m.sc petroleum economics
DESCRIPTION
Basic introduction to petroleum economicsTRANSCRIPT
PETROLEUM ECONOMICS
BY
G.C.ENYISCHOOL OF COMPUTING, SCIENCE AND ENGINEERING
UNIVERSITY OF SALFORD
MANCHESTER, UK.
AIMS
To introduce the basic concepts and background for the financial and economic assessment of projects within the petroleum industry.
OBJECTIVES• Be able to calculate the NPV of a project
including the collection of all necessary data, carry out Decision Tree Analysis and be able to select the best option from several possibilities.
• Be able to assess risk and uncertainty related to projects and carry out probabilistic resource calculations.
• Be able to carry out simple portfolio management decisions under conditions of uncertainty, including economic, technical and political risk.
TEXTS
• Petroleum Evaluations and Economic Decisions: Arthur W. McCray, Prentice-Hall, Englewood Cliffs, New Jersey.
• Risk Analysis and Management of Petroleum Exploration Venture: Peter R. Rose, AAPG, ISBN 0-89181-663-1.
• Economics of Worldwide Petroleum Production: F.H. Allen and R.D. Seba, OGCI, ISBN 0-930972-17-1.
OUTLINE
INTRODUCTION
ESTIMATION OF OIL AND GAS RESERVES
CASH FLOW ANALYSIS
TIME VALUE OF MONEY
PROFITABILITY OF A VENTURE
PRODUCTION ECONOMICS
RISK AND UNCERTAINTY
INTRODUCTION• The Engineering economy and engineering economics or
engineering economic analysis are all used interchangeably to denote the study of the economics of engineering systems.
• Engineering economy is an applied economics course. Since the application is engineering systems this economics course is taught by engineering faculty.
• As future engineers, no matter what type, you will sooner or later have to deal with problem situations similar to the ones covered in this course. At the end of the course you will be equipped with analytical skills that you can use to solve problems of an economic nature.
• Why I need to do economics?• "Is it not enough for me to be a good
engineer? I am not an accountant.• I will ask the accountant in my company to
do that work for me.
• Why do I need to study economics?• "Is it not enough for me to be a good
engineer? I am not an accountant.• I will ask the accountant in my
company to do that work for me.
ECONOMIC DECISION
ROLE OF THE PETROLEUM ECONOMIST
To advise on the economic attractiveness of these opportunities, taking into account the many uncertainties regarding reservoir behavior, development costs, future energy prices and relationships with governments.
He will also be involved in some or all of the following activities: - Lease Bidding - Selection of "best" option - Reporting - Unitization discussions - Fiscal changes - Contracts
ECONOMIC ANALYSIS AND DECISION MAKING
The primary objective of any business organization (oil and gas) is not merely to produce goods and services (oil and gas) BUT rather to make a profit – the maximum profit.
OTHERS- Expansion in production capacity
- Increase in market share
- Diversification of activities
- Continuous survival of the organization
RELATIONSHIP WITH OTHER DISCIPLINES
WHERE IS THE MISSING LINK ?
RELATIONSHIP WITH OTHER DISCIPLINES
Economics
Environmental
Reservoir
Engineering
Process
Engineering
Production
Engineering
Exploration and Geology
Well
Engineering
DECISION MAKING ENVIRONMENT
The environment within which decision making takes place can be logically divided into three parts or states:
•Certainty•Risk •Uncertainty
DECISION MAKING ENVIRONMENT
Certainty exists when one can specify exactly what will happen during the period for which the decision is being made. Risk refers to a situation where one can specify a probability distribution over possible outcomes. Uncertainty refers to the condition when one cannot specify the relative likelihood of the outcomes.
1 Prioritize projects. 2 Re-evaluation of priorities in allocation of investment funds by the company. 3 Planned change in development or production methods that consequently may affect the production rate and ultimate recovery. 4 Assessment of value of assets for taxation purposes.
Whatever the reason for conducting an economic evaluation, with limited financial resources and a specific set of corporate objectives, any company must select the best investment opportunities from among those available
WHY DO WE MAKE ECONOMIC EVALUATION
The economic analysis should lead toward an unbiased answer to two questions:
1 Does the particular investment project seem to satisfy the stated objectives of the firm? 2 Is this project “better” or “worse” than other possible projects?
WHY DO WE MAKE ECONOMIC EVALUATION
Even if there were only one investment opportunity under review, it must favourably compare with other profit-generating activities – This is the concept of opportunity cost – the advantage forgone due to alternative use of investment funds
WHY DO WE MAKE ECONOMIC EVALUATION
In addition to factors normally considered in capital investments, some of the characteristics of oil and gas that may affect the results of economic analysis are:
1 The long lead time from geologic discovery to full use of the resource (5 – 12 years)2 The political and social environment in the region ( takeovers, shutdown of operations)3 Tax burden and special allowances customary in oil and gas accounting4 The heterogeneous nature of deposits ( no two deposits are identical)5 The nonrenewable nature of oil and gas resources
CHARACTERISTICS OF OIL AND GAS RESOURCES
ASPECTS OF LEASING * OIL AND GAS ARE MINERALS AND PART OF LAND:
HOME GOVERNMENT (HG) OR LANDOWNER’S (LO) LEGAL RIGHT – IF HE SAYS NO THEN – NO SHOW.
In some countries – Govt owns the mineral rights and only Govt can explore the minerals unless it transfers right to another. If this happens we say that Govt gives another a CONCESSION.
THREE COMMON OPTIONS FOR HG/LO
* Lease interest * Mineral interest * Royalty interest
LEASE INTEREST-There will be written agreement b/w HG (lessor) and the Petroleum company (lessee) granting legal interest in HG property.
-The right will revert to LO at the end of the lease term.
-The lease is granted for explicit period (primary term) and for as long as petroleum is found in paying quantity.
-The LO reserves certain rights and privileges
* Bonus payment * Royalty payment
* Reversion of right * Surface rights
* Delayed rental
MINERAL RIGHTS
- LO is the owner of mineral right.
- LO may choose to develop or sell right to mineral to second party through a lease.
ROYALTY INTEREST
- LO is granted fraction of production free of costs
LICENSES AND LEASES
• OIL-EXPLORATION LICENSE (OEL)
A non-exclusive right to explore for and produce petroleum within area of grant. Whoever finds oil first reports to the HG/LO. Others will leave.
• OIL-PROSPECTING LICENSE (OPL)
Exclusive right to explore and prospect for petroleum within area of grant
• OIL-MINING LEASE (OML)
Permits lessee use of land to explore and dispose of petroleum discovered within leased area.
This is the Ultimate in petroleum exploration and production
TYPE OF OIL AND GAS CONTRACTS
* CONCESSIONARY
- Allows private (coy) ownership of oil and gas discovered through transfer of rights and payments of bonuses, royalties, taxes to Govt.
- No more prevalent
TYPE OF OIL AND GAS CONTRACTS
* JOINT VENTURE
- Risk shared by Govt and Coy
- Objective is to increase HG take
- Better control of your money and assets
• PRODUCTION SHARING CONTRACT (PSC)
-Coy assumes risk of exploration
- At commercial discovery, Govt steps in and becomes partner.
- Production first used to repay expenses (cost oil).
- Coy then receives share of remainder ( to be determined by contract)
- Remaining oil is divided into: > Tax oil – (PPT Obligations) > Interest (profit) oil – True value of contract to coy.
TYPE OF OIL AND GAS CONTRACTS
* SERVICE CONTRACTS (SC)
-Principle is same as PSC
-Service Coy takes care of exploration
- At discovery, Govt pays actual exploration cost, but remains sole owner of discovered reserves.
-Govt may buy part of the production
TYPE OF OIL AND GAS CONTRACTS
ESTIMATION OF OIL AND GAS RESERVES
Volumetric MethodThis is applied in a new field for rough estimates. No production history is required. We need only geological data like porosity, water saturation etc.
Where: A = Area of the reservoir (Acres); h = Formation thickness (ft)= Porosity ; Swi = Water Saturation
Boi = Initial oil formation volume factor (res bbl/STB)
Bgi = Initial gas formation volume factor (res ft3/Scf)G = Gas initial in place (Scf)
N = Oil initial in place (STB) ER = Recovery factor
WORKED EXAMPLE
A well was drilled into an oil reservoir. Well logs indicate that the reservoir has a thickness of 105 feet, average porosity of 18.5 percent and average water saturation of 25 percent. Analysis of offset wells production in the area indicate that this well will drain 160acres with a recovery efficiency of 15 percent, and the initial oil formation volume factor is 0.8 STB/res bbl. What are the recoverable oil reserves.
SOLUTION
N = [7758 x 160 x 105 x 0.185 x (1- 0.25) x 0.15] / 1.25
N = 2,170,068 STB
CASH FLOW
TERMS AND CONCEPTS
*Revenues – funds received by the coy during the period under consideration
*Costs and Expenses – money spent by doing business that must be paid from the revenues received by the coy.
*Tangible costs – Expenditures for items such as well equipment, casing, wellhead etc. These costs are charged against income through depreciation.
*Intangible costs – Expenditures not represented by physical equipment (Items with value but you can not touch). They are not capitalized for tax purposes.
TERMS AND CONCEPTS
*Depreciation – decline in value of equipment due to wear and tear of normal use.
*Royalty – right to oil and gas in place that entitles its owner to a specific fraction in kind or cash.
*Salvage value – amount of money realised at the time a used item is sold.
*Amortization – costs of certain assets (patents, pollution control devices) are charged against income over a period of time.
*Cost Depletion – reduction in value of the investment in producing oil and gas acreage (money spent for mineral rights).
TERMS AND CONCEPTS
*Farm-out – the assignment (subcontract) of part or all of an oil, natural gas or mineral interest to a third party which gives the farmees a potential profit that they would not otherwise have access to. Government approval is required.
*Working capital – money set aside to be drawn on as needed to facilitate and insure smooth operation. The net flow of working capital in and out of the operation is zero. Each company determines the proper amount of working capital it needs for smooth operation without tying up too much capital.
EXPENDITURESThe total expenditures incurred in producing oil and gas wells may be divided into two groups:
- the total capital cost (expenditure)
- the total operating cost (expenditure)
TOTAL CAPITAL EXPENDITURE (CAPEX)
The total cost of installed facilities which cannot be deducted for tax purposes, but for which depreciation is allowed by the tax authorities.
It includes all expenditures required to drill and complete the well and to provide the well with production facilities required to lift the oil and gas from the bottom of the well to the surface and to transport it from the well head to the terminal.Also included are all future expenditures required to keep the well on production (other than operating costs).
TOTAL CAPITAL EXPENDITURE (CAPEX)
It includes costs such as:
Drilling costs (including casing)Well equipment (well head connections, tubing, lift equip)Installation of pumping unitsGathering lines and tanksWater and gas injection systemsCompression stations
CAPEX are classified as tangible or intangible expense:
Tangible expenses are cost of physical equipment and are tax deductible only by depreciation.
Intangible expenses are expenditures not represented by physical equipment. These items are not capitalised for tax purposes (eg: land survey, site development, access roads, well logging/testing, etc)
OPERATING COSTS (OPEX)The expenditure incurred by producing an oil or gas well after it has been drilled and completed is called the operating cost. It is divided into two categories:
• DIRECT OPERATIND COSTS
These are costs (expenses) directly chargeable to individual leases except taxes. Labour and material costs for operation, maintenance, workovers, gas processing plants, salt-water disposal systems and injection plants.
•TAXES
Vary widely throughout the world.
Severance taxes: They include conservation and production taxes. They are levied by governments and are based on production volume
Ad valorem taxes: These include property taxes
OVERHEADS
Costs not directly assigned to any unit of production but are incurred as a result of general operations (R&D, Administration and Management, Debt interest).
INCOME TAXES
The net revenue before income tax (net revenue after expenses) is determined by subtracting total expenditures before income tax from total revenue. The council, state and federal taxes are subtracted from the net revenue before income tax to give after tax net cash flow.
CASH FLOW DIAGRAM
Corporation cash
Working capital Direct investment
Operations
Borrowed capitals
R & D
Sales revenue
Dividends to shareholders
Income from Patents, R&D
Outside investment
Operating costs
Gross profit
Other deductions
Amortisation
Depletion
Depreciation
Net profit Income taxTaxable income
Cash flow
Companies involved in the exploration and development of crude oil and natural gas have the option of choosing between two accounting approaches: the "successful efforts" (SE) method and the "full cost" (FC) method. These differ in the treatment of specific operating expenses relating to the exploration of new oil and natural gas reserves.
CASH FLOW ANALYSIS
The accounting method that a company chooses affects how its net income and cash flow numbers are reported. Therefore, when analyzing companies involved in the exploration and development of oil and natural gas, the accounting method used by such companies is an important consideration.
CASH FLOW ANALYSIS
The successful efforts (SE) method allows a company to capitalize only those expenses associated with successfully locating new oil and natural gas reserves. For unsuccessful (or "dry hole") results, the associated operating costs are immediately charged against revenues for that period. The alternative approach, known as the full cost (FC) method, allows all operating expenses relating to locating new oil and gas reserves - regardless of the outcome - to be capitalized.
CASH FLOW ANALYSIS
According to the view behind the SE method, the ultimate objective of an oil and gas company is to produce the oil or natural gas from reserves it locates and develops so that only those costs relating to successful efforts should be capitalized. Conversely, because there is no change in productive assets with unsuccessful results, costs incurred with that effort should be expensed.
CASH FLOW ANALYSIS
On the other hand, the view represented by the FC method holds that, in general, the dominant activity of an oil and gas company is simply the exploration and development of oil and gas reserves. Therefore, all costs incurred in pursuit of that activity should first be capitalized and then written off over the course of a full operating cycle. The choice of accounting method in effect receives regulatory approval.
CASH FLOW ANALYSIS
NEW PROJECT CASH FLOW PROFILE
Abandonment
Primary Development
Exploration
AppraisalProduction
Redevelopment
time0
+
Cu
mu
lati
ve C
ash
flow
s
= Final Investment Decision (incl. economics)
= Economic Analysis
NET CASH FLOW (NCF) CALCULATIONS
NCF = Gross Revenue - royalty - operating expenses (well repairs/work-over ) - overheads (internal costs) - taxes (property/severance/conservation) - production or not. - capex
= Net Revenue after expenses - state and federal income tax
= Net Cash Flow
NET CASH FLOW (NCF) CALCULATIONS
NCF = Gross Revenue - Expenses (opex, overhead, royalty, taxes ) - Depreciation - Depletion - Capex = Taxable Income - Income taxes For Accountant = NET PROFIT + Depreciation + Depletion For Economist = NET CASH FLOW
WORKED EXAMPLE
From volumetric calculations, the recoverable reserves for a proposed well are 15 million barrels of oil. A joint venture agreement between the host government and the IOC allows the host government 51% of the after tax profit. Determine the host government take if the following economic conditions prevail.Oil price = $18 / bbl; Capex = $ 75 million; Opex = $ 30 million; Royalty = 20%; Depreciation = $ 50 million; Tax rate = 75%.
SOLUTION
Revenue = 15 million x $18 = $ 270.00 millionRoyalty (20% of Revenue) = 54.00 million **Opex = 30.00 millionCapex = 75.00 millionDepreciation = 50.00 million Before tax profit = 61.00 million Tax (75%) = 45.75 million **After tax profit = 15.25 millionJVA ( 51%) = 7.78 million **HG take = 107.53 million
DEPRECIATION DEPLETION AND AMORTIZATION
Depreciation, Depletion and Amortization are the means of recovering investment in certain types of property in before tax basis.
DEPRECIATION
A reduction in the value of an asset over time, due in particular to wear and tear. It is a non-cash expense that reduces the value of an asset over time. Provision should be made for depreciation of fixed assets.
DEPRECIATION DEPLETION AND AMORTIZATION
Depreciation, Depletion and Amortization are the means of recovering investment in certain types of property in before tax basis.
METHODS OF COMPUTING DEPRECIATION
Straight Line
Double Declining Balance
Sum of the Years Digits
WORKED EXAMPLEA drilling bit with an estimated life of 5 years is purchased for $33,000. Its salvage value at the end of the fifth year is estimated to be $3000. Calculate the annual depreciation using the three methods.
SOLUTION
Straight-Line MethodYear Cost Less Annual Cumu
Salvage Allowance Allowance1 30,000 6,000 6,0002 30,000 6,000 12,000 Sum of the Years Digits Method3 30,000 6,000 18,000 Year Cost Less Annual Cumu 4 30,000 6,000 24,000 Salvage Allowance Allowance5 30,000 6,000 30,000 1 30,000 10,000 10,000
2 30,000 8,000 18,000Double Declining Balance Method 3 30,000 6,000 24,000Year Unrecovered Annual Cumu 4 30,000 4,000 28,000
Cost Allowance Allowance 5 30,000 2,000 30,0001 33,000 13,200 13,2002 19,800 7,920 21,1203 11,880 4,752 25,8724 7,128 2,851 28,7235 4,277 1,277 30,000
In DDB, the permissible allowance during the fifth year is $1277. The Cumu can not exceed the equipt cost less its salvage value.
The accounting method that a company chooses affects how its net income and cash flow numbers are reported. Therefore, when analyzing companies involved in the exploration and development of oil and natural gas, the accounting method used by such companies is an important consideration. The computation of depreciation and its effect on cash flow is shown in the next slide.
EFFECTS OF DEPRECIATION ON CASH FLOW
WORKED EXAMPLE A B C
Sales $1,000,000 $1,000,000 $1,000,000Operating Cost 200,000 200,000 200,000Depreciation 50,000 50,000 000,000
Taxable Income 750,000 750,000 800,000
Income Tax (50%) 375,000 375,000 400,000
Net Revenue 375,000 375,000 400,000 + Depreciation 50,000 00,000 00,000
CASH FLOW 425,000 375,000 400,000
A = Depreciation taken and added B = Depreciation taken but not added C = Depreciation NOT taken
DEPRECIATION DEPLETION AND AMORTIZATION
DEPLETIONAn accounting method that companies use to allocate the cost of extracting natural resources such as, minerals and oil from the earth. Depletion is calculated for tax-deduction and bookkeeping purposes. Unlike depreciation and amortization, which mainly describe the deduction of expenses due to the aging of equipment and property, depletion is the actual physical depletion of natural resources by companies.Cost depletion is calculated by taking the property's basis, total recoverable units and number of units sold into account. Percentage depletion looks at the property's gross income and taxable income limit.
METHODS OF COMPUTING DEPLETIONAfter the life of the well. How will the operator survive? HG/LO should give some allowance to keep going until new discovery – Concept of Depletion.
Cost Depletion Percentage Depletion (% of Gross Income/Revenue) 50% of Taxable Income
NOTE: Only ONE of the three will be used in the calculation. The taxpayer must deduct the larger of cost depletion and percentage depletion.
COST DEPLETION
Where:
CD = Annual cost depletion allowance B = Adjusted basis of the property ( C – CDprev) P = Units of production sold or for which payment was received during tax year R = Recoverable units of production remaining at the end of the tax year C = Project cash flow
WORKED EXAMPLEThe purchase price of a producing property was $150,000. Engineering estimate of the recoverable reserves is 1,000,000 barrels. Determine the cost depletion if the yearly depletion for two years in the life of the project is 50,000 barrels.
SOLUTION For Year 1: Production = 50,000 bbls Cost Depletion = $150,000{ 50,000 / 1,000,000} = $7,500
For Year 2: Production = 50,000 bbls Cost Dep. = ($150,000 - $7,500) { 50,000 / 1,000,000 – 50,000} = $7,500
PERCENTAGE DEPLETION
• Specified % of Gross Income
• Calculate 50% of taxable income before depletion
• Can not exceed 50% of taxable income before depletion
COMPUTATION OF DEPLETION ALLOWANCE ASSUMING PERCENTAGE DEPLETION (15%) Properties A B C
Gross Income $3,937,500 $4,200,000 $3,150,000Operating Cost -1,200,000 -2,400,000 -2,000,000Depreciation -600,000 -650,000 -550,000Taxable Income b/4 depletion 2,137,500 1,150,000 600,000Depletion AllowancesCost depletion 435,000 450,000 425,000Percentage depletion at 15% 590,625 630,000 472,50050% of taxable income 1,068,750 575,000 300,000Allowable depletion -590,625 -575,000 -425,000Taxable Income $1,546,875 $575,000 $175,000
EXAMPLE 1
DEPRECIATION DEPLETION AND AMORTIZATION
AMORTIZATIONIt refers to spreading an intangible asset's cost over that asset's useful life. For example, a patent on a piece of oilfield equipment usually has a life of 17 years. The cost involved with creating the equipment is spread out over the life of the patent, with each portion being recorded as an expense on the company's income statement.
CLASSWORK
Consider an oil field to be developed. The first and second year outputs were 3.6 and 1.8 million barrels of crude oil respectively and the per barrel cost of the oil was $24.00. One-eighth of this amount was paid as royalty to the landowner. The first and second year operating costs were $18,000 and $9,000 respectively, overheads was $8,000 each year, taxes for years 1 and 2 were $7,600 and $3,800 respectively. Depreciation allowance was $7,500 yearly while depletion was $8,000 for year 1 and $4,000 for year 2. The capital investment for this field was $22,000. Assuming income tax at 50%, generate the field cash flow.
SOLUTION
Year 1 Year 2
Revenue 75,600 37,800
Operating costs -18,000 -9,000
Overheads -8,000 -8,000
Taxes -7,600 -3,800
Depreciation -7,500 -7,500
Depletion -8,000 -4,000
Taxable income 26,500 5,500
Income tax at 50% -13,250 -2,750
Net profit 13,250 2,750
Depreciation +7,500 +7,500
Depletion +8,000 +4,000
Capital investment -22,000 0
After Tax Net Cash Flow
6,750 14,250
The revenue and cost items are listed and the cash flows generated in thousands of dollars are shown.
TIME VALUE OF MONEYA basic concept in economic analysis is that money has a time value. A sum of money now is normally worth more than an equal sum of money at some future date.
Long lead time between initial investment in exploration and development of oil and gas resources and the inflow of revenue when the fields are fully productive implies dealing with different values of money because of different time.
TIME VALUE OF MONEY
INVESTMENT TERMINOLOGY
•The Principal is the amount of money borrowed or invested.
• The terms of a loan are the length of time or number of periods the loan is outstanding and the repayment rate.
• The rate of interest is the percentage of the Principal the borrower pays the lender per time period
INTEREST FORMULAS
The symbols used for interest formulas are:
i = interest rate per interest period (%)n = number of interest periods (years)P = present sum of money ($)F = future sum of money form “n” interest periods from present date ($) A = end of period payment in a uniform series continuing for the coming “n” periods ($)
SINGLE PAYMENT COMPOUND AMOUNT FACTORIf a capital sum P (the principal) is placed on compound interest at a rate “i” compounded annually. What will it grow to in “n” years?
Principal for first year = P
Interest for first year = iP
Sum at the end of first year = P + iP = P(1 + i)
Interest for second year = iP(1 + i)
Sum at the end of second year = P(1 + i) + iP(1 + i) = P(1 +2i + i2) = P(1 + i)2
Similarly, for “n” years:
The Sum “F”at the end of “n” year = F = P(1 + i)n
The factor (1 + i)n is the single payment compound amount factor.
SINGLE PAYMENT PRESENT VALUE (WORTH) FACTOR
The present value is the worth today of $P due sometime in the future. It is the amount that must be deposited at compound interest today to grow to $F in the future. It is the reciprocal of compound amount. It is expressed as:
The factor 1/(1 +i)n is the single payment present value factor.This process of converting future income into present value or present worth is called discounting. The single payment present value factor is also called the discount factor.
ji 1/1FactorDiscount
DISCOUNT FACTORS
• Convert future values of revenue, expense, or investment into present values
• Used in the calculation of ROR, NPV, and DPI
SINGLE PAYMENT PRESENT VALUE (WORTH) FACTOR
EXAMPLES
1) If a sum of $25,000 is invested at the interest rate of 8% per year for 10 years, what will it grow to?
P = $25,000, i = 8%/yr, n = 10 yrs , F?: F = 25,000(1 + 0.08)10 = $53,972.50
2)To receive $10,000 in the future 20 years from now, how much should I deposit today at 10% interest per year? F = $10,000, i = 10%, n = 10 yrs , P?: P = 10,000[ 1/(1.10)20 = $1,486.00
Assume you have a choice of receiving $65,000 today or $70,000 one year from now. You could invest the $65,000 in a 9% interest bearing account. Which do you take?
PV = $70000 / (1+0.09)1 = $64,220 < $65,000
or
FV = $65000 * (1+0.09)1 = $70,850 > $70,000
So, would you take the $65,000 today?
Example – Present Value
CONTINUOUS INTEREST FORMULAS
Many people believe that it is more representative of actual business conditions to treat those transactions which occur fairly uniformly throughout the year as continuous cash flows.
Because these cash flows are continuous and earnings are created uniformly through the year, interest is also treated continuously in such cases.
CONTINUOUS CASH FLOW AND CONTINUOUS COMPOUNDING
PROFITABILITY OF A VENTUREThis is the yardstick for measuring the productivity of individual investment. Companies usually consider the possible benefits they may derive from ventures before investing money. The financial benefits, expressed by the profitability of the investments are measured by profitability criteria, profit indicators or economic yardsticks.
PROFITABILITY OF A VENTUREThere are two kinds of yardsticks:
Screening – which ventures meet the minimum qualifications to be considered for investment. Ranking – which of two or more mutually exclusive ventures is the most desirable.
NOTE: No single criterion tells us everything about profitability. So we normally choose the criterion that gives the management the
maximum amount of information about economic factors.
PROFITABILITY OF A VENTUREPAYOUT (PAYBACK) PERIOD
This is the time required for the cumulative net earning to equal the initial investment. It measures the speed with which invested funds are returned to the business.The shorter the period, the better and the higher the project is rated.
PROJECT A B Investment 250,000 250,000 Annual Income 50,000 75,000 Payout 250,000/50,000 250,000/75,000 = 5.00 years = 3.33 years
Project B, with a shorter payout period would be the better investment proposal.
DISCOUNTED PROFIT-TO-INVESTMENT RATIO (DPR)
It is defined as the ratio of total net profit to the investment.
i = minimum acceptable ROR
It is used when money is limited but you have several investments options.
STRATEGY > Maximize DPR
NET PRESENT VALUE (NPV)
The net present value (NPV) or net present worth profit is the algebraic sum of all net cash flows when discounted to time zero using a single discounting rate.
STRATEGY FOR SELECTION 1)Accept projects that maximize NPV profit and reject all project having negative NPV profit (except to meet certain objectives – pollution control to meet standards)2)The greater the positive NPV for a project, the more economically attractive it is.
PROFITABILITY OF A VENTURE
WORKED EXAMPLEThe cost of putting a well on stream is $1,500,000. The after tax cash flows generated by the investment for six years are:
The end of year convention is used. Annual compounding is also used. Using an average reinvestment rate of 15%, calculate the net present profit of the cash
flow.
Year Cash Flow (Revenue) ($)
1 1,000,000
2 800,000
3 600,000
4 400,000
5 200,000
6 100,000
Total 3,100,000
SOLUTIONYear Net cash flow Discount Factor Discounted C-Flow
($) i= 0.15 ($)0 -1,500,000 1.0000 -1,500,0001 1,000,000 0.8696 869,9602 800,000 0.7561 604,8803 600,000 0.6575 394,5004 400,000 0.5718 228,7205 200,000 0.4972 99,4406 100,000 0.4323 43,230
NPV i=0.15 740,730
CONCLUSIONThe NPV discounted at 15% is positive. This means that the six years cash revenues are preferred to our initial investment of $1,500,000 if the discount rate is 15%. If we invest the $1,500,000 we would make a 15% rate of return plus increase our net worth by $740,730 over 6 yrs.
NET PRESENT VALUE (NPV)• The NPV takes account of all earnings throughout
the expected life of the asset. When comparing alternatives with different expected lives, assumption is made in the evaluation of the future rates that a company’s fund can earn.
• For this criterion, it remains a problem to determine the minimum acceptable rate of return that projects are expected to earn to justify investment of the business’s funds.
• The rate of return should be above the cost of capital to the firm. If not, no need to invest.
NET PRESENT VALUE (NPV)The minimum acceptable rate of return to use in the NPV calculation is usually set by top management after consideration of at least some of the following factors:1.Future investment opportunities and their anticipated rate of earnings.2.If investment capital borrowed, i* must at least exceed the interest rate of the loan, or should at least exceed the average cost of capital.3.Corporate growth objectives (the rate at which management has set for annual growth rate of treasury) should be taken into account.
MID-YEAR PAYMENT
EXAMPLE (MID-YEAR PAYMENT)
The capital cost of natural gas treatment plant is $31,000 and the earning life of the plant will be 6years. The net incomes in these 6 years will be $5,000; $12,000; $13,000; $12,000, $12,000, and $8,000 respectively. Calculate the undiscounted per cent profit and payout time, the discounted values using a discount rate of 10% and the rate of return. Assume that income is paid as a lump sum at the midpoint of the year.
SOLUTIONYear Undis- Cumu Un- Undis- Discount Factor Dis- Cumu Discounted
discounted discounted discounted counted Discounted profitnet income net income profit net income net income
1 5,000 5,000 (26,000) 1/(1.1)1/2 = 0.9535 4,768 4,768 (26,232) 2 12,000 17,000 (14,000) 1/(1.1)3/2 = 0.8668 10,402 15,170 (15,830) 3 13,000 30,000 (1,000) 1/(1.1)5/2 = 0.788 10,244 25,414 (5,586) 4 12,000 42,000 11,000 1/(1.1)7/2 = 0.716 8,592 34,006 3,006 5 12,000 54,000 23,000 1/(1.1)9/2 = 0.651 7,812 41,818 10,818 6 8,000 62,000 31,000 1/(1.1)11/2 = 0.592 4,736 46,554 15,554
From the Table: Undiscounted Profit = $62,000 - $31,000 = $31,000 Undiscounted % Profit = $31,000/$31,000 x 100 = 100%
Similarly: Discounted Profit = $46,554 - $31,000 = $15,554 Discounted % Profit = $15,554/$31,000 x 100 = 50.2%
-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
0 2 4 6 8
Cu
mu
lati
ve
Pro
fit
Time (Year)
Cumulative Profit vs Time plot
Undiscounted
Discounted at 10%
From the graph of Cumulative profit versus time:
Undiscounted Payout time = 3.15 years
Discounted Payout time = 3.65 years
Plotting the Cumulative discounted net income against various discount rates gives the project ROR as 27.6%
ROR
Capital cost of project
DISCOUNTED CASH FLOW RATE OF RETURN (DCFROR)
It is defined as the discount rate that makes the NPV of a project equal to zero. It is also known as internal rate of return (IRR), rate of return (ROR). It is expressed as:
Or in the continuous form as:
PROCEDURE TO CALCULATE DCFRORIt is calculated by a trial-and-error series of calculations
•List the annual cash flow.
• Select a discount rate and list the discount factors.
• Calculate the present value of each annual cash flow and add the discounted values to obtain the NPV of the cash flow.• If the NPV is positive, select a higher discount rate. If negative, select a lower discount rate.• After several trials and the zero NPV is bracketed, interpolate to find the DCFROR.
WORKED EXAMPLEThe cost of putting a well on stream is $1,500,000. The after tax cash flows generated by the investment for six years are:
The end of year convention is used. Annual compounding is also used. Calculate
the DCFROR for the cash flow.
Year Cash Flow (Revenue) ($)
1 1,000,000
2 800,000
3 600,000
4 400,000
5 200,000
6 100,000
Total 3,100,000
SOLUTIONThis involves trial and error computation. The final stages of the computation are as follows:
Yr NCF DFactor DCF DFactor DCF($) i= 0.35 ($) i= 0.45 ($)
0 -1,500,000 1.0000 -1,500,000 1.0000 -1,500,0001 1,000,000 0.7407 740,740 0.6897 689,6552 800,000 0.5487 438,957 0.4756 380,4993 600,000 0.4064 243,865 0.3280 196,8104 400,000 0.3011 120,427 0.2262 90,4875 200,000 0.2230 44,603 0.1560 31,2036 100,000 0.1652 16,520 0.1076 10,759
NPV i=0.35 105,112 NPV i=0.45 -100,587
SOLUTION
Interpolating between 0.35 and 0.45: DCFROR = 0.35 + {105,112/(105,112 + 100,587)} (0.10) = 40.11%
Hence investing $1,500,000 to buy the future series of six annual revenues is equivalent to investing $1,500,000 in a project that pays 40.11% compound annual interest.
PRESENT VALUE PROFILE
Much of the confusion that results from the use of profitability criteria can be eliminated by plotting the present value profit versus the discount rate.
This curve is called the present value profile.
The present value profile for the prospect considered in the last worked example is as shown below.
0 160000015 74073035 10511245 -100587
-2000000
200000400000600000800000
10000001200000140000016000001800000
0 10 20 30 40 50
NPV
Discount Rate
PRESENT VALUE PROFILE
PRESENT VALUE PROFILE
PRESENT VALUE PROFILE
The point where the profile crosses the discount axis is the ROR of about 40%.
For discount rates less than 40% , NPV is positive hence accept if the cost of capital is less than 40%.For discount rates greater than 40%, NPV is negative, hence reject the prospect.
Changes in the initial investment simply shift the profile in the vertical direction by the amount of this change.
PROFITABILITY OF TWO PROPOSALS
Compare the profitability of the following two investment proposals:
•Proposal A: An investment of $100,000 today to receive $120,000 continuously in one year.
•Proposal B: An investment of $100,000 today to receive $200,000 continuously in seven years.
Use continuous compounding method.
Rate NPV of NPV of (j) A B
0 20000 1000005 17049 6875010 14195 4583315 11434 2382120 8762 762925 6176 -557430 3673 -1642435 1250 -2541240 -1096 -3291545 -3368 -3922950 -5567 -44583
Data for preparation of the present value profile are shown below using the continuous compounding relationship.
Profitability of two investments proposals
Rate A B0 20000 1000005 17049 68750
10 14195 4583315 11434 2382120 8762 762925 6176 -557430 3673 -1642435 1250 -2541240 -1096 -3291545 -3368 -3922950 -5567 -44583
-60000
-40000
-20000
0
20000
40000
60000
80000
100000
120000
0 20 40 60
NPV
Discount Rate
PV Profiles for Proposals A & B
Proposal A
Proposal B
Profitability of two investments proposals
The present value profiles for proposals A and B are shown below
Profitability of two investments proposals
Proposal A has a discounted cash flow rate of return of 37.5% and a net profit of $20,000 while Proposal B has a discounted cash flow rate of return of 22.8% and a net profit of $100,000.
Using the profit-to-investment ratio, B is a better option than A. However, P/I does not reflect the time-rate pattern of income from the prospects. This is one of the weakness of the P/I ratio.
Profitability of two investments proposals
The discounted cash flow rate of return indicates A to be better proposal, while the NPV at 15% indicates B to be the better proposal.The present value profiles give the whole picture. The profile intersect at a discount rate of 19.5%. This is the break-even point.
NOTE:B/w: 0-19.5: B is good At 19.5: Both are goodB/w: 19.5-40.11: A is good > 40.11: Both are not good
CONFLICT BETWEEN PROFIT INDICATORS
> Determine (Y-X)> Handle by PV indicator
For PV @ 10%: Project Y is better than X DCF : Project X is better than Y Which ONE do we choose? Determine the PV of (Y-X); if positive then Y is better.
Hence: Y is better than X
Yr X Y Y-X0 -85 -87 -21 100 38 -622 38 383 38 38
Total 15 27 12DCF 38% 21% 12%
PV@10% 10 13 3
INCREMENTAL CASH FLOW
Note
Primary production is better since it has lower PBP and higher P/I at i of 20%.If i =20%, and (Y-X) is 28%, then we can do waterflooding (optional).If i = 30%, and (Y-X) is 28%, then do not waterflood.
Yr X-Primary Y-Flooding Y-X0 -20 -260 -2401 100 70 -302 90 200 1103 80 400 3204 70 100 305 60 70 10
Total 380 580 200PBP 0.2 yrs 2 2.5P/$ 19 2.23 0.83DCF > 100% 74% 28%
ACCELERATION PROJECTSAn acceleration project is defined as a project applied to an already existing profitable venture in order to bring future net income forward in time.
The economic justification for accelerating lies in the fact that the accelerated income is earned in fewer years than the un-accelerated, so that discounting will have less effect on the accelerated than un-accelerated. Hence discounted profit from the accelerated project might exceed that from the original project.
Problems when no new reserves are generated.
The existence of two ROR further complicates the interpretation of the profit indicators.
EXAMPLE
The estimated future net incomes for a certain project are shown below. The project is under consideration for acceleration, and the estimated future net incomes are also shown. The capital cost involved in undertaking the acceleration is $3000. Determine the discounted profit and payback time, draw a curve of difference in cumulative discounted net incomes (accelerated less un-accelerated) against discount rate, and find the rate of return if the earning power of the company is 10% per cent/year. Assume that income is paid as lump sum at the midpoint of the year.
Year Cash Flow Accelerated DF = 10% DCF Acc-DCF Cumu-DCF Cumu-ADCF
1 4000 7000 0.9535 3814 6675 3814 66752 5000 15000 0.8668 4334 13002 8148 196773 4000 6000 0.788 3152 4728 11300 244054 6000 2000 0.716 4296 1432 15596 258375 3000 0.651 1953 17549 258376 3000 0.592 1776 19325 258377 2000 0.538 1076 20401 258378 1000 0.489 489 20890 258379 1000 0.445 445 21335 25837
10 1000 0.404 404 21739 25837
SOLUTION
A graph of cumulative discounted net incomes for both accelerated and un-accelerated are shown. From the graph, payback time is about 0.45 years.The difference between the total annual income of accelerated and un-accelerated is $4098. Allowing for $3000 needed to start the project the discounted profit is $1098 or 36.5%
Cost of acceleration Project
A graph of the difference in total discounted net incomes against discount rate crosses the discount rate axis twice giving rise to two ROR at 6 and 255%. The project is acceptable between the two limits and rejected outside the limits
Cost of acceleration project
ROR ROR
RISK AND UNCERTAINTY
Risk refers to a situation where one can specify a probability distribution over possible outcomes. Uncertainty refers to the condition when one cannot specify the relative likelihood of the outcomes.Many of the things that we do fall into these categories. The drilling of an exploratory oil well is only an example where both the cost and the uncertainty regarding success are so great that they cannot be ignored.
RISK AND UNCERTAINTY
There are no decision methods that eliminate risk and uncertainty. The utilisation of the methods discussed here will provide the necessary tools to evaluate, quantify and understand risk and uncertainty so that engineers and managers can devise a decision strategy to minimise the firm’s exposure to risk and uncertainty.
RISK AND UNCERTAINTY
Where uncertainties are great, and where there is no recognised way of taking them into account, decision making becomes difficult.Judgment of some kind must be made. One is forced to make assumptions and predictions, otherwise there is no basis for a decision.The criteria used may be adjusted upward or downward according to the feelings about particular ventures.
RISK AND UNCERTAINTYWhen an organisation undertakes project in which it has little or no recent experience, there will be three distinct areas of uncertainty.
-Timing of the project and the cash flow it is expected to generate- Direct outcome of the project ( accomplishment)- The side effects of the project (its unforeseen consequences)
There is little one can do to eliminate the uncertainty. Decisions must be taken in the face of the uncertainty.
We try to reduce such uncertainty by analysing the risk associated with it.
Risk analysis does not remove the ambiguity, it simply describes it in a way that provides decision maker with a useful insight into their nature.
RISK AND UNCERTAINTY (CONT’D)
A risk is any uncertain event that, if it occurs, could prevent the project realising the expectations of the stakeholders as stated in the agreed business case of the project definition.
A risk that becomes a reality is treated as an ISSUE
Every risk always has a cause and if it occurs, a positive or negative consequence sets in.
Many risks are well hidden away in the schedule and unless you look for them, will impact your efforts at a time you least expected.
WHAT IS IMPACTED ?
1)Cost – the overall cost of the project.2)Schedule – the time the project will take.3)Scope – the project deliverables and quality of the work.
STEPS TOWARDS RISK ANALYSIS1)ONE-POINT-ANALYSIS (Best Estimate)2)WEIGHTED AVERAGE SENSITIVITY (Expected Value)
ONE-POINT-ANALYSIS
Consider an opportunity to acquire an exploration concession for a considerable sum of money. An analysis must first be made to ascertain discovery that will offset all financial outlays and yield an adequate return on expended capital.The traditional approach is to perform the reserve in place using volumetric reserve formula for best estimate values for the individual petrophysical parameters. Through a combination of experience, intuition, judgment and consensus the manager must then decide if the profitability is large or not.This type of one-point analysis gives acceptable results in many cases where the uncertainty is not large. Unfortunately such projects are very scarce in oil and gas industry.
STEPS TOWARDS RISK ANALYSIS
ONE-POINT-ANALYSIS
• Risk treated as judgment factor• No quantitative assessment risk• Does not recognize possibility of failure
Example Reserves NPV 400 Mbbls $6,000
Avoid Statements such as:1) We have good idea of the formation2) This is about as sure as a wildcat can be3) This is pretty risky – moderately risky – high risk and so on.
STEPS TOWARDS RISK ANALYSIS
WEIGHTED AVERAGE SENSITIVITY (Expected Value)
To aid decision making under conditions of uncertainty, we assign a chance or probability of occurrence to the possibility of a certain outcome. These probability are commonly used to quantify uncertainty. It is important to realise that they are merely a way of expressing personal feelings about uncertainty and have no objective reality.
STEPS TOWARDS RISK ANALYSISThe following methods will help us to obtain probability estimates:
1.Subjective probability estimates are a common way of expressing the degree of risk and uncertainty. The estimates represent personal opinion based on available statistical data or on the analyst’s feeling.2.The use of past success ratios is the most common method of estimating probabilities.
STEPS TOWARDS RISK ANALYSIS
• The expected value (monetary, utility) of an outcome is the product obtained by multiplying the probability of occurrence of the outcome and the conditional value (or worth) that is received if the outcome occurs.
• The expected value of an outcome is the algebraic sum of the expected values of each possible outcome that occur if the decision alternative is accepted.
• It can be positive, zero or negative. It is the numerical criterion used to compare competing decision choices.
• The decision maker must select only one of the available alternatives
WEIGHTED AVERAGE SENSITIVITY• Probability of occurrence assigned to outcomes• Probability must sum to 1.0• “Best estimate” assigned highest probability• Expected value (EV) obtained by weighting• Individual EV added to give project EV• Accept project if EV is positive
Example:
Reserves NPV Probability EV
0 Mbbl 500 M 0.15
75 M 200 Mbbl 3,000 M 0.30
900 M 400 Mbbl 6,000 M 0.35
2100 M 600 Mbbl 9,000 M 0.20
1800 M 1.00 EMV =
4,725 M
A young graduate has received job offers from two companies: Shell and Schlumberger. He plans to work for 4 years, quit and return to the university.
Shell offers $ 30k p/a, Schlumberger offers $ 50k p/a.
Given above information, what should he do ?
Decisions and Probability (Risk) graduate 1
The graduate should go for Schlumberger because 4 * $50k is more than 4 * $30k
FALSE 0
120 120
Accept Job
200
TRUE 1
200 200
The Graduate
Shell
Schlumberger
Decisions and Probability (Risk) graduate 2
The graduate decides to ask around a bit how graduates that joint either Shell or Schlumberger some years ago are doing today. His fact finding shows:
100% of those who joined Shell are still with the company
80% of those who joined Schlumberger burned out and quit, on the average after 6 months and need a 6 months recovery period. All then find a job paying $85k.
20% of those who joined Schlumberger are still with the company
Given above information, what should he do ?
Decisions and Probability (Risk) graduate 3
TRUE 1
120 120
Accept Job
120
80.0% 0
85 85
FALSE Survive
0 108
20.0% 0
200 200
The Graduate(2)
Shell
Schlumberger
Burn out
Doing fine
The graduate realizes that his expectation earning with Schlumberger is only [0.8x85 + 0.2x200] = $108k, $12k less than with Shell.
He should join Shell.
Decisions and Probability (Risk) graduate 4
LIMITATIONS OF EMVThe assumption is that a decision maker will want to choose a project that has the highest EMV. The analyses assume that decision makers will want to “play the average” on all deals regardless of the potential negative consequences that might result. BUT IS THIS TRUE?
• Purely mechanical (judgment, experience of Decision Maker NOT incorporated)
• Failure to take into account the different financial circumstances of investors
• EMV is good model for RISK NEUTRAL DECISION MAKER.
• Need to incorporate ATTITUDES and FEELINGS of decision maker.
UTILITY THEORYUtility theory states that each individual has a measurable preference when faced with choices among alternatives uncertainty, which is called his “utility”.
It has unit called utiles.
The relationship between utiles and dollars is called an individual’s utility function (curve).
The function is strictly personal and differs among individuals.
UTILITY THEORY
It recognises that the second increment of a substance may have generally less value (utility) to a person than the first increment.
Different people will of course have different regard or desire for the same substance.
Thus each person would have his individual utility curve or function.
UTILITY CONCEPTS - RECOMMENDED PROCEDURE
The recommended procedure for determining a person’s utility function is to find a “point of indifference”- when the decision maker has no preference among several alternatives and accepts them as possessing the same utility. This point is determined by questioning the decision maker about his preference when confronted with two monetary alternatives.
The zero point on the vertical scale is generally interpreted as a point of indifference or neutrality about money.
Positive, upper values on the vertical axis denote increasing desirability and the negative portion of the scale denotes an increasing dislike for the corresponding amounts of money.
UTILITY CONCEPTS – PROPERTIES 1
The utility scale is dimensionless and its magnitude is arbitrary.
The horizontal scale can be in any units of money (NPV, etc).
The curve shows an increasing function and occupies the first & third quadrants only.
The curve merely describes a person’s preferences and attitudes for money and does not imply a comparison among individuals. It does not imply that he is wrong for having the attitude or that he should change his attitude about money.
The shape of the curve reflects the attitudes and preferences of the decision maker. If he was totally impartial to money his utility would be a straight line passing through the origin.
SHAPES OF VARIOUS PREFERENCE CURVES
(b) Shows a conservation attitude for risk taking.
(d) Shows a risk taking attitude.
(f) Totally impartial to risk – Anything goes.
UTILITY CONCEPTS – PROPERTIES 2
The shape in the first quadrant indicates the decision maker’s attitudes toward risks. A concave downward in the first quadrant shows a conservative attitude for risk taking.
A curve that bends sharply upward in the first quadrant is representative of a risking- seeking attitude.
Utility theory has the property of expectation. We can compute expected utility value (EUV) for a decision alternative by multiplying the utility values and the probabilities of occurrence.
The EUV is the decision parameter used by the decision maker to accept or reject the alternative. The decision rule is to select the alternative that maximises EUV.
EXAMPLEA company is planning to embark on a drilling venture. The possible outcomes of the venture are given below and the utility curve of the company is attached:
Outcomes Probability Alternatives Drill Farm Out (1/8 RI) Dry Hole 0.4 -200,000 0 5 BCF 0.6 +600,000 +50,000
Using the EMV concept, we obtain
EMV of Drill = (0.4)(-200,000) + (0.6)(600,000) = $280,000
EMV of Farm Out = (0.4)(0) + (0.6)(50,000) = $30,000 Drill is the preferred choice.
TYPICAL CURVE FOR A COMPANY
Using the EUV computation gives:
EUV of Drill = (0.4)(-8) + (0.6)(4) = -0.80 utiles
EUV of Farm Out = (0.4)(0) + (0.6)(0.6) = 0.36 utiles Farm Out is the preferred choice.
The difference between the EMV and EUV decisions occurs because the potential loss of $200,000 overrides the potential gain of $600,000.
Without the use utility theory, the company would have made the wrong decision.
DECISION TREES ANALYSISA line (pictorial) representation of a sequence of events and possible outcomes.
The main problem is too many branches in the future.The point from which two or more branches emanate is called a Node.Two types of Node:
DECISION NODE: represented by a square. The decision maker dictates which branch is taken.CHANCE NODE: represented by a circle. Chance determines which outcome will occur.
DECISION TREES ANALYSIS• The trees normally reads from left to right and are
drawn in the same order as the actual sequence in which the decision choices and chance events occur in the real world.
• The ends of a decision tree are called terminal points. Indicating that there are no further decisions or chance events beyond that point.
• The evaluation of the outcomes starts from the terminal point of each branch and moves from right to left.
• The decision criterion at any decision node is to take the branch of alternative that maximises expected value.
DECISION TREES ANALYSIS
Umbrella Problem
Carry umbrella
Leave umbrella
Chance Node
Rain
Rain
No Rain
No Rain
Stay Dry
Stay Dry
UnnecessaryBurden
Get Wet
DecisionNode
Event
DECISION TREE ANALYSIS
An investor is planning to buy a pizza restaurant near the university campus. If he buys the restaurant, there are three possible outcomes: a low demand, a medium demand and a high demand for pizza. There is a 60% chance of a low demand with a resulting loss of $25,000; a 30% chance of a medium demand and realising a NPV profit of $50,000 and a 10% chance of a high demand and realising a NPV profit $150,000. Calculate the expected value of outcomes.
Low
Don’tBuy
Medium
HighBuy
PIZZA RESTAURANT
Outcome Probability NPV
Low 0.6 -25,000Medium 0.3 50,000High 0.1 150,000
EMV of Buy = (0.6)(-25,000) + (0.3)(50,000) + (0.1)(150,000) = + $15,000EMV of Don’t Buy = $ 0
The decision criterion at any decision node is to take the branch that maximizes expected value. Hence the preferred option is to BUY.
($-25,000)
($50,000)
($150,000)
($0)
EXAMPLE
A company has a nontransferable short-term option to drill on a certain plot of land. This option is the only business deal which the company is involved now. Two recent dry holes elsewhere have reduced the company’s liquid assets to $130,000, and John Doe the president of the company must decide within two weeks if drilling is to commence by then. Doe has three possible choices: 1 Drill immediately 2 Pay to have a seismic test run, then, depending on the result, decide whether or not to drill. 3 Let the option expire
The cost of seismic test is $30,000 and the well can be drilled for $100,000. Another oil company has promised to buy any oil discovered for $400,000. A geologist states that there is a 0.55 probability that there will be oil if a well is drilled immediately. Data on the reliability of seismic tests indicate that if the test result is favourable the probability of finding oil will increase to 0.85, but if unfavourable it will fall to 0.10. The geologist has also said that there is a 0.60 probability that the result will be favourable if a test is made. If you were Mr. Doe what will you do?
SOLUTION
The EMV at the top branch: (0.85)(+$400,000) + (0.15)($0) = $340,000Compare with the EMV of don’t drill = $100,000 (The maximum EMV of $340,000 is chosen for the top node.)
The EMV at the middle branch: (0.10)(+$400,000) + (0.90)($0) = $40,000Compare with the EMV of don’t drill = $100,000 (The maximum EMV of $100,000 is chosen for the middle node.)
The EMV at the bottom branch: (0.55)(+$430,000) + (0.45)($30,000) = $250,000Compare with the EMV of don’t drill = $130,000 (The maximum EMV of $250,000 is chosen for the bottom node.)
The EMV at the last top branch: (0.60)(+$340,000) + (0.40)($100,000) = $244,000Compare with the EMV of don’t drill = $250,000 (The maximum EMV of $250,000 is chosen for the last node.)
Don’t take seismic test
Take seismic
test
Take seismic
test
Don’t take seismic test
Test unfavourable
Test unfavourable
Test favourable
Test favourable
Drill
Drill
Drill
Drill
Drill
Drill
Don’t drill
Don’t drill
Don’t drill
Don’t drill
Don’t drill
Don’t drill
Oil
No Oil
Oil
Oil
Oil
Oil
Oil
No Oil
No Oil
No Oil
No Oil
No Oil
$130,000
$30,000
$400,000
$430,000
$100,000
$100,000
$400,000
$400,000
$430,000
$400,000
-$100,000
-$100,000
-$100,000
-$100,000
-$100,000
-$100,000
$30,000
$244,000
$250,000
0.6
$100,000
$340,000
0.4
0.45
0.55
0.90
0.10
0.15
0.85
$0
$0
Doe’s Decision
Doe’s Decision Tree
0.6
0.4
0.85
0.15
0.10
0.90
0.45
0.55
+$244,000 (REJECT)
+$250,000 (ACCEPT)
Don’t Take seismic
test
Take seismic test
DOE’S CHOICE
The two choices open to Doe are “drill without seismic” for an expected net income of $250,000 OR “drill with seismic” for an expected income of $244,000.
Doe should have his company drill immediately without taking any seismic test.
CONCLUDING REMARKSThe uncertainties in geology will always be as the Creator made them. How the problems of decision making in petroleum engineering are solved depend on how well engineers and managers apply new ideas, knowledge and technology.Petroleum exploitation is always an exciting and challenging game – a game of chance but also of change. Chi U. Ikoku
THANK YOUAND
GOODLUCK