 182 3.492
Project A needs 1 year to recover 2.000 € and project B, 2 years. If the company use 1 year payout as the criteria to choose investments alternatives, it will choose only project A. If company uses 2 years payout as criteria, it will accept both projects. As we can see, the payout criteria give different answer than npv. The reason is because payout gives same weight to all cash flows generated before to the recovery period. In the next example all projects have same payout. But project B has a bigger npv than project A for any discount rate (1 .000 € in years 1 and 2 have more value than 2.000 € in year 2). And project C has a bigger npv than projects A and B. Project A B C
C0 -2.000 -2.000 -2.000
C1 +1.000
+1.000
C2 +1.000 +2.000 +2.000
C3 +5.000 +5.000 +5.000
Payout
2 years 2 years 2 years
NPV @ 10%
3.492 3.409 74.867
When a company uses the payout criteria has to establish a time limit. If use a limit without considers the length of the projects, it will tend to approve too many short projects. If the average length of the projects is too long the company will accept some projects with npv negative. On the contrary, if projects are short the company will reject some of them with positive npv.
As an example, it will be considered a project with the following cash flows: Co= - 4.000; C1= 2.000; C2= 4.000 NPV + 200
+ 100 IIR = 28% 10%
20%
40%
50%
Discount rate
- 100
- 200
If opportunity cost of the capital is less than IRR, 28%, the npv will be positive. If it is equal to IRR the npv will be zero and if is bigger than IRR the project’s npv will be negative. IRR criteria will give same answer than npv if the npv of a project is a decreasing function of discount rate. But not all cash flows have the quality that npv decrease while discount rate increase. Example: Project
A B
C0
-1.000 1.000
C1
1.500 -1.500
IRR
50% 50%
NPV @ 10%
364 -364
If we choose based on IRR criteria both projects are equally attractive. But it is clear that they are not. In project A we pay a certain amount of money, or we lend money at 50% interest rate. In project B we receive money, or we borrow at 50% interest rate. When people lend money wish the highest interest rate as possible. On the contrary, when people borrow always tried to pay the lowest interest rate. It is what banks do. The interest rates of active are higher than interest rates of passive. If we drawing the discounted cash flows of project B we will see that npv increase while discount rate rise. It is clear that in these circumstances the IRR does not work. Other problem that it is possible to find with IRR criteria is when certain types of cash flows have more than one discount rate, which satisfies the definition of rate or return. Examples of cash flows, which lead to multiple rates of return, are those projects requiring a large expenditure at a later point in the life of the project. A necessary condition to have multiple rates of return is a second sign reversal in the cumulative cash position. But a second sign reversal is not a sufficient condition. It also depends on when the second reversal occurs and the magnitude of negative cash flows causing the reversal.
NPV + 1.000
IRR = 15,2%
-25%
-1.000
0%
25%
50%
Discount rate
IRR = -50%
As we can see in the drawing the cash flow of the following example, there are two solutions that make npv equal to zero: -50% y 15,2%. Co = -1.000, C1 = 800, C3 = 150, C4 = 150, C5 = 150, C6 = -150 In cash flows having multiple rates of return there is no way to establish which, if any, of the rates is the correct, or true IRR. And we must aware that in exploration and production these circumstances can occur when it is considered the abandon cost of a project. Moreover, it is possible to find cases where do not exist any IRR, such as the following example shows. Project D C0 = 1.000 C1 = -3.000 C2 = 2.500 IRR = no NPV (10%) = 339 Other problem that can arise is, when decision maker is choosing among different alternatives to make the same project, or simply, when he is analysing mutually exclusive projects. Project E
C0 = - 10.000
C1 = 20.000
IRR = 100
NPV (10%) = 8.182
Project F
C0 = - 20.000
C1 = 35.000
IRR = 75
NPV (10%) = 11.818
Project E can be, for instance, an industrial process manually controlled and project F, same process but automatically controlled. Both projects are good, but results are opposite depended on the criteria used. In cases like this, the way to solve the dilemma is analyse the IRR of incremental cash flow. First, it will be necessary to study the IRR of cash flow of the smaller project. Then, it will analyse if is worthy to go ahead with the additional investment of 10.000. The incremental cash flow will be:
Incremental cash flow C0 = -10.000 C1 =15.000 =15.000 IRR = 50 NPV (10%) = 3.636 All these examples have helped to show how to solve some of the discrepancies that appear when are compared the results obtained with npv or IRR criteria. At same time they make clear that, sometimes, the IRR is not a useful measure of profitability to classified projects of different size. DISCOUNTED PROFIT-TO-INVESTMENT RATIO (DPR). To sidestep the weakness of npv being independent of the absolute size of cash flows, it is advantageous to use the
criterion called Discounted Profit-to-Investment Ratio, which is the dimensionless ratio obtained by dividing npv by the present value of the investment. Project’s net present value Discounted profit to investment =
= DPR Investment
The ratio is interpreted as the amount of discounted net profit generated in excess of the average opportunity rate per monetary unit. Characteristics of dpr ratio ratio include:
It has all of advantages of npv plus providing a measure of profitability per monetary unit invested.
It is a suitable measure of value for ranking and comparing investment opportunities. Some authors conclude that the dpr is is the most representative measure of true earning potential of an investment.
The dpr ratio will always be positive or zero, but never negative.
It should be reasonably obvious that use of a single discount rate gives a more realistic measure of true profitability than does a rate of return. This implies the superiority of npv. And since rarely companies have unlimited supply of money, and on the other hand they work on budget restrictions, we must consider the importance of trying to choose investments that will give the maximum gain per unit of money invested. This leads to the investment strategy of maximizing the discounted profit-to-investment ratio. If we consider the following fol lowing example with three projects, and the opportunity cost is 10%. Project
A B C
C0
C1
C2
-10 -5 -5
30 5 5
5 20 15
NPV 10%
21 16 12
Based on npv criteria all three projects must be approved. But, if it is established that the maximum budget expenditure is 10, it is not possible to carry out all the projects together. Projects B and C have lower npv than project A, but the addition of npv of projects B and C is bigger than the npv of A.
The discounted profit-to-investment ratio is useful to select investment opportunities under the constraint of limited capital, when it is essential to gain the most profit per monetary unit invested. Project
Investment
A B C
NPV @ 10%
-10 -5 -5
Index
21 20 15
2,1 3,2 2,4
Project B has the highest index, the next higher is project C. If budget establish a limit of 10, both projects must be selected. Unfortunately the application of these criteria can have some problems. One of the most important is when the constraint affects to more than one variable. We will see it in the next example. The budget limit of 10 is extended to the years 0 and 1 and it is enlarge the number of projects with a new one D. Project
A B C D
C0
C1
C2
NPV @ 10%
-10 -5 -5 0
30 5 5 -40
5 20 15 60
21 16 12 13
Index
2,1 3,2 3,4 0,4
One solution can be to accept projects B and C, but in that case it is not possible to approve project D because go beyond the budget constrain in year 1. If it is accepted project A, that provide a cash flow of 30 in year 1, t will be possible go ahead with project D, obtaining a profitability index lower than projects B and C but with a higher total npv. This fault is produced because there are more than one limit. It is not possible to anlysed with this criteria a mutually exclusive projects or a project which is dependent of another. This simplicity of this method can compensate their limitation, which can be solved using the lineal programmation.
RISK ANALYSIS AND OIL EXPLORATION The measures of investment worth considered previously were all non-risk parameters. The criteria did not include explicit statements about the degree of risk or uncertainty associated with a given investment. We are all aware, however, that oil exploration involves a great deal of risk and uncertainty. Modern risk, as it is now applied in international petroleum exploration, utilizes principles of statistics, probability theory, and utility theory, which began to be recognized as significant subdisciplines of mathematics and philosophy during the 16th, 17th, and 18th centuries. The applications for early studies concerned games and gambling, then interested to actuarial and insurance companies. Petroleum exploration is a process of repeated trials under conditions of uncertainty, each trial requiring a substantial commitment of investment capital. As such, the casino analogy is apt, but because it is not certainly what the odds are, or the size of the prize, it is necessary to employ modern science and technology to refine the “bets” as: Stratigraphy,
Geochemistry, Geophysics, Drilling technology and Reservoir technology. The systematic employment of statistics and probability theory in exploration did not begin until mid-1960s, led by Exxon, Shell, and Arco. By the late 1970s, companies like Chevron, BP, and Elf, as well as some governmental agencies, IFP, USGS, were also beginning to employ risk analysis in their explorations evaluations. In early 1990s, a technological explosion in risk analysis took place because most modern oil and gas companies saw the need for systematic management of their exploration portfolios on a worldwide basis. Today the methodologies of exploration risk analysis used by most oil companies have converged to the status of a generally accepted technology. BASIC PRINCIPLES OF STATISTICS. Risk is somewhat of a catchall term, in that we
may have the need to quantify or asses many types of risks: risk of an exploratory or development dry hole; political risk, risk to future oil/gas prices, risk that a discovery will not be a large enough to recover initial exploration costs, environmental risk, etc. The problems relating to making exploration decisions under conditions of risk and uncertainty have been with this industry since the oil business began. Early attempts to define risk were pretty informal and usually involved adjectives rather than probabilities. Later the new discipline of statistical decision theory began to emerge, and exploration decision makers began to take note of the potential benefits of decision analysis. The problem involved in using decision analysis is where do we get all the probabilities required to solve a decision tree or compute an EMV. Risk analysis is, probably, the weakest link of the overall decision process. But what is our alternative? Even though risk analysis is tough, the alternative of ignoring it is untenable. This requires that we attempt to improve our expertise at evaluating risk and communicating our findings in a clear, concise manner to the decision maker. Depending on the grade of information that the decision maker has about all parameters, which defined an event, in our case, an investment, it is possible to distinguish three situations:
When all variables can have just one state. That is, the probability of occurrence is 1.
When the variables are aleatories. The values are known in terms of probability.
Total uncertainty. The decision maker does not know the probability of occurrence of the different parameters of the event.
Until now, the word probability has mentioned many times, the assessment of the probabilities of occurrence for each possible outcome, without being very specific about its definition. Now is the time to remind some basic principles of statistics. Deterministic or causal phenomenons are those that keeping constant all factors the results always will be equal. On the contrary, aleatory or stochastic phenomenons are those that although all factors are kept constant the results have variations It is knew that when aleatory phenomenons are repeated a large number of times it is possible to find certain rules in their behaviour, proving that there are certain laws, the law of large numbers, giving stability to these phenomenons. Statistics is the science that studies these types of phenomenon. If Statistics analysed events that are repeated many times, trying to find its regularity it is clear that any study should based on watching experiments or samples. Sample space is a set or list of all the possible things that can occur from an experiment, chance phenomenon, or a decision under uncertainty. It is also called a population. Event is defined as a part of the sample space whose occurrence is of special interest. An
event may be defined in any way we please, and it may contain one, two or more of the elements of sample space. The size of the sample space is the number of events that form the population and it can be finite or infinite. It is obvious that it is not possible to study all the events in infinite or almost infinite samples. That is the reason why it is necessary to use a small sample and then to extend the conclusions to the whole sample. The Statistics try to find regularity that appear in certain phenomena and also, to forecast their behaviour. As an example suppose we have a standard Spanish deck, which consist in 40 cards, and we are considering a wager involving the withdrawal of a card at random from the deck. In this case there are 40 elements in the sample space. In petroleum exploration is possible to define a sample spaces like: the number of structures which have oil in a basin, the number of producing wells in a field, or all the possible values of recoverable reserves in a structure. Now, it is necessary to define what mean a probability number, or a probability of occurrence. There are three main definitions which can be given to express probability: relative frequency, or statistical; a classical, or objective definition; and a subjective definition.
Relative frequency definition of profitability: It is the long run ratio of the number of
times the event has occurred divided by the total number of times the experiment has been repeated. An alternative definition is that probability is the ratio of the number of
elements defined as the event divided by the total number of elements in the sample space. Examples of this might be: the probability of withdraw a “queen” is 4/40 in the Spanish
deck, or a wildcat success ratio in hydrocarbons exploration. There are some chance phenomena of interest where a probability cannot be computed in this manner. What is the probability of an earthquake occurring certain future date in a concrete place? How would we determine its value? This phenomenon is not a repetitive process that could be experiment with a study. It is necessary to consider an alternative definition of probability. called the classical or objective definition.
Classical or Objective Definition of Probability. It is defined as a measure of the
degree to which available evidence supports a given hypothesis. This measure is determined by purely objective logic. The usual way we think about risk in oil exploration is an example of this meaning of profitability. The explorationists hypothesize that a structure has oil, or a given level of reserves, and they look at all the evidence which supports the hypothesis: the nearby structure has oil, rock strata appear correlative, etc. Then, by purely objective logic, the probability is determined as the degree to which this evidence supports the hypothesis “Structure has oil”.
From a practical viewpoint this definition may be difficult to use because explorationists are usually not free of human emotion about their hypothesis. This leads to a third definition of profitability.
Subjective Definition of Probability. It is a personal opinion of the likelihood that an
event will occur. A subjective probability estimate represents the extent to which an individual thinks an event is likely to occur. It is a degree of belief . Subjective probability estimates are sometimes used where past statistical data are not available and/or the information is of an indirect nature. These estimations are influenced by a person’s biases, emotions or past experiences, etc. It is also known as “a priori” probability and correspond an honour place in its use to the
economist John Maynar Keynes. And because the decision maker never is a situation of total uncertainty, this idea of profitability has been restored to use in the analysis of economic decisions. From mathematics viewpoint subjective probability does not exist, but in the real world of hydrocarbons exploration, often, it is the only way to consider the probability because technical people do not have enough information. In oil and gas exploration risk analysis the tree definitions of profitability are used and people will not have to concern about which of tree is the most appropriate to use. There are other important statistical terms that it is necessary to remind as:
Equally likely events. Two or more events are said to be equally likely if they have the
same probability of occurrence. When we are playing with a die, the probability of
obtains 1, 2 ... or 6 is the same and equal to 1/6. The probability distribution of this event is uniform
Mutually exclusive events. Events are mutually exclusive if the occurrence of any
given event excludes the occurrence of all other events. Mutually exclusive events have no points of the sample space in common. When it is drilled a wildcat well and it is unsuccessful implies that it is impossible to find 100 M of oil.
Independent events. Two or more events are independent if the occurrence one
event in no way affects, or are affected by the occurrence of the other events. An example is flipping a coin, which has no memory and each flip is a new experiment. Whatever has happened previously has no effect on the probability of a head or tail on the next flip.
Conditional probability. When two or more events are not independent they are said
to be dependent. Conditional probability is the probability of an event given that some other has already occurred. The last two definitions are very important from oil exploration viewpoint, and it is necessary to be very precise about the distinction between independent or dependent event in risk analysis. PROBABILITY THEORY.
The probability is a measure of the grade of certainty that someone has about the chance of occurrence for a possible outcome. The probability theory has a set of rules of operation in the same sense that the number system has a set of rules of operation: addition, multiplication, etc, that now is useful to remind briefly. Total probability or addition theorem.
For a number of events, which are mutually exclusive, the probability of any one of the events occurring is the sum of the individual probabilities. P(S1 + S2 + S3) = P(S1) + P(S2) + P(S3) The probability of event S1 and/or event S2 is equal to the probability of S1 occurring plus the probability of occurrence of S2 minus the probability of both S1 and S2 occurring. P(S1 + S2) = P(S1) + P(S2) - P(S1 S2) Compound probability or multiplication theorem.
This theorem is used to find the probability of two events occurring in sequence, or simultaneously. The theorem is interpreted as: the probability of S1 and S2 occurring is equal to the probability of S2, given that event S1 has occurred, multiplied by the probability S1 occurring in the first place. P(S1 S2) = P(S2/S1) P(S1)
The term P(S2/S1) is called a conditional probability. This theorem applies, for both, independent and dependent events. Define event S1 as drawing a “king” in the Spanish deck on the first draw, and event S2 a “queen” on the second draw. Assume for the moment that the first card is not replaced in de deck prior to the second draw. What is the probability of both events occurring? What is P(S2/S1)? The likelihood of drawing a “king” on the first draw is 4/40. Since the card is not replaced in
the deck there are only 39 remaining cards on the second draw, and the likelihood of drawing a “queen” on the second draw is 4/39. Hence, it is possible compute the
probability of events S1 and S2, (4/40) (4/39). The sequence in this example is said to be dependent. But, if the first card is placed back in the deck the probability of draw a “queen” on the second draw is 4/40. So, using the multiplication theorem we obtain now that the probability of events S1 and S2, is (4/40) (4/40). If a series of events are independent the probability that all the events will occur simultaneously is the product of the individual probabilities of occurrence. As an example of exploration involving conditional probabilities, we can think in an explorationist who is analysing a drilling “prospect” in a field. There has been 20
successful gas completions drilled in the field having reserves ranging from 3-6 Bcf per well. The field appears to have some rather complex stratigraphic variations and it is difficult to predict the reserves. As an attempt to determine probabilities he tabulated the reserves as follows: Reserves volume 3 Bcf
Nº of wells 7
Percent 35%
4 Bcf
7
35%
5 Bcf
4
20%
6 Bcf
2
10% 20
100%
After detailed study and comparisons with nearby correlative areas he concluded that the probability of finding gas is about 25%. The probability of finds gas and that the level of reserves would be 3 Bcf is: P(S1 S2) = P(S2/S1) P(S1); Probab gas and 3Bcf reserves = 0.25 x 0.35 Bayes’ Theorem
Often, at the time of making the decision there may have been little or no information available upon which to base the probability estimates. Because of this it may be important to revise, or reassess these initial probability estimates as new information becomes available. The Statistical method to revise probability estimates from new information is calls Bayesian Analysis.
The theorem is easily derived from the addition and multiplication theorems already discussed. S1
A
S1 ∩ H
S2
Sn
Sn ∩ H
An explorationist defines a mutually exclusive events series, S1, S2,... , Sn, which initial probabilities of occurrence are P(S1), P(S2),... , P(Sn). These estimates are called “a priori” probabilities. H is an event, occurrence of something, which gives new information allowing to revise the
initial values of the probabilities. And now the explorationist must reassess the initial estimates obtaining new values called “a posteriori" probabilities, which can be computed
from the following equation: P(Si/H) = P(Si) P(H/Si) / Σ P(Si) P(H/Si) Let’s consider a numerical example. Suppose the exploration department has made a
geological analysis of 12 seismic anomalies of about equal size. Because the information the company have is poor, there is uncertainty about how many of the anomalies will contain oil, and establish several possible states of nature S1: 7 anomalies contain no oil and 5 anomalies contain oil; P(S1) = 0,33 S2: 9 anomalies contain no oil and 3 anomalies contain oil; P(S2) = 0,67 The company decide to drill a wildcat on one of the twelve anomalies and it turns out to be a dry hole. How can this new information be used to revise our original estimates of the likelihood of each of hypothesized states of nature? We will use Bayes’ Theorem to gain an insight and restimate the “a priori” probabilities and computing the conditional probabilities. What is the probability that the first anomaly drilled will be dry? P(S1) = 7/12 = 0.58. And, what is the probability that the second anomaly drilled will be dry? P(S2) = 9/12 = 0.75. What is the revised probability that S 1 is the true state of nature given the evidence of one dry hole? That is, P(S1/H)? P(S1/H) = P(H/S1) P(S1) / P(H/S1) P(S1) + P(H/S2) P(S2)
P(S1/H) = (0,58)(0,33) / (0,58)(0,33) + (0,75)(0,67) = 0,28 What is the revised probability that S 2 is the true state of nature given the evidence of one dry hole? That is, P(S2/H)? P(S2/H) = P(H/S2) P(S2) / P(H/S1) P(S1) + P(H/S2) P(S2) P(S2/H) = (0,75)(0,67) / (0,58)(0,33) + (0,75)(0,67) = 0,72 S1: 7 anomalies no contain oil and 5 yes; P(S1) = 0.33; P(S1/H) = 0.28 S2: 9 anomalies no contain oil and 3 yes; P(S2) = 0.67; P(S2/H) = 0.72 1.00 1.00 ANALYSIS BASED ON THE CONDITION OF DEPENDENT EVENTS (Sampling with replacement)
It is very important to distinguish the analysis based on dependent or independent events. But, how can it is possible to tell if a real world series of wells are independent or dependent events? To answer this question let’s consider an experiment in which the 40 cards of a Spanish deck are thoroughly shuffled and then laid face down on a table. For this analogy we’ll
assume that each card represents a geologic prospect in a basin. Let’s suppose further that all the “gold” represent oil productive prospects and all the rest:
spades, cups, etc correspond to prospects having no oil or gas. To complete the analogy supposes that selecting a card (which is face down initially) and turning it face up is equivalent to drilling a prospect. Before any wells are drilled what is the likelihood of finding oil? As we know, the answer is 10/40. Suppose the card turned up was a “gold”. No w what is the likelihood of the second card turn up also being a “gold”? As long as there are 39 faces down left, the answer is 9/39.
This probability is a conditional probability. The sequence of turning up the two cards in the manner just described is said to be a series of dependent events. Nature has distributed n prospects in a basin, some of which have oil and some are dry. As we drill each prospect we are, in essence, turning one of the cards face-up to see if it is oil or dry. But this card is then left face up and there is one less in the sample space of outcomes on the next trial. In the real world once a prospect has been drilled it is removed from the total of those remaining to be drilled. Each system is one of sampling without replacement. What would be equivalent analog be if the card experiment represented a series of independent events? The experiment would be the same, and on the first card selected the odds of a “gold” would be 10/40. Then, the card is faced down before selecting another card and the odds of the second card being a “gold” would be exactly the same 10/40.
This last analog, clearly, does not apply to the real world because of the fact that once a prospect is drilled, and observe weather it has oil, it is not possible to “un-drill”. As result of this, it is obvious that a sequence of drilling several exploration wells is a sampling without replacement process. The probabilities of what is left to find at any point are dependent upon what has been found thus far. As an example, suppose that exploration department has identified 10 prospects of which 30% were estimated to have oil. What is the probability of finding two discoveries in a 5 well exploration program? Suppose the first two anomalies tested were oil productive and the next three were dry. Using symbols P = productive and D = dry, the sequence would be P, P, D, D, D. What is the probability of this sequence occuring? The likelihood of the first anomaly selected being oil productive, all other factors equal, is 3/10. The conditional probability of the second anomaly being oil, given the first was oil is 2/9. The conditional probability of the third being dry is 7/8. The conditional probability of the fourth anomaly being dry is 7/8, given that two oil anomalies had been found plus one of the dry anomalies is 6/7. Finally, the conditional probability of the fifth anomaly being dry, given that two of the four already tested had been found to be dry is 5/6. The likelihood that this entire sequence of P, P, D, D, D. could occur is the product of these five probability terms: 3/10 x 2/9 x 7/8 x 6/7 x 5/6 = 3/72. Is this the answer to our original question? Definitely not. This is the probability of one particular way to obtain 2 discoveries in 5 wells, but there are other sequences which also could occur: P, D, P, D, D, or P, D, D, P, D, etc. There are 10 mutually exclusive ways of achieving two discoveries in five trials. The probability of each sequence, based on the condition of sampling without replacement, dependent events, 3/72. Applying the addition theorem we will sum 10 times the probability of each sequence ant it will result 30/72. ANALYSIS BASED ON THE CONDITION OF INDEPENDENT EVENTS (Sampling without replacement)
While we have just tried to demonstrate that the realities of the drilling of a sequence of exploration wells is one of dependent events, there are several special instances where the parallel system of independent events applies. When each exploration well in the n well program is in a different basin, and the case where geology varies so rapidly that each well drilled is nearly a separate reservoir.
RISK, UNCERTAINTY AND ESTIMATING. Risk and uncertainty are inherent aspects of investing in petroleum exploration ventures. The tasks in serial exploration decision making are to be consistent in dealing with risk and uncertainty, and to perceive uncertainty realistically, reducing it where possible. Mineral exploration can be defined as a series of investment decisions, whether to acquire additional technical data, geological, geophysical, engineering or drilling, and/or additional mineral interests. The most critical decision in petroleum exploration is not which prospect to drill; it is which basin or trend to explore. A play is a family of geologically similar fields, discoveries, prospects and leads. In order to understand the principles of play analysis it is necessary first, understand the risks analysis of prospects, simply because plays are aggregates of geologically similar prospects. Once the exploration trend has been selected, the first step is the identification of drilling prospect by geoscientists. It requires geotechnical skill and creative imagination. After the exploration prospect has been identified, there are key tasks involved throughout the life cycle of petroleum exploration and development. The second step is measuring value of producible reserves, estimating the chance of hydrocarbon accumulation and estimating the profitability of the project. Finally, the third step consists of implementation and management of exploration projects as business ventures, and includes additional tasks: acquisition strategies, determining the terms under which the company would commit to explore, and portfolio management, choosing which prospects should include in the annual drilling program to maximize economic return. Each decision should produce a progressively clearer determination of risk versus reward, and support timely management action concerning the inferred mineral deposit o accumulation. An idealistic definition of exploration might be a series of investment decisions made with decreasing uncertainty. Some authors used risk and uncertainty as synonymous, others considered them to be separate and distinct factors. Risk connotes the threat of loss . Risk decisions weigh the level of investment against four considerations: net financial assets, chance of success/failure, potential gain and potential loss. The last three considerations must rely on estimates of probabilities that some conditions may occur. In other words, uncertainty refers to the range of probabilities that some conditions may exist or occur . Every exploration decision involves considerations of both risk and uncertainty. Risk comes into play in deciding how much we are willing to pay for additional data or mineral interests, considering the high impact of front-end costs on project profitability. Uncertainty is intrinsically involved in all geotechnical predictions about the range of magnitude of the inferred mineral deposit, the chance of discovery, and the cost of finding and developing it. Once prospects have been identified, the problem in serial exploration decision is twofold:
to be consistent in the way we deal with risk and uncertainty, and to perceive uncertainty accurately and reduce it where possible.
One of the problems is how to express the technical uncertainties realistically, and in a form by which they can be utilized in economic equations and subjected to evaluation. The most common convention in use today by modern petroleum corporations involves the formulation of a range of anticipated values for a given parameter with probabilities, ordinarily 90%, 50% and 10%. For example, the geologists may believe there is a 90% chance that the anticipated payzone will be more than 10 feet thick, and she may be 50% confident that it will be more than 20 feet thick, but she is only 10% sure that it could be more than 40 feet thick. The same procedure may be applied to any parameter: productive area, initial production rate, decline rate or drilling costs. Such estimates must rely on objective considerations of all relevant data: maps, cross sections, geophysical data, borehole log interpretations, etc. The concept of expected value, that we will see immediately, offers an effective way to evaluate risk ventures.
DECISION ANALYSIS Consider the operator of a casino containing a certain number of gaiming devices and table: the odds on each game are well known to the owner, and they are set to be slightly in his favor. He is playing a repeted-trial game in which the expected value of each trial, for him, is positive. When expected value is positive, it is an investment when expected value is negative, it is a game. If the casino operator knows the number of tables, the number of players in an evening, and the house rules, he can predict with considerable precision what his profit will be. He is not a gambler, any more than a life insurance company is. He is an investor . The casino analogy may be distasteful to petroleum managers, but it is actually a pretty fair analog to centralized drilling portfolio. The diversity of investments opportunities, such as drilling wells, enhanced recovery projects or property acquisitions, could be likened to the various types of games such as roulette, blackjack, etc. Repeated trials at the roulete are analologous to the prospects in the annual exploration portfolio. And, finally, the casino operator cannot predict which spin of the wheel will produce a “win”, as exploration manager cannot predict which prospect will be a discovery. However, there are some significant differences between operating a casino and annual exploration portfolio. The actual odds on every drilling venture cannot certainly known; they can only be estimated. But the ability of the firm’s explorers to estimate chance correctly can be
measured and improved. The basic problem is that different explorers, in different geologic areas, are estimating prospect reserves, profitability and chance of success. This calls for the adoption of consistent methods throughout the company.
There are fewer wells in the drilling portfolio than there are spins of the roulette wheel. Most exploration portfolio contains only about 10 to 100 exploration wells. The payoff at the gaming table is inmediate and the payoff at the wellhead is long-term and subject to fluctuations in price and politics. THE EXPECTED VALUE CONCEPT. The oil exploration has frequently been given the dubious distinction of being the “classic” example of decision making under uncertainty .
Each time he decides to drill a well the decision maker is playing a game of chance in which he has no assurance that he will win. Decision analysis considers the element of risk and uncertainty in a quantitative manner and provides a means to incorporate the dimension of risk into a logical and consistent decision strategy under conditions of uncertainty. The cornerstone of Decision Analysis is the expected value concept, a method for combining profitability estimates with quantitative estimates of risk to yield a risk-adjusted decision criterion. This method of analysis whereby the various consequences of each decision can be evaluated and compared. All formal strategies for decision making under uncertainty rest on the expected value concept. A decision to drill could result in a dry hole, or a marginal discovery, or a giant discovery. Decision making under uncertainty always involves at least two possible outcomes for each decision alternative. Each outcome has some likelihood of occurrence, but none is certain to occur. If we knew exact values for all parameters, which affect overall profitability, we would be able to compute an exact value of project profitability. Such calculation would be called deterministic value of profitability. If we do not exact values for each of the parameters the computation is said to be stochastic. If the consequences of all possible decision alternatives could be computed exactly the process of decision would be much simpler. It is the unknown resulting from our inability to measure or predict values of the profit before the events happen that makes the decision making process complicated. Quantitative statements about risk and uncertainty are given as numerical probabilities, or likelihoods of occurrence. Probabilities are decimal fractions in the interval zero to one. An event, which is certain to occur, has a probability of occurrence of 1, and an event that cannot occur has a probability of 0. A decision alternative is an option or choice available to the decision maker. Each decision alternative will have at least two outcomes. Two definitions are important to the understanding of the expected value concept. Expected value of an outcome is the product obtained by multiplying the probability of occurrence of the outcome and the conditional value that is received if the outcome occurs. This product can be expressed in various ways, when it is expressed as monetary profit and losses, usually it is called expected monetary value EMV.
The word conditional means that the value will receive only if that particular outcome occurs. That is, the value received is conditional upon the occurrence of the outcome. Expected value of a decision alternative is the algebraic sum of the expected values of each possible outcome that could occur if the decision alternative is accepted. The expected value of a decision alternative can be positive, zero, or negative. And it is the numerical criterion used to compare competing decision choices available to the decision maker. The decision rule for expected monetary value choices is: when choosing among several mutually exclusive decision alternatives select the alternative having the highest positive expected monetary value (EMV). If the decision maker consistently selects the alternative having the highest positive expected monetary value his total net gain from all decisions will be higher than his gain realized from any alternative strategy for selecting decisions under uncertainty. Examples: Outcome Dry Hole Producer
Outcome Dry Hole 2 Bcf 5 Bcf
Probability Outcome 0.4 0.6 1.0 Probability Outcome 0.7 0.2 0.1 1.0
Conditional Monetary Value
Expected Monetary Value
- 200.000 $ + 600.000 $
- 80.000 $ +360.000 $ +280.000 $
Conditional Monetary Value
Expected Monetary Value
- 50. 000 $ +100. 000 $ +250. 000 $
- 35. 000 $ + 20. 000 $ + 25. 000 $ +10. 000 $
Expected Value of decision
E MV
MEANING AND INTERPRETATION OF EXPECTED VALUES. The decision rule means
that, all other factors equal, the decision maker should accept the alternative, which maximises expected value. The expected value of a decision alternative is interpreted to mean the average monetary over a series of repeated trials. The key words in this interpretation are per decision and repeated trials If the decision maker were presented with a repeated series of prospects having the same risk and profit values as those of first previous example his overall profit from the series of repeated trials would average 280.000 $ per decision if, in each instance, he had accept the drill option.
Suppose he had presented 100 “prospects”, and suppose further that he elected to drill
each of them. The most probable results of the 100 well drilling series would be 40 dry holes and 60 producers. His net revenues from producer wells would be 60 x 60.000 = 36.000.000. His losses in 40 dry holes would be 40 x 200.000 = 8.000.000. His net profit, would be 36.000.000 – 8.000.000 = 28.000.000. His average profit per decision would be 28.000.000/100= 280.000, the expected monetary value of the decision alternative drill. If this meaning of the expected value of a decision alternative is accepted it should be obvious why the decision rule is to accept the alternative having the highest EMV. The average profit received per decision is not as much if any alternative with a lower EMV is accepted. The expected value of a decision alternative is really just a weighted arithmetic average profit that he would expect if the decision was repeated over a series of trials. The weighting factors in the actual computation of EMV are the probability numbers. But the usual case in oil business, and in general in economy, is that there is only one prospect and in this case the EMV represents a profit per decision. Why does this mean, if anything? Does the repeated trial clause rule out its use in business decisions where nearly every decision choice has different risk and profit levels? We just proved that expected value concepts might be useful for repeated events as flipping coins, but not when we are in economical events, as drilling decisions, where every trial has different probabilities and profitabilities. The answer to the above questions is that it is possibly to apply this concept to business decisions if it is recognized that the repeated trial can be satisfied by continued investment decisions. If the decision maker consistently selects the alternative having the highest positive expected monetary value his total net gain from all decisions will be higher than his gain realized from any alternative strategy for selecting decisions under uncertainty. This statement is the absolutely essential for any justification of the use of expected value in business decisions. So we see that this concept is more nearly a strategy for consistent decision making than an absolute measure of profitability.
DECISION TREE ANALYSIS In many occasions exploration opportunities involve only a single decision that is made at time “zero”. This decision would be, for example, “drill”. Once the decision is made there
are no decision options with which the decision maker becomes involved. There are, however, certain decision alternatives of a more complex nature that can’t be analysed in a simple EMV computation. Consider the basic, initial decision of whether to
bid on a lease. The immediate decision choices are bid or not bid. But if the decision maker bids, and wins the tract, he then has a decision regarding whether to drill immediately or run more seismic. It becomes obvious that the initial decision is but a link in a chain of future decision options and contingencies. And all of these future options must be considered when evaluating the feasibility of bidding. The simple decision whether to bid has suddenly become quite complex with future decisions options and “what if’s” at every step of the anticipated
exploitation of the lease.
These types of decisions require a slight modification in our thinking with respect to the expected value concept. The mechanical steps to determine expected values for the initial choices are slightly different. The analysis involves constructing a diagram showing all the subsequent chance events and decision options that are anticipated. These diagrams look very much a drawing of a tree, and now are given the name decision tree analysis. A decision tree is merely a pictorial representation of a sequence of events and possible outcomes. The decision tree illustrates the decision alternatives.
Dry hole
2 Bcf Drill
Don’t drill
5 Bcf
The trees normally read from left to right and are drawn in the same order as the actual sequence in which the decision choices and chance events occur in the r eal world. The point from which two or more branches emanate is called a node. A node surrounded by a square denotes a decision node, a point at which the decision maker dictates which is followed. An encircled node is called a chance node, a point where chance determines the outcome. Any number of decision alternatives or outcomes can emanate from a given decision or chance node. The next step in constructing a decision tree is that we must associate probabilities of occurrence to all the branches radiating from chance nodes and we must specify conditional values received at the endpoints of the tree. When indicating probabilities on a decision tree we must adhere to two important rules. First, the sum of the probabilities around a given chance node must add to 1.0. Ad second, no probabilities are shown on the branches emanating from a decision node.the probabilities around a chance node indicate the relative likelihoods as to which specific outcome will occur. The specific path that occurs from a decision node, however, is not a function of chance, but rather the result of an explicit choice by the decision maker.
SOLVING A DECISION TREE Decision tree analysis is one the few things we solve by starting at the end and working backward. We start by making an expected value computation using the terminal around the last chance node in the tree.
Dry hole -50 000 $ 0.7
A
2 Bcf -100 000 $
0.2
Drill
B
0.1 5 Bcf +250 000 $
Don’t drill
0$
For our example we first make an EMV calculation at point A EMV A= (0.7)(-50 000 $)+(0.2)(+100 000 $)+(0.1)(+250 000 $)= +10 000 $ Next we proceed backward (to the left) in the tree to the next node B. Now we make a decision as if the decision maker were actually standing in B. That is, his choices at decision node B could be represented schematically with the next tree. + 10 000 $ Drill
B Don’t drill
0$
Note that the EMV + 10 000 $ at chance node A is used to represent, or replace all the tree beyond that point. The decision rule at any decision node is to select the alternative (branch) which has the highest EMV. In this case it would be to drill. Each time we come to a chance node we make an EMV calculation, and each time we come to a decision node we make a hypothetical decision. This process is continued until the initial, time-zero decision node is reached, at which time the tree has been solved. In our example there was nothing to the left of decision node B, so the tree was solved at that point.
Decision tree is pretty simple and logical. As far as the definitions and mechanics of solution are concerned it is simple. The difficulties usually arise in being able to correctly organize and draw the trees for decisions of a more complex nature. The advantages of this form of analysis include the following points: All contingencies and possible decision alternatives are defined and analysed in a consistent manner. The complex decision is broken into a series of small parts, then the parts are reassembled to provide a rational basis for the initial decision. Such an analysis provides a better chance for consistent action in achieving a goal over a series of decisions. That is, each step in the sequence has been analysed ahead of time. Any decision, no matter how complicated, can be analysed by the method. The decision tree can be used to follow the course of events. At any decision node, if conditions have changed, the remaining alternatives can be re-analysed to develop a new strategy for that point forward.
PROBABILITY DISTRIBUTIONS. A part of petroleum exploration risk analysis is the concept of profitability distributions. Distributions are useful to describe in a very concise graph the range of possible values a variable can have as well as the probabilities of these values occurring. First it is necessary to give some definitions. Random variable: A parameter or variable, which can have more than one possible
value, is called a random variable. Random variables may be thought of as those variables whose values cannot be predicted with certainty at the time of decision making. For each possible value of the random variable there is associated a likelihood, or probability of occurrence. Random variables are sometimes called stochastic variables to denote the fact that the likelihoods of the values occurring are stochastic, or probabil istic in nature. If the value of a variable is known or can be predicted with certainty at the time of decision making the variable is called a deterministic variable. The values of a random variable can be positive or negative. Each value will have a certain probability of occurrence and different values can have same probability. The adjective random implies that the values of a variable have specific probabilities of occurrence, and it does not mean that the variable itself is random, or randomly distributed. Examples of random variables in petroleum exploration include the possible values of net pay thickness, ultimate reserves or net profit from a drilling prospect. Probability distribution: Is a graphical representation of the range and likelihoods of
occurrence of possible of possible values that a random variable can have. Probability distributions can be discrete or continuous, depending on the nature of the random variable. The horizontal axis of a probability distribution is the random variable and its
appropriate units and range of values. The height of probability distributions above the horizontal axis is proportional to the probability of occurrence of the values of the random variable. An example of a continuous probability distribution is given in the next figure. It is continuous in the sense that any value of recoverable reserves within the range of Xmin and Xmax is possible. The parameter on the vertical axis, f(x), is called a probability density function, and the area under all probability distributions is by definition 1. Another characteristic of all probability distributions is that the probabilities are always zero or positive. This means that the probability function never goes below the horizontal axis. Continous distribution
Discrete distribution P(x). Probability of occurrence.
f(X)
Xmin
Random variable: reserves in X field
Xmax
10
12
14
16
18
20
22
Random variable: nº of oil estructures in the Y basin
The continuous distribution that describes a random variable can have infinite numerical values within a giving range. Their theoretical limits of the probability density function are +/- . For a random variable having limits such as drawed before the probability density function is simply defined zero from to Xmin and zero from Xmax to + . Another technical point with continuous probability functions distributions is that it is only meaningful to talk in terms of the probability of a range of values of X and not specific value of an X. For a continuous random variable the probability of occurrence of a specific value is, theoretically, zero. On the contrary, there are some random variables, which can have only specific numerical values. The probabilities distributions, which describe random variables of this type, are called discrete distributions. Any random variable whose values result from counting is an example of a variable that would be described as a discrete probability distribution: number of producing wells in a field, etc. With discrete distributions the sum of the p(x) terms for each possible value of the random variable must be exactly one: Σ0n p(x) = 1.
CUMULATIVE FREQUENCY DISTRIBUTIONS . Every probability distribution can be expressed in an equivalent graphical form called a cumulative frequency distribution. There are two principal reasons for expressing distributions in their cumulative frequency form:
If we have a cumulative frequency distribution we can read any areas under the probability distribution.
In the mechanics of the risk analysis method called simulation it will be necessary convert distributions of possible values for each random variable into their equivalent cumulative frequency form.
For example, we tabulated net pay thickness data from 20 wells in a basin Y. Range of Thickness 50-80 81-110 111-140 141-170 171-200
Frecuency 4 7 5 3 1 20
Relative Frecuency 0.20 0.35 0.25 0.15 0.05 1.00
Cum. relative frecuency 0.20 0.55 0.80 0.95 1.00
Cum. percent
20% 55% 80% 95% 100%
To represent the data as a cumulative frequency distribution it is necessary to plot the cumulative frequencies of column 4 versus the upper limit of each range. The cumulative frequency less than or equal to the minimum possible value of the random variable will always be 0, and the cumulative frequency less than or equal to the maximum value of the random variable will always be 1.
50
80
100
110
140
170
200
SINGLE VALUE PARAMETERS OF DISTRIBUTIONS Although a random variable can normally assume many possible numerical values there are certain specific values, which can tell us important information about the entire probability distribution. At this moment it is only necessary to consider two of the single value parameters of distributions: a) a parameter which describes central tendency o average values of the random variable, and b) a parameter which describes the variability, or range within which the random variable is distributed.
Measures of central tendency.
Parameters, which describe central tendency, can provide information about average values of random variable. The measures most commonly used are: the mean, median and mode. Mean: The weighted average value of the random variable where the weighting factors are
the probabilities of occurrence. It is synonymous to the expected value of a distribution and to the arithmetic average of a set of statistical data. If we are dealing with a distribution of net monetary value profit the mean value of this profit distribution is exactly equal to EMV. All probability distributions, discrete or continuous, have a mean value. The units of the mean are the same as the units of the random variable. The symbols used for the mean value are: or x. From a statistical point of view the mean value is, by far, the most important single value measure of central tendency, and it is very important in decision analysis because it is, by definition, equivalent to expected value, the basis for decision making under uncertainty Median: The value of a random variable, which divides the area under the probability
distribution into two equal parts. The probability of the random variable being less or equal to the median is 0.5. The probability of the random variable being greater than to the median is also 0.5. The median value is not as representative a measure of central tendency, average, as the mean, because is not affected by the magnitudes of the values of the random variable. It only tells us the value of the variable such that half of the possible values will be smaller and half of the values will be larger. Mode: The mode is the value of the random variable, which is most likely to occur. It is the
value of the random variable located under the highest, peak value of the probability distribution curve. Distributions can have more than one mode. From risk analysis point of view the mode does not have much value. However, the mode value is referenced frequently in the decision making process when it is referred to the most likely or most probable value of the random variable. In general, the mean, median and mode are all different values for a given distribution. One exception to this is continuous distributions that are symmetrical in shape. In these cases the mean, median and mode values will be coincident. Examples of these cases include the normal and uniform distributions.
Measures of variability.
The mean value of a distribution tells us important information about the average or expected value of the random variable, but it does not tell us anything about the spread, or variability of other possible values of the variable on either side of the mean. Will the range of possible values of the variable be very small with all the values located at or near the mean, or will the range be very large with possible values much larger or smaller than the mean? The most important of the single value measures of variability is standard deviation.
Standard deviation: Each possible value of a random variable is located a given distance
from the mean, as measured along the horizontal axis. These distances are called deviations about the mean. The mean value of the squared deviations about the mean is called variance, and standard deviation is defined as the nonnegative square root of the variance. All distributions have a standard deviation and its units are identical to the units of the random variable. The symbols for standard deviation and variance are σ and σ2 respectively. The physical significance of the standard deviation is that it tells us the degree of spread, or dispersion of distribution on either side of the mean value.
A
f(X)
B
X
In this figure the standard deviation of the narrow distribution A is less than standard deviation of distribution B. From statistical point of view standard deviation is by far the most important measure of dispersion, or variability. In fact, certain distributions such as the normal and lognormal can be completely and uniquely defined by simply specifying the mean value and the standard deviation. Other measures of variability such as the range, mean deviation, percentiles, etc, are much less useful in petroleum exploration risk analysis.
DISTRIBUTIONS ANALYSIS
OF
INTEREST
IN
EXPLORATION
RISK
There are several specific distributions which appear rather frequently in exploration analysis and it is necessary describe briefly their characteristics. Normal distribution. It is probably one of the most common and widely used distributions
in statistics and probability. It is a continuous probability distribution having a symmetrical shape similar to a bell. Statistics is routinely taught to students by employing the normal distributions.
The Central Limit Theorem states that distributions resulting from the natural addition of independent random variables will be normal, a frequency distribution will tend to take the form of the familiar bell-shaped curve, in which the vertical axis is ordinarily expressed as a percentage of the total, and the horizontal axis is an arithmetic scale expressing some variable. Specific characteristics of the normal distribution include:
The distribution is completely and uniquely defined by the two single value parameters and σ.
The mode (most likely value), median (value of the random variable which divides the distribution into two equal parts), and the mean are all equal.
The distribution curve is symmetrical and the inflection points of the curve occur at values of the random variable corresponding to + σ and - σ. All normal distributions have 0.6826 of total area under the curve within the limits +- σ. The area under the curve between the limits +- 2σ is 0.9544 for all normal distributions, and the area within the limits of +- 3σ is 0.9974. Cumulative frecuency
f(X)
- σ
+ σ
X
X
The theoretical limits of all normal distributions are - and + . In practice the distribution is truncate at values of the random variable corresponding to 4 or 5 standard deviations on the basis of the random variable outside 4 or 5 standard deviations become infinitesimally small.
The cumulative frequency graph of a normal distribution, when plotted on coordinate graph paper, has the shape of a symmetrical “s” as shown in the figure.
Lognormal distribution. Even though students of mathematical statistics have long know
the significance of the Central Limit Theorem, the lognormal distribution in petroleum science has only gained wide acceptance during the past decade. This theorem provides that distributions resulting from natural multiplication of independent random variables will be lognormal (see page 6). The lognormal distribution is a continuous probability distribution that tends to form a symmetrical bell-shaped curve, similar to a normal except that is skewed to one side. The distribution can be skewed in either direction.
Frecuency
Mode Median Mean
f(X)
X
The lognormal distribution can be skewed as shown in the figure describes a random variable which has a small chance of large numerical values and a large chance of smaller numerical values of the variable. Some examples of random variables that can sometimes be represented by lognormal distributions include thickness of sedimentary beds, oil recovery in a given formation and reserves per well in a sedimentary basin.
Cumulative frecuency
Another convention for presenting the same data is the cumulative probability distribution, in which the vertical axis is 0-100% and horizontal axis displays a dimensional variable. The power of cumulative probability distribution is that, conceptually at least, it represents the full universe of all possible outcomes, 100%, and probability is expressed as a cumulative percent of some outcome “equal to or less than” or “equal to or more than” a particular value. Thus the cumulative probability distribution is especially useful as a predictive tool. Specific characteristics of the lognormal distribution include:
The distribution is completely and uniquely defined by the two single value parameters and σ.
If a random variable, x, is lognormally distributed, the logarithms of the numerical values of x are normally distributed. That is, if it is make the transformation y = ln x, where x is a lognormally distributed random variable, the distribution of the transformed variable, y, will be normally distributed.
The theoretical limits of all normal distributions are - and + . In practice the distribution is usually truncated at values of the random variable where the distribution curve is nearly asymptotic with the abscissa.
The cumulative frequency graph of a lognormal distribution, when plotted on a special graph paper called lognormal probability paper, will plot as a straight line.
The meaning of standard deviation of a lognormal distribution is the same as with any other distribution, the larger the value of σ the greater the range of the variable.
The most common application of lognormal distributions in exploration risk analysis will be to describe reserve data, recovery data and formation thickness data.
PREFERENCE THEORY CONCEPTS The theory relates to an extension of the expected value concept in which the decision maker’s attitudes and feelings about money are incorporated into a quantitative decision parameter, looking for a more realistic measure of value than the EMV. The real-world application of preference theory is still very controversial and its value in the decision making context is questioned by some scholars and many businessmen. When we studied EMV criterion for decision making we pointed out this criteria implied that the decision maker was totally impartial to money. And therein lies the central issue, people are not impartial to money. Rather, they have specific attitudes and feelings about money, which depend on the amounts of money, their personal risk preferences and immediate or longer term personal objectives. The result of all this is that the simple, easy to use concept of EMV and its decision rule of maximizing EMV may not provide the most representative decision criterion, because it is not included any consideration of the particular attitudes and feelings the decision maker associates with money. It is easy to mention a number of situations in which EMV does not provide a clear-cut decision strategy:
Imagine that the EMV for a drilling venture is positive but the potential loss from a dry hole is greater than the decision maker can afford. Should he follow and drill, with the hopes of not getting dry hole?
With same data and probably same decision, using EMV criterion, some decision makers are conservative in their preferences for taking risk, but others may be gamblers.
On the flip of a fair coin would receive 2$ if a head occurs and lose 1$ if a tail occurs. Would you accept this gamble? Would you accept the game in case your fortune is 10 million $ and you will receive 20 million $ more if a head occurs and lose 10 million $ if a head occurs?
Which are the answers? Most people will answer yes in case of a 1$ game but no, in case of 10 million $. In terms of EMV would have both been to accept both games. Now consider two different gambling situations. As before assume that your personal funds are being used.
You have saved 5$ to spend for an evening of entertainment. You are then offered the chance to participate in a coin-flip gamble in which you receive an additional 5$ if a head occurs and lose the 5$ you have saved if a tail occurs. Would you accept this gamble?
You are desperate to see the NBA final. You have 5$, but the tickets costs 7,5$. You are offered the chance to participate in a coin-flip gamble in which you receive an additional 5$ if a head occurs, and lose your 5$ if a tail occurs. Would you accept this gamble?
What are the answers to these two gambles? The usual reactions are that some would take the first gamble, but nearly everyone would accept the second. On the basis of EMV both gambles have same value, which presumably means the decision maker is neutral or indifferent to each gamble. This suggests that immediate or long term represent another non-monetary consideration in the decision process. All of this is positive evidence that people simply are not impartial to money. The desirability and preferences we associate with various amounts of money are not proportional to the quantities of money. This observation is not recent. In the XVII century was famous the Saint Petersburg Paradox. This Paradox involves the following gamble: Player A pays 1$ to player B for the privilege of playing the game. The game continues until the f irst tail appears on flip of a fair coin. Player A receives 1$ for each head that occurs prior to occurrence of the first tail. Player A can repeat playing the game as long as he desires, but each time he must pay the 1$ stake. Question: Should A play the game? How much does he stand to gain if he does? Solution:
Probably Outcome 1/2 1/4 1/8
Outcome T HT HHT …
…
Reward to Player A 0 1 2 …
EMV A = (1/2 * 0) + (1/4 * 1) + (1/8 * 2) + …+ (- 1) EMV A = (1/4) + (2/8) + (3/16) + …+ (- 1) = 1 + (-1) = 0 Player A’s expected winnings are zero. Over a series of games he will neither win nor lose any money. In the terminology of mathematical game theory this is called a “fair game”.
Now we will change slightly the game. Player A receives 1$ for one head, 2$ for two heads, etc., each time doubling the previous payoff. With this exception, the game is played as before, and player A should be required to pay a higher stake since his winnings are higher. Question: How much can player A afford to pay to play this revised game and still expect
to at least break even? Solution:
Outcome T HT HHT HHHT …
Probably Outcome 1/2 1/4 1/8 1/16
Reward to Player A 0 1 2 4
…
EMV A = (1/2 * 0) + (1/4 * 1) + (1/8 * 2) + (1/16 *4) + …+ (- stake)
…
EMV A = (1/4) + (1/4) + (1/4) + …+ (- stake) = + (- stake) If player A offered an infinitely large stake each time he plays his overall expectation would be zero. For any stake less than infinite player A’s EMV would be positive. And player A’s gain is player B’s loss.
Do you believe that? How much would you offer to player B to play the game? If you were player B would you have played if player A offered you 100$ each time? 1000$? 1.000.000$? The Paradox implied that player A could offer any amount of money and still win in the long run and player B should never accept the gamble, because his EMV will always be negative. For most people the reverse situation would apply: the more money player A offered the more probable it was that A would lose in the long term, and the more player A offered the more likely it would be player B would accept the money and offer to play the game. The Swiss Mathematician, Daniel Bernoulli, studied this Paradox and about 1738 concluded that an individual’s preference for money is inversely pr oportional to the amount he already has. The mathematical implication is that the correlation between the amounts of money and the corresponding preferences for money follows the shape of a logarithmic function. To solve the paradox he computed an expected value in which the rewards to player A were expressed as the logarithm of 2$, 4$, etc. With this modification the series become convergent and has a finite sum and one could compute the monetary value of the stake player A should offer which would reflect his value system of diminishing preference with increasing wealth. Thus do not imply that EMV is invalid as a decision parameter. Rather, we have suggested that all of us have certain attitudes and feelings about money, which EMV does not consider.
EMV is a completely valid decision parameter if the decision maker is totally impartial to money. But very few, if any, are completely impartial to money. Most have specific feelings about it caused by factors as asset position, risk preferences, goals, etc.
The decision maker has two choices with regard to applying quantitative criteria to petroleum exploration investments. Use EMV and include attitudes and feelings in an informal, non-quantitative manner. Or incorporate his beliefs into a quantitative decision parameter having all the characteristics of the expected value concept and use the resulting numerical parameter as a basis for decision making.
THE MATHEMATICAL BASIS FOR PREFERENCE THEORY
This theory was developed by two Princeton University mathematicians, von Neumann and Morgenstern. Their theory is about of strategies against an opponent or adversary, or game theory as is called in mathematical circles. They concluded that person’s value
system regarding money included various emotional attitudes and feelings and developed the mathematical basis for what we here call preference theory.
A mathematical theory has as its basis one or more axioms. An axiom is simply a statement, or starting point from which the theory is developed. Von Neumann and Morgenstern started with eight axioms. We won’t go into details of this, other than to
mention two or three of them to illustrate their general nature:
If an individual has two choices, A or B he either prefers A to B, or he prefers B to A, or he is indifferent between A and B.
If an individual has three choices, A, B, and C and if he prefers A to B and prefers B to C, then he prefers A to C.
Given three choices, A, B, and C such that A is preferred over B, and B is preferred over C, there is some combination of A and C where A occurs with probability p and C occurs with probability (1-p) such that the combination with A and C as possible outcomes will be preferred over the non-risk alternative of B. Similarly, there is some value of p such that the non-risk alternative B, will be preferred over the combination of A and C.
The authors of this theory proved that if a decision maker accepts the eight axioms as the basis of rational decision it is possible to describe his attitudes about money in a simply function o curve.
Increasing preference
Increasing amounts of money
This function is mathematically unique up to a linear transformation. This means that the scales of the preference curve are arbitrary until numerical values of two points have been specified. There are several important properties of the preference curve:
The vertical preference scale is dimensionless and reflects only the relative desirability of an amount of money. The zero point on the vertical scale is generally interpreted as a point of indifference about of money. Positive values on the vertical denote desirability and negative ones denotes dislike for the corresponding amounts of money.
The horizontal scale can be in units of money such NPV, etc.
The curve is a monotonically increasing function. This means that the vertical parameter increases in numerical value as the amounts of money increase.
The preference curve is based on an individual’s preferences and does not imply a
comparison among individuals.
The shape of the preference curve reflects preferences of the decision maker. If he were totally impartial to money his preference curve would be a straight line passing through the origin.
Same as EMV concept, preference theory has the property of expectation. We can multiply probabilities of occurrence by the relative preference and compute an expected preference value for a decision alternative.
The expected preference value of a decision alternative is the decision parameter used by the decision maker to accept or reject the alternative. The decision rule is to select the decision alternative, which has the highest positive expected preference value.
The expected preference value, EMV, of a decision choice represented a “weighted average profit”. In preference theory the expected value of a decision alternative represents a measure of “weighted average preference”. The decision rule suggests that the manager select projects, which maximize this “weighted average desirability”.
Decision Analysis Using EMV
Decision Analysis Using Preference Theory
Define decisions alternatives and outcomes.
Define decisions alternatives and possible possible outcomes.
Determine numerical probabilities of occurrence for each outcome.
Determine numerical probabilities of occurrence for each outcome.
Compute a conditional monetary profit or loss for each outcome.
Compute a conditional monetary profit or loss for each outcome.
Multiply probabilities of occurrence of each outcome by conditional monetary values.
Read preference values corresponding to each conditional monetary profit or loss from preference values. Multiply probabilities of occurrence of each outcome by corresponding
Compute algebraic sum of the expected monetary values of all
possible outcomes to yield the decision parameter EMV of decision alternative.
preference values.
Select alternative which maximizes EMV.
Compute algebraic sum of the expected preference values of all possible outcomes to yield the decision parameter expected preference value of decision alternative. Select alternative which maximizes expected preference value.
The only difference between the two concepts is that in EMV we multiply probabilities by the monetary values to be received whereas in preference theory we multiply probabilities by the preference values which correspond to the monetary values to be received. We can probably all agree that people are not impartial to money and the question is how these attitudes could be incorporated into the quantitative decision process. The preference curve and resulting decision analysis techniques are just descriptive. The curve is merely a description of the decision maker’s attitudes, it does not prescribe what his
preferences should be, nor does it mean that he is wrong for having his particular preferences.
PETROLEUM EXPLORATION RISK ANALYSIS METHODS. As we already mentioned risk implies the need to quantify many types of risks: risk of an exploratory or development dry hole; political risk, risk to future oil/gas prices, risk that a discovery will not be a large enough to recover initial exploration costs, environmental risk, etc. The purpose will be to discuss the strengths and weaknesses of each method, so that you will be in a better position to judge the conditions for which each method can be used. We should remind that there are very few absolutes in petroleum exploration risk analysis. Answers to “what if” questions are very important and may provide the basis for a rational
decision, even though some of the specific probabilities are not known to three decimal place accuracy. The problem in risk analysis can be stated quite simply. For the drilling prospect being considered what are the probabilities of occurrence of all possible levels of profitability? What are the chances of a dry hole? What are the probabilities that estimated future oil prices will occur? Since an acceptable investment must have a reasonably good chance of making a profit the various outcomes of interest are expressed in levels of profitability, rather than just such as 100 MMB, 500 MMB, etc. But the uncertainties relating to possible reserves levels are, in many cases, a major unknown in the decision. As we consider solutions to the problem we must bear in mind certain characteristics which are unique to the petroleum exploration decision process.
With regard to reserve level probabilities we cannot explicitly describe the process which originally generated the distribution of petroleum accumulations. This is a handicap to us because it means that we will probably never be able to develop an exact probabilistic model to serve as an analog to the exploration process.
The drilling of a sequence of wells is a series of dependent events based on a sampling without replacement process.
Probability estimates must often be made on the basis of very little or no statistical data or experience. Additional data in petroleum exploration are usually from additional wells or seismic, and we normally can not afford to delay decisions until there is a sufficient amount of data upon which to base our probability estimates.
With regard to the economic factors and the prediction of probabilities we have an equally complex situation to deal with. The volatility of the world crude prices, for example, can be very difficult to predict. The effects of inflation, shortages of steel for plataforms, casing for wells, etc must be considered when determining ultimate value of a discovery.
Geologyis a very abstract science. An explorationist must try to recreate in his mind how ancient river deltas existed, how the seas regressed, erosion occurred, etc. But at the end of his analysis he is now being to quantify his feelings about the prospect in terms of probabilities. Not an easy task.
These considerations certainly make the task of estimating probabilities in exploration uniquely complex and difficult.
GLOSARY OF ECONOMIC EVALUATION NOMENCLATURE Acquisition of unproved properties. Costs incurred to purchase, lease or otherwise
acquire a property, including costs of lease bonuses and options to purchase or lease properties, the portion of cost applicable to minerals when land, including mineral rights, is purchased in fees, brokers’ fees, recording fees, legal costs and other costs incurred in
acquiring properties. Acquisition of proved properties. Costs incurred to purchase or otherwise acquire
proved oil and gas reserves in place, including production payments payable in-kind. Costs include cash and other forms of consideration, brokers’ fees, legal costs, etc. Exploration costs. Costs incurred in identifying areas that may warrant examination and
in examining specific areas that are considered to have prospects containing oil and gas reserves, including costs of drilling exploratory wells and exploratory-type stratigraphic test wells. Exploration costs may be incurred both before acquiring the related property (sometimes referred to in part as prospecting costs) and after acquiring the property. Principal types of exploration and applicable operating costs of support equipment and facilities and other costs of exploration activities are:
Costs of topographical, geographical and geophysical studies, rights of access to properties to conduct those studies and salaries and other expenses of geologists, geophysical crews and others conducting those studies. Collectively, these are frequently referred to as geological and geophysical or G&G costs.
Costs of drilling exploratory-type stratigraphic test wells.
Costs of carrying and retaining undeveloped properties, such as delay rentals, ad valorem taxes on properties, legal costs for title defense and the maintenance of land and lease records.
Dry hole contributions and bottom hole contributions.
Costs of drilling and equipping exploratory wells. An exploratory well is a well drilled to find and produce oil or gas in an unproved area, to find a new reservoir in a field previously found to be productive of oil or gas in another reservoir, or to extend a known reservoir. Generally, an exploratory well is any well that is not a development well, service well or a stratigraphic test well.
Costs of drilling exploratory-type stratigraphic test wells.
Development costs. Costs incurred to obtain access to proved reserves and to provide
facilities for extracting, treating, gathering and storing the oil and gas. More specifically, development costs, including depreciation and applicable operating costs of support equipment and facilities and other costs of development activities, are costs incurred to:
Gain access to and prepare well locations for development drilling, including surveying well locations for the purpose of determining specific development drilling sites, clearing ground, draining, road building and relocating public roads, gas lines and power lines, to the extent necessary in developing the proved reserves.
Drill and equip development wells, development-type stratigraphic test wells and service wells, including the costs of platforms and of well equipment such as casing, tubing, pumping equipment and the wellhead assembly. A development well is a well drilled within the proved area of an oil and gas reservoir to the depth of a stratigraphic horizon known to be productive.
Acquire, construct and install production facilities such as lease flow lines, separators, treaters, heaters, manifolds, measuring devices and production storage tanks, natural gas cycling and processing plants and central utility and waste disposal systems.
Provide improved recovery systems.
Production costs. Costs incurred to operate and maintain wells and related equipment
and facilities, including depreciation and applicable operating costs of support equipment and facilities and other costs of operating and maintaining those wells and related equipment and facilities. They become part of the cost of oil and gas produced. Examples of production costs (sometimes called lifting costs) are:
Costs of labor to operate the wells and related equipment and facilities.
Repairs and maintenance.
Materials, supplies and fuel consumed and supplies utilized in operating the wells and related equipment and facilities.
Property taxes and insurance applicable to proved properties and wells and related equipment and facilities.
Severance taxes.
Proved oil and gas reserves . Proved oil and gas reserves are the estimated quantities of
crude oil, natural gas and natural gas liquids (including natural gas liquids attributable to plant ownership interests) which geological and engineering data demonstrate with reasonable certainty to be recoverable in future years from known reservoirs, under existing economic and operating conditions, i.e., prices and costs as of the date the estimate is made. Prices include consideration of changes in existing prices provided by fixed contractual arrangements, but not escalations based upon future conditions (e.g., inflation).
Reservoirs are considered proved if economic producibility is supported by either actual production or a conclusive formation test. The area of a reservoir considered proved includes (i) that portion delineated by drilling and defined by gas-oil and/or oilwater contacts, if any, and (ii) the immediately adjoining portions not yet drilled but which can be reasonably judged as economically productive on the basis of available geological and engineering data. In the absence of information on fluid contacts, the lowest known structural occurrence of hydrocarbons controls the lower proved limit of a reservoir.
Reserves which can be produced economically through application of improved recovery techniques (such as fluid injection) are included in the “proved” classification when successful testing by a pilot project, or the operation of an installed program in the reservoir, provides support for the engineering analysis on which the project or program was based.
Estimates of proved reserves do not include the following: (i) oil that may become available from known reservoirs but which is classified separately as “indicated additional reserve”; (ii) crude oil, natural gas and natural gas liquids, the recovery of
which is subject to reasonable doubt because of uncertainty as to geology, reservoir characteristics or economic factors; (iii) crude oil, natural gas and natural gas liquids that may occur in undrilled prospects; and (iv) crude oil, natural gas and natural gas liquids that may be recovered from oil shales, coal, gilsonite and other sources. Changes in proved reserves include the following:
Extensions and discoveries. Additions to proved reserves that result from extension
of the proved acreage of previously discovered (old) reservoirs through additional drilling periods subsequent to discovery and discovery of new fields with proved reserves or of new reservoirs of proved reserves in old fields.
Improved recovery. Changes in reserve estimates resulting from application of
improved recovery techniques. Revisions represent changes in previous estimates of proved reserves, either upward or downward, resulting from new information (except for an increase in proved acreage) normally obtained from development drilling and production history or resulting from a change in economic factors.
Revisions of previous estimates.
Production.
Purchase of minerals in place.
Sales of minerals in place.
Proved developed oil and gas reserves . Proved developed oil and gas reserves are
reserves that can be expected to be recovered through existing wells with existing equipment and operating methods. Additional oil and gas expected to be obtained through the application of fluid injection or other improved recovery techniques for supplementing the natural forces and mechanisms of primary recovery should be included as “proved developed reserves” only after testing by a pilot project or after the operation of an
installed program has confirmed through production response that increased recovery will be achieved. Proved undeveloped reserves . Proved undeveloped oil and gas reserves are reserves
that are expected to be recovered from new wells on undrilled acreage or from existing wells where a relatively major expenditure is required for recompletion. Reserves on undrilled acreage shall be limited to those drilling units offsetting productive units that are reasonably certain of production when drilling. Proved reserves for other undrilled units
can be claimed only where it can be demonstrated with certainty that there is continuity of production from the existing productive formation. Under no circumstances should estimates for proved undeveloped reserves be attributable to any acreage for which an application of fluid injection or other improved recovery technique is contemplated, unless such techniques have been proved effective by actual tests in the area and in the same reservoir. Tangible assets; they are assets which may be appraised by inspection. These include
buildings, machinery and equipment of all types, which depreciate in value with age and usage. Costs that ordinarily have some a salvage value. Intangible assets; Intangible assets are those that include all types of minerals. No value
may be established by direct inspection and the asset not necessarily depreciate with time. It loses value only when produced and furthermore cannot be replaced. Or costs that ordinarily do not have a salvage value. The exact differentiation between a tangible (capital) asset and an intangible asset is somewhat arbitrary. Depletion; It describes the production of a wasting asset, which, in turn, reduces in value
as the remaining supply decreases. Lease bonuses; A lease bonus is a cash payment to the potential lessor by a potential
lessee as an inducement to give a lease on a property. They may be of several types: Signature bonus. Payable upon signing the contract with the Government. Production bonus. Payable as an agreed upon the achievement of a stated level of
production. Royalty; It is the interest of a party owning minerals in the ground where another party
(the working interest) has gained the right to capture such minerals under a lease agreement. Farm-out Agreement; This is the name applied to a specific form of assignment wherein
the lessee grants a conditional interest to a third party in consideration for the development of a prospect within a specified length of time on given acreage. Carried Interest; A carried interest is an agreement between two more partners whereby
one party (carried party) does not share in the working interest revenue until a certain amount of money has been recovered by the other party (carrying party). Working Interest; It is an interest that is liable for the cost of developing and operating a property. It is a company’s portion of total revenue and also represents the company’s
toward investment and operating costs. Operating Interest; The operating interest is the interest charged with operational
responsibility of the lease. This interest handles all accounting, charging or remitting to each interest its pro-rata share of expenses and profits.
Incremental Economics; As used in investment evaluation, this term usually refers to the
algebraic difference between two cash flow streams. Depreciation; It is an annual reduction of income reflecting the loss in useful value of
capitalized investments by reason of wear and tear. Depletion; It is a reduction in income reflecting the exhaustion of a mineral deposit. It is
allowable to prevent the taxation of a capital asset as ordinary income. Allowable Depletion; The amount of depletion that may be claimed as an expense in a
given year. It can be shown as: remaining investment x
Annual production Remaining reserves
Expended Expenditures; Those which are deducted from income in the year of
expenditure. Capital; Expenditures that may not be completely deducted from income in the year in
which they are made (office equipment, cars, machinery, etc). Capitalized Expenditures; Those which are deducted from income over the years of
useful life. The unit-of-production method; This method is used to depreciate lease, well equipment
and facilities that has a life largely controlled by th physical depletion of reserves. The amount to be deducted each year may be expressed as: (C – D) x
R P
C = the cost of equipment D = accumulated depreciation P = barrels or millions of cubic feet produced during the year R = recoverable barrels, or millions of cubic feet, remaining in the reservoir at yearend.
OIL INDUSTRY ACRONYMS API: American Petroleum Institute API gravity: Scale expressing the gravity or density of liquid petroleum products. Crude
oil is often described in terms of "lightness" or "heaviness" by an index called the API gravity. A high number denotes a "light" crude, and vice versa. Degrees API Gravity = (141.5/Specific Gravity at 60 Deg. F) - 131.5) AAPG: American Association of Petroleum Geologists BBLs: barrels of oil Bcf : Billion cubic feet (109) Bcfd: billion cubic feet per day BOE: Barrels of oil equivalent BTU: British thermal unit CAPEX: Capital expenditure (Investment) Cf : Cubic feet CPI: Consumer price index CT: Corporation tax DD&A: Depreciation, Depletion and Amortization DoE: US Department of Energy EIA: Energy Information Administration, division of US Department of Energy EMV: Expected monery value EOR: Enhanced oil recovery E&P: Exploration and production EU: European Union FPS: Floating production, storage FPSO: Floating production storage and offloading system Ft: Foot (feet) GAAP: = Generally Accepted Accounting Principles
Gal: Gallon GHG: Greenhouse gases GOM: Gulf of Mexico GOR: Gas oil ratio GTL: Gas-to-liquids conversión HP: Horsepower IADC: International Association of Drilling Contractors In: Inch IEA: International Energy Agency IOC: International oil company IOR: Improved oil recovery IPE: International Petroleum Exchange (London) IRR: Internal rate of return JOA: Joint operating agreement JV: Joint venture kW: Kilowatt kWH: Kilowatt-Hour LNG: Liquified natural gas, refrigerated for shipping LPG: Liquified petroleum gas (propane and butane) MB: Millions of barrels MBD or MBPD: Millions of barrels per day MD: Measured Depth MOU: Memorandum of Understanding MWD: Measurement while drilling Natural Gasoline: Condensate (mostly C5+) NGL: Natural gas liquids (ethane, propane, butane, isobutene) (C3-C4 and some C5+)
