Advanced Petroleum Economics Staber

600.019 Advanced Petroleum Economics Lecture Notes

Originaly prepared by Stephan Staber, 2007, Leoben Revised by Stephan Staber, October 2008, Vienna Revised by Stephan Staber, September 2009, Vienna Revised by Stephan Staber, October 2010, Vienna Revised by Stephan Staber, September 2011, Vienna © Economics and Business Management, University of Leoben, Stephan Staber

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Preface ■ These lecture notes can be seen as a reasonable supplement for the lecture “Advanced Petroleum Economics”. ■ Because of didactic reasons placeholder can be found instead of most figures in these lecture notes. The figures are presented and discussed in the lessons. Subsequently this is not a complete manuscript and consequently not sufficient for the final examination. ■ For further reading and examination prparation the following books are recommended: ▪ Allen, F.H.; Seba, R. (1993): Economics of Worldwide Petroleum Production, Tulsa: OGCI Publications. ▪ Campbell Jr., J.M.; Campbell Sr., J.M.; Campbell, R.A. (2007): Analysing and Managing Risky Investments, Norman: John M. Campbell. ▪ Newendorp, P.; Schuyler, J. (2000): Decision Analysis for Petroleum Exploration. Vol. 2nd Edition, Aurora: Planning Press.

■ The interested student finds the full list used literature at the end of this document. © Economics and Business Management, University of Leoben, Stephan Staber

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Why Advanced Petroleum Economics? ■ The content of teaching is based on your knowledge gained in the lecture „Petroleum Economics“! ■ Required knowledge: ▪ Time Value of Money Concept consult „Allg. Wirtschafts- und Betriebswissenschaften 1“ and „Petroleum Economics“ ▪ Measures of Profitability consult „Allg. Wirtschafts- und Betriebswissenschaften 1“ and „Petroleum Economics“ ▪ Financial Reporting and Accounting Systems consult „Allg. Wirtschafts- und Betriebswissenschaften 2“ and „Petroleum Economics“ ▪ Basic Probability Theory and Statistics consult „Statistik“ and „Petroleum Economics“ ▪ Reserves Estimation consult „Reservoir Engineering“ and „Petroleum Economics“

© Economics and Business Management, University of Leoben, Stephan Staber

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Lecture Outline ■ Cash Flow and Costs ■ Profitability and Performance Measures ■ Expected Value Concept ■ Decision Tree Analysis ■ Probability Theory ■ Risk Analysis ■ Sensitivity Analysis


Page 4

Setting the scene… ■ What are the core processes of an E&P company?

Fig. 0: Core processes in an E&P company

■ What are potential decision criteria/ decision influencing factors regarding e.g. a field development approval decision? © Economics and Business Management, University of Leoben, Stephan Staber

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Cash Flow and Costs

Cash Flow and Costs ■ Net Cash Flow= Net Annual Revenue – Net Annual Expenditure (both cash) ■ Costs: ▪

Capital expenditure (CAPEX)

▪

Operating expenditure (OPEX)

▪

Abandonment Costs

▪

Sunk Costs

▪

Opportunity Costs

Fig. 1: Cash Flow Projection

© Economics and Business Management, University of Leoben Cf. Allen and Seba (1993), p. Mian (2002a), p. 86ff.

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Capital Expenditure (CAPEX) ■ ■ ■

…one-time costs …occurring at the beginning of projects Classification by purpose: ▪ ▪ ▪ ▪ ▪ ▪

■

Classification by purchased items: ▪ ▪ ▪ ▪ ▪

■

Exploration costs (capitalized portion) Appraisal costs Development costs Running Business costs Abandonment costs Acquisition costs Facility costs Wells/ Drilling costs Pipeline costs G&G costs (mainly seismic) Signature bonus

Classification and wording differ from company to company

© Economics and Business Management, University of Leoben

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Operational Expenditure (OPEX) ■ ■ ■

…occur periodically …are necessary for day-to-day operations …consist typically of: ▪ ▪ ▪ ▪

Utilities Maintenance of facilities Overheads Production costs, e.g.: ▪ ▪ ▪ ▪

▪ ▪

■

Treatment Costs Interventions Secondary recovery costs Water treatment and disposal costs

(Hydrocarbon-)Evacuation costs Insurance costs

Classification and wording differ, but often: ▪ ▪

Production cost per unit = OPEX/production volume [USD/bbl] Lifting cost per unit = (OPEX + royalties + expl. expenses + depreciation)/sales volume [USD/bbl]

© Economics and Business Management, University of Leoben Cf. Mian (2002a), p. 126ff.

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Types of Cost Estimates ■

▪

Linked to the stage of development

▪

Based on the available information

Order of Magnitude Estimate ▪

■

Optimization Study Estimate ▪

■

■

Data: Location, weather conditions, water depth (offshore), terrain conditions (onshore), distances, recoverable reserves estimate, number and type of wells required, reservoir mechanism, hydrocarbon properties Also based on scaling rules but with more information and for individual parts

Budget Estimate ▪

Engineers create a basis of design (BOD)

▪

Contractors are invited for bidding

▪

Result is a budget estimate

Control Estimate ▪

Actual expenditure is monitored versus the budget estimate

▪

If new information is available, then the development plan is updated


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Accuracy and Cost Overrun ■

■

Main reasons for Cost Overrun ▪

Contractor delay

▪

Unforeseen difficulties

▪

New information may change the project

Accuracy improves over time ▪

Major improvement occurs when the BOD is frozen

Fig. 2: Accuraccy of cost estimates

Fig. 3: Probability of cost overrun

© Economics and Business Management, University of Leoben From Mian (2002a), p. 139ff.

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Contingency and Allowance ■

Contingency ▪

■

Budget for the unknown unknowns

Allowances ▪

Budget for the known unknowns

▪

…are probable extra costs

▪

E.g. for material, identified risks, foreseeable market or weather conditions, new technology, growth…

▪

The value is often taken from the 10% probability budget estimate

Fig. 4: One possible statistical view on contingency and allowance


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Measures of Profitability and Performance

Popular Criteria ■ Three which ignore time-value of money: ▪ Net Profit ▪ Payout (PO) ▪ Return on Investment (undiscounted profit-to-investment ratio)

■ Others which recognize time-value of money: ▪ ▪ ▪ ▪

Net present value profit Internal rate of return (IRR) Discounted Return on Investment (DROI) Appreciation of equity rate of return

■ Some criteria might have alternate names, but these are the common ones in petroleum economics

© Economics and Business Management, University of Leoben, Stephan Staber Cf. Newendorp, Schuyler (2000), p. 9ff.

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Prospect Cashflow Example ■ This example helps to understand the measures of profitability (Taxation is excluded from this analysis for simplicity) Investment:

$268,600 for completed well; $200,000 for dry hole

Estimated recoverable reserves:

234,000 Bbls; 234 MMcf gas

Estimated average producing rate during first two years:

150 BOPD

Future Expenditures:

Pumping Unit in year 3, $10,000; Workover in year 5, $20,000

Working interest in proposed well:

100%

Average investment opportunity rate:

10%

Type of discounting:

Mid-project-year

Year

Estimated oil Production, Bbls

Annual Net Revenue*

Future Expenditures

Net Cash Flow

1

54,750

$132,900

$132,900

2

54,750

132,900

132,900

3

44,600

107,600

4

29,200

69,200

5

18,900

43,500

6

12,900

28,600

28,600

7

7,800

15,900

15,900

8

5,200

9,400

9,400

9

3,700

5,600

5,600

10

2,200

1,900

1,900

234,000

$547,500

10,000

97,600 69,200

20,000

$30,000

23,500

$517,500

*Annual Net Revenue = Annual Gross Revenue – Royalties – Taxes – Operating expenses

© Economics and Business Management, University of Leoben From Newendorp, Schuyler (2000), p. 14f.

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Net Profit ■ Net Profit=Revenues – Costs = Cash Receipts – Cash Disbursements ■ Prospect Cashflow Example: ▪ $547,500 – $298,600 = $248,900

■ Strengths: ▪ Simple ▪ Project profits can be weighted, e.g., (n x average = total)

■ Weaknesses: ▪ Does not recognize the size of investment ▪ Does not recognize the timing of cash flows © Economics and Business Management, University of Leoben, Stephan Staber Cf. Newendorp, Schuyler (2000),p. 9ff.

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Payout (PO) 1/2 ■ The length of time which elapses until the account balance is exactly zero is called payout time. ■ If one tracks the cumulative project account balance as a function of time he gets the so-called cash position curve. ■ All other factors equal a decision maker would invest in projects having the shortest possible payout time. Fig. 5: Cash position curve


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Prospect Cashflow Example ■ Unrecovered portion of the initial investment: ▪ $268,600 – $132,900 = $135,700

■ Unrecovered portion of the investment at the end of year 2: ▪ $135,700 – $132,900 = $2,800

■ Assuming constant cashflow rates the portion of year 3 required to recover this remaining balance: ▪ $2,800 / $97,600 = 0.029

■ Payout time: ▪ 2.029


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Payout (PO) 2/2 ■

Strengths: ▪ ▪

■

Fig. 6: Weakness 1

Simple Measures an impact on liquidity

Weaknesses: 1. 2. 3.

Payout considers cashflows only up to the point of payback. Especially troublesome with large abandonment costs Project profits cannot be weighted: (n x average ≠ total)

Fig. 7: Weakness 2

Fig. 8: Weakness 3

Fig. 9: Variation 1

Fig. 10: Variation 2


Fig. 11: Variation 3

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Return on Investment (ROI) ■ Reflects total profitability! ■ Sometimes called: ▪

ROI =

∑ NCF Investment

(undiscounted) profit-to-investment ratio

■ Strengths: ▪

Recognizes a profit in relation to the size of investment

▪

Simple

■ Weaknesses: ▪

Accounting inconsistencies

▪

Continuing investment is not represented properly

▪

Project ROI cannot be weighted: (n x average ROI ≠ total ROI)

© Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 9ff.

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Return on Investment (ROI) - Variations 1. Using “maximum out-of-pocket cash” instead of investment

2. Return on Assets (ROA): ROA =

Fig. 12: Maximum out-of-pocket cash

AverageNetIncome AverageBookInvestment

■ Prospect Cash Flow Example: ▪

($517,500 – $268,600) / $268,600 = 0.927


Fig. 13: ROA

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Net Present Value ■ Money received sooner is more worth than money received later! ■ The money can be reinvest in the meantime! (Opportunity cost of capital) ■ The present value can be found by: ▪ PV = FV (1+i)-t ▪ ▪ ▪ ▪ ▪

PV… Present Value of future cashflows FV… Future Value i… Interest or discount rate t… Time in years (1+i)-t… Discount factor


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Discount rate ■

Two philosophies what this rate should be:

1. Opportunity cost of capital (OCC) ▪

The average yield we can expect from funding other projects. This is the rate at which one can reinvest future cash.

2. Weighted-average cost of capital (WACC) ▪

The marginal cost of funding the next project. This is calculated as an weighted-average cost of a mixture of equity and debt.


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Net Present Value ■ Prospect Cash Flow Example: Year

Net cashflow

Discount factor 10%

10% discounted cashflow

0

-$268,600

1.000

-$268,600

1

+$132,900

0.953

+$126,700

2

+$132,900

0.867

+$115,200

3

+$97,600

0.788

+$76,900

4

+$69,200

0.716

+$49,500

5

+$23,500

0.651

+$15,300

6

+$28,600

0.592

+$16,900

7

+$15,900

0.538

+$8,600

8

+$9,400

0.489

+$4,600

9

+$5,600

0.445

+$2,500

10

+$1,900

0.404

+$800

Fig. 14: e.g. profitable, but neg. NPV

$148,400 = NPV @ 10%

Fig. 15: Major weakness of NPV


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(Internal) Rate of Return (IRR) ■ Sometimes:

Year

Net cashflow

Discount factor 40%

40% discounted cashflow

0

-$268,600

1.000

-$268,600

1

+$132,900

0.845

+$112,300

▪ Internal yield

2

+$132,900

0.604

+$80,300

▪ Sometimes: Profitability index (PI)

3

+$97,600

0.431

+$42,100

4

+$69,200

0.308

+$21,300

5

+$23,500

0.220

+$5,200

6

+$28,600

0.157

+$4,500

7

+$15,900

0.112

+$1,800

8

+$9,400

0.080

+$700

9

+$5,600

0.057

+$300

10

+$1,900

0.041

+$100

▪ Discounted rate of return

■ IRR is the discount rate such that the NPV is zero ■ Prospect Cash Flow Example: (trail-and-error procedure)

$0 IRR = 40%


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Discounted Return on Investment (DROI) ■ Sometimes: ▪ Discounted profit to investment ratio (DPR, DPI, or DPIR) ▪ Present value index (PVI)

DROI =

NPV PV _ of _ Investment

▪ Sometimes: Profatibility Index (PI)

■ DROI is the ratio obtained by dividing the NPV by the present value of the investment ■ Prospect Cash Flow Example: ▪ DROI = $148,400 / 268,600 = 0.553


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Discounted Return on Investment (DROI) ■ Strengths: ▪ All advantages of NPV (such as realistic reinvestment rate, not trail and error procedure) ▪ Providing a measure of profitability per dollar invested ▪ Suitable for ranking investment opportunities ▪ Only meaningful if both signs of the ratio are positive

■ Ranking investments with DROI gives a simple and often good enough portfolio ■ But there are a couple of considerations around that might optimize one’s portfolio: ▪ ▪ ▪ ▪

Synergies Fractional participation Strategic and option values Game-theoretical thoughts


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Appreciation of Equity Rate of Return ■ Also: Growth rate of return ■ Idea: ▪ ▪ ▪

Reflecting the overall net earning power of an investment Assumes the reinvestment at a lower rate (e.g. 10%) than the true rate of return (e.g. 40%) As a consequence the overall rate of return is less!

■ Baldwin Method: 1. Calculate a compound interest factor for each year: (1+i)n , where i is the discount rate for the opportunity cost of capital and n is always the number of years reinvested (midyear) 2. Calculate the appreciated value of the net cash flows. The sum is the total value of the cash flows at the end of the last project year. 3. Solve this equation for iae: Investment*(1+iae)N=Σ Αppr. value of NCFs © Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 9ff.

Page 28

Appreciation of Equity Rate of Return ■ Prospect Cash Flow Example using the Baldwin Method: Year

Net cashflow

Number of years reinvested

Compound interest factor, 10%

Appreciated value of net cashfliws as of end of project

1

+$132,900

9.5

2.475

+$328,900

2

+$132,900

8.5

2.247

+$298,600

3

+$97,600

7.5

2.045

+$199,600

4

+$69,200

6.5

1.859

+$128,600

5

+$23,500

5.5

1.689

+$39,700

6

+$28,600

4.5

1.536

+$43,900

7

+$15,900

3.5

1.397

+$22,200

8

+$9,400

2.5

1.269

+$11,900

9

+$5,600

1.5

1.153

+$6,500

10

+$1,900

0.5

1.049

+$2000 $1,081,900

■ $268,600 (1+iae)10=$1,081,900 ■ Appreciation of equity rate of return = iae = 0.1495 © Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 9ff.

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Net Present Value Profile Curve

Fig. 16: Net Present Value Profile Curve

■ NPV and rate of return not necessarily prefer the same ranking! © Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 9ff.

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Net Present Value Portfolios ■ Due to limited statements of single measures portfolios are established ■ Common are “x” vs. NPV portfolios

Fig. 17: IRR vs. NPV Portfolio

Fig. 18: DROI vs. NPV Portfolio


Fig. 19: Cash Out vs. NPV Portfolio

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Rate Acceleration Investments ■ Typical for the petroleum industry! ■ Investments which accelerate the cashflow schedule ■ Examples: ▪ ▪

Infill drilling Installing large volume lift equipment

■ Simple calculation example: Year

Present cashflow

Accelerate d cashflow

Incrementa l cashflow

Discount factor, 10%

Discounted incremental cashflows, 10%

0

0

-$50

-$50

1.000

-$50.00

1

+$300

+$500

+$200

0.953

+$190.60

2

+$200

+$400

+$200

0.867

+$173.40

3

+$200

0

-$200

0.788

-$157.60

4

+$100

0

-$100

0.716

-$71.60

5

+$100

0

-$100

0.651

-$65.10 +$19.70


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Multiple choice review questions Past costs which have already been incurred and cannot be recovered are called… O CAPEX. O OPEX. O Abandonment costs. O Sunk costs.


Page 33

Multiple choice review questions The expected return forgone by bypassing of other potential investment projects for a given capital is called… O weighted average cost of capital (WACC). O opportunity cost of capital. O profit. O half-life.


Page 34

Multiple choice review questions The length of time which elapses until the account is balanced of e.g. a development project is called… O maximum-out-of-pocket-cash. O net present value. O return on investment. O payout.


Page 35

Expected Value Concept

Expected Value Concept (EVC) ■ Previously discussed measures were all “no risk” parameters ■ But petroleum exploration involves a high degree of risk! ■ Two way out: ▪

Doing intuitive risk analysis or

▪

trying to consider risk and uncertainty in a logical, quantitative manner.

■ Expected value concept combines profitability estimates and risk estimates © Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 71ff.

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Risk and Uncertainty ■ Risk: ▪ ▪

Addresses discrete events (e.g. discovery or dry hole) Can be both: A threat or an opportunity

■ Uncertainty: ▪ ▪

Result depends on unknown circumstances (e.g. oil price) Occurrence probability of an event is not quantifiable

■ Deterministic: ▪

Calculations using exact values for their parameters are called deterministic

■ Stochastic: ▪

Calculations which use probabilities within their model are called stochastic

© Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 71ff and Laux (2003), p. 105.

Page 38

Definitions and EVC ■ Expected Value (EV): ▪

The EV is the probability-weighted value of all possible outcomes.

■ Expected Monetary Value (EMV): ▪ ▪

The EMV is the expected value of the present values of the net cashflows EMV = EV (NPV)

■ “Conditional” ▪ ▪

In this context “conditional” means that a value will be received only if a particular outcome occurs. Often it is omitted!

■ Simple Example: ▪

EV Cost of Stuck Pipe = P(Stuck Pipe) * (Cost to remedy Stuck Pipe)

■ More generally:

EMV =

∑ P(outcome _ i) × NPV

Outcome _ i

all _ i


Page 39

EMV Example ■

Situation in a drilling prospect evaluation: ▪

Probability of a successful well 0.6

▪

Two decision alternatives: ▪

Farm out: A producer is worth $50,000, a dry hole causes no profit or loss

▪

Drilling the well: A dry hole casts $200,000, a hit brings (after all costs) $600,000 Decision Alternatives Drill

Outcome

Probability outcome will occur

Conditiona l monetary value

Farm Out

Expected monetary value

Condition al monetary value


Dry hole

0.4

-$200,000

-$80,000

0

0

Producer

0.6

+$600,000

+$360,000

+$50,000

+$30,000

■

EMV Decision Rule: ▪

+$280,000

+$30,000

=EMV (drill)

=EMV (farm out)

Fig. 20: Cumulative result for drill decisions

When choosing among several mutually exclusive decision alternatives, select the alternative having the greatest EMV.


Page 40

Characteristics of the EVC ■ Mutually exclusive outcomes ■ Collectively exhaustive outcomes ■ The sum of probabilities for one event must be one ■ Any number of alternatives can be considered ■ Normally values are expressed in monetary profit, therefore “expected monetary value” ■ The EMV does not necessarily have to be a possible outcome


Page 41

Risked DROI EMV Risked _ DROI = EV ( PV _ of _ Investment )

Cf.

DROI =

NPV PV _ of _ Investment

■ Reasonable under limited capital constraints


Page 42

Concerns about the EV Concept ■ ■ ■ ■

Is there a need to quantify risk at all? No benefit seen in using the EV! We don’t have probabilities anyway… Every drilling prospect is unique, therefore we have no repeated trail! ■ Isn’t EV only suitable for large companies? ■ For sure other concerns override EV! ■ “…EMV is not perfect. It is not an oilfinding tool, and it is not (…) the ‘ultimate’ decision parameter.” © Economics and Business Management, University of Leoben Newendorp, Schuyler (2000), p. 119. Cf. Newendorp, Schuyler (2000), p. 71ff.

Page 43

Decision Tree Analysis

Simple Decision Tree Example ■ Decision trees are necessary if sequent decision must be made ■ Decision tree analysis is an extension of the EMV concept Decision Alternatives Drill Possible Outcome

Probability outcome will occur

Outcome

Don‘t Drill


Outcome


Dry hole

0.7

-$50,000

-$35,000

0

0

2 Bcf

0.2

+$100,000

-$20,000

0

0

5 Bcf

0.1

+$250,000

-$25,000

0

0

1.0

EMV = +$10,000

EMV = $0

Fig. 21: Simple decision tree (partially completed)

■ There is no scale to decision trees © Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 127ff.

Page 45

Decision Tree Symbols ■ There exist two different nodes (forks) ▪

Decision node (or activity node) - squares

▪

Chance node (or event node) - circles ▪

Terminal nodes (last chance node of a branch)

Fig. 22: Simple decision tree (partially completed with correct symbols)


Page 46

Decision Tree Completion ■ Associate probabilities to all chance nodes ■ Place the outcome value to all branch ends

Fig. 23: Simple decision tree (completed)

■ Three important rules: ▪ ▪ ▪

Normalization requirement: The sum of all probabilities around a chance node must be 1.0 There are no probabilities around decision nodes The end nodes are mutually exclusive


Page 47

Decision Tree Solution ■ Start at the back of the tree and calculate the EMV for the last chance node. ■ The expected value is written above the node ■ The decision rule for a decision node is to choose the branch with the higher EMV

Fig. 24: Simple decision tree (solved)


Page 48

Case Study: Decision Tree Analysis

Fig. 25: Case Study: Decision Tree


Page 49

Advantages of Decision Tree Analysis ■ The complexity of a decision is reduced ■ Provides a consistent action plan ■ Decision problems of any size can be analysed ■ Forces us to think ahead ■ If conditions change the situation can be re-analysed ■ Logical, straight-forward an easy to use


Page 50

Probability Theory

Concept of Probability ▪

Probability Theory enables a person to make an educated guess

■ Objective Probability 1. Classical approach: ▪ ▪ ▪ ▪ ▪

Derives Probability measures from undisputed laws of nature Requires the identification of the total number of possible outcomes (n) Requires the number of possible outcomes of a wanted event (m) Probability of occurrence of an event: P(A)=m/n Three basic condition must be fulfilled: equally likely, collectively exhaustive and mutually exclusive

2. Empirical approach: ▪ ▪ ▪ ▪

Derives Probability measures from the events long-run frequency of occurrence The observation is random A large number of observations is necessary The following mathematical relationship is valid: P(A)=limnÆ∞ (m/n)

■ Subjective Probability ▪

Based on impressions of individuals

© Economics and Business Management, University of Leoben Cf. Mian (2002b), p. 84ff.

Page 52

Probability Rules ■

Complementation Rule: ▪

■

P(A)+P(Ā)=1

Addition Rule:

Fig. 39: Vann diagram showing two mutually exclusive events

▪ For simultaneous trails 1. Events are mutually exclusive: ▪ ▪

P(A∪B)=P(A)+P(B) P(A∩B)=0

2. Events are partly overlapping: ▪ ▪

■

P(A∪B)=P(A)+P(B)-P(A∩B) P(A∩B)=P(A)+P(B)-P(A∪B) (=P(AB))

Fig. 40: Vann diagram showing of partly overlapping events

Multiplication Rule: ▪ ▪

For consecutive trails Independent events: ▪

▪

P(AB)=P(A) x P(B)

Dependent events: ▪

P(AB)=P(A) x P(B|A)

© Economics and Business Management, University of Leoben Cf. Mian (2002b), p. 84ff. and http://cnx.org/content/m38378/latest/?collection=col11326/latest

Fig. 41: Vann diagram showing union two events

Page 53

Example “Addition Rules” ■

Assume 50 wells have been drilled in an area with blanket sands. The drilling resulted in (a) 8 productive wells in Zone A, (b) 11 productive wells in Zone B, and (c) 4 productive wells in both Zones. With the help of Venn diagrams and probability rules, calculate the following: 1. 2. 3. 4.

■

Number of wells productive in Zone A only, Number of wells productive in Zone B only, Number of wells discovered, and Number of dry holes.

Solution: ▪ 1. 2. 3. 4.

n(S)=50; n(A)=8; n(B)=11; n(A∩B)=4 n(A∩B)=n(A) - n(A∩B)=8 - 4=4 n(Ā∩B)=n(B) - n(A∩B)=11 - 4=7 n(A∪B)= n(A) + n(B) - n(A∩B)=8+11 - 4=15 n(S) - n(A∪B)=50 - 15=35


Fig. 42: Vann diagram for example “Addition Rules”

Page 54

Example “Multiplication Rules” ■ 10 prospective leases have been acquired. Seismic surveys conducted on the leases show that three of the leases are expected to result in commercial discoveries. The leases have equal chances of success. If drilling of one well is planned for each lease, calculate the probability of drilling the first two wells as successful discoveries. ■ Solution: ▪

W1 is the first, W2 the second well.

▪

P(W1)=3/10

▪

P(W2|W1)=2/9

▪

P(W1W2)= 3/10 x 2/9=6,67%


Page 55

Bayes’ Rule ■ Beyesian analysis addresses the probability of an earlier event conditioned on the occurrence of a later event P( Ai B ) =

■ Where: ▪ ▪

P (B Ai )⋅ P( Ai )

∑ P(B A )⋅ P( A ) k

i =1

i

i

P(Ai|B)=posterior probabilities and P(Ai)=prior event probabilities

■ Bayes’ theorem is used if additional information results in revised probabilities. © Economics and Business Management, University of Leoben Cf. Mian (2002b), p. 84ff.

Page 56

Theoretical Example “Bayes’ Rule” ■

■

One box contains 3 green and 2 red pencils. A second box contains 1 green and 3 red pencils. A single fair die is rolled and if 1 or 2 comes up, a pencil is drawn from the first box; if 3, 4, 5 or 6 comes up, then a pencil is drawn from the second. If the pencil drawn is green, then what is the probability it has been from the first box? Solution: ▪ ▪ ▪

P(B1)=1/3 and P(B2)=2/3 In box 1: P(G)=3/5 and P(R)=2/5 In box 2: P(G)=1/4 and P(R)=3/4

⎛3⎞ ⎛1⎞ ⎜ ⎟⋅⎜ ⎟ P(G Bi )⋅ P(Bi ) 6 ⎝5⎠ ⎝3⎠ P (Bi G ) = k = = 54,55% = ⎛ 3 ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞ ⎛ 2 ⎞ 11 ( ) ( ) P G B P B ⋅ ⎜ ⎟⋅⎜ ⎟ + ⎜ ⎟⋅⎜ ⎟ ∑ i i ⎝5⎠ ⎝3⎠ ⎝ 4⎠ ⎝ 3⎠ i =1


Fig. 43: Probability tree for the theoretical example “Bayes’ Rule”

Page 57

Page 57

Offshore Concession Example “Bayes’ Rule” ■ We have made a geological and engineering analysis of a new offshore concession containing 12 seismic anomalies all about equal size. We are uncertain about how many of the anomalies will contain oil and hypothesize several possible states of nature as follows: ▪ ▪

E1: 7 anomalies contain no oil and 5 anomalies contain oil E2: 9 anomalies contain no oil and 3 anomalies contain oil

■ Based on the very little information we have, we judge that E2 is twice as probable as E1. ■ Then we drill a wildcat and it turns out to be a dry hole. The question is: “How can this new information be used to revise our initial judgement of the likelihood of the hypothesized state of nature?” © Economics and Business Management, University of Leoben Cf. Newendorp, Schuyler (2000), p. 318ff.

Page 58

Offshore Concession Example “Bayes’ Rule”

Fig. 44: Solution of the offshore concession example


Page 59

Probability Distributions ■

Stochastic or random variable: ▪

■

The pattern of variation is described by a probability distribution

Probability distributions: ▪

Discrete (Stochastic variable can take only a finite number of values) Widely used in petroleum economics: ▪ ▪ ▪ ▪

▪ ▪

Binomial Multinomial Hypergeometric Poisson

Continuous (Stochastic variable can take infinite values) Widely used in petroleum economics: ▪ ▪ ▪ ▪

Normal Lognormal Uniform Triangular


Page 60

Binomial Distributions ■ ■

Applicable if an event has two possible outcomes n! Equations: C xn = P( x ) = C xn ⋅ p x ⋅ q n − x ▪ ▪ ▪ ▪ ▪ ▪

■

x!⋅(n − x )! Where, P(x)=probability of obtaining exactly x successes in n trails, p=probability of success, q=probability of failure, n=number of trails considered and x=number of successes

Example: ▪

A company is planning six exploratory wells with an estimated chance of success of 15%.What is the probability that (a) the drilling will result in exactly two discoveries and (b) there will be more than three successful wells.

Fig. 45: Solution of the “six exploratory wells” example


Page 61

Multinomial Distributions ■

Applicable if an event has more than two possible outcomes

■

Equations:

P (S ) =

N! P1k1 P2k2 ...Pmkm k1!k 2 !...k m !

▪

Where,

▪

P(S)=probability of the particular sample,

▪

p=probabilities of drawing types 1, 2, …m from population,

▪

N=k1+k2+…+km=size of sample,

▪

k1, k2, …,km=total number of outcomes of type 1, 2, …,m

▪

m=number of different types


Page 62

Multinomial Distributions - Example 1/2 ■

■

In a certain prospect, the company has grouped the possible outcomes of an exploratory well into three general classes as (a) dry hole (zero reserve), (b) discovery with 12 MMBbls reserves, and (c) discovery with 18 MMBbls reserves. Each of these categories probabilities of 0.5, 0.35, and 0.15 were assigned, respectively. If the company plans to drill three additional wells, what will be the probabilities of discovering various total reserves with these three additional wells? Solution: ▪ ▪ ▪ ▪

P(S ) = ▪ ▪

m=3; N=3; P1=0.5; P2=0.35; P3=0.15 k1=number of wells giving reserves of zero k2=number of wells giving reserves of 12 MMBbls k3=number of wells giving reserves of 18 MMBbls

N! 3! 3 ⋅ 2 ⋅1 P1k1 P2k2 P3k3 = 0.52 0.351 0.150 = ⋅ 0.25 ⋅ 0.35 ⋅1 = 0.263 k1!k 2 !k3! 2!1!0! 2 ⋅1 ⋅1 ⋅1 Corresponding reserves=2x0+1x12+0x18=12MMbbls Expected reserves=0.263x12MMBbls=3.15MMBbls


Page 63

Multinomial Distributions - Example 2/2 k2

k1

k3

Probability

Reserves

Probability

Exp. Reserves

P(S)

[MMBbls]

Of Reserves ≥

[MMBbls]

3

0

0

0.125

0

1.000

0.000

2

1

0

0.263

12

0.875

3.150

2

0

1

0.113

18

0.613

2.025

1

2

0

0.184

24

0.500

4.410

1

1

1

0.158

30

0.316

4.725

1

0

2

0.034

36

0.159

1.215

0

3

0

0.043

36

---“---

1.544

0

2

1

0.055

42

0.082

2.315

0

1

2

0.024

48

0.027

1.134

0

0

3

0.003

54

0.003

0.182

1,000


20.700

Page 64

Hypergeometric Distributions ■

Application in statistical sampling, if trails are dependent and selected, is from a finite population without replacement

■

Equation: ▪ ▪ ▪ ▪ ▪

■

⎛ C ⎞⎛ N − C ⎞ ⎟ ⎜⎜ ⎟⎟⎜⎜ x ⎠⎝ n − x ⎟⎠ ⎝ P(x ) = ⎛N⎞ ⎜⎜ ⎟⎟ ⎝n⎠

Where, N=number of items in the population C=number of total successes in the population n=number of trails (size of the sample) x=number of successes observed in the sample

Example: ▪

A company has 10 exploration prospects, 4 of which are expected to be productive. What is the probability 1 well will be productive if 3 wells are drilled. Fig. 46: Solution of the “Hypergeometric distribution” example


Page 65

Poisson Distributions ■

Good for representing a particular event over time or space

■

Equation:

■

▪ ▪ ▪ ▪

P(x ) =

λx

e −λ

x! Where, λ=average number of occurrence per interval of time or space x=number of occurrences per basic unit of measure P(x)=probability of exactly x occurrences

Examples:

▪ Assume Poisson distribution! 1. If a pipeline averages 3leaks per year, what is the probability of having exactly 4 leaks next year? 2. If a pipeline averages 5 leaks per 1000 miles, what is the probability of having no leaks in the first 100 miles?

Fig. 47: Solutions of the “Poisson distribution” examples


Page 66

Normal Distributions ■ ■

Linear systems, like NCF, approximate a normal distribution, regardless of the shape of subordinate variables like OPEX, CAPEX, taxes, etc… Probability density function: ▪ ▪ ▪

■

1 e σ 2π

2

Example: ▪

■

Where, μ=mean σ=standard deviation

f (x ) =

1 ⎛ x−μ ⎞ − ⎜ ⎟ 2⎝ σ ⎠

Porosities calculated from porosity logs of a certain formation show a mean porosity of 12% with standard deviation of 2.5%. What is the probability that the formation’s porosity will be (a) between 12% and 15% and (b) greater than 16%.

Solution: ▪

By means of the standard normal derivate (Z) and probability tables

Z=

X −μ

σ

© Economics and Business Management, University of Leoben Cf. Campbell et al. (2007) p. 218ff and Mian (2002b), p. 99ff.

Fig. 48: Solutions of the “Normal distribution” example

Page 67

Lognormal Distributions ■ ■

The occurrence of oil and gas reserves is approximately lognormal distributed (the same as return on investments, insurance claims, core permeability and formation thickness) Y=ln(X) …is normal distributed

Fig. 49: Lognormal distribution


Page 68

Uniform Distributions ■

Equal probability between a minimum and a maximum

f (x ) =

1 xmax − xmin

Fig. 50: Probability density function and cumulative distribution function of a uniform distribution


Page 69

Triangular Distributions ■ ■

■

Used if an upper limit, a lower limit, and a most likely value can be specified Equation: 2

⎧ ⎛ X−X ⎞ ⎛ X mod − X min ⎞ min ⎟⎟ ⋅ ⎜⎜ ⎟⎟, X min ≥ X ≥ X mod ⎪ ⎜⎜ X X X X − − ⎪ min ⎠ min ⎠ ⎝ max F ( x ) = ⎨ ⎝ mod 2 ⎪ ⎛⎜ X max − X ⎞⎟ ⎛⎜ X max − X mod ⎞⎟ ⎪1 − ⎜ X − X ⎟ ⋅ ⎜ X − X ⎟, X mod ≥ X ≥ X max Example: ⎩ ⎝ max mod ⎠ ⎝ max min ⎠

▪

■

A bit record in a certain area shows the minimum and maximum footage, drilled by the bit to be 100 and 200 feet, respectively. The drilling engineer has estimated, that the most probable value of the footage drilled by a bit will be 130 feet, and the footage which is drilled follows triangular distribution. What is the probability that the bit fails within 110 feet?

Solution:

Xmin=100; Xmod=130; Xmax=200; X=110

⎛ X − X min ⎞ ⎟⎟ F ( x ) = ⎜⎜ ⎝ X mod − X min ⎠

2

2

⎛ X − X min ⎞ ⎛ 110 − 100 ⎞ ⎛ 130 − 100 ⎞ ⎟⎟ = ⎜ ⋅ ⎜⎜ mod ⎟ ⋅⎜ ⎟ = 0.033 = 3.33% ⎝ X max − X min ⎠ ⎝ 130 − 100 ⎠ ⎝ 200 − 100 ⎠


Fig. 51: Probability density function and cumulative distribution function of a triangular distribution

Page 70

Tests of Goodness of Fit ■ With these tests one can analyse whether a sample emanates from a certain population or not. ■ Chi-squared-Test

For continuous and discrete data Need to define bins

■ Kolmogoroff-Smirnow-Test

For continuous No need to define bins

■ Anderson-Darling-Test

For continuous No need to define bins

■ Root-Mean-Square-Error

For continuous and discrete data No need to define bins

■ The probability of a sample data drawn from a certain distribution is measured by P-values (called observed significance level)

© Economics and Business Management, University of Leoben Cf. Mian (2002b), p. 99ff and PalisadeCorporation (2002), p. 148ff.

Page 71

Risk Analysis

Risk Management in E&P Projects ■ Example for key points of a risk management policy:

Risk management is an integrated part of project management Every project faces risks from the very beginning The ability to influence and manage risk is higher the earlier identified Risk management supports the achievement of the project’s objectives The project manager – and development manager in case of composite projects – is accountable for managing project’s risks Risk management is a continuous process The selective application of risk management tools supports risk management Proper risk management involves multi-discipline teams Taking calculated risk consciously generates value Risk can be quantified by multiplying the probability that the unfavourable event happens with the severity (financial exposure) of possible consequences Risk auditing is subject to project peer reviewing

■ In risk analysis one can distinguish between:

Qualitative risk analysis Quantitative risk analysis


Page 73

Qualitative Risk Analysis ■ Risk management is understood as

Identifying potential project threats, Reducing the probability that negative events occur (prevention), and Minimizing the impact of the occurrence of negative events (mitigation).

■ The process: Id ic tif en n io at

M on ito

rin g

Policy


As

se ss m

en t

Standards

Re Pla spon nn se ing

Page 74

Bow-Tie Diagram

Fig. 51a: Bow-Tie Diagram

Bow-tie diagrams are used for in depth analysis of major risk issues. Especially when the cause-effect-chain of a risk issue is too complicated to be overlooked due to multiple threats, consequences, and barrier opportunities, bow-ties reduce the complexity and help to understand the coherence of the risk issue. © Economics and Business Management, University of Leoben

Page 75

Risk Matrix (for projects) Probability

Consequence

Never heard of in Heard of in E&P E&P industry industry

Cost

Schedule

Scope

>= EUR 10 mn

> 6 months delay

Total change in project scope or leading to desastrous quality

1

Catastrophic

>= EUR 2 mn up to < 10 mn

2 - 6 months delay

Major change in project scope or leading to bad project quality

2

Major

>= EUR 100.000 up to < 2 mn

2 week - 2 month delay

Moderate change in project scope or leading to inferior quality

3

Moderate

>= EUR 10.000 up to < 100.000

2 days - 2 weeks delay

Minor change in project scope or leading to inferior quality

4

Minor

< EUR 10.000

< 2 days delay

Marginal change in project scope and quality

5

Slight

No consequence

No consequence

No consequence

Has occured in company

Has occured several times in company

Occurs frequently in company

A

B

C

D

E

Improbable

Unlikely

Seldom

Probable

Frequent

High

Medium

Low

Fig. 51b: Bow-Tie Diagram


Page 76

Basic Problems of Risk Analysis ■ ■ ■ ■ ■

Incomplete understanding Not independent trails Little data or experience Price instability Geology as an art

■ These factors make the judgement of probabilities in petroleum exploration difficult.


Page 77

Judging Probability of Recovery ■ What is the wildcat success ratio? ■ Derive from past success rates ■ Calculate the geologic risk factor Considered factors:

Source Migration Timing Thermal Maturity Reservoir (porosity and permeability) Trap Seal

■ P(wildcat discovery)=P(trap) x P(source) x P(porosity and permeability) x etc.


Page 78

Three Level Estimation of Risk

■ Is used instead of two discrete levels: Dry hole Average discovery

■ The three levels are: Low Medium High


Page 79

Monte Carlo Simulation ■ Numerical procedure ■ Random numbers provide computer-aided an artificial sample ■ Pioneers:

Earl George Buffon John von Neumann

■ Software packages in use:

@Risk Cristal Ball


Page 80

Monte Carlo Process ■ Workflow:

Define variables

Develop the deterministic projection model

Sort the input variables in two groups

Define distributions for random numbers

Perform the simulation trails

Calculate EMV and preparing graphical displays

Input Data

Sampling of Input Data via Probability Distributions

Computing Outputs (e.g.: NPV)

i=n?

no

yes Evaluation of Output Probability Distribution

In Monte Carlo simulations risky events and values are modelled by means of probability distributions and repeating relevant calculations a sufficiently number of times using random numbers in order to end up with calculated probability distributions for output variables. © Economics and Business Management, University of Leoben Cf. Zettl (2000), p. 43 and Newendorp, Schuyler (2000), p. 397ff.

Result Interpretation and Decision

Page 81

Random Numbers ■ Sources of random numbers:

Mechanical experiment Noise in nature (really random) Table of random number (boring book!) (Pseudo) Random number generator (pseudo random)

■ Uniformly distributed numbers between 0 and 1 ■ If computers offer to set the “seed” value, the random numbers are reproducible


Page 82

Sampling ■ Monte Carlo Sampling

Fig. 52: Monte Carlo Sampling

■ Latin Hypercube Sampling

Fig. 53: Latin Hypercube Sampling


Page 83

Result Interpretation ■ The result is a probability distribution of the output value ■ Received statistical measures:

Measures of location: mean, median, mode… Measures of dispersion: range, interquantile range, standard deviation, variance… Measures of shape: modality, skewness, kurtosis…

Fig. 57: Hidden relationship between input and output shape of distribution

Fig. 58: Possible output probability distribution of a Monte-Carlo-Simulation


Page 84

Main Fields of Application ■ Risked Costs ■ Risked Economics ■ Risked Schedule


Page 85

Selected Measures of Risk ■ Risk Adjusted Capital (RAC)

Maximum amount of money that can be lost (with a certain confidence)

■ Value-at-Risk (VaR)

Difference between the mean and the maximum amount of money that can be lost (with a certain confidence)

■ Return on Risk Adjusted Capital (RORAC)

Relation between expected profit (e.g. mean) and the maximum amount of money that can be lost (with a certain confidence)

Fig. 59: Selected Measures of Risk

■ Different definition in literature! © Economics and Business Management, University of Leoben Cf. Gleißner (2004) and Homberg, Stephan (2004)

Page 86

Risked Schedules ■ Stochastic Inputs:

Durations of project tasks Start dates of project tasks Predecessor links Calendar Global variables

■ Outcome:

Fig. 59a: Risked Gantt Chart

Ranges, P10, P50, P90, and expected end dates Probability of meeting a deterministic schedule

Fig. 59b: Important issue in risking schedules

Within probabilistic schedule analyses, a closer look on the project schedule is taken by means of a Monte Carlo simulation. © Economics and Business Management, University of Leoben

Page 87

Sensitivity Analyses

Sensitivity Analysis ■ A way to handle uncertainty ■ Demonstrates the significance of uncertain elements in economic evaluations ■ Typical items for sensitivity analysis:

Investment

Operating costs

Reserve size

Production rates

Prices

etc.

© Economics and Business Management, University of Leoben Cf. Allen, Seba (1993), p. 213.

Page 89

Deterministic Sensitivity Analysis ■

Where the range of outcome is known but not the probability

■

Input parameters in an economic model are changed over a certain range

■

Y-axis represents an economic yardstick

■

X-axis represents the fractional change of the input parameters

■

Does not depict interrelations between input parameters Fig. 60: Spider Diagram

© Economics and Business Management, University of Leoben Cf. Allen, Seba (1993), p. 213ff.

Page 90

Probabilistic Sensitivity Analysis ■

The input parameters of an economic valuation model have probability distribution

■

Correlation- or Regression-Coefficients of every input parameter and the output are calculated

■

Visualisation is normally done in a tornado diagram

■

Does depict interrelations between input parameters

Fig. 61: Correlation diagram

Fig. 62: Tornado Diagram


Page 91

Literature

Allen, F.H.; Seba, R. (1993): Economics of Worldwide Petroleum Production, Tulsa: OGCI Publications. Campbell Jr., J.M.; Campbell Sr., J.M.; Campbell, R.A. (2007): Analysing and Managing Risky Investments, Norman: John M. Campbell. Clo, A. (2000): Oil Economics and Policy, Boston/Dordrecht/London: Kluwer Academic Publisher. Dahl, C.A. (2004): International Energy Market - Understanding Pricing, Politics and Profits, Tulsa: Penn Well. Deffeyes, K.S. (2005): Beyond Oil - The view from Hubbert's Peak, New York: Hill and Wang. Dias, M.A.G. (1997): The Timing of Investment in E&P: Uncertainty, Irreversibility, Learning, and Strategic Considerations. In: 1997 SPE Hydrocarbon Economics and Evaluation Symposium. Dallas, TX: SPE. Dixit, A.K.; Nalebuff, B.J. (1997): Spieltheorie für Einsteiger - Strategisches Know-how für Gewinner, Stuttgart: Schäffer-Poeschel Verlag. Gleißner, W. (2004): Die Aggregation von Risiken im Kontext der Unternehmensplanung. In: Zeitschrift für Controlling und Management. Vol. 48, Nr. 5: S. 350-359. Homburg, C.; Stephan, J. (2004): Kennzahlenbasiertes Risikocontrolling in Industrie und Handelsunternehmen. In: Zeitschrift für Controlling und Management. Vol. 48, Nr. 5: S. 313-325. Johnston, D. (2003): International Exploration Economics, Risk, and Contract Analysis, Tulsa: Pann Well. Laux, H. (2003): Entscheidungstheorie. 5. Auflage, Berlin Heidelberg: Springer. Mian, A.M. (2002a): Project Economics and Decision Analysis - Volume I: Deterministic Models, Tulsa: PennWell. Mian, A.M. (2002b): Project Economics and Decision Analysis - Volume II: Probabilistic Models, Tulsa: PennWell. Newendorp, P.; Schuyler, J. (2000): Decision Analysis for Petroleum Exploration. Vol. 2nd Edition, Aurora: Planning Press. PalisadeCorporation (2002): @Risk - Advanced Risk Analysis for Spreadsheets. Vol. Version 4.5, Newfield: Palisade Corporation. Zettl, M. (2000): Application of Option Pricing Theory for the Valuation of Exploration and Production Projects in the Petroleum Industry. Leoben: Montanuniversität Leoben, Dissertation.


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Advanced Petroleum Economics Staber

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