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    Chapter 7 Petroleum Economics

    Contents7.1 INTRODUCTION ....................................................................................................................... 3

    ROLE OF THE PETROLEUM ECONOMIST............................................................................ 4 Lease bidding............................................................................................................................ 4 Selection of "best" option.......................................................................................................... 4 Reporting................................................................................................................................... 4 Unitisation discussions.............................................................................................................. 4 Fiscal changes .......................................................................................................................... 4 Contracts ................................................................................................................................... 4 THE METHOD .......................................................................................................................... 5 THE REQUIRED INFORMATION AND ITS ACCURACY........................................................ 7

    EXPLORATION ECONOMICS ................................................................................................. 9

    REFERENCES........................................................................................................................ 10

    7.2 PROJECT CASH FLOWS ...................................................................................................... 12

    INTRODUCTION..................................................................................................................... 12 CASHIN................................................................................................................................... 12 THE TECHNICAL COSTS...................................................................................................... 12 GOVERNMENT TAKE............................................................................................................ 12 DEPRECIATION ..................................................................................................................... 13 CASH SURPLUS CALCULATION.......................................................................................... 14 CASH SURPLUS AND NET INCOME.................................................................................... 15 THE NET APPROACH............................................................................................................ 16

    7.3 PROJECT PROFITABILITY ................................................................................................... 18

    INTRODUCTION..................................................................................................................... 18 VALUING A CASHFLOW........................................................................................................ 18 THE DISCOUNTED CASH FLOW METHOD......................................................................... 19 THE MECHANICS OF DISCOUNTING.................................................................................. 20 THE DISCOUNT RATE........................................................................................................... 20 PROFITABILITY INDICATORS .............................................................................................. 21 EARNING POWER................................................................................................................. 22 DISCOUNTING A CASHFLOW WITH AN HP CALCULATOR .............................................. 23

    7.4 INFLATION.............................................................................................................................. 24

    A PRICE INDEX...................................................................................................................... 24 THE INFLATION RATE........................................................................................................... 25 THE INFLATION RATE........................................................................................................... 26 TYPES OF MONEY................................................................................................................ 26 THE STAGES IN THE ECONOMIC EVALUATION................................................................ 27 EXCHANGE RATES AND INFLATION .................................................................................. 28 CURRENCY CHANGES AND CASHFLOWS ........................................................................ 29

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    2001 Shell International Exploration and Production B.V. Page 2

    7.5 UNIT COSTS AND BREAKEVEN PRICES........................................................................... 30

    INTRODUCTION..................................................................................................................... 30 UNDISCOUNTED UNIT COSTS ............................................................................................ 30 DISCOUNTED UNIT COSTS ................................................................................................. 31 BREAKEVEN PRICES............................................................................................................ 32 NET UNIT COSTS.................................................................................................................. 33

    7.6 GUIDELINES FOR THE PRESENTATION OF ECONOMICS............................................... 35

    EXAMPLE OF A GROUP BUDGET PROPOSAL .................................................................. 35 Shell Share.............................................................................................................................. 35 Total Requirement................................................................................................................... 35 GENERAL............................................................................................................................... 36

    7.7 DISCOUNT FACTORS ........................................................................................................... 37

    List of Figures

    7.1 Shells Capital Expenditure in the Period 1972-1991 3 7.2 Breakdown of the Revenues of a Medium Cost Oil Field 6 7.3 Production Forecast 6 7.4 The Cumulative Cashflow 7 7.5 The Cumulative Cashflow (at 15$/bbl) 9 7.7 Profit from a Project An Accountants View 16 7.8 Cumulative Cashflow and Economic Indicators 22 7.9 Present Value Profile 22 7.10 Type of Money 28 7.11 Currencies and Type of Money 29 7.12 Breakeven Prices 34

    List of Tables7.1 Calculation of a Price Index 25 7.2 Apparent Discount Rates for Various RT-Discount Rates and Inflation 27

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    7.1 INTRODUCTION

    "The objectives of the Royal Dutch/Shell Group of Companies are to engage efficiently,responsibly and profitably in the oil, gas, chemicals, coal, metals and selected other

    businesses, and to play an active role in the search for and the development of other sources ofenergy."

    So begins the Group's Statement of General Business Principles, which then discussesresponsibilities to 4 groups of interested parties: shareholders, employees, customers, andsociety as a whole. In line with these objectives very large investments are made annually,particularly in the Exploration and Production Function, as seen in Figure 7.1.

    The annual rate of "upstream" investment rose very fast in the 1970s and has averaged $ 5 billionsince 1980. The lean years 1986-87 reflect the oil price collapse, whilst the peaks in 1979, 1985and 1989 include major acquisitions in the USA, Colombia and Nigeria. Excluding acquisitions,total 1972-91 investments were about $ 75 billion. Such sums spent in finding and developingnew oil and gas fields should lead to the creation of enough production capacity to offset thedecline of existing sources. The funds must, of course, be invested profitably. Quoting again fromthe Business Principles:

    "Profitability is essential to discharging these responsibilities and staying in business. It is ameasure both of efficiency and of the ultimate value that people place on Shell products andservices. It is essential for the proper allocation of corporate resources and necessary to supportthe continuing investment required to develop and produce future energy supplies to meetconsumer needs. Without profits and a strong financial foundation it would not be possible to fulfilthe responsibilities outlined above. (....) Criteria for investment decisions are essentiallyeconomic, but also take into account social and environmental considerations and an appraisal ofthe security of the investment.

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    ROLE OF THE PETROLEUM ECONOMIST

    Investment opportunities are regularly proposed to E & P management. They may involve thedevelopment of a newly discovered oil or gas field, or exploration for hydrocarbons in a new area.There may also be the chance of a farm-in or farm-out deal or even the acquisition of an entire

    company, like Belridge in 1979 or HOCOL in 1989.

    It is the petroleum economist's job to advise on the economic attractiveness of theseopportunities, taking into account the many uncertainties regarding reservoir behaviour,development costs, future energy prices and relationships with governments. He will also beinvolved in some or all of the following activities:

    Lease bidding

    Often the company has to bid in order to acquire acreage. The bidding parameter may be the sizeof a signature bonus, the Group's share of production, a price discount for domestic supplies, etc.The economist will help establish the value of this parameter.

    Selection of "best" option

    Usually a choice has to be made between development options. There may be more than oneproduction method (water or gas injection, beam pumps, gaslift), development plan (underwatercompletion or deviated drilling from a platform) or evacuation method (truck, rail, pipeline, tanker).Profitability plays an important part in such decisions.

    Reporting

    The project proposals of operating companies are formally presented to EP management at theannual Programme Discussions. Prior to this, the Data Books are prepared, setting out thetechnical and economic merits of the proposals. In addition, where the proposed expenditureexceeds the chief executive's discretionary limit, a formal budget proposal (known as a Return502F) will have to be submitted for approval.

    Unitisation discussions

    If a field straddles the boundaries of several license blocks held by different licensees, theproduction of the field will be shared between the various parties. This sharing involves frequentunitisation discussions, in which the economist normally takes part.

    Fiscal changes

    If fiscal changes are being discussed within or with the host government, the petroleumeconomist will inform his management on the economic consequences.

    Contracts

    These may cover the sale of hydrocarbons, the sale or purchase of the right to use facilities suchas pipelines, or the purchase of services or materials from third parties.

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    THE METHOD

    The petroleum economist basically sees the proposed venture as a "black box", which initiallyabsorbs shareholders' investment funds and later generates money that reaches them in the formof dividends. Inside the black box the investments are turned into steel, concrete, facilities, etc.;oil sales revenues are received; and operating costs, royalties and taxes are paid. The forecast of

    the annual amounts of money absorbed or generated is called the cashflow of the venture. Theexample in Figure 7.2 illustrates the relation between revenues, technical costs, host governmenttake and cashflow for a venture whose major parameters are shown in Figure 7.3 and theaccompanying table.

    The oil price assumption of $30 per barrel is high, as the evaluation of this project preceded the1986 fall in oil prices. The effect of lower oil prices is discussed later.

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    Development of this 26 million barrel, medium-cost oilfield would lead to the cashflow of Figure7.2. The dominant cost element in the early years is the capital expenditure ($100m) needed tobuild the platform, production facilities and pipeline and to drill and complete the wells. Theremaining technical costs cover maintenance, lifting, treatment, transportation, insurance andoverheads: these operating costs are dominant during the last years of the venture, and are the

    eventual cause of abandonment of the field.

    The largest single cost element is generally the host government take, in this exampleconsisting of royalty and taxes. The relative magnitude of the various cashflow items can be

    judged from a cumulative cashflow, as shown in Figure 7.4.

    This cumulative cashflow curve also illustrates several of the so-called profitability indicators. The investor can see from figure 7.4 that he will have to invest $ 70 million (the depth of the cashsink, or exposure), which will be retrieved in total after the payout time of 6.3 years, and that theproject will have earned him a cash surplus of $ 83 million by the time the field is abandonedafter 18 years.

    The most important profitability indicators, however, result from discounting the cashflow. In thisprocess the cashflow elements of later years are reduced by a discount factor reflecting the timevalue of money. The Present Value Cash Surplus is the sum of the discounted cashflow andrepresents the value of the project to the investor. The Earning Power is a measure of theproject's return on capital.

    THE REQUIRED INFORMATION AND ITS ACCURACY

    In order to analyse a project economically, the petroleum economist will build an economic modelof the venture, normally using a computer. The model parameters will be based on informationgathered from various departments of the company and a large part of the economist's time canbe devoted to this data gathering.

    The accuracy of the information obtained varies considerably. With limited well data, only roughguesses can be made and the accuracy will be rather poor. As more and more appraisal and/ordevelopment wells are drilled, the accuracy of the estimates will gradually improve. In view of this

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    uncertainty, the most probable outcome of the venture is defined as the Base Case . Theeconomic results for this base case should be regarded with some reserve.

    In order to appreciate the effect of possible variations on the base case, a set of "sensitivities" aredefined, evaluated and analysed. Typical examples are: different oil/gas price assumptions;

    alternative reserves estimates; different production behaviour; increased capital expenditure; changes in operating expenses; delayed production start-up.

    Study of such sensitivities reveals the project's vulnerability to parameter variations. Measurescan then be taken to limit the most damaging sensitivity (or reduce its chance of occurrence). If,for instance, the economics are very sensitive to the reserves estimate, a suitably placedappraisal well could limit the risk. If the main risk is "capex overrun", special attention needs to bepaid to cost optimisation and realistic budgeting.

    As regards the oil price, this is so unpredictable that it is now standard practice to repeat theeconomics at (typically) three different "screening values". Figure 7.5 shows the cumulativecashflow graph for the example of Figure 7.2, with the $30/bbl oil price assumption replaced by ascreening value of $15/bbl. The payout time increases to 8 years, total revenues drop by morethan 50% and government take is much reduced. The economic lifetime of the project has shrunkby 5 years to 13 years, reducing the total amount of oil recovered. Finally it can be seen that thecash surplus has dropped to a dangerously low level, which threatens the overall viability of theproject.

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    For very large projects, such as development of the Troll field offshore Norway, a statisticalapproach called "Monte Carlo" analysis is sometimes used to study the combined effect ofparameter variations. A multitude of possible outcomes of the venture is analysed and the resultspresented in the form of expectation curves. As computing power increases, this method may beapplied to smaller projects.

    EXPLORATION ECONOMICS

    Uncertainty of outcome is most pronounced for exploration ventures. For this reason a statisticalapproach, similar to techniques used in gambling theory, is often used. The exploration costs,such as bonuses, seismic and drilling, are compared with the prices of lottery tickets. The PresentValues of the possible results are regarded as the prizes. As in a lottery, it is important to have anidea of the probability of getting the rewards.

    The range of possible geologic results and their probabilities can be deduced from the presenceof reservoir rock, source rock, cap rock and structures in the licence area. Computer programslike PAQC digest this information, generating expectation curves for the reserves. For arepresentative set of outcomes rough development plans will be conceived and economicallyanalysed. The results will again be presented in the form of expectation curves and statisticalproperties such as the Expected Monetary Value and the required probability of success.

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    REFERENCES

    For course participants who are sufficiently intrigued and want to learn more about this subject, alist of useful books and publications is given for further reading.

    R.G. Lipsey and P.O. Steiner, "Economics"

    (Harper & Row, New York, 6th Edition, 1981) General textbook on macro- and micro-economics,not specifically related to oil.

    The "Campbells", "Mineral Property Economics":

    Vol. 1. Economics Principles and Strategies (1978) Vol. 2. Energy Sources and Systems (1978)Vol. 3. Petroleum Property Evaluation (1978) Petroleum Evaluation for Financial Disclosures(1982) Campbell Petroleum Series, Norman, Oklahoma (USA 73072) Very thorough on theeconomic and financial basis, and a good introduction to the required petroleum engineeringfoundations.

    A.P.H. van Meurs, "Modern Petroleum Economics"

    (Van Meurs & Associates Ltd., Ottawa, Canada, 1981) Interesting because it considers not onlythe viewpoint of a private oil company but also that of a State Oil Company and a producinggovernment.

    P.G. Moore and H. Thomas, "The Anatomy of Decisions"

    (Penguin Books Ltd., Harmondsworth, Middlesex, England, 1984) Discusses decision trees andtheir statistical basis, which are required for evaluating exploration proposals.

    P.D. Newendorp, "Decision Analysis for Petroleum Exploration"

    (Petroleum Publishing Company, Tulsa, USA 1976) A standard reference text for ExplorationEconomics.

    S.H. Schurr and B.C. Netschert, "Energy in the American Economy 1850-1975"

    (John Hopkins Press, Baltimore, 1960) An economic study of the history of oil in USA.

    R.E. Megill, "An Introduction to Risk Analysis"

    (PennWell Publishing Company, Tulsa, Oklahoma, 1984) Good introductory text for risk analysisplus some useful comments on competitive lease bidding.

    R.E. Megill, "An Introduction to Exploration Economics"

    (PennWell Publishing Company, Tulsa, Oklahoma, 1979) A simple but interesting introduction. Also: "Evaluating and Managing Risk - A Collection of Readings" (Sci Data Publishing, Tulsa,Oklahoma, 1985) A collection of 14 articles taken from several magazines, journals, etc., dealingwith subjects ranging from Investment Indicators to Bidding Strategies. Recommended.

    O.E.C.D., "OECD Economic Outlook"

    (Organisation for Economic Co-operation and Development (OECD), Paris, France. Publishedsemi annually.) Contains forecasts of the inflation rates in the OECD member Countries.

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    International Monetary Fund, "International Financial Statistics"

    (I.M.F., Washington D.C., USA, published monthly). Excellent source of information on historiceconomic data of virtually all countries.

    SIPM, "Exploration Bulletin" - Articles by R.M. Jonkman:

    Bulletin no. 253 (1990/6), page 15: Exploration Economics; Bulletin no. 255 (1991/2), page 17:Value and Cost of Appraisal; Bulletin no. 259 (1991/6), page 20: Finding Costs and the Value ofReserves.

    SIPM-EPC, "Petroleum Contracts" (1992). SIPC-FN/PL, Manual of Investment Evaluation.

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    7.2 PROJECT CASH FLOWS

    INTRODUCTION

    A project cashflow is a model of the financial consequences of an investment. It covers a project'sentire life, making it possible to derive measures of value and economic performance, which are

    based on the project as a whole. It is therefore exempt from the accountant's need to introducenon-cash items, such as depreciation of asset value, to obtain meaningful measures of short-termperformance. It is simply an assessment of money required or money generated. The figures areobtained, generally on an annual basis, by subtracting the cashout (the sum of payments madeon behalf of the venture, comprising technical costs and government take) from the cashin (the sum of payments received as a result of the venture) to give the cash surplus or cashdeficit. The initial deficits have to be supplied by the investors in the project; the subsequentsurpluses accrue to them as their remuneration.

    CASHIN

    The main cashin element is the company's share of the gross revenues derived fromhydrocarbon sales. To model this, the economist needs a production forecast and a set ofassumptions about prices. Given the impossibility of forecasting the long-term oil price, it is usualto take a representative constant level for the "marker crude", deriving the corresponding pricesof local crude, gas and NGL with appropriate formulas.

    Other possible cashin items include: partner payments, notably by State oil companies coming in after a project has started and

    refunding their share of prior costs; payments for use of project assets by another (own or third-party) venture. e.g. a pipeline

    tariff paid or allocated; payments for acquisition of an interest in the venture.

    THE TECHNICAL COSTS

    Project costs are either capital expenditure (capex) or operating expenses (opex). In principleexpenditure is capitalised if it creates an asset with a lifetime of more than one year, whereas thecost of short-lived assets, perishable goods and services is opex. The exact definitions, however,depend on the local tax legislation.

    Typical capital items are platforms, production facilities, pipelines and production wells. Typical operating costs are maintenance, insurance, lifting, well repairs and workovers, tanker rentals,and tariffs paid for using a third-party pipeline. Overheads too are a significant opex element.Capex is predominant in a project's early years.

    GOVERNMENT TAKE

    Host Government Take depends on the contract terms and the local fiscal system. In traditionalsystems the company pays a royalty, based on the value of oil and gas recovered, plus one ormore taxes levied on "taxable income". Under production-sharing arrangements the company'sshare of produced hydrocarbons is limited by a cost-related formula; tax and even royalty may belevied as well.

    Royalty is normally a percentage of gross revenues from the sale of hydrocarbons, and may bedue in cash or in kind. It is payable from the start of production onwards.

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    Tax is a percentage of taxable income, which is calculated by subtracting fiscally allowable costsfrom revenues:

    TAXABLE INCOME = REVENUES - FISCAL COSTS (1)

    The fiscal costs are defined in the host country's fiscal legislation. Royalties and opex arenormally allowed in the fiscal year in which they are incurred. Capex is replaced by the

    depreciation allowance (see next section), which is intended to spread the cost deduction overthe life of the asset and so reflect its gradual loss of value.

    FISCAL COSTS = ROYALTY + OPEX + FISCAL DEPRECIATION (2)

    Tax is usually the main cashout item in the middle period of a project's life. It is due only whenthere is a fiscal profit. As this can only be determined after the end of the fiscal year, settlement isoften much later than receipt of the corresponding revenue. Advance provisional payments may,however, be required. The economist must know the mechanism, and assign tax payments to theperiods when they are actually made.

    In years when fiscal costs exceed revenues, there is a fiscal loss. However, where tax isassessed on a corporate basis and the company as a whole is already tax-paying, a project'sfiscal loss means a reduction of the company's profit and tax bill: the fiscal costs of the project areeffectively being claimed against corporate income, and the incremental tax attributable to theproject is negative and will appear as a plus in the project cashflow. If the company is not ataxpayer, or if "ring-fencing" applies, then the project must be seen in isolation, and in that caseits fiscal losses are carried forward to be offset against profits later on. Over the life of the projectthe total tax bill is still the same, but the deferment of tax relief has an adverse effect on theeconomics.

    DEPRECIATION

    The depreciation allowance, or fiscal depreciation, is not itself an element of the cashflow. Its onlyrole is in the calculation of tax; and it should be noted that the allowance claimed for that purpose,being determined by local legislation, is different from the "Group rules" depreciation used byaccountants when determining profits and book values according to a procedure common to allGroup operating companies.

    Three types of depreciation scheme are the most common in fiscal legislations:

    1. Straight Line Method: The assets are depreciated in equal amounts over a number ofyears, e.g. 25% of initial value each year for 4 years. Depreciation may start as soon asmoney is spent, or may have to wait until the asset involved is in use.

    2. Declining Balance Method: Each year a fixed percentage (e.g.25%) of the nondepreciatednet book value at the end of the previous year is depreciated (again, it may or may not benecessary to wait until the asset concerned is in service). This construction results in having

    incompletely depreciated assets at the end of the venture. Generally, these undepreciatedbalances are claimable in full in the final year.

    3. Depletion Method: In this system - also known as the Unit-of-Production method -depreciation is calculated as the book value (non-depreciated assets) at the end of theprevious year multiplied by the ratio of the current year's production to the reserves at thebeginning of the year. The depreciation per barrel remains constant unless total recoverablereserves change, when the method can lead to complications.

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    2001 Shell International Exploration and Production B.V. Page 14

    Since depreciation reduces taxable income, fast depreciation leads to a lower tax bill in the earlyyears of a project, thus improving its early cashflow at the expense of its later cashflow. This hasa beneficial effect on the economics. Of the systems described, the simple straight-line method isthe most favourable from this point of view.

    CASH SURPLUS CALCULATION

    A project's cash surplus (or deficit) in any one year is given by

    CASH SURPLUS = REVENUE -OPEX-CAPEX -ROYALTY TAX (3)

    In a typical tax/royalty system,

    ROYALTY = ROYRATE * REVENUE (4)

    TAX = TAXRATE * (REVENUE - ROYALTY - OPEX - FISC. DEPR.) (5)

    Suppose, for example, that in a particular year

    production = 15 million bbl oil price = $18/t)bl

    capex = $75 million royalty rate = 20%opex = $30 million tax rate = 75%

    We need to know the fiscal depreciation, which depends on previous capex. Assume, for thepurpose of this illustration, that it is $50 million - arising, for instance, from a 5-year straight-linerule with prior capex of $175 million: (175+75) * 20% = 50.

    Calculate revenue, technical cost, and government take:

    Revenue =15mbbl x $18/bbl = $270 million

    Capex = 75

    Opex =30

    Technical cost = $ 105 million

    Royalty = 20% x $270 million = 54

    Taxable income:

    (revenue) 270

    (royalty) 54

    (opex) 30

    (depreciation) 50

    (fiscal costs) 134

    (taxable income) 136

    Tax =75% x $136 million =102

    Government take = $ 156 million

    The cash surplus is therefore $ 270 m-$105 m-$156 m = $9 million

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    2001 Shell International Exploration and Production B.V. Page 15

    CASH SURPLUS AND NET INCOME

    The accounting profit, or net Income , is generally defined as

    NET INCOME = REVENUE-OPEX-DEPRECIATION-ROYALTY-TAX (6)

    In which, as already mentioned, the depreciation is not necessarily the same as the fiscal

    depreciation allowance. Suppose, nevertheless, that in the example given above they are equal.Then the net income for the year in question is

    $270m - $30m - $50m - $54m - $102m = $34 million

    The element common to the cash surplus and net income formulas is called the CashGeneration:

    So, CASHGEN = REVENUE - OPEX - ROYALTY TAX (7)

    and CASH SURPLUS = CASHGEN - CAPEX (8)

    NET INCOME = CASHGEN DEPRECIATION (9)

    In our example the cash generation is $ 84 million, of which $ 75 million is used in capitalinvestment. Depreciation, however, is only $ 50 million, giving a $ 34 million net income. Whencapex exceeds depreciation, cash surplus is less than net income; when depreciation exceedscapex, cash surplus is greater than net income. Their totals over a project's life are equal, but thenet income lies in a narrower range of values.

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    THE NET APPROACH

    The step-by-step method of building annual cashflows simulates in detail the financialtransactions relating to a project. The method is easy to program with appropriate computersoftware. In the days before such software was available the calculations were time-consuming(especially when sensitivities had to be calculated too), and to speed up the analysis, frequentuse was made of the net approach described below. This approach is still of value as it enablesthe main sensitivities to be quickly evaluated on hand calculators. It will be illustrated for atax/royalty system, but can also be adapted to production sharing.

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    Going back to equations (3) - (5) and combining them, we get the following formula:

    CASH SURPLUS = (1 -TAXRATE) * {(1 - ROYRATE) * REVENUE - OPEX}

    - {CAPEX - TAXRATE * FISCAL DEPRECIATION} (10)

    This can be rewritten as

    CASH SURPLUS = NET REVENUE - NET CAPEX - NET OPEX (11)

    where the "net" terms are defined as follows:

    Net revenue is the revenue remaining after royalty and tax (before any reduction for allowablecosts) have been paid:

    NET REVENUE = (1 -TAXRATE) * (1 - ROYRATE) * PRICE * PROD (12)

    Net capex is the actual capital expenditure minus the tax relief on this expenditure:

    NET CAPEX = CAPEX - TAXRATE * DEPRECIATION (13)

    Net opex is likewise the actual operating expenses minus the related tax relief:

    NET OPEX = (1-TAXRATE)* OPEX (14)

    Changes in production profile, oil price or royalty rate affect Net Revenue only, whilst changes inthe capex or in the depreciation rules affect Net Capex only, and changes in opex affect NetOpex only. The power of this in sensitivity analysis will now be seen.

    If the net approach is used in the example given earlier, the following is obtained:

    NET REVENUE = (1-0.75) x (1-0.20) x 18 x 15 = $ 54.0m

    NET CAPEX = 75-0.75x50 = $ 37.5m

    NET OPEX = (1-0.75) x 30 = $ 7.5m

    NETTECH. COST =$ 45.0 mCASH SURPLUS = $ 9.0 m

    The result is, of course, the same as before; but one can now see immediately that (for instance)a 20% cut in the production rate would reduce the cash surplus by 20% of $ 54m, or $ 10.8m, orthat doubling the opex would reduce the surplus by $ 7.5 m. These conclusions could not havebeen drawn so easily with the step-by-step method.

    The above formulae can be used both on an annual basis and on a cumulative project basis. Itshould however be clearly understood that, although a change in the level of the revenues doesnot affect the tax relief on capital expenditure, it may affect very significantly the timing of thatrelief if the company is not already a taxpayer. By using the net approach one ignores part of the

    effect of the possible carrying forward of fiscal allowances. The result is that sensitivities maytend to be understated.

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    7.3 PROJECT PROFITABILITY

    INTRODUCTION

    Most upstream project cashflows follow a standard pattern: they show a series of cash deficitsduring the investment phase, followed by a series of cash surpluses during the production phase.

    The surpluses may be interrupted if there is a major mid-life investment (compressors, secondaryrecovery), and there may well be a deficit year when the project is abandoned; but broadlyspeaking, a typical project involves investing in the short term in the expectation of earning steadysurpluses in the long term. To decide if it is profitable we need a means of consistently valuingsums of money spent or received at different times over a long period.

    The key lies in the concept of the cost of capital . Venture capital comes, in the first instance,from shareholders and lenders. By combining their required rewards in suitable proportion, theoverall cost of capital can be assessed in % per year. This then sets a marker, which the overallbusiness return should exceed. Now if capital is applied to a specific project we forgo theopportunity to use it for other investments, from which - on average - a return matching the cost ofcapital should have been obtainable. The project is only worth doing if its reward exceeds that ofthe alternative investment. Its value is measured by the extent to which it exceeds.

    VALUING A CASHFLOW

    Suppose, just for simplicity, that our cost of capital is 10% per year. Consider the followingpotential project cashflow ($m):

    Year 1 2 3 4 5 6 7

    Cash -50 -145 70 65 60 45 25

    Let us see how closely we could reproduce this cashflow by making an alternative investmentat10%p.a.lfwe

    invest the indicated amounts in years 1 and 2; add, each year, 10% to the balance invested; withdraw the indicated amounts in years 3 to 6; withdraw all of the final balance in year 7 (or make it up if negative),

    then the alternative investment develops as follows:Year 1 2 3 4 5 6 7Interest accrued 5 20 15 10 5 1Investment 50 145Withdrawals -70 -65 -60 -45 -11Balance 50 200 150 100 50 10 0

    Our cashflow from this is -50 -145 70 65 60 45 11

    The project is better than this alternative investment, as it brings us an extra $ 14 million in thelast year.

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    We could make the alternative cashflow match the project exactly in years 1-7 by investing somemoney in year 0. If we invest $ 7 million, the above table becomes:Year 0 1 2 3 4 5 6 7Interest accrued 1 6 21 16 11 6 2Investment 7 50 145Withdrawals -70 -65 -60 -45 -25

    Balance 7 58 209 160 111 62 23 0Our alternative cashflow is now -7 -50 -145 70 65 60 45 25

    The project is better than this by precisely the $ 7 million that it does not require us to spend inyear 0. This $ 7 million is in a real sense the value of the project: it is the maximum, which weought to be prepared to pay to acquire its cashflow.

    THE DISCOUNTED CASH FLOW METHOD

    How was the figure $ 7 million arrived at? It is simply the amount which would have to be put intothe alternative investment in year 0, in order to produce in year 7 enough extra money to bridgethe gap between (a) the $11 million that would otherwise be available from that investment and(b) the $ 25 million expected from the project. In other words it is the sum which, if put oncompound interest at 10% for 7 years, would grow to $14 million. Now the compound interestformula states that, if an amount C is invested fort years at an interest rate expressed as afraction r, it will increase to Ct , where:

    The reader may verify that 14x1.10 ^ = 7 (more accurately 7.2).We call the result of formula (2) the Present Value (PV) of C^. The process of converting a futurevalue to a present value in this way is called discounting. The discount rate (r) and the reference date must always be stated. In our example, $ 7 million is the 10% PV at year 0 (of$14 million in year 7).

    If we discount separately (at 10%) the seven annual elements of the project cashflow, and addtogether the results, we shall arrive at the same $ 7 million PV which we previously got bydiscounting the difference between project cashflow and alternative cashflow. The reason is thatthe alternative cashflow is 'itself neutral (has zero PV) at this discount rate: the discountingprocess cancels out the interest additions. This procedure of discounting each year's surplus (ordeficit) separately, and adding, is the normal way to calculate the PV of a cashflow and its result

    is known as the PV Cash Surplus (PVCS) or Net Present Value (NPV). Applied to our example,the procedure gives a PVCS of

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    THE MECHANICS OF DISCOUNTING

    The discounting operation can be performed in several ways:

    (a) by the direct method illustrated above;

    (b) the same, but getting the multipliers from a table of Discount Factors;

    (c) by a streamlined and much less error-prone version of method (a), suitable for calculators ofthe HP1 IC type and described at the end of this chapter;

    (d) by using appropriate computer software.

    The tables required for method (b) are included in section 7.7. It will be observed that the table foreach discount rate has two parts, headed Full Year Discounting and Half Year ShiftDiscounting. So far in this chapter we have worked with whole years, which is appropriate (i) ifmoney movements occur at annual intervals or (ii) if it is a fair approximation to assume that theyare uniformly spread over the year. For the long projects typical of E&P, the latter assumption isusually perfectly valid within the accuracy of our modelling. We then use the full year factors: forinstance, to discount at 10% from year 7 to year 0 the required factor is found from the 10% tableto be 0.51316. Our reference date is effectively 1st July of the reference year. This is the normalEP practice.

    Half year shift factors are needed 'if, for instance, we are evaluating a proposal to spend money(capex) at the end of year 0 for an immediate and continuous benefit (opex reduction). Todiscount the benefit in years 1, 2 etc. we can take 1/7/0 as reference date and use full yearfactors; but then the capex should be discounted just half a year, which is achieved using the halfyear shift factor for year 1 = 0.95346.

    THE DISCOUNT RATE

    The NPV can be calculated for any discount rate (r). When r is equal to the cost of capital, theNPV is, as we saw earlier, a real measure of project value. However, it is not enough just toscreen projects (require them to have a positive NPV) at this discount rate. More is needed tooffset the fact that there is often a substantial gap between the aggregate cashflow expected onthe basis of investment proposals and the overall cashflow of the Upstream Sector. This gapreflects the erosion of project profitability by various influences at field, opco and Sector level -respective examples being the imposition of new environmental standards, expenditure oncompany infrastructure, and the costs of research and technological development.

    For such reasons the NPV at the cost of capital should not be just positive, but substantiallypositive. In general, the NPV decreases as the discount rate increases. Accordingly, a discountrate substantially higher than the cost of capital is normally used for project screening. TheNPVs are reported at both rates (as well as at 0%) and at various oil prices - a "grid" of valuesproviding a framework for judgment.

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    PROFITABILITY INDICATORS

    The main measures of a venture's profitability are the Net Present Values shown on the "grid". Anumber of other useful indicators can also be derived from the cashflow and its elements.

    The annual cashflow itself provides an essential portrait of the project and should always be

    presented in support of the economics, at least in pictorial form. The only useful indicatorobtainable directly from it is the economic life, i.e. the time until the cashflow turns permanentlynegative. This corresponds to the production rate falling below the economic limit orabandonment rate, which (in a tax/royalty system) is found by equating revenue with royalty plusopex. The economic life should be checked against the concession expiry date.

    More information can be derived from the cumulative cashflow. This is a running total of theannual figures (so its values apply at the end of each year), and it finally arrives at the ultimatecash surplus. On the way, it tells us:

    - the exposure, or maximum value of the cumulative cash deficit: this is the amount theinvestor would stand to lose if the project were to be terminated by some disaster at themost unfavourable moment;

    - the payout time, or time until the cumulative cashflow turns positive: this indicates how longthe investor will take to recover his original investment.

    Neither of these, however, is true indicators of profitability as they take no account of whathappen later in the project's life.

    All of the quantities discussed so far are expressed in money or in years. In order to be able tocompare projects of different sizes and scopes, it is useful to have a measure expressed as aratio. A convenient one is the Profit / Investment Ratio or PIR, defined by

    PIR = Ultimate Cash Surplus Capital Expenditure (17)

    (Note that the term "profit" is here misused.) The ratio can also be defined on a PV basis, e.g.

    8% PIR = 8% PV Cash Surplus -- 8% PV Capex (18)

    In the latter form it is a good measure of reward per unit of value invested.

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    EARNING POWER

    The NPV of a project depends, of course, on the discount rate applied. Provided that the projecthas a conventional cash flow, in which all of the deficit years precede the first surplus year, theNPV will decrease as the discount rate increases. It will be positive at low enough rates(assuming that the ultimate cash surplus, or 0% NPV, is itself positive) and it will be negative athigh rates as the discounting will then bear much more heavily on the surpluses than on thedeficits. There is, therefore, one particular discount rate for which the NPV will be zero. In Shellcompanies this rate is generally called the Earning Power; elsewhere it is more often referred toas the Internal Rate of Return, or IRR.

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    The earning power may be found by plotting NPV against discount rate; such a plot is called apresent value profile. The earning power is read off where the curve crosses the axis. Somecomputer software and some calculators (the HP12C, but not the HP11C), have functions, whichdo the IRR calculation by iterative methods.

    For a conventional cashflow the following are true:

    - if the discount rate is less than the earning power, the NPV will be positive;

    - if the discount rate is more than the earning power, the NPV will be negative.

    Herein lies the convenience of this profitability indicator. If a project has an earning power of 20%,it is not necessary to have established whether (for instance) 12%, 15% or 18% is the properdiscount rate to be used for screening; provided we know that the screening rate is less than20%, the project is economically justified.

    Thus the earning power is basically a screening tool. It is not a suitable criterion when comparing,ranking, or optimising projects. Its other value is as an indicator of robustness: this will not bepursued here, but, broadly speaking, the higher a project's earning power the greater degree ofrisk it can withstand.

    When the cashflow is not conventional the PV profile may cross the axis several times, givingmultiple "earning powers". Sometimes it may be obvious which one is meaningful but usually it isbest to stick to NPVs and leave earning powers alone. A typical example is an accelerationproject, where an incremental investment is made in order to recover some oil earlier than itwould otherwise have been recovered: the reward is the gain in the PV of the revenue. The NPVwill be negative at 0%, positive - 'if the project has any merit - for a range of discount rates, andultimately negative again. In such cases "earning power" is meaningless, and the economicdecision has to be based on the nature of the range of positive NPVs.

    DISCOUNTING A CASHFLOW WITH AN HP CALCULATOR

    Determining an NPV with an HP calculator simple. We first fill the "stack" with copies of the 1 -year discount factor; then, whenever multiplication by an unspecified quantity is invoked, thisfactor is used and regenerated. To discount at 15%, prime the calculator as follows:

    1.151/x

    ENTERENTERENTER

    The cashflow is then fed in backwards. Suppose it runs from year 1 to year N. The cash surplusfor year N is entered, followed by x (multiplication); this has the effect of discounting it back to themiddle of year N-1. Year N-1 's cash surplus is then entered followed by + and then by x: thisyields the combined NPV of years N and N-1, discounted back to year N-2. One continues in thisway (replacing + by-in deficit years) until finally the year 1 deficit is entered, followed by - and x,

    giving the NPV of the total cashflow with reference date the middle of year 0. As an example ofthe method, let us discount at 15% the cashflow

    (10) 5 4 3 2 1

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    Immediately after priming (see above), the keystrokes are1x2+x3

    +x4+x

    10-x and the result is 0.857

    7.4 INFLATION

    So far the subject of inflation has not been mentioned. For a multinational company like Shell, thediscount rate for a venture in an inflation-prone country would have to be set appreciably higherthan the discount rate for a low inflation country elsewhere. Such an approach would be rathercumbersome for an investor who wishes to compare projects in different countries with differentinflation rates. For this reason Shell has opted for another approach. The cashflow is calculated inthe normal (nominal) currency of the country involved. This cashflow will then be corrected for theeffects of inflation and converted into dollars, before the profitability indicators are evaluated. Inthis way, the present values and earning powers of various projects in different countries can becompared directly without worrying about currency translations and local inflation rates.

    A PRICE INDEX

    The world's economies have often experienced periods of prolonged and rapid changes in pricelevels. Over the long swing of history price levels have sometimes risen and sometimes fallen. Inrecent decades, however, the course of prices has always been upward. The price level can bemeasured by an index of the economy's prices. A "price index number" for a given year is definedas the ratio of the cost of purchasing a "shopping basket" of commodities in that year to the costof purchasing that same basket in the "base year", multiplied by 100. In table 7.3 an index iscalculated for a simple case.

    The three most common indices are the "consumer price index" (CPI), which covers commoditiesbought by the typical consumer; the "producer price index" (PPI), which covers wholesale prices;and the "gross domestic product" (GDP) deflator, which covers everything produced and soldwithin the economy. The IMF statistics usually report the GDP deflator, which is often taken asthe general rate of inflation (GRI).

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    THE INFLATION RATE

    The annual rate of inflation is defined as the percentage rate of change in the yearly average ofsome price index from one year to the next.

    The rate of inflation for the example shown in Table 7.1 would be 23.4%. The rate of inflation isnot constant. It varies with time, location and the composition of commodities in the basket

    TYPES OF MONEY

    For an economic evaluation in the presence of inflation, the Shell Group of companies make useof four basically different "types of money", possibly in more than one currency. The most familiartype is the "money of the day" (MOD), also called nominal money or current money. This is themoney, which as coins, bank notes and cheques, changes hands all over the world in exchangefor goods and services. It has the (face) value as printed or stamped on it. Its purchasing powerwill change with time, as seen in the preceding paragraphs. To overcome this varying purchasing

    power of money of the day, the "real terms" (RT), or "constant value money" (CVM) money wasintroduced. This imaginary money keeps the same purchasing power at different moments intime.

    As a unit of real terms money one can use any currency, provided that a reference date is added,e.g. US dollars of 1.1.1991 or Dutch Guilders of 1.7.1990. Although in principle every date can bechosen as a reference date, in practice one normally takes either January 1st, or July 1st as areference date. To convert a MOD-price into a RT-price, one merely has to divide by the ratio ofthe price indices:

    Observe that this relation is similar to the discounting equation described in section 7.3.

    The third type of money is the "present value", of money promised or due in the future. This isobtained from the forecast amounts by "discounting", in order to account for foregone "alternativeinvestment opportunities" and risk. If this discounting is applied to the RT-cashflow, the discountrate is referred to as the "real terms discount rate", r.

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    EXCHANGE RATES AND INFLATION

    If free trade exists between two countries "A" and "B" and the exchange rate is not subject togovernment regulation, then one may expect a relation between the purchasing power of therespective currencies and the exchange rate. Goods bought in country "A" and sold unchanged incountry "B" cannot make an excessive profit or others would follow the example, which wouldeventually lead to an adjustment of the exchange rate. If it were impossible to make any profitwith such transactions, the following equation would hold:

    In real terms money the exchange rate will remain constant if there are no restrictions to freetrade, i.e. there is purchasing power parity.

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    It may be concluded that in the long term the above equation is reasonably valid but fairly largeshort term fluctuations may occur also depending on interest rate differentials and balance ofpayment movements. If the free trade assumption is violated, as is the case e.g. for East-Westtrade, deviations of the equation can be very large.

    In such cases there exists often a "black money market", where the exchange rate is probably

    closer to the theoretical rate than the official rate. Under normal situations the above mentionedtheoretical relation is commonly used to predict future exchange rates for cashflow purposes.

    CURRENCY CHANGES AND CASHFLOWS

    In most operating companies cashflows will be made in the local currency, since taxes need to becalculated and paid in the local currency. Some of the capital assets may be acquired locally, butin many cases foreign manufacturers and contractors will be involved, which will be paid in theirown currency if so desired. The resulting cashflow has to be presented in RT US dollars. Andfinally, for budget purposes, the capital requirements of the project have to be presented in bothMOD US dollars and in MOD of the local currency. This diversity of currencies together with thefour "types of money", results in a fairly complex evaluation procedure. Since the exchange ratesare constant in real terms money, the actual calculation converts all data to RT before a currencytranslation (Figure 7.11).

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    7.5 UNIT COSTS AND BREAKEVEN PRICES

    INTRODUCTION

    By "unit costs" we mean costs determined on a per barrel basis - gross or net of tax, discountedor undiscounted, as appropriate. The concept is useful for

    - comparing the costs of projects of different sizes;

    - establishing the breakeven oil price for a project;

    - setting the tariff for the use of a shared facility;

    - assessing the relative severity of tax systems.

    It also leads to the PV Unit Cash Surplus, or NPV per barrel, another profitability indicator thatcould be used (for instance) to

    - rank projects when the long-term constraint is not money but production;

    - assess, by comparing with the company's estimate of "finding costs", whether the barrelsproduced are paying for their own replacement.

    UNDISCOUNTED UNIT COSTS

    To illustrate unit costs we shall use the following cashflow, in $ million:

    The $1329 million cashin is generated by the production of 66.4 million bbl of oil. Dividing thesetwo values gives the Unit Cashin of $20/bbl, which in this case is of course the same as the oilprice: if, however, we were assuming a price that varied with time, then the Unit Cashin wouldrepresent a weighted average.

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    Dividing the $1147 million cashout by the total production gives $ 17.27/bbl. This is the UnitCashout - the total of Unit Technical Cost (UTC) and unit government take. The differencebetween Unit Cashin and Unit Cashout is the Unit Cash Surplus, amounting to 20 - 17.26 =$ 2.73/bbl, which could also have been obtained by dividing the Ultimate Cash Surplus by thetotal production.

    Here are the (undiscounted) unit figures for all the components of our cashflow:

    Of the $20 revenue generated by one barrel, $10.37 (52%) goes in government take and $6.89(34%) in technical cost, leaving 14% as cash surplus. The technical cost element is (on thisundiscounted basis) about equally split between capex and opex.

    DISCOUNTED UNIT COSTS

    The discounted or PV Unit Technical Cost, etc., are the Present Value counterparts of the unitfigures discussed above. The PV Unit Technical Cost is the ratio of PV technical cost (i.e. PVcapex + PV opex) to PV production. For the example cashflow the PV unit figures at discountrates of 0%, 8% and 15% are given below. At 0%, of course, they reproduce the figures alreadyshown.

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    On a discounted basis the PV unit capex is now much more important than the PV unit opex.Further, the PV unit capex increases with the discount rate, as lightly discounted capex is dividedby heavily discounted barrels. The PV unit opex, however, is effectively a weighted average; asthe discount rate increases, the later years lose weight; and since the opex per barrel is highest inthose years, the PV unit opex goes down. The PV unit cashout increase is entirely due to theincrease in PV unit capex: "up front" capital has a strong effect on PV Unit Technical Cost.

    BREAKEVEN PRICES

    In calculating breakeven prices the usefulness of the Discounted Unit Cost concept is clearlydemonstrated. "Breakeven", at a given discount rate, occurs when the NPV is exactly zero;

    equivalently, the Earning Power is equal to the discount rate. The condition for breakeven isPV(CASHIN) = PV (CASHOUT)

    or PV (PRICE * PRODUCTION) = PV (CASHOUT)

    If the entire production is sold at a constant price, this condition becomes

    PRICE * PV (PRODUCTION) = PV (CASHOUT)

    or PRICE = PV (CASHOUT) / PV (PRODUCTION)

    = PV (UNIT CASHOUT)

    On an after-tax basis this is not a very useful formula since the cashout includes tax and royalty,

    which themselves depend on price. On a pre-tax basis, however, the cashout is simply capexplus opex. It follows that breakeven on a pre-tax, or total project, basis will occur if

    PRICE = PV {UNIT (CAPEX + OPEX)}

    In other words,

    PRE-TAX BREAKEVEN PRICE = PV UNIT TECHNICAL COST

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    The 15% PV UTC should always be shown in the economics section of budget proposals, inaddition to the profitability indicators discussed in Chapter 7.3.

    NET UNIT COSTS

    An alternative way to present unit costs is based on the "net approach":

    CASH SURPLUS = NET REVENUE - NET CAPEX - NET OPEX

    Dividing all terms by the total production:

    UNIT CASH SURPLUS = UNIT NET REV. - UNIT NET CAPEX -UNIT NET OPEX

    where

    UNIT NET REVENUE = (1 - TAXRATE) x (1 - ROYRATE) x UNIT REVENUE

    UNIT NET CAPEX = UNIT CAPEX-TAX RATE x UNIT DEPRECIATION

    UNIT NET OPEX = (1 - TAXRATE) x UNIT OPEX

    For the example given above, we find:

    This table shows the increasing dominance of the PV Unit Net Capex term at higher discountrates. It also allows the breakeven price to be calculated on a full after-tax basis. For breakeven,

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    PV UNIT NET CASH SURPLUS = 0

    or

    PV UNIT NET REVENUES = PV UNIT NET TECH. COST

    If the price is constant this becomes

    (1 - TAXRATE) * (1 - ROYRATE) * PRICE = PV UNIT NET TECH. COST

    In other words, the breakeven price on a full after-tax basis equals the PV Unit NetTechnical Cost "grossed up" for tax and royalty:

    Implicit in the use of this formula is the assumption that - at least approximately - the PV Unit NetTechnical Cost, and notably the PV (i.e. timing) of depreciation, is independent of the oil price.Where this is not true - e.g. in a "newcomer" situation where early revenues may not cover thedepreciation allowance in full, causing it to be partly carried forward - the breakeven price has tobe ascertained by rerunning the full cashflow model and using graphical or trial and errormethods. The same applies under more complicated fiscal systems, or when the PV unit opexand/or PV unit capex are themselves significantly price-dependent via the assumed impact of theoil price on costs (e.g. fuel) or on the timing of abandonment.

    For the example above, recalling that tax = 70% and royalty = 20%,

    BREAKEVEN PRICE AT 15% = 3.86/ {(1 - 0.70) * (1 - 0.20)}

    = $16.1 /BBL

    The amount by which the breakeven price exceeds the PV UTC (the difference, in this example,between $16.1 and $ 8.66) is one measure of the impact of the fiscal system. The adjoiningdiagram shows the separate impacts of royalty and tax at various discount rates.

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    7.6 GUIDELINES FOR THE PRESENTATION OF ECONOMICS

    The guidelines for the presentation of economics in Programme Documentation and in GroupBudget Proposals are given respectively in two Shell Group procedures, EP-59000 (updatedannually) and the "Financial Procedure Manual". They should be read by those who prepareproposals for the larger projects, which require the approval of SIPM and SIPC.

    Typically a Group Budget Proposal would comprise a summary, as shown below.

    EXAMPLE OF A GROUP BUDGET PROPOSAL

    GROUP BUDGET PROPOSAL (Example based on MIE (3.8.2) slightly modified)

    COMPANY : Shell Projects (Production)

    GROUP EQUITY INTEREST : 100% SECTOR/CATEGORY: Upstream gasproduction.

    FOR : The engineering and drilling costs of developing

    the G2-A and G2-B offshore gasfields.

    KEY FACTORS:Concession : Discovery date: June '88 Expiry date: Dec. 2017

    Shell interest : 60% - operator

    Partner : Chexxacon40%

    Expected recovery : 8.5 mrd m3 (Shell share 5.1 mrd m3)

    FINANCIAL DIMENSIONS (all figures in millions MOD; 1 US $=Q 2.00 at 1.7.92)

    Shell Share 100%

    LC US$ LC US$

    Total Requirement 100 50 166 83

    Previous firm appropriation 4 2 6 3

    This Proposal 96 48 160 80

    Total Overrun Total

    Phasing (Shell share figures) '92 '93 '94 '95 '96 Later 50/50 Allowance 90/10

    LC 4 40 30 22 - - 96 14 110

    US$ 2 20 15 11 - - 48 7 55

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    SUMMARY ECONOMICS

    (US$ million RT 1.7.92 based on 50/50 estimates)

    Key assumptions * Standard gas contract terms; price * Load factor 0.67

    * Tax 50% based on oil-related formula. * Inflation 4%

    Dubai Net Present Value RTEP Key Sensitivities

    price (Shell share) Prod.

    Capex 90/10 Sales-20% delay 1 year

    US$/bbl 0% 8% 15% % NPV RTEP NPV RTEP NPV RTEP

    8% % 8% % 8% %

    12 106 39 11 19 34 18 23 16 29 17

    15 179 68 24 23 63 22 50 20 56 21

    20 301 116 46 32 111 31 92 28 101 30

    BEP 6.0 7.9 9.5

    UTC 5.3 6.4 7.4

    Payout time: 6 years

    Other sensitivities: Pipeline tariff $3 instead of $2/boe -> NPV ($15,8%) = $ 58 million.

    GENERAL

    The G2 offshore concession consists of 2 fields, both of which are overpressured "turtleback"structures in sandstone. The platform, above the G2-A field, will be a single train minimumfacilities production platform in line with latest industry techniques. The G2 platform has beenselected as the nodal point for this system, providing space for receiving and launching facilities.

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    7.7 DISCOUNT FACTORS

    The following formulae are used to calculate Discount Factors:

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