Economic Evaluation for Oil and Gas Exploration

7/25/2019 Economic Evaluation for Oil and Gas Exploration

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Centro Superior de Formacin Repsol Exploration & Production

KEY CONCEPTS ON

ECONOMIC EVALUATION

AND

DECISION ANALYSIS

OF

EXPLORATION - PRODUCTION

PROJECTS


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ACKNOWLEDGEMENTS

Special thanks to:

Marco Antonio Guimares Dias, professor of Industrial Engineering Departament ofPontifcia Universidade Catlica do Rio de Janeiro, because his opinion has been key inthe bibliography selection.

Amparo Cervera, professor of Market Research and Techniques of the BusinessAdministration Department of the Valencia University, because she gave me the access tothe Library of Harvard Business School, in Boston.

Clara Cardone,Director of the Master of Business Administration Program at the Carlos IIIUniversity 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. Basic principles of statistics: sample space, event, relative frequence probability,

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 of independent events (sampling withoutreplacement)

Risk, uncertainty and estimating.

Decision analysis. The expected value concept. Meaning and interpretation of expected values. Decision tree analysis. Solving a decision tree.


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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

distributionsPreference theory concepts.

The mathematical basis for preference theory.

Glosary of economic evaluation nomenclature


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INTRODUCTION

Exploring for new reserves of oil and gas natural is a long-term economic priority formankind. New reserves must be located to provide economically viable and politicallysecure 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 wellsare dry holes and are abandoned when drilling is completed, with only a fraction of themleading to commercial developments of new oil and gas reserves.

The volatility of oil prices has raised major questions regarding the economic sense ofexploration program. The financial and regulatory environments for petroleum explorationhave become increasingly complex in recent years. Political risk may also be an importantconsideration in many foreign countries.

Concerted evaluation of new exploration opportunities will not remove many of the difficultto predict risks and uncertainties, but it can improve the economic efficiency of explorationinvestments, 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 economicmerit of investments made in exploring for new reserves of oil and gas in environments oftechnical uncertainty. It strives to embrace the spectrum of business disciplines andtechnological 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, operationaland financial factors are considered in the normal evolution of petroleum exploration. It is apractitioners treatment, concentrating on the assembly and analysis of the best availableinformation 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 theimplications 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 theonly criterion used; unquantifiable factors sometimes underlie major strategic moves.


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EXPLORATION ECONOMICS

Is defined as quantifying our expectations, in financial terms, with respect to exploring forand 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 nationalpetroleum agencies, the conventional definition of successmeans simply that a well wascompleted and did produce some hydrocarbons. But, geological success is not necessarilythe same as commercial success or even economic success. It is well-known the phrasegeological success but economic failure. The standard definitions of successs containsome possible outcomes:

Geological success, meaning that a reservoired accumulation was found that was atleast large enough to support a flowing test. In onshore any well that flows is likely to becompleted, but many such small reservoirs encountered offshore are often reported asshows.

Commercial success or completion success. The exploratory well was completedbecause anticipated future production revenues will return a profit on the cost ofcompleting and operating it, but not on the costs of exploratory drilling, leasing, andseismic, which are thus viewed as sunk cost and not recoverable. This is an economicsuccess 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 whichaverage 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, plusa reasonableprofit. Some authors said this is an economic success on full-cycle basis,defined as theeconomics of discovering and developing an oil/gas prospect including the risk cost of dryholes.

The motive for being in the petroleum exploration business is to make a financial profit. Itis clear the necessity of to find ideas, methods or criteria to measure the ventures

attractiveness.

The decision maker needs tools to distinguish those investment proposals that are not justa geological success, but large enough to produce the necessary revenues to recover allthe expenditure, plus a certain level of profit to attract investors and, at the same time,generate sufficient economic resources to continuing exploring.


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EXPLORATION SUCCES CHANCE.

Petroleum geologist generally agree that for a subsurface accumulation of hydrocarbons toexist, there must be porous and permeable reservoir rock, hydrocarbons that have movedfrom 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 bepresent. This paradigm becomes the fundamental basis for employing geologic chancefactors in estimating probability of geologic success.

Serial multiplication of all factors produces a decimal serial fraction equivalent to theprobability that a hydrocarbons accumulation is present, which is the probability ofgeological 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 = 0.72Chance of prospect structure = 0.60Chance of permeable reservoir = 0.50Chance of trapping seal = 0.40Composite chance of hydrocarbon discovery = 0.0864

Chance that hydrocarbons will be oil = 0.75Chance of oil discovery = 0.0648 or 6,48%

This link chain determine the shape of the probability distribution. The Central LimitTheorem provides that distributions resulting from natural multiplication of independentrandom variables will be lognormal. The lognormal distribution in petroleum science hasgained wide acceptance recently (see pag 42).

Dry hole risk broken in two major categories. Primary risk is defined as the perceived levelof 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 initialdiscovery 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 individualprospect will be a discovery within an already successful exploration play.

Independent prospects are defined as secondary risk exploration targets where adiscovery in any prospect does not materially change expectations regarding the chanceof making a discovery in exploring follow-up prospects.

Dependent prospects are defined as primary risk in any one of the prospects significantlyenhances the perceived chances for making follow-up discoveries. In some cases, failureto make a discovery in a proximity risk prospect can result in a downgrading of discoveryexpectations for follow-up prospects.


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EXPLORATION CONSIDERATIONS

Exploration lands provide the necessary physical base for natural resource companies todevelop and undertake exploration programs to find new reserves of crude oil and natural

gas. Consequently, oil companies place a heavy emphasis on accumulating largeinventories of petroleum lands in attractive geological areas, which are considered to havea good potential for yielding new petroleum discoveries. Attempts are usually made todistribute the land holdings over a number of areas having differing types of petroleumprospects and sometimes contained in a variety of political and administrative settings.

Exploration lands are usually made available by host governments to oil companiesthrough different ways. There are a number of key considerations linking land holdingswith 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 grantedby government discretion through negotiations and are based on the programs thecompanies commit to carry out in exploring them.

Often the up-frontcosts to acquire such land are relatively low, and the companies arerequired to carry out extensive work programs in order to maintain control of a significantportion of the granted lands for an extended period of time. In other countries oilcompanies must bidconsiderable funds up-front and in competition with one another toobtain land rights for oil and gas exploration, absorbing considerable funds, which couldotherwise be utilized in undertaking exploration, work.

Oil companies also sell and/or trade interests in lands to other oil companies forconsiderations of cash or for work which one company commits to undertake on anothercompanys behalf. Farmins and farmouts are particularly important land allocationmechanism because of large land holdings and work commitments of some companiesand the benefits often gained in broadening the number of participants to bring freshexploration ideas to an area to share the burden and opportunity of the extensive andcostly work programs.

The cost of acquiring land interest, whether by direct purchase or by farmin, plays animportant role in the economic viability of many exploration opportunities. In some casesthe acquisition costs can be quite high in relation to the potential economic returns fromthe land acquired, and because these costs represent expenditures at very outset of along program, they can weigh heavily against the ultimate program value when the timevalue of those expenditures is considered.

Areal extent. Petroleum exploration companies generally seek large tracts of land onwhich to carry out explorations activities. On average, only small fractions of initially soughexploration land remain attractive after early exploration surveys are completed. Becauseland selection often has to be made before the general geological potential of an area isknown, oil companies seek large tracts to increase the probability that at least a portion oftheir lands will ultimately turn out to be geologically attractive and worth drilling.


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Large land holdings in an active exploration area also mean that if a discovery is made inthe general area, the company will have a reasonable good chance of having a groundfloor interest in some of the follow-up exploration potential stemming from the initialdiscovery. A large land spread is an oil companys insurance that it will have its fair shareof exploration and production activity in the future.

Permit term.The term of an exploration permit or license relates to the amount of time anoil company has to explore a concession or contract area before it either converts itsexploration 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 casesare considerably longer.

During the exploration permit stage, an oil company normally conducts a series of jobs inorder to evaluate the lands and determine whether they are to be dropped or retained inthe form of a production lease. These front-end exploration costs have an extremelyimportant impact on economic viability of a project.

Work obligations. A company, which is awarded an exploration concession or contractarea normally, is required to undertake a pre-specified amount of exploration work in orderto retain longer term rights to at least part of the territory awarded. This requirementsusually takes the form of a work commitment which may be specified in terms of totalinvestment (budget) or total exploration effort, including geophysical surveys and drillingnumber of wells (work program), which a company must achieve on a specified explorationblock in a specified period of time.

These work commitments are the host governments return for awarding the blocks forexploration, and play a very important economic role in the overall outcome of investments

made on these lands. Predetermining an appropriate work program for a relativelyunexplored block is difficult to do effectively, and frequently the commitments turn out to beeither insufficient to test the true potential of a block or to be too onerous (too much worktoo fast) to be justified based on a blocks true economic potential.

The important difference between discretionary work programs and mandatory workprograms has a fundamental impact on exploration economics, and is often not givensufficient 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 pre-

specified time points. This forces a company to assess the value of the lands, from aregional perspective, as early as possible in order to retain the most promising portions forfuture exploration work.

From a host government viewpoint, this encourages early exploration activity and keeps alarge portion of lands in circulation allowing other companies with different explorationideas to lease and explore them.

Working and carried interests.Working interests refers to the percentage participation acompany has in a petroleum concession or contract area. Normally, a company pays itsfull 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 workinginterests in the lands.


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In certain cases where a company, the farmee, is farming in on the interest of anothercompany, the farmor, the farmee may spend all of certain exploration expenditureobligations of the farmor in order to earn a portion of the farmors interest in certain lands.In such cases the farmor is carried through the exploration expense by the farmee. Oncethe farmee has earned its interest by fully meeting its expenditure obligations, it will be aworking interest partner alongside the farmor, and both companies will share futureexpenditure on the lands in accordance with their respective working interests.

Operating environment considerations. The physical environment and surroundings, inwhich oil exploration, development and production activities take place, play an importantrole 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 itis in a remote area, if the terrain is inhospitable, such a mountainous or desert, andwhether 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 itis in, and what range of weather and oceanographic conditions can be expected over timeon the proposed location. These factors will bear heavily on the type and cost of facilitiesrequired to drill the exploration well and particularly to develop a discovery, and willsignificantly affect time requirements, capital and ultimately the potential economicattractiveness of the prospect.

In both cases, onshore and offshore, when costs or investments are high, sometimesresulting 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 orderto reduce the unit operating and transportation costs.

Finally, discovery of natural gas instead of oil can result in more difficult logistical problemin gathering and transporting the production. Consequently, it is imperative that the natureof the operating environment is fully appreciated and considered in the evaluation ofpetroleum exploration prospect.


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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 Companys overall organization.What is the relationship ofthe 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 itis not possible to find funds, at reasonable price, or there is no room in the companysbudget.

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 toconsider 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 comefrom 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 theirproduction life is an extremely important factor affecting the potential viability of exploration

programs.


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The oil price is notoriously difficult to forecast. Oil supply and demand curves are nottypical of most comodities and the supply of oil is influenced by OPEC policy, whocurrently produce about 40% of the worlds oil supply.

Economists would say that oil demand is inelastic, meaning that demand is not verysensitive to price changes. This is because there are very few immediate substitutes for oilin the short term.

On the other hand, oil price fluctuations are beyond the control of oil companies, and mostcompanies no longer use past oil trends for forecasting.

Gas prices differ from oil prices in that they are often contractually agreed with the buyer atthe outset of a project. The price per unit may have a fixed and variable componet, withthe variable componet being linked to the oil price, thus partly indexing the gas sales priceto the crude oil price.

Energy and the Economy

At least since the time of the first oil shock in October 1973, economists have struggled tounderstand the ways that disturbances to the supply and demand balance in energymarkets influence economic growth and inflation.

At the most basic level, oil and natural gas are just primary commodities, like tin, rubber, oriron ore. Yet energy commodities are special, in part because they are critical inputs to avery wide variety of production processes of modern economies. They provide the fuel thatdrives 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 grossdomestic product (GDP) largely because of our limited ability to adjust the amount ofenergy 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 thevariety of machines that we buy. Those decisions, in turn, influence the growth andcomposition 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 spotprices. Thus, unlike in earlier episodes, the significantly higher relative price of energy thatwe 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 capacityof the economy. That outcome would occur, for example, if high energy costs makebusinesses less willing to invest in new capital or cause some existing capital to becomeeconomically obsolete. All else being equal, these effects tend to restrain the growth oflabor productivity, which in turn implies that real wages and profits will be lower than theyotherwise would have been.

Under the assumption that energy prices do not move sharply higher from their alreadyhigh 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 shocksof the past few years with only a few dislocations.


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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 pricescan simultaneously slow economic growth while raising inflation.

An increase in oil prices slows economic growth in the short run primarily through itseffects on consumer spending.

At the same time that higher oil prices slow economic growth, they also create inflationarypressures. Higher prices for crude oil are passed through to increased prices for therefined products used by consumers, such as gasoline and heating oil. When oil pricesrise, people may try to substitute other forms of energy, such as natural gas, leading toprice increases in those alternatives as well.

The rise in prices paid by households for energy--for example for gasoline, heating oil, andnatural gas--represent, of course, an increase in the cost of living and in price inflation. Ajump 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 andexpectations of inflation down. They attempted to contain the inflationary effects of the oil-price shocks by engineering sharp increases in interest rates, actions which had theconsequence of sharply slowing growth and raising unemployment, as in the recessionsthat began in 1973 and 1981.

To the extent that households and business owners expect that the Central Banks willkeep inflation low, firms have both less incentive and less ability to pass on increasedenergy 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 tocreate new, energy-saving technologies and for energy consumers to adopt them. Themarket for alternative fuels is growing rapidly and will help to shift consumption away frompetroleum-based fuels. Governments can contribute to these conservation efforts byworking to create a regulatory environment that encourages the growth in energy suppliesin 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 impacton the U.S. and global economy that previously believed. The reason is that the petroleumconsumption to gross domestic product and energy to gross domestic product ratios havefallen sufficiently in the past few years to make the economy far less sensitive to priceincreases than anytime in history. To say it another way, energy prices could go muchhigher 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 consumptionGDP ratio in the United States will fall tonearly half the current level by 2025 in the base case. This implies that by 2025, theeconomy 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.


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MEASURES OF PROFITABILITY

This chapter considers the meaning and uses of measures of profitability, the parametersused by decision maker to order, accept, reject, or compare investments proposals. Theseparameters 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 ordimensions of investment projects that are pertinent to the decision maker.

A good measure of profitability must be suitable for comparing and ranking investmentopportunities. And it should provide means of telling whether profitability exceeds someminimum, such as the cost of capital or the firms 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 theywere received at the same period of time. These indicators are not accurate but, often, arevery useful.

And those which consider the time-value of money and use the compound and discountfactors to homogenize the current of cash flows, which are received at different periods oftime.

Cash flows are defined as movements of money into or out the treasury. A goodunderstanding of cash flows in and out of the treasury is essential to the proper use andinterpretation 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 revenuesequal 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 generatedearly 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 shortestpayout.

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 economicanalysis of exploration opportunities. It is a useful parameter to compare the relative ratesof receipt of revenues early in the projects, but it is not a parameter that reflects ormeasures all the dimensions of profitability, which are relevant in capital expendituredecisions.

When cash flows are constant, the payout period will be equal to the quotient between theinitial investment Cand the cash flow S; P = C/S.


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PROFIT-TO-INVESTMENT RATIO.It is a measure that does reflect total profitability. It isdefined as the ratio of total undiscounted net profit to investment. It is a dimensionlessnumber relating the amount of new money generated from a project per monetary unitinvested. It is sometimes called the return-on-investment, or ROI.

Total salesCostsInvestment (Capex) = Net Cash flow

Net Cash flowProfit-to-investment ratio ( ROI ) =

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 issometimes computed using the maximum amount of cash invested in, but not yetrecovered from the project as the term in the denominator. This investment term is calledthe maximum out of pocket cashand 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 ofincome from the project.

Example, consider Prospects A and B. Each has the same profit-to-investment and payoutratios.

Prospect A Prospect B

Producing rate at early projects life 150 Bbl/d 150 Bbl/d

Costs: $/month 575 $ 575 $Investment 150.000 $ 150.000 $Payout: months 14,3 Same 14,3Recoverable Reserves 200.000 Bbls 243.000 BblsProducing Life 15 years 30 yearsTotal Revenues 2,4 M$ 2,9 M$(2,92 $/Bbl, 12,5 % royalty and 5% tax)Total Costs 103.500 $ 207.000 $Revenues - Costs 382.000 $ 382.000 $Net Profit 212.000 $ 212.000 $Profit-to-Investment Ratio 1,41 Same 1,41

Most decision makers, if given a choice would prefer A over B because prospect A returnstotal income in one-half time. Thus it should obvious that a missing dimension in theseparameters 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 threeyears or 4$ in 10 years. Which would you prefer?


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TIMEVALUE OF MONEY CONSIDERATIONS

The usual method of relating the time-rate patterns of future cash flows to some measureof profit is by use of time-value of money concepts: compoundingand 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 calleda compound interest factor.By dividing both sides of the equation by (1 + i)nwe 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 ofabove equation.

It is very important to recognize that C and S are equivalent in value, even thoughseparated in time by nyears.

Thus, 100$ invested at 10% compound interest will appreciate in 146.4$ at the end of 4years. 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 4years 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 monetarysums is the present time, or time zero. Consequently, equation (2) will be used morefrequently.

We normally speak of compound or discount rates in terms of the nominal interest rate peryear. If the investment earns interest once a year the nominal and effective interest are thesame. 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 introducethose that measure or reflect the time-rate patterns of cash flows and the time-value ofmoney, providing a better quality analysis.


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RATE OF RETURN. One of the more widely used profit indicators in recent years. It hasbeen given many different names, including discounted rate of return, internal rate ofreturn (IRR), marginal efficiency of capital.

It is the interest rate, which equates the value of all cash inflows to the cash out- lays whenthese 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 thepresent value of investments.

The rate of return calculation is made after the series of anticipate future cash flows to bereceived 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 ( projects 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 bedefined 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 areequal, P = C/S, we can infer that the internal rate of return is equal to the reciprocal ofpayout.

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 ofreturn there is no way to establish which (if any) it is the correct. In situations like thisthe analysis should be made using other criteria such as net present value.


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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 oftenmisunderstood or ignored by those who assume the criterion. To illustrate this pointconsider the following investment project:

C = initial investment = 8.000S1= net cash flow at year 1 = 1.000S2= net cash flow at year 2 = 3.000S3= net cash flow at year 2 = 5.000

-8.000 + + + r = 4.54% = IRR

If we suppose that the first cash flow is reinvested at 20% and the second at 10% theIRR would be

But if cash flow were reinvested at 3%, the IRR would be

-8.000+ =0 r = 4.5% = IRR

If cash flows remain in the security box of the company, the IRR would be

-8.000+ =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 return10% and 30% respectively. The discount factor in a common period of time will behigher for the investment opportunity with lower internal rate of return, and apparently amonetary unit received from the project with lower internal rate of return has morevalue than a monetary unit received from the other. But, in reality, the value of amonetary 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 cashrevenues.

-8.000+ =0 r = 6.75% = IRR(1+r)3

1.000 1.2 + 3.000 1.1 + 5.000

1.000 1.03 2 + 3.000 1.03 + 5.000

(1+r)

1.000 + 3.000 + 5.000

(1+r)3

(1+r)

1.000

(1+r)

3

(1+r)

3.000 5.000


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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 andprofit to investment ratio, primarily because it includes the time value of money concept. Itis a useful measure of the relative profitability of investments having approximately thesame total life and cash flow patterns. Its primary weaknesses as a measure of trueprofitability 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, previouslyspecified discount rate is used for all economic analysis. It is usually called the averageopportunity 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 ofreturn is that is computed using a more realistic appraisal of future investmentopportunities.

- C + S1/( 1 + i0)1+ S2/( 1+ i0 )

2+ + Sn/( 1 + i0)n = A (npv) ( 4 )

Ais, by definition, the net present value discounted at the average opportunity rate. One ofthe advantages of npv over rate of return is that it is computed using a more realisticappraisal 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 isrealistic of the firms ability to invest capital, then it follows those investment opportunities,which have a negative npv,should be rejected.

Characteristics of npvas 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 addedfact that the reinvestment assumption is satisfied because the discount ratepresumably reflects future investment opportunities.

If npv=0, then the investment is yielding an internal rate of return (IRR) equal todiscount rate used i0. If it is negative it means that the investment will yield a rate ofreturn less than i0. If positive, the sum represents present value cash worth in excessof making a rate of return equal to i0.

The npvis independent of size of cash flows.

The npv concept can be used to evaluate investment alternatives in which all of thecash flow terms are negative. In this instance the preferred decision option will have

the least negative present value.


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Specifying the rate to use for npvcomputations is sometimes not an easy procedure.The usual first reaction is to check the overall corporate annual earning rate in pastyears. But, it may not be realistic because the desired rate is what future investedcapital will earn. Predictions of the rate at which future revenues can be reinvestedinvolve an element of uncertainty. The discount rate for npvcalculations is usually setby 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 theinterest rate being paid on the loan.

If the capital comes from several sources (internally generated funds, debt andequity), 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 iscompletely satisfied and based on time-value money system. It is meaningful for all typesof 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 C0 C1 C2 C3 Payout NPV @ 10%A -2.000 +2.000 1 year - 182B -2.000 +1.000 +1.000 +5.000 2 years 3.492

Project A needs 1 year to recover 2.000 and project B, 2 years. If the company use 1year 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, thepayoutcriteria give different answer than npv. The reason is because payout gives sameweight to all cash flows generated before to the recovery period.

In the next example all projects have same payout. But project B has a biggernpv

thanproject A for any discount rate (1.000 in years 1 and 2 have more value than 2.000 inyear 2). And project C has a bigger npvthan projects A and B.

Project C0 C1 C2 C3 Payout NPV @ 10%A -2.000 +1.000 +1.000 +5.000 2 years 3.492B -2.000 +2.000 +5.000 2 years 3.409C -2.000 +1.000 +2.000 +5.000 2 years 74.867

When a company uses the payout criteria has to establish a time limit. If use a limit withoutconsiders the length of the projects, it will tend to approve too many short projects. If theaverage length of the projects is too long the company will accept some projects with npvnegative. On the contrary, if projects are short the company will reject some of them withpositive npv.


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As an example, it will be considered a project with the following cash flows:

Co= - 4.000; C1= 2.000; C2= 4.000

If opportunity cost of the capital is less than IRR, 28%, the npvwill be positive. If it is equalto IRR the npvwill be zero and if is bigger than IRR the projects npvwill be negative. IRRcriteria will give same answer than npvif the npvof a project is a decreasing function ofdiscount rate.

But not all cash flows have the quality that npv decrease while discount rate increase.Example:

Project C0 C1 IRR NPV @10%A -1.000 1.500 50% 364B 1.000 -1.500 50% -364

If we choose based on IRR criteria both projects are equally attractive. But it is clear thatthey 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. Whenpeople lend money wish the highest interest rate as possible. On the contrary, whenpeople borrow always tried to pay the lowest interest rate. It is what banks do. The interestrates of active are higher than interest rates of passive.

If we drawing the discounted cash flows of project B we will see that npvincrease whilediscount 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 flowshave more than one discount rate, which satisfies the definition of rate or return. Examplesof cash flows, which lead to multiple rates of return, are those projects requiring a largeexpenditure at a later point in the life of the project. A necessary condition to have multiplerates of return is a second sign reversal in the cumulative cash position. But a second signreversal is not a sufficient condition. It also depends on when the second reversal occursand the magnitude of negative cash flows causing the reversal.

Discount rate

NPV

10% 20% 40% 50%

IIR = 28%

+ 200

+ 100

- 100

- 200


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As we can see in the drawing the cash flow of the following example, there are twosolutions 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, ofthe 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 followingexample 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 differentalternatives to make the same project, or simply, when he is analysing mutually exclusiveprojects.

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 areopposite depended on the criteria used.

In cases like this, the way to solve the dilemma is analyse the IRR of incremental cashflow. First, it will be necessary to study the IRR of cash flow of the smaller project. Then, itwill analyse if is worthy to go ahead with the additional investment of 10.000. The

incremental cash flow will be:

NPV

Discount rate

IRR = -50%

IRR = 15,2%

0%-25%

+ 1.000

-1.000

50%25%


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Incremental cash flow C0= -10.000 C1=15.000 IRR = 50 NPV (10%) = 3.636

All these examples have helped to show how to solve some of the discrepancies thatappear when are compared the results obtained with npv or IRR criteria. At same timethey make clear that, sometimes, the IRR is not a useful measure of profitability toclassified projects of different size.

DISCOUNTED PROFIT-TO-INVESTMENT RATIO (DPR). To sidestep the weakness ofnpvbeing independent of the absolute size of cash flows, it is advantageous to use thecriterion called Discounted Profit-to-Investment Ratio, which is the dimensionless ratioobtained by dividing npv by the present value of the investment.

The ratio is interpreted as the amount of discounted net profit generated in excess of theaverage opportunity rate per monetary unit.

Characteristics of dprratio include:

It has all of advantages of npvplus providing a measure of profitability per monetaryunit invested.

It is a suitable measure of value for ranking and comparing investment opportunities.Some authors conclude that the dpris 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 realisticmeasure 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 theywork on budget restrictions, we must consider the importance of trying to chooseinvestments that will give the maximum gain per unit of money invested. This leads to theinvestment strategy of maximizing the discounted profit-to-investment ratio.

If we consider the following example with three projects, and the opportunity cost is 10%.Project C0 C1 C2 NPV 10%A -10 30 5 21B -5 5 20 16C -5 5 15 12

Based on npv criteria all three projects must be approved. But, if it is established that themaximum 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 Cis bigger than the npv of A.

Projects net present valueDiscounted profit to investment = = DPR

Investment


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Thediscounted profit-to-investment ratio is useful to select investment opportunities underthe constraint of limited capital, when it is essential to gain the most profit per monetaryunit invested.

Project Investment NPV @ 10% IndexA -10 21 2,1

B -5 20 3,2C -5 15 2,4

Project B has the highest index, the next higher is project C. If budget establish a limit of10, both projects must be selected.

Unfortunately the application of these criteria can have some problems. One of the mostimportant is when the constraint affects to more than one variable. We will see it in thenext example. The budget limit of 10 is extended to the years 0 and 1 and it is enlarge thenumber of projects with a new one D.

Project C0 C1 C2 NPV @ 10% IndexA -10 30 5 21 2,1B -5 5 20 16 3,2C -5 5 15 12 3,4D 0 -40 60 13 0,4

One solution can be to accept projects B and C, but in that case it is not possible toapprove project D because go beyond the budget constrain in year 1. If it is acceptedproject A, that provide a cash flow of 30 in year 1, t will be possible go ahead with projectD, 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 anlysedwith 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 usingthe lineal programmation.


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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 uncertaintyassociated 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 ofstatistics, probability theory, and utility theory, which began to be recognized as significantsubdisciplines of mathematics and philosophy during the 16th, 17th, and 18th centuries.The applications for early studies concerned games and gambling, then interested toactuarial and insurance companies.

Petroleum exploration is a process of repeated trials under conditions of uncertainty, eachtrial requiring a substantial commitment of investment capital. As such, the casino analogyis 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 beginuntil mid-1960s, led by Exxon, Shell, and Arco. By the late 1970s, companies likeChevron, BP, and Elf, as well as some governmental agencies, IFP, USGS, were alsobeginning to employ risk analysis in their explorations evaluations.

In early 1990s, a technological explosion in risk analysis took place because most modernoil and gas companies saw the need for systematic management of their explorationportfolios on a worldwide basis. Today the methodologies of exploration risk analysis usedby 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 wemay have the need to quantify or asses many types of risks: risk of an exploratory ordevelopment dry hole; political risk, risk to future oil/gas prices, risk that a discovery willnot be a large enough to recover initial exploration costs, environmental risk, etc.

The problems relating to making exploration decisions under conditions of risk anduncertainty have been with this industry since the oil business began. Early attempts todefine risk were pretty informal and usually involved adjectives rather than probabilities.

Later the new discipline of statistical decision theory began to emerge, and explorationdecision 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 probabilitiesrequired to solve a decision tree or compute an EMV. Risk analysis is, probably, theweakest link of the overall decision process. But what is our alternative? Even though riskanalysis is tough, the alternative of ignoring it is untenable. This requires that we attemptto 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 threesituations:


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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 ofthe different parameters of the event.

Until now, the word probability has mentioned many times, the assessment of theprobabilities of occurrence for each possible outcome, without being very specific about itsdefinition. Now is the time to remind some basic principles of statistics.

Deterministic or causal phenomenons are those that keeping constant all factors theresults always will be equal. On the contrary, aleatory or stochastic phenomenons arethose 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 ispossible 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 thatstudies these types of phenomenon. If Statistics analysed events that are repeated manytimes, trying to find its regularity it is clear that any study should based on watchingexperiments or samples.

Sample spaceis 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.

Eventis defined as a part of the sample space whose occurrence is of special interest. Anevent may be defined in any way we please, and it may contain one, two or more of theelements 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 infinitesamples. That is the reason why it is necessary to use a small sample and then to extendthe conclusions to the whole sample. The Statistics try to find regularity that appear incertain phenomena and also, to forecast their behaviour.

As an example suppose we have a standard Spanish deck, which consist in 40 cards, andwe are considering a wager involving the withdrawal of a card at random from the deck. Inthis case there are 40 elements in the sample space.

In petroleum exploration is possible to define a sample spaces like: the number ofstructures which have oil in a basin, the number of producing wells in a field, or all thepossible values of recoverable reserves in a structure.

Now, it is necessary to define what mean a probability number, or a probability ofoccurrence. There are three main definitions which can be given to express probability:relative frequency, or statistical; a classical, or objective definition; and a subjectivedefinition.

Relative frequency definition of profitability: It is the long run ratio of the number oftimes the event has occurred divided by the total number of times the experiment hasbeen repeated. An alternative definition is that probability is the ratio of the number of


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elements defined as the event divided by the total number of elements in the samplespace.

Examples of this might be: the probability of withdraw a queen is 4/40 in the Spanishdeck, or a wildcat success ratio in hydrocarbons exploration.

There are some chance phenomena of interest where a probability cannot be computed inthis manner. What is the probability of an earthquake occurring certain future date in aconcrete place? How would we determine its value? This phenomenon is not a repetitiveprocess that could be experiment with a study. It is necessary to consider an alternativedefinition of probability. called the classical or objective definition.

Classical or Objective Definition of Probability. It is defined as a measure of thedegree to which available evidence supports a given hypothesis. This measure isdetermined by purely objective logic.

The usual way we think about risk in oil exploration is an example of this meaning ofprofitability. The explorationists hypothesize that a structure has oil, or a given level ofreserves, and they look at all the evidence which supports the hypothesis: the nearbystructure has oil, rock strata appear correlative, etc. Then, by purely objective logic, theprobability is determined as the degree to which this evidence supports the hypothesisStructure has oil.

From a practical viewpoint this definition may be difficult to use because explorationistsare usually not free of human emotion about their hypothesis. This leads to a thirddefinition of profitability.

Subjective Definition of Probability. It is a personal opinion of the likelihood that anevent will occur. A subjective probability estimate represents the extent to which anindividual thinks an event is likely to occur. It is a degree of belief.

Subjective probability estimates are sometimes used where past statistical data are notavailable and/or the information is of an indirect nature. These estimations are influencedby a persons biases, emotions or past experiences, etc.

It is also known as a priori probability and correspond an honour place in its use to theeconomist John Maynar Keynes. And because the decision maker never is a situation oftotal 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 ofhydrocarbons exploration, often, it is the only way to consider the probability becausetechnical people do not have enough information.

In oil and gas exploration risk analysis the tree definitions of profitability are used andpeople 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 thesame probability of occurrence. When we are playing with a die, the probability of


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obtains 1, 2 ... or 6 is the same and equal to 1/6. The probability distribution of thisevent is uniform

Mutually exclusive events. Events are mutually exclusive if the occurrence of anygiven event excludes the occurrence of all other events. Mutually exclusive eventshave no points of the sample space in common. When it is drilled a wildcat well and itis unsuccessful implies that it is impossible to find 100 M of oil.

Independent events. Two or more events are independent if the occurrence oneevent in no way affects, or are affected by the occurrence of the other events. Anexample 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 onthe next flip.

Conditional probability. When two or more events are not independent they are saidto 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 isnecessary to be very precise about the distinction between independent or dependentevent in risk analysis.

PROBABILITY THEORY.

The probability is a measure of the grade of certainty that someone has about the chanceof occurrence for a possible outcome.

The probability theory has a set of rules of operation in the same sense that the numbersystem has a set of rules of operation: addition, multiplication, etc, that now is useful toremind briefly.

Total probability or addition theorem.

For a number of events, which are mutually exclusive, the probability of any one of theevents occurring is the sum of the individual probabilities.

P(S1 + S2 +S3) =P(S1) + P(S2) + P(S3)

The probability of event S1and/or event S2is equal to the probability of S1occurring plus

the probability of occurrence of S2 minus the probabilityof both S1and S2occurring.

P(S1 + S2) =P(S1) + P(S2) - P(S1S2)

Compound probability or multiplication theorem.

This theorem is used to find the probability of two events occurring in sequence, orsimultaneously. The theorem is interpreted as: the probability of S1 and S2 occurring isequal to the probability of S2, given that event S1 has occurred, multiplied by the probabilityS1occurring in the first place.

P(S1S2) = P(S2/S1) P(S1)


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The term P(S2/S1) is called a conditional probability. This theorem applies, for both,independent and dependent events.

Define event S1as drawing a king in the Spanish deck on the first draw, and event S2aqueen on the second draw. Assume for the moment that the first card is not replaced inde deck prior to the second draw. What is the probability of both events occurring? Whatis P(S2/S1)?

The likelihood of drawing a king on the first draw is 4/40. Since the card is not replaced inthe deck there are only 39 remaining cards on the second draw, and the likelihood ofdrawing a queen on the second draw is 4/39. Hence, it is possible compute theprobability of events S1 andS2, (4/40) (4/39). The sequence in this example is said to bedependent. But, if the first card is placed back in the deck the probability of draw a queenon the second draw is 4/40. So, using the multiplication theorem we obtain now that theprobability of events S1 and S2, is (4/40) (4/40).

If a series of events are independent the probability that all the events will occursimultaneously is the product of the individual probabilities of occurrence.

As an example of exploration involving conditional probabilities, we can think in anexplorationist who is analysing a drilling prospect in a field. There has been 20successful gas completions drilled in the field having reserves ranging from 3-6 Bcf perwell. The field appears to have some rather complex stratigraphic variations and it isdifficult to predict the reserves. As an attempt to determine probabilities he tabulated thereserves as follows:

Reserves volume N of wells Percent3 Bcf 7 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 theprobability of finding gas is about 25%. The probability of finds gas and that the level of

reserves would be 3 Bcf is:

P(S1S2) = 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 informationavailable upon which to base the probability estimates. Because of this it may be importantto revise, or reassess these initial probability estimates as new information becomesavailable. The Statistical method to revise probability estimates from new information is

calls Bayesian Analysis.


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The theorem is easily derived from the addition and multiplication theorems alreadydiscussed.

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 prioriprobabilities.

His an event, occurrence of something, which gives new information allowing to revise theinitial values of the probabilities. And now the explorationist must reassess the initialestimates obtaining new values called a posteriori" probabilities, which can be computedfrom the following equation:

P(Si/H) = P(Si) P(H/Si) / P(Si) P(H/Si)

Lets consider a numerical example. Suppose the exploration department has made a

geological analysis of 12 seismic anomalies of about equal size. Because the informationthe company have is poor, there is uncertainty about how many of the anomalies willcontain 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 bea dry hole. How can this new information be used to revise our original estimates of thelikelihood of each of hypothesized states of nature?

We will use Bayes Theorem to gain an insight and restimate the a priori probabilities andcomputing 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 S1is the true state of nature given the evidence of onedry hole? That is, P(S1/H)?

P(S1/H) = P(H/S1) P(S1) / P(H/S1) P(S1) + P(H/S2) P(S2)

S1 S2 Sn

S1 H SnH

A


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P(S1/H) = (0,58)(0,33) / (0,58)(0,33) + (0,75)(0,67) = 0,28

What is the revised probability that S2is 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) = 0.721.00 1.00

ANALYSIS BASED ON THE CONDITION OF DEPENDENT EVENTS (Sampling withreplacement)

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 ordependent events?

To answer this question lets consider an experiment in which the 40 cards of a Spanishdeck are thoroughly shuffled and then laid face down on a table. For this analogy wellassume that each card represents a geologic prospect in a basin.

Lets 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 analogysupposes that selecting a card (which is face down initially) and turning it face up isequivalent to drilling a prospect. Before any wells are drilled what is the likelihood offinding oil? As we know, the answer is 10/40.

Suppose the card turned up was a gold. Now what is the likelihood of the second cardturn 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 themanner 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 prospectwe are, in essence, turning one of the cards face-up to see if it is oil or dry. But this card isthen left face up and there is one less in the sample space of outcomes on the next trial. Inthe real world once a prospect has been drilled it is removed from the total of thoseremaining to be drilled. Each system is one of sampling without replacement.

What would be equivalent analog be if the card experiment represented a series ofindependent events? The experiment would be the same, and on the first card selectedthe odds of a gold would be 10/40. Then, the card is faced down before selecting anothercard and the odds of the second card being a gold would be exactly the same 10/40.


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This last analog, clearly, does not apply to the real world because of the fact that once aprospect is drilled, and observe weather it has oil, it is not possible to un-drill. As result ofthis, it is obvious that a sequence of drilling several exploration wells is a sampling withoutreplacement process. The probabilities of what is left to find at any point are dependentupon what has been found thus far.

As an example, suppose that exploration department has identified 10 prospects of which30% were estimated to have oil. What is the probability of finding two discoveries in a 5well 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 isthe probability of this sequence occuring? The likelihood of the first anomaly selectedbeing oil productive, all other factors equal, is 3/10. The conditional probability of thesecond 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 thefourth anomaly being dry is 7/8, given that two oil anomalies had been found plus one ofthe 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 likelihoodthat this entire sequence of P, P, D, D, D. could occur is the product of these fiveprobability 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 oneparticular way to obtain 2 discoveries in 5 wells, but there are other sequences which alsocould occur: P, D, P, D, D, or P, D, D, P, D, etc. There are 10 mutually exclusive ways ofachieving 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 itwill result 30/72.

ANALYSIS BASED ON THE CONDITION OF INDEPENDENT EVENTS (Samplingwithout replacement)

While we have just tried to demonstrate that the realities of the drilling of a sequence ofexploration wells is one of dependent events, there are several special instances wherethe parallel system of independent events applies.

When each exploration well in the n well program is in a different basin, and the casewhere geology varies so rapidly that each well drilled is nearly a separate reservoir.


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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 acquireadditional technical data, geological, geophysical, engineering or drilling, and/or additionalmineral interests.

The most critical decision in petroleum exploration is not which prospect to drill; it is whichbasin 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 necessaryfirst, understand the risks analysis of prospects, simply because plays are aggregates ofgeologically similar prospects.

Once the exploration trend has been selected, the first step is the identification of drillingprospect by geoscientists. It requires geotechnical skill and creative imagination. After theexploration prospect has been identified, there are key tasks involved throughout the lifecycle of petroleum exploration and development.

The second step is measuring value of producible reserves, estimating the chance ofhydrocarbon accumulation and estimating the profitability of the project.

Finally, the third step consists of implementation and management of exploration projectsas business ventures, and includes additional tasks: acquisition strategies, determining theterms under which the company would commit to explore, and portfolio management,choosing which prospects should include in the annual drilling program to maximizeeconomic return.

Each decision should produce a progressively clearer determination of risk versus reward,and support timely management action concerning the inferred mineral deposit oaccumulation. An idealistic definition of exploration might be a series of investmentdecisions 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 thelevel of investment against four considerations: net financial assets, chance ofsuccess/failure, potential gain and potential loss. The last three considerations must relyon estimates of probabilities that some conditions may occur. In other words, uncertaintyrefers to the range of probabilities that some conditions may exist or occur.

Every exploration decision involves considerations of both risk and uncertainty. Riskcomes into play in deciding how much we are willing to pay for additional data or mineralinterests, considering the high impact of front-end costs on project profitability. Uncertaintyis intrinsically involved in all geotechnical predictions about the range of magnitude of theinferred 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:


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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 aform by which they can be utilized in economic equations and subjected to evaluation. Themost common convention in use today by modern petroleum corporations involves theformulation 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 pay-zone will be more than 10 feet thick, and she may be 50% confident that it will be morethan 20 feet thick, but she is only 10% sure that it could be more than 40 feet thick. Thesame 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 allrelevant data: maps, cross sections, geophysical data, borehole log interpretations, etc.

The concept of expected value, that we will see immediately, offers an effective way toevaluate risk ventures.

DECISION ANALYSIS

Consider the operator of a casino containing a certain number of gaiming devices andtable: the odds on each game are well known to the owner, and they are set to be slightlyin his favor. He is playing a repeted-trial game in which the expected value of each trial, forhim, is positive. When expected value is positive, it is an investment when expected valueis 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. Heis 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 prettyfair analog to centralized drilling portfolio.

The diversity of investments opportunities, such as drilling wells, enhanced recoveryprojects or property acquisitions, could be likened to the various types of games such asroulette, blackjack, etc.

Repeated trials at the roulete are analologous to the prospects in the annual explorationportfolio. And, finally, the casino operator cannot predict which spin of the wheel willproduce a win, as exploration manager cannot predict which prospect will be a discovery.

However, there are some significant differences between operating a casino and annualexploration portfolio.

The actual odds on every drilling venture cannot certainly known; they can only beestimated. But the ability of the firms explorers to estimate chance correctly can bemeasured and improved. The basic problem is that different explorers, in different geologic

areas, are estimating prospect reserves, profitability and chance of success. This calls forthe adoption of consistent methods throughout the company.


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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-termand subject to fluctuations in price and politics.

THE EXPECTED VALUE CONCEPT. Theoil exploration has frequently been given thedubious 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 inwhich he has no assurance that he will win.

Decision analysis considers the element of risk and uncertainty in a quantitative mannerand provides a means to incorporate the dimension of risk into a logical and consistentdecision 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-adjusteddecision criterion. This method of analysis whereby the various consequences of eachdecision can be evaluated and compared. All formal strategies for decision making underuncertainty 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 foreach decision alternative. Each outcome has some likelihood of occurrence, but none iscertain 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 calleddeterministicvalue of profitability. If we do not exact values for each of the parametersthe computation is said to be stochastic.

If the consequences of all possible decision alternatives could be computed exactly theprocess of decision would be much simpler. It is the unknown resulting from our inability tomeasure or predict values of the profit before the events happen that makes the decisionmaking process complicated.

Quantitative statements about risk and uncertainty are given as numerical probabilities, orlikelihoods 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 thatcannot occur has a probability of 0.

A decision alternative is an option or choice available to the decision maker. Each decisionalternative 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 ofoccurrence of the outcome and the conditional value that is received if the outcomeoccurs. 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.


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The word conditional means that the value will receive only if that particular outcomeoccurs. 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 ofeach 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 isthe numerical criterion used to compare competing decision choices available to thedecision maker.

The decision rule for expected monetary value choices is: when choosing among severalmutually exclusive decision alternatives select the alternative having the highest positiveexpected 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 gainrealized from any alternative strategy for selecting decisions under uncertainty.

Examples:

Probability Conditional ExpectedOutcome Outcome Monetary Value Monetary Value

Dry Hole 0.4 - 200.000 $ - 80.000 $Producer 0.6 + 600.000 $ +360.000 $

1.0 +280.000 $

Probability Conditional ExpectedOutcome Outcome Monetary Value Monetary Value

Dry Hole 0.7 - 50. 000 $ - 35. 000 $2 Bcf 0.2 +100. 000 $ + 20. 000 $5 Bcf 0.1 +250. 000 $ + 25. 000 $

1.0 +10. 000 $

MEANING AND INTERPRETATION OF EXPECTED VALUES. The decision rule meansthat, all other factors equal, the decision maker should accept the alternative, whichmaximises expected value. The expected value of a decision alternative is interpreted tomean the average monetary over a series of repeated trials. The key words in thisinterpretation are per decisionand repeated trials

If the decision maker were presented with a repeated series of prospects having the samerisk and profit values as those of first previous example his overall profit from the series ofrepeated trials would average 280.000 $ per decision if, in each instance, he had acceptthe drill option.

ExpectedValue

of decision

E MV


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Suppose he had presented 100 prospects, and suppose further that he elected to drilleach of them. The most probable results of the 100 well drilling series would be 40 dryholes 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 36.000.0008.000.000 = 28.000.000. His average profit per decision would be28.000.000/100= 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 beobvious why the decision rule is to accept the alternative having the highest EMV. Theaverage profit received per decision is not as much if any alternative with a lower EMV isaccepted. The expected value of a decision alternative is really just a weighted arithmeticaverage profit that he would expect if the decision was repeated over a series of trials. Theweighting 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 oneprospect and in this case the EMV represents a profit per decision. Why does this mean, ifanything? Does the repeated trial clause rule out its use in business decisions wherenearly every decision choice has different risk and profit levels? We just proved thatexpected value concepts might be useful for repeated events as flipping coins, but notwhen we are in economical events, as drilling decisions, where every trial has differentprobabilities and profitabilities.

The answer to the above questions is that it is possibly to apply this concept to businessdecisions if it is recognized that the repeated trial can be satisfied by continued investmentdecisions. If the decision maker consistently selects the alternative having the highestpositive expected monetary valu

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Economic Evaluation for Oil and Gas Exploration

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