OCS Study 

MMS 2004-016 

 

Coastal Marine Institute 

Fiscal System Analysis: 

Concessionary and Contractual Systems 

Used in Offshore Petroleum Arrangements 

Cooperative Agreement 

Coastal Marine Institute 

Louisiana State University 

U.S. Department of the Interior 

Minerals Management Service 

Gulf of Mexico OCS Region 
U.S. Department of the Interior Cooperative Agreement 

Minerals Management Service Coastal Marine Institute 

Gulf of Mexico OCS Region Louisiana State University 

OCS Study 

 MMS 2004-016 

 

Coastal Marine Institute 

Fiscal System Analysis: 

Concessionary and Contractual Systems 

Used in Offshore Petroleum Arrangements 

Authors 

Mark J. Kaiser 

Allan G. Pulsipher 

March 2004 

Prepared under MMS Contract 

1435-01-01-30951-18178 

by 

Center for Energy Studies 

Louisiana State University 

Baton Rouge, Louisiana 70803 

Published by 
iii 

DISCLAIMER

This report was prepared under contract between the Minerals Management Service 

(MMS) and Louisiana State University’s Center for Energy Studies. This report has been 

technically reviewed by MMS. Approval does not signify that the contents necessarily 

reflect the view and policies of the Service, nor does mention of trade names or 

commercial products constitute endorsement or recommendation for use. It is, however, 

exempt from review and compliance with MMS editorial standards. 

REPORT AVAILABILITY 

Extra copies of the report may be obtained from the Public Information Office (Mail Stop 

5034) at the following address: 

 

 U.S. Department of the Interior 

 Minerals Management Service 

 Gulf of Mexico OCS Region 

 Public Information Office (MS 5034) 

 1201 Elmwood Park Boulevard 

 New Orleans, Louisiana 70123-2394 

 Telephone Number: 1-800-200-GULF 

 1-504-736-2519 

CITATION 

Suggested citation: 

Kaiser, M.J. and A.G. Pulsipher. 2004. Fiscal system analysis: Concessionary and 

contractual systems used in offshore petroleum arrangements. U.S. Department 

of the Interior, Minerals Management Service, Gulf of Mexico OCS Region, New 

Orleans, La. OCS Study MMS 2004-016. 78 pp. 
v 

ACKNOWLEDGMENTS 

The advice, patience, and critical comments of Radford Schantz, Kristen Strellec, and 

Stephanie Gambino are gratefully acknowledged. Radford Schantz suggested the initial 

formulation of the problem considered in this paper, and special thanks also goes to 

Thierno Sow of the MMS for generating the cash flow parameters for the Na Kika and 

the Girassol field developments. This paper was prepared on behalf of the U.S. 

Department of the Interior, Minerals Management Service, Gulf of Mexico OCS region, 

and has not been technically reviewed by the MMS. The opinions, findings, conclusions, 

or recommendations expressed in this paper are those of the authors, and do not 

necessarily reflect the views of the Minerals Management Service. Funding for this 

research was provided through the U.S. Department of the Interior and the Coastal 

Marine Institute, Louisiana State University. 
vii 

ABSTRACT 

The manner in which the fiscal terms and parameters of a contract impact system 

measures are complicated and not well understood, and so the purpose of this report is to 

quantify the influence of private and market uncertainty on concessionary and contractual 

fiscal systems. An analytic framework is developed that couples a cash flow simulation 

model with regression analysis to construct numerical functionals associated with the 

fiscal regime. A meta-modeling approach is used to derive relationships that specify how 

the present value, rate of return, and take statistic vary as a function of the system 

parameters. The critical assumptions involved in estimation, the uncertainty associated 

with interpretation, and the limitations of the statistics are also examined. 

The report is divided into two parts. In Chapter 1, the concessionary system is examined 

and the deepwater Gulf of Mexico Na Kika field development is considered as a case 

study. In Chapter 2, the contractual fiscal system is considered with the deepwater 

Angola Girassol field development as a case study. 
ix 

TABLE OF CONTENTS 

 Page 

List of Figures.................................................................................................................. xiii 

List of Tables .....................................................................................................................xv 

Chapter 1: Concessionary Systems 

1.1. Introduction..............................................................................................................1 

1.2. The Stages of an Oil and Gas Venture.....................................................................3 

1.3. Fiscal System Classification ....................................................................................5 

 1.3.1. Concessionary Systems..................................................................................5 

 1.3.2. Fiscal Components of Concessionary Systems..............................................5 

1.4. Cash Flow Analysis of a Royalty/Tax Fiscal Regime .............................................6 

 1.4.1. After-Tax Net Cash Flow Vector...................................................................6 

 1.4.2. Cash Flow Components .................................................................................6 

1.5. Economic and System Measures .............................................................................8 

 1.5.1. Economic Indicators ......................................................................................8 

 1.5.2. The Take Statistic ..........................................................................................9 

 1.5.3. Annual Government and Contractor Take...................................................10 

 1.5.4. Cumulative Discounted Government and Contractor Take.........................11 

 1.5.5. The Characteristics of Take .........................................................................12 

1.6. Meta-Modeling Methodology................................................................................14 

1.7. A Functional Analytic Approach to System Measures..........................................15 

 1.7.1. Development Scenario.................................................................................15 

 1.7.2. Regression Model Results............................................................................16 

 1.7.3. Valuation Strategy .......................................................................................17 

 1.7.4. Sensitivity Analysis .....................................................................................17 

1.8. Elements of Fiscal Design .....................................................................................18 

 1.8.1. Equivalent Fiscal Regimes...........................................................................18 

 1.8.2. Feasibility Constraints .................................................................................19 

 1.8.3. Feasible Domain ..........................................................................................20 

 1.8.4. Progressive Fiscal Regimes .........................................................................21 
x 

TABLE OF CONTENTS (continued) 

 Page 

1.9. Deepwater Gulf of Mexico Case Study: Na Kika..................................................22 

 1.9.1. Na Kika Deepwater Development ...............................................................22 

 1.9.2. Development Scenario.................................................................................22 

 1.9.3. Deepwater Royalty Relief............................................................................23 

 1.9.4. Regression Model Results............................................................................23 

 1.9.5. The Impact of Royalty Relief ......................................................................25 

1.10. Conclusions............................................................................................................26

Chapter 2: Contractual Systems 

2.1. Introduction............................................................................................................27

2.2. The Licensing and Negotiation Process.................................................................28 

2.3. Background Information........................................................................................32 

 2.3.1. Contractual Systems.....................................................................................32 

 2.3.2. Fiscal Components of Contractual Systems ................................................32 

2.4. Cash Flow Analysis of a Production Sharing Agreement .....................................32 

 2.4.1. After-Tax Net Cash Flow Vector.................................................................33 

 2.4.2. Cash Flow Components ...............................................................................33 

 2.4.3. Sliding Scales...............................................................................................36 

2.5. Economic and System Measures ...........................................................................36 

 2.5.1. Economic Indicators ....................................................................................36 

 2.5.2. Government and Contractor Annual Take...................................................37 

 2.5.3. Government and Contractor Discounted Take ............................................38 

2.6. Generalized Fiscal System Analysis......................................................................38 

 2.6.1. Terms of a Contract .....................................................................................38 

 2.6.2. System Functionals ......................................................................................39 

 2.6.3. Meta-Modeling Methodology......................................................................40 

2.7. A Functional Analytic Approach to System Evaluation........................................42 

 2.7.1. Development Scenario.................................................................................42 

 2.7.2. Regression Modeling Results ......................................................................42 

 2.7.3. Profit Oil Sliding Scale ................................................................................44 
xi 

TABLE OF CONTENTS (continued)

 Page 

2.8. Deepwater Angola Case Study: Girassol...............................................................45 

 2.8.1. The Angola Play ..........................................................................................45 

 2.8.2. Angolan Production Sharing Agreements ...................................................45 

 2.8.3. Block 17 Deepwater Development ..............................................................46 

 2.8.4. Development Scenario.................................................................................47 

 2.8.5. The Design Space ........................................................................................47 

 2.8.6. Regression Model Results............................................................................49 

2.9. Conclusions............................................................................................................52 

References ....................................................................................................................53 

Appendix A Concessionary Systems Figures and Tables ..............................................57 

Appendix B Contractual Systems Figures and Tables ...................................................65 
xiii 

LIST OF FIGURES 

Figure Description Page 

A.1 The Na Kika Field Development ...............................................................59 

A.2 The Na Kika Host Platform and Subsea Well Configuration....................59 

B.1 Typical Bid Evaluation and Negotiation Process in Licensing 

 Agreements ............................................................................................67 

B.2 Angola Oil License Blocks ........................................................................68 

B.3 The Girassol FPSO ....................................................................................69 

B.4 The Girassol Development Plan ................................................................70 
xv 

LIST OF TABLES

Table Description Page

A.1 Projected Production, Capital Expenditures, and Operating 

 Expenditures for a Hypothetical 40 MMbbl Field................................60 

A.2 Regression Models for Contractor Take, Present Value, and Internal 

 Rate of Return for a Hypothetical 40 MMbbl Field .............................60 

A.3 Projected Production, Capital Expenditures, and Operating 

 Expenditures for the Na Kika Field Development................................61 

A.4 The Design Space of the Na Kika System Parameters ..............................62 

A.5 The Impact of Royalty Relief on Contractor Take, Present Value, and 

 Internal Rate of Return for the Na Kika Field Development................62 

A.6 Statistical Data for the Na Kika Regression Models .................................63 

B.1 Projected Production, Capital Expenditures, and Operating 

 Expenditures for a Hypothetical 40 MMbbl Field................................71 

B.2 The Design Space of the System Parameters.............................................71 

B.3 Contractor Take, Present Value, and Internal Rate of Return for a 

 Hypothetical 40 MMbbl Field–Model I Results...................................72 

B.4 Contractor Take, Present Value, and Internal Rate of Return for a 

 Hypothetical 40 MMbbl Field–Model II Results..................................73 

B.5 Projected Production, Capital Expenditures, and Operating 

 Expenditures for the Girassol Field Development................................74 

B.6 The Design Space for the Girassol Field Development.............................75 

B.7 Angolan Profit Oil Split (1990) .................................................................75 

B.8 A Generalized Profit Oil Split Functional .................................................76 

B.9 Girassol Regression Model I Results.........................................................76 

B.10 Girassol Regression Model II Results........................................................77 

B.11 Girassol Regression Model III Results ......................................................78 
1 

CHAPTER 1: CONCESSIONARY SYSTEMS 

1.1. Introduction 

The economics of the upstream petroleum business is complex and dynamic. Each year 

anywhere between 25-50 countries in the world offer license rounds; 20-30 countries 

introduce new model contracts or fiscal regimes; and nearly all countries revise their tax 

laws during their annual budgetary process. There are more fiscal systems in the world 

than there are countries because 

• Numerous vintages of contracts may be in force at any one time, 

• Countries typically use more than one arrangement, and 

• Contract terms are often negotiated and renegotiated as political and economic 

conditions change, or as better information becomes available. 

The focus of fiscal system analysis depends upon your perspective. From the host 

government’s point of view, focus is usually maintained on the division of profit (take) 

between the contractor and government. From the operator’s perspective, economic 

measures such as the present value and rate of return describing the expected profitability 

of the project are of primary interest. 

There is a wide degree of uncertainty inherent in the computation of any economic or 

system measure associated with a field, and the only time that take, present value, or rate 

of return can be calculated with certainty is after the field has been abandoned and all the 

relevant revenue and cost data made public. Only in the case of “perfect” information, 

when all revenue, cost, royalty and tax data is known for the life of the field can 

profitability and the division of profits be reliably established. 

Unfortunately, as most casual observers of the oil/gas industry are aware, it is rare indeed 

when the net cash flow from a real asset is available outside the firm, and rarer still if it is 

made public. Cash flow and cost information is proprietary. Operators on federal leases 

are required to report production data to the government on a well basis, and so the 

revenue and royalty stream on a structure, field, and/or property basis can be readily 

estimated, but the revenue stream is only half of the equation, and the all-important and 

ever-elusive cost data – including capital and operating expenditures, depreciation 

schedules, financing costs, interest on payments, decommissioning cost, etc. – need to be 

inferred. The reliability of the inference represents one of the primary limitations 

associated with the accurate computation of the economic and system measures 

associated with a field. 

The computation of economic and system measures requires each of the revenue and 

expense items to be estimated and forecast over the life of the project. Imperfect 

information, incomplete knowledge, and private/market uncertainty dictate the terms of 

the correspondence. The manner in which these forecasts are performed, relying on both 

art and science, opinion and fact, rules-of-thumb and advanced quantitative modeling, 
2 

depends critically on the assumptions of the user. Most of the relevant economic 

conditions of a fiscal regime, regardless of its complexity, can be modeled, and thus the 

sophistication of the contract terms themselves usually do not represent an impediment to 

the analysis. The uncertainty is elsewhere. 

Several sources of uncertainty exist: 

• Geologic uncertainty, 

• Production uncertainty, 

• Price uncertainty, 

• Cost uncertainty, 

• Investment uncertainty, 

• Technological uncertainty, 

• Strategic uncertainty. 

A detailed and realistic field description is the first and most important estimate that must 

be made. The size, shape, productive zones, fault blocks, drive mechanisms, etc. of the 

reservoir must be estimated with as much accuracy as possible since they determine the 

capacity of the structure and the required number and location of wells. Estimates of 

production rates can be based on geologic conditions at the reservoir level, decline curve 

analysis or similar techniques. Forecast production is only used as a guideline, however, 

since investment activity can dramatically alter the form of the production curve as well 

as recoverable reserves. Hydrocarbon price, development cost, technological 

improvements, and demand-supply relations impact the revenue of a lease and investment 

planning. Strategic objectives of a corporation are generally unobservable, 

nonquantifiable, and can vary dramatically over time. 

The types of estimates that can be performed depend on the stage of development of the 

project and the design and planning information available. Initial cost and production 

estimates typically fall between “order-of-magnitude” estimates (on the order of 25%-

50% accuracy) and “conceptual development plan” estimates (on the order of 15%-25% 

accuracy). The uncertainty associated with the value of the system measures will almost 

always fall within a broad range, and in the worst case, the range itself may be unknown. 

The purpose of this Chapter is to develop an analytic framework to quantify the influence 

of private and market uncertainty on the economic and system measures associated with a 

field. A “meta-modeling” approach is employed to construct regression models of the 

system measures in terms of various exogeneous, fiscal, and user-defined parameters. In 

meta-modeling, a model of the system is first constructed, and then meta data is 

generated for variables simulated within a specified design space. Linear models are then 

constructed from the meta data. Meta-modeling is not a new construct, but as applied to 

fiscal system analysis is new, useful, and novel, being an especially good way to 

understand the structure and sensitivity of fiscal systems to various design parameters. 

The outline of the Chapter is as follows. In Chapter 1.2 and Chapter 1.3, background 

material on the basic stages of an oil and gas venture and the two primary fiscal systems 
3 

of the world’s petroleum licensing arrangements are briefly outlined. In Chapter 1.4, the 

general framework of cash flow analysis governed by a royalty/tax fiscal regime is 

developed. The take measure is defined and critically examined in Chapter 1.5, and in 

Chapter 1.6, the meta-modeling approach is outlined. The basic elements of fiscal system 

design are presented in Chapter 1.7 for a hypothetical oil field, and in Chapter 1.8, formal 

definitions of equivalent and progressive fiscal regimes are provided. The notion of a 

feasible domain is also introduced. In Chapter 1.9, the Gulf of Mexico deepwater field 

development Na Kika is presented as a case study, and in Chapter 1.10, conclusions 

complete the Chapter. 

1.2. The Stages of an Oil and Gas Venture 

A model oil and gas venture can be considered to consist of distinct stages separated in 

time as follows (Gerwich, 2000): 

I. Leasing, 

II. Exploration, 

III. Appraisal, 

IV. Development, 

V. Production, 

VI. Decommissioning. 

In the United States, an oil company acquires mineral rights from the government or 

private landowner, while outside the U.S. a host government typically grants a license 

(lease, or block area) or enters into a contractual arrangement with an operator to develop 

a field without owning the mineral resources. The contractor or operator refers to an oil 

company, contractor group, or consortium. The host government is represented by a 

national oil company, an oil ministry, or both. 

After acquiring leasing rights, the oil company will carry out geological and geophysical 

investigations such as seismic surveys and core borings. Seismic acquisition is usually 

performed by contractors who specialize in providing the service to industry. The 

company’s geophysical staff process and interpret the data in-house or it may be 

contracted out to another contractor or the same contractor who acquired the data. If a 

play appears promising, exploratory drilling is carried out. A drill ship, semi-submersible, 

jack-up, or floating vessel will be used depending on the location of the field, rig supply 

conditions, and market rates. The purpose of exploration is to discover the presence of oil 

and gas. 

If hydrocarbons are discovered, further delineation wells may be drilled to establish the 

amount of recoverable oil, production mechanism, and structure type. The number of 

wells required to develop the reserves depends on a tradeoff between risked capital and 

expected production. Generally speaking, the more wells a company is willing to drill 

(risked capital), the faster the rate of extraction and revenue generation. Development 

planning and feasibility studies are performed and the preliminary development plan will 

form the basis for cost estimation. 
4 

If the appraisal is favorable, and a decision is made to proceed, then financial 

arrangements will need to be made and the next stage of development planning 

commences using site-specific geotechnical and environmental data. Studies are carried 

out using one or more engineering contractor-construction firms, in-house teams, and 

consultants. Once the design plan has been selected and approved, the design base is said 

to be “frozen,” and venders and contractors are invited to bid for tender. Environmental 

impact statements are prepared and submitted to the appropriate government agencies. 

The operator lets contracts for the development according to the following segments: 

Design of the substructure, 

Design of the deck, 

Design of the pipeline, 

Fabrication of the substructure, 

Fabrication of the deck, 

Procurement of pipe, 

Procurement of process equipment, 

Installation of platform, 

Installation of equipment, 

Installation of pipeline, 

Hookup, 

Production drilling. 

Several of these activities may be combined and awarded to one contractor depending 

upon the type and location of activity, the requirements of the contract, contractor 

specialization, and the supply and demand conditions in the region at the time. 

Following the installation, hookup, and certification of the platform, development drilling 

is carried out and production started after a few wells are completed. Subsea completions 

may be used to produce from appraisal wells before field development. Early production 

is important to generate cash flow to relieve some of the financial burden of the 

investment. Workovers must be carried out periodically to ensure the continued 

productivity of the wells, and water/gas injection may be used to enhance productivity at 

a later time. 

At the end of the useful life of the field, which for most structures occurs when the 

production cost of the facility is equal to the production revenue (the so-called “economic 

limit”), a decision is made to decommission. Decommissioning represents a liability as 

opposed to an investment, and so the pressure for an operator to decommission a 

structure is not nearly as strongly driven as installation activities. In most instances, 

properties are divested and decommissioning liability is transferred to the new owner 

(although liability is never completely dissolved by this action). For a successful removal, 

operators generally begin planning one or two years prior to the planned date of 

decommissioning. 

 
5 

1.3. Fiscal System Classification 

1.3.1. Concessionary Systems: Governments decide whether resources are privately 

owned or whether they are state property. Under a concessionary system (also called a 

royalty/tax system), the government or land owner will transfer title of the minerals to the 

oil company which is then subject to the payment of royalties and taxes. The royalty and 

tax rates are normally specified in the country or state’s legislation (and are thus 

transparent) and are the same for all companies (no negotiations involved). The fiscal 

terms of royalty/tax systems are not necessarily “fixed,” however, because governments 

frequently change1 their petroleum laws and taxation levels, and in some instance, terms 

of a royalty/tax system may be subject to negotiation. Sliding scale features and various 

levels of taxation may exist peculiar to one country or another; e.g., see (Barrows, 1983; 

Barrows, 1994; Johnston, 1994b), but most royalty/tax systems are fairly straightforward 

to understand. 

1.3.2. Fiscal Components of Concessionary Systems: The concession was the first 

system used in world petroleum arrangements and can be traced to silver mining 

operations in Greece2 in 480 B.C. (Anderson, 1998). The earliest petroleum 

concessionary agreements consisted only of a royalty. As governments gained experience 

and bargaining power, contracts were renegotiated, royalties increased, and various levels 

of taxation were added. Today there are numerous fiscal devices and sophisticated 

formulas to capture rent. 

In the traditional concessionary system, the company pays a royalty based on the value of 

the recovered mineral resources, and one or more taxes based on taxable income. In its 

most basic form, a concessionary system has three components: 

1. Royalty, 

2. Deduction, 

3. Tax. 

The royalty is normally a percentage of the gross revenues of the sale of hydrocarbons 

and can be paid in cash or in kind. Royalty represents a cost of doing business and is thus 

tax-deductible. Other deductions typically include operating cost, depreciation of 

capitalized assets, and amortization. The revenue that remains after the fiscal cost has 

been deducted is called taxable income. 

The definition of fiscal costs is described in the legislation of the country. Royalties and 

operating expenditures are normally expensed in the year they occur, and depreciation is 

calculated according to the tax legislation. The taxable income under a concessionary 

agreement is normally taxed at the country’s basic corporate tax rate. Special royalty 

incentive programs and tax rates may also apply. 

 

1

 Changes may act in favor of operators (such as occurs with royalty relief and accelerated depreciation 

schedules) or act against operators (as would occur with an increase in the tax rate). 2

 The mines of Laurium were owned by the State but were leased to its citizens for one talent and a rent (or 

tribute) of one twenty-fourth of the output, in bullion. 
6 

 The exact manner in which costs are capitalized or expensed depends on the tax regime 

of the country and the manner in which rules for integrated and independent producers 

vary. The successful-efforts and full-cost methods used in U.S. oil and gas accounting are 

discussed in detail in (Gallun et al., 2001). If costs are capitalized, they may be expensed 

as expiration takes place through abandonment, impairment, or depletion. If expensed, 

costs are treated as period expenses and charged against revenue in the current period. 

The primary difference between the two methods is the timing of the expense against 

revenue and the manner in which costs are accumulated and amortized. 

1.4. Cash Flow Analysis of a Royalty/Tax Fiscal Regime 

The terms and conditions of concessionary systems vary widely and may employ various 

sophisticated formulas to determine royalty and taxation levels, but underneath the 

diversity and complexity of terms, concessionary systems are fairly uniform in their 

treatment of royalty and tax obligation. The intent of the following discussion is to 

describe the elements common to most royalty/tax systems. 

1.4.1. After-Tax Net Cash Flow Vector: The net cash flow vector of an investment is 

the cash received less the cash spent during a given period, usually taken as one year, 

over the life of the project. The after-tax net cash flow associated with field f in year t is 

computed as 

NCFt = GRt − ROYt − CAPEXt − OPEXt −TAXt , 

where, 

NCFt = After-tax net cash flow in year t, 

GRt = Gross revenues in year t, 

ROYt = Total royalties paid in year t, 

CAPEXt = Total capital expenditures in year t, 

OPEXt = Total operating expenditures in year t, 

TAXt = Total taxes paid in year t. 

The after-tax net cash flow vector associated with field f is denoted as 

( ) ( , ,..., ) NCF1 NCF2 NCFk NCF f = , 

and is assumed to begin in year one (t = 1) and run through field abandonment (or 

divestment) at t = k. The after-tax net cash flow vector serves as the basic element in the 

computation of take and the economic measures associated with the field. 

1.4.2. Cash Flow Components: The gross revenues in year t due to the sale of 

hydrocarbons is defined as 

GRt = gt

o

 Pt

o

 Qt

o +gtg

 Pt

g

 Qt

g 
7 

where, 

gt

o

, gt

g

 = Conversion factor of oil (o), gas (g) in year t, 

Pt

o

, Pt

g

 = Average oil, gas benchmark price in year t, 

Qt

o

, Qt

g

 = Total oil, gas production in year t. 

The conversion factor depends primarily on the API gravity and the sulfur content of the 

hydrocarbon, and is both time and field dependent. The hydrocarbon price is based on a 

reference benchmark expressed as an average over the time horizon under consideration. 

The total amount of production in year t is expressed in terms of barrels (bbl) of oil, cubic 

feet (cf) of gas, or barrels of oil equivalent3 (BOE). 

Oil and gas streams can be valued individually or combined into one product stream. For 

Qt

o

 and Qt

g

 expressed in BOE, define 

g

t

o

t

o

t

t Q Q

Q

+

α = = Proportion of hydrocarbon production in year t that is oil, 

g

t

o

t

g

t

t Q Q

Q

+

1−α = = Proportion of hydrocarbon production in year t that is gas. 

A weighted average hydrocarbon price for a combined oil and gas production stream is 

computed as 

g

t

g

t t

o

t

o

t t

w Pt = α g P + (1−α )g P = Weighted average hydrocarbon price in year t. 

The equivalence between the individual and combined product streams is clear from the 

following relation: 

(Q Q ) P (Q Q ) Q Q

g P Q g P Q GR g P Q g P Q g

t

o

t

w

t

g

t

o

g t

t

o

t

g

t

g

t

g

t

o

t

o

t

o

g t

t

g

t

g

t

o

t

o

t

o

t t + = + 















+

+ = + = . 

The gross revenues adjusted for the cost of basic gathering, compression, dehydration and 

sweetening form the base of the royalty: 

ROYt = R (GRt – ALLOWt). 

The total allowance cost is denoted by ALLOWt and includes allowances set by regulation 

for the cost of gathering, compression, dehydration, and sweetening of the hydrocarbon 

stream. The royalty rate R, 0 ≤ R ≤ 1, depends upon the location and time the tract was 

leased and the incentive schemes, if any, in effect. The “typical” federal royalty rate in 

the United States is R = 1/8th (12.5%) onshore and R = 1/6th (16.67%) offshore. 

 

3

 Barrels of oil equivalent is the amount of natural gas that has the same heat content of an average barrel of 

oil. One BOE is about 6 Mcf of gas. 
8 

Capital expenditures (CAPEX) are the expenditures incurred early in the life of a project, 

often several years before any revenue is generated, to develop and produce 

hydrocarbons. CAPEX typically consist of geological and geophysical costs; drilling 

costs; and facility costs. Capital costs may also occur over the life of a project, such as 

when recompleting wells into another formation, upgrading existing facilities, etc. These 

cost are usually of a considerably smaller magnitude and duration than the initial capital 

expenditures. 

Operating expenditures (OPEX) represent the money required to operate and maintain the 

facilities; to lift the oil and gas to the surface; and to gather, treat, and transport the 

hydrocarbons. In many fiscal systems, no distinction is made between operating costs and 

intangible capital costs, and both are expensed. 

Taxable income (TAX) is determined as the difference between net revenue and operating 

cost; depreciation, depletion, and amortization; intangible drilling costs; investment 

credits (if allowed), interest in financing (if allowed), and tax loss carry forward (if 

applicable). Depletion is seldom allowed although some countries allow capital costs and 

bonuses to be expensed. In the United States, state and federal taxes are determined as a 

percentage of taxable income, usually ranging between 35%-50%, and here denoted by 

the value T, 0 ≤ T ≤ 1: 

 

( / ) t t t OPEXt DEPt CFt TAX = T NR − CAPEX I − − − , 

where, 

NRt = GRt − ROYt = Net revenue in year t, 

CAPEX / Intangible capital expenditures in year It = t,

DEPt =Depreciation, depletion, and amortization in year t, 

CFt = Tax loss carry forward in year t. 

The tax and depreciation schedule is normally legislated and will vary significantly from 

country to country. In the United States, all or most of the intangible drilling and 

development cost may be expensed as incurred, whereas equipment cost must be 

capitalized and depreciated. Tax losses in the U.S. may be carried forward for at least 

three years. 

1.5. Economic and System Measures 

1.5.1 Economic Indicators: The purpose of economic evaluation is to assess if the 

revenues generated by the project cover the capital investment and expenditures and the 

return on capital is consistent with the risk associated with the project and the strategic 

objectives of the corporation. Economic analysis requires a commitment of both time and 

monetary resources, and the degree to which procedures for capital expenditures are 

formalized is a function of company size, capital budget, and number of projects under 

consideration. Large firms tend to use a central review committee; formal written capital 

budgeting procedures; and a post audit on completed projects. Small firms tend not to 
9 

institutionalize such procedures (Boudreaux et al., 1991; Pohlman et al., 1987). The 

primary analytic techniques utilize a time value of money approach; e.g., see (Dougherty, 

1985; Mian, 2002; Seba, 1987). 

For field f and fiscal regime denoted by F, the present value (PV(f, F)) and internal rate of 

return (IRR(f, F)) of the cash flow vector NCF(f) is computed as 

PV(f, F) ∑=

− + =

k

t

t

t

D

NCF

1

1 (1 ) , 

IRR(f, F) = {D | PV ( f , F) = 0}, 

where D is the (discount) rate that equates the present value to zero. A profitability 

index, or investment efficiency ratio, normalizes the value of the project relative to the 

total investment and is calculated as 

PI(f, F) PV(TC)

PV(f,F) = . 

The present value provides an evaluation of the project’s net worth to the contractor in 

absolute terms, while the rate of return and profitability index are relative measures used 

to rank projects for capital budgeting. Economic values are not intended to be interpreted 

on a stand-alone basis, but should be used in conjunction with other system measures and 

decision parameters. A combination of indicators is usually necessary to adequately 

evaluate a contract’s economic performance. 

1.5.2. The Take Statistic: The division of profit between the contractor and government 

is referred to as “take.” Take is a fiscal statistic as opposed to an economic measure, and 

so generally matters most to the host government. In fact, since take does not provide a 

direct indication of the economic performance of a field, the contractor holds only 

secondary interest in its value. Further, unlike the economic measures which are 

generally well-established, general confusion surrounds the application and interpretation 

of take. “Take” is commonly cited throughout the trade and academic press (Johnston, 

2002a; Johnston, 2000; Johnston, 1994a; Johnston, 1993; Khin and Liang, 1993; Van 

Meurs and Seck, 1995; Van Meurs and Seck, 1997; Rapp et al., 1999; Smith, 1993; 

Smith, 1987; Wood, 1990a; Wood, 1990b;Wood, 1993) and various texts (Allen and 

Seba, 1993; Barrows, 1983; Barrows, 1994; Johnston, 1994b; Kemp, 1987; Van Meurs 

and Seck, 1995; Thompson and Wright, 1984; Van Meurs, 1971), and because of the 

commercial interest involved, strong opinions abound4

. 

It is commonly accepted that the level of government take is inversely proportional to the 

overall quality of the investment opportunity. In a purely competitive world, countries 

 

4

 The following quote is especially revealing: “I believe the government take statistic suffers from both 

under-use and over-use. When people are unaware of the weaknesses (and I believe few are intimate with 

all the weaknesses associated with the ‘take’ statistics), then over-use is extremely likely.” (Johnston, 

2002a). 
10 

with favorable geologic potential, high wellhead prices, low development costs, and low 

political risk will tend to offer tougher fiscal terms than areas with less favorable 

geology, low wellhead prices, high development cost, and high political risk. The 

economic strength and political stability of the country, oil supply balance, regional 

market demands, global economic conditions, and financial health of the oil sector also 

influence fiscal terms and the value of take5

. It is important to remember, however, that 

countries with harsh fiscal regimes or the greatest success probability provide no 

guarantees in the profitability of the play. A “tough” contract may be highly profitable, 

while a very “favorable” contract may not be. Good geologic projects do not always 

translate to profitable ventures. 

Rutledge and Wright (1998) claim that a 50%-50% split between government and 

contractor was considered a fair value before the two oil shocks, but after the creation of 

OPEC, companies began to accept some erosion of their take. A study performed by 

Petroconsultants in 1995 showed that in more than 90% of 110 countries examined, 

government take ranged from 55%-75%. Other studies have shown similar results; e.g., 

(Johnston, 1994b; Kemp, 1987; Van Meurs and Seck, 1995; Van Meurs and Seck, 1997). 

 

1.5.3. Annual Government and Contractor Take: The total cost in year t, TCt , is 

defined as 

TCt = CAPEXt + OPEXt , 

and the total profit is the difference between the gross revenues and total cost: 

TPt = GRt − TCt . 

If the total profit in year t is written 

TPt = CTt + GTt , 

then the contractor and government take is computed as, 

CTt = TPt − ROYt − TAXt = Contractor take in year t, 

GTt = ROYt + TAXt = Government take in year t. 

The contractor and government take in year t, expressed in percentage terms, is 

defined as 

 

5

 It is important to remember, however, that countries with harsh fiscal regimes or the greatest success 

probability provide no guarantees in the profitability of the play. A “tough” contract may be highly 

profitable, while a very “favorable” contract may not be. Good geologic projects do not always translate to 

profitable ventures. 
11 

t

t c

t TP

CT

τ = , 

t

t g

t TP

GT

τ = . 

Take varies as a function of time over the life history of a field. Three cases arise 

depending on the value of gross revenue and total profits: 

• GRt = 0: c

t τ = -1; 

• GRt > 0, TPt < 0: c

t τ < 0; 

• GRt > 0, TPt > 0: 0 ≤ c

t τ ≤ 1. 

During the installation and development phase of a project, and before production begins, 

gross revenue is zero and total profit is negative. In this case, take is not defined, or by 

convention is set equal to c

t τ = −1. As production begins GRt > 0, and if GRt > TCt, then 

TPt > 0 and the division of profit can be computed; i.e., in this case, 0 ≤ c

t τ ≤ 1. If 0 < GRt

< TCt, the government take is positive but CTt < 0. In this case, g

t τ > 1 and ct τ < 0 since 

c

t τ + gt τ = 1. 

1.5.4. Cumulative Discounted Government and Contractor Take: Cumulative 

discounted government and contractor take through year x, x = 1,..., k, is computed as 

, ( ) ( )

( ) ( )

, ( ) ( )

( ) ( )

PV CT PV GT

PV GT PV

PV CT PV GT

PV CT PV

x x

g x

x

x x

c x

x

+ =

+ =

τ

τ

 

where, 

PVx(CT) = = + ∑=

−

x

t

c t

t

D

CT

1

1 (1 ) Present value of contractor take through year x, x = 1,..., k, 

PVx(GT) = = + ∑=

−

x

t

g t

t

D

GT

1

1 (1 ) Present value of government take through year x, x = 1,..., k, 

c D = Discount factor for contractor, 

g D = Discount factor for government. 

The choice of what discount factor to use is an important decision for companies 

evaluating projects since selecting c D “too high” may result in “missing” good 

investment opportunities, while selecting c D “too low” may expose the firm to 

unprofitable or risky investments; e.g., see (Allen and Seba, 1993; Deluca, 2003; 
12 

Ehrhardt, 1994). The government6

 does not (nor should not) value money in the same 

way as companies, and so generally speaking, g c D ≤ D . Undiscounted take7

 is computed 

by setting c D = g D = 0. Discounted take is computed by assuming c D = g D ≠ 0, or by 

considering c D and g D as decision parameters which range over specified design 

intervals. At the time of abandonment x = k, c c PVk ( and . τ ) = τ ( ) g g PVk τ = τ

1.5.5. The Characteristics of Take: The computation of take depends critically on the 

ability to forecast the expected cash flow for the project. Unfortunately, estimating the 

cash flow of a prospective project is highly uncertain, and even under the best conditions, 

is based on incomplete and often unobservable information. In the GOM, the royalty and 

tax parameters of the fiscal regime are legislated, while in most concessionary 

agreements take is a negotiated quantity that depends on the economic conditions and 

prospectivity believed to exist at the time the contract is negotiated8. If economic, 

geologic, or political conditions change, the contract may be renegotiated. If the take 

statistic is used to characterize a field following development, the risk capital of the 

exploration program needs to be incorporated in the analysis. 

Take can be characterized as: 

• Take is a site-specific quantity that varies with numerous system parameters 

unique to the site, including but not limited to, the size and quality of discoveries, 

the time the field was developed, the life and profitability of the field, and the 

development plan of the operator. 

• Take is an uncertain quantity since it is based on field parameters which are 

themselves uncertain, such as estimated reserves, development and operational 

plans, and cost structure; unknown parameters such as the cost of capital; 

exogenous parameters such as crude oil prices, inflation, currency exchange rates, 

local and global economic conditions, and regulatory changes; and user-defined 

 

6

 The Office of Management and Budget of the U.S. government suggests using a 5.8% discount factor in 

the evaluation of federal projects. 

7 One of the reasons why take statistics are usually quoted on an undiscounted basis is perhaps due to the 

misguided belief that the user does not have to select a value for c D ; in fact, the default condition is itself 

a selection (and not a very good one): c D = g D = 0. In general, due to the structure of most fiscal regimes 

the contractor share of undiscounted profits is greater than the contractor share of discounted projects; i.e., 

c τ ( c D = 0, g D = 0) > c τ ( c D > 0, g D > 0), 

and similarly, 

g τ ( c D = 0, g D = 0) < g τ ( c D > 0, g D > 0).

Thus, if profits are undiscounted, the contractor will overestimate and the government will underestimate 

its take contribution. Fortunately, this is usually tolerable since the value of take as a stand-alone statistic 

matters more to governments than contractors, and from the government’s perspective, using an 

undiscounted take provides a lower-bound (conservative) estimate on the expected value. 

8

 This adds a complicating dimension to the interpretation of take, since take encompasses the perception of 

the risk associated with field development at the time the contract is negotiated. 
13 

preferences. The terms that determine take are identical, or nearly identical, to the 

economic measures of the system, and the variability associated with the 

computation of take is considered to have the same order-of-magnitude as the 

present value and rate of return measures. 

• Take is an unobservable quantity since field data is normally considered 

confidential and the cost history of fields is usually not maintained by operators or 

shared outside the firm. The only time that take or any economic indicator 

associated with a field can be calculated with certainty is after the field has been 

abandoned and all the relevant revenue and cost data made public. The fiscal 

terms of a contract and the inability to model contractual terms such as training 

commitments, domestic market obligations, carries and other factors that impact 

the cash flow (investment in working capital, working capital recovery, interest 

payment, repayment of principle) contribute to the uncertain and unobservable 

nature of the measure. 

• Take is a biased, unverifiable, and nontransparent quantity since it is based upon 

incomplete, uncertain, and unobservable information. Under most circumstances 

there is no way to “check” or “validate” the computed measure, and since the 

calculation is typically performed without reference to the model assumptions 

involved, the measure is usually not transparent. Only in the case of “perfect” 

information, when all revenue, cost, royalty and tax data is known for the life of 

the field can the division of profits between the contractor and government be 

reliably established. Only in the case of perfect information can take be calculated 

in a statistically meaningful manner. 

 

• Take is a fiscal statistic as opposed to an economic statistic, and so generally 

matters more to the host government than the contractor. Take is of secondary 

interest from the contractor’s perspective since it does not provide a direct 

indication of the economic performance of the field. 

• Take is often a negotiated quantity that depends upon the strength, knowledge, 

experience, and bargaining position of the oil company and host government, the 

perception of the risk associated with the field development at the time the 

contract was written, and the availability of opportunities worldwide. For 

contractual fiscal systems, “model” contracts are used as a starting point for 

negotiation, and the final negotiated fiscal terms are not normally disclosed or 

released to the public. 

• Take is inconsistent relative to standard economic measures since it is frequently 

computed/reported on an undiscounted basis. There can be a significant difference 

in the computation of take depending on the manner in which the cash flow 

elements are discounted. 
14 

1.6. Meta-Modeling Methodology 

The impact of changes in system parameters is usually presented as a series of graphs or 

tables that depict the measure under consideration (present value, rate of return, take, 

etc.) as a function of one or more variables under a “high” and “low” case scenario; e.g., 

(Smith, 1993; Wood, 1990a; Wood, 1990b; Wood, 1993). While useful, this approach is 

generally piecemeal and the results are anchored to the initial conditions employed. The 

amount of work involved to generate and present the analysis is also nontrivial, and the 

restrictions associated with geometric and tabular presentations of multidimensional data 

are significant; e.g., on a planar graph at most three or four variables can be examined 

simultaneously. A more general and concise approach to fiscal system analysis, which is 

also believed to be new, is now presented. 

 

The value of take, present value, and internal rate of return varies with the selection of the 

price of oil (Po), the price of gas (Pg), the royalty rate (R), the tax rate (T), the contractor 

discount factor ( c D ), and the government discount factor ( g D ), in a complicated manner, 

but it is possible to understand the interactions of the variables and their relative influence 

using a constructive modeling approach. The methodology is presented in three steps. 

Step 1. Bound the range of each variable of interest (X1 ,X2 ,...) = (Po

, Pg, R, T, 

,

c D g D ,...) within a design interval, Ai < Xi < Bi, where the values of Ai and Bi

are user-defined and account for a reasonable range of the historic uncertainty 

associated with each parameter. The design space Ω is defined as 

Ω = { ) ( ,..., X 1 Xk | Ai ≤ Xi ≤ Bi, i = 1,..., k}. 

Step 2. Sample the component parameters (Po, Pg, R, T, ,

c D g D ) over the design space 

Ω and compute the economic and system measures 

( f , c τ F) c =τ (Po

, Pg, R, T, ,

c D g D ), 

PV(f, F)= PV(Po, Pg, R, T, ,

c D g D ), 

and 

IRR(f, F)= IRR(Po

, Pg, R, T, ,

c D g D ), 

for each parameter selection. 

Step 3. Using the parameter vector (Po

, Pg, R, T, , c D g D ) and computed functional 

values, of , ( f c τ F), PV(f, F), and IRR(f, F) construct a regression model based 

on the system data: 

 , φ( f F)= k + αPo

 + β Pg + γR + T D D , c g δ + ε + θ

for each functional φ( f , F)= { , ( f c τ F), PV(f, F), IRR(f, F)}. 
15 

This procedure is sometimes referred to as a “meta” evaluation since a model of the 

system is first constructed, and then meta data is simulated from the model in accord with 

the design space specifications. The cash flow meta data are then analyzed and linear 

models describing the system constructed of linear models do not suffice to adequately 

represent the meta data, then non-linear terms can be incorporated into the analysis. 

The design base, cost structure, and production profile is assumed fixed, and so the 

relationships derived relate to the manner in which the system variables interact under a 

given development plan and fiscal regime. A good rule of thumb is to sample until the 

regression coefficients “stabilize.” If the regression coefficients do not stabilize, or if the 

model fits deteriorate with increased sampling, then the variables are probably spurious 

and linearity suspect. After the regression model is constructed and the coefficients 

(k,α,β, γ,δ, ε,θ) determined, if the model fit is reasonable and the coefficients 

statistically relevant, the value of the system measures , φ( f F) can be estimated for any 

value of (Po, Pg, R, T, Dc, Dg) within9 the design space Ω . 

1.7. A Functional Analytic Approach to System Measures 

In the case of perfect information, the computation of the economic and system measures 

associated with a field will not depend on the individual performing the calculation. In 

reality, however, the computation of present value, rate of return, and take is strongly 

dependent on the level of system information available and the assumption set of the 

user. Examples provided in the literature typically represent hypothetical developments 

under “reasonable” assumptions, and continuing in this tradition, we illustrate the general 

approach on a specific field development. 

To investigate the impact of a royalty/tax fiscal system for a specific field, it is necessary 

to calculate the after-tax cash flow under the fiscal system and to examine the factors that 

influence the economic performance of the field. 

1.7.1. Development Scenario: The development scenario selected is for an oil field with 

reserves estimated at 40 MMbbl and a projected 11-year life. The costs, production, and 

production prices are assumed fixed and the capital and operating expenditures are 

estimated under the base case P50 reserves10. The cash flow shown in Appendix Table 

A.1 is extracted from Johnston (Johnston, 1994b). 

 

Total capital costs are $101M distributed as (20%, 13%, 43%, 25%) over the first 4 years 

of the project’s cash flow. Capital expenditures are assumed to comprise 18% intangibles 

(services) and 82% tangibles (facilities, equipment, etc.). The tangible capital costs are 

depreciated straight line over 5 years. Estimated operating costs during the life of the 

project are $117M, which represents on average about $3/bbl full cycle cost. OPEX is 

 

9

 Extrapolating the functional relations outside the design space may be warranted in specific situations, but 

if the design volume changes dramatically, it is necessary to repeat the analysis for the new specification. 10 The P50 reserves number represents an estimate that has a 50% chance of being larger (or smaller) than 

the value provided.
16 

initially stable at around $2.5/bbl and is forecast to increase significantly near the end of 

the life of the field. 

 

The royalty regime is calculated as a percentage R, 0 ≤ R ≤ 1, of gross revenues, and the 

income tax is calculated as a percentage T, 0 ≤ T ≤ 1, of taxable income. Tax losses are 

carried forward from a previous year if negative. The fiscal terms are assumed to be 

described completely by the values of R and T; i.e., there are no royalty/tax holidays, 

domestic market obligations, government participation, or negotiated terms. The inflation 

rate per cash flow stream is assumed to be zero. The oil price and the contractor and 

government discount factors, c D and g D , 0 ≤ c D , g D ≤ 1, is assumed constant 

throughout the life of the field. The conversion factor gt

o is assumed to be unity, and the 

allowance term ALLOWt is set equal to zero. 

1.7.2. Regression Model Results: Regression models are constructed for , ( f c τ F), PV(f, 

F), and IRR(f, F) for 100, 500, 1000, and 5000 values sampled uniformly over the design 

space Ω defined as 

Ω = {(Po

, R, T, c D , g D )| 10 ≤ Po ≤ 30, 0.10 ≤ R ≤ 0.30, 0.25 ≤ T ≤ 0.45, 

 0.15 ≤ c D ≤ 0.40, 0.10 ≤ g D ≤ 0.20}. 

The design space constrains the variation of the parameter set, and can be interpreted 

geometrically as a 5-dimensional “hyper” parallelpiped in Euclidean space E5

; the 

“volume” of Ω, V(Ω), correlates with the magnitude of the system variability. 

 

The model results are shown in Appendix Table A.2. For the most part, the regression 

coefficients quickly stabilize with increased sampling. The 500 data point simulation is 

considered representative: 

(f,F) 36.1 2.8P 84.5R 71.7T 163.4D 43.1D , c o c g τ = + − − − + =2 R 0.75, 

PV(f,F) 74.3 5.2P 129.2R 99.1T 318.1D 21.0D , o c g = + − − − + =2 R 0.93, 

IRR(f,F) 16.9 1.7P 44.1R 30.7T 85.3D 2.3D , o c g = + − − − + =2 R 0.98. 

All the coefficients have the expected signs and are statistically significant except the 

government discount factor. Contractor take, present value, and the internal rate of return 

all increase with an increase in commodity price, and decline as royalty and tax rates 

increase. This behavior is not unexpected, since an increase in the commodity price 

(holding all other factors such as cost and production fixed) will increase the profitability 

of the field. If the royalty and/or tax rate increases, the government will acquire a greater 

percentage of revenue, which will decrease the profitability of the field, and 

subsequently, contractor take. 

As the contractor’s discount factor is increased, the economics of field development 

become progressively worse, and eventually, uneconomic. If the royalties and taxes 

collected by the government are discounted at a higher rate, the contractor take and 

economic measures of the field will increase. 
17 

1.7.3. Valuation Strategy: To determine the impact of fiscal terms on project economics 

an operator will typically compare several economic measures under different 

development scenarios. For illustration, however, only the present value functional is 

used to evaluate a prospect’s net worth. 

 

Definition. The value to an operator of field f under the fiscal regime F ) (R,T is defined 

as 

V(F ) (R,T ) = PV(f, F). ■

Example. For P = $20/bbl, c D = 15%, and g D = 10%, the present value of field f under 

the development scenario previously outlined is computed as 

PV( f, F ) (R,T ) . = 132.7 −129.2R − 99.1T

The fiscal regime defined by ) (R,T = (0.1667, 0.20) yields the present value 

PV (f, F(0.1667, 0.20)) = $91.3M. ■

To compare a field under two fiscal regimes, the contractor will compare the present 

value functionals. 

Definition. For field f, the fiscal regime F ) (R,T is preferred to the fiscal regime F(R,T )

if 

V(F ) (R,T , F(R,T ) ) = PV(f, F , (R,T)) − PV ( f F(R,T ) ) > 0. 

If V(F ) (R,T , F(R,T ) ) < 0, the contractor will prefer F(R,T ) to F ) (R,T , and if

V(F ) (R,T , F(R,T ) ) = 0, then F ) (R,T and F(R,T ) are fiscally equivalent and the 

contractor will exhibit no preference between the fiscal regimes. ■

Example. For P = $20/bbl, c D = 15%, and g D = 10%, the present value of field f under 

the fiscal regime defined by (R,T ) = (0.125, 0.35) yields the present value 

PV (f, F(0.125, 0.35)) = $81.9M. 

The contractor will prefer the fiscal regime defined by R = 16.67% and T = 20% and 

should be “willing to pay” up to the market value $9.4M to maintain (or negotiate) this 

arrangement. ■ 

1.7.4. Sensitivity Analysis: From the regression models shown in Appendix Table A.2, 

a 1% increase in the royalty rate impacts take, present value, and the rate of return 

slightly more than a 1% increase in the tax rate. Royalty comes “off the top” and is based 

on production and not profits, while tax receipts are profit-based. One reason why the 

impact of royalty is not more significant is due to the design space restriction: royalty is 

limited to a range bounded above by the tax rate, and thus, the royalty rate parameters 
18 

selected from their design interval will on average have a smaller absolute value than the 

tax rate, and subsequently, a smaller relative impact. The impact of the contractor 

discount factor is also interesting, since on a relative basis we observe that a 1% increase 

in the discount factor has about three times the impact of a royalty or tax rate change. 

1.8. Elements of Fiscal Design 

There are many applications of regression modeling to the design of efficient and flexible 

royalty/tax systems. In this chapter the main elements of fiscal design are briefly 

highlighted. 

 

1.8.1. Equivalent Fiscal Regimes: There are many ways to extract economic rent, but 

none of the arrangements is inherently more profitable than any other, and all petroleum 

arrangements can be made fiscally equivalent. For field f and fiscal regime F ) (R,T , the 

notion of equivalency is defined in terms of the system functional φ(f). 

Definition. The fiscal regime F ) ( , φ( f ) R T is said to be φ(f)-equivalent to the fiscal regime 

F *) ( *, φ( f ) R T , F ) ( , φ( f ) R T ~ F *) ( *, φ( f ) R T , if ) φ(R,T =φ(R*,T*) . ■

Example. Consider the parameter specification defined by Po = $20/bbl, c D = 15%, and 

g D = 10%. Contractor take is described by 

R T R T c τ ( , ) = 71.9 − 84.5 − 71.7 , 

and so for the fiscal regime defined by R = 10% and T = 30%, c τ (0.10, 0.30) = 41.9%. 

For the fiscal system F defined by R* and T* = 20%, to maintain “take” equivalence R* 

must satisfy the relation 

(R*,T*) = 57.6 − 84.5R* = 41.9 = c τ (R,T) c τ ; 

i.e., R* = 18.6%, and F c τ (0.10, 0.30) ~ F c τ (0.186, 0.20). Similarly, for the fiscal system 

defined by R*= 12.5% and T*, to maintain take equivalence, 

(R*,T*) = 61.3 − 71.7T* = 41.9 = c τ (R,T) c τ ; 

i.e., T* = 27.1%, and F c τ (0.10, 0.30) ~ F c τ (0.125, 0.271). ■

The exact manner in which equivalency is maintained is determined by the functional 

relationship established for the field and the fiscal regime under consideration. 

Example. Consider the parameter specification (Po

, c D , g D ) = (20, 0.15, 0.10). The rate 

of return measure is described by 

 

IRR(R T ,T) = 38.3 − 44.1R − 30.7 , 
19 

and analogous to c τ -equivalency, the IRR-functional computed for ) (R,T = (0.10, 0.30) 

yields IRR(0.10, 0.30)= 24.7%. For the fiscal system F defined by R* and T* = 20%, 

IRR-equivalence is maintained through the following relation: 

IRR(R*,T*) = 32.2 − 44.1R* = 24.7 = IRR(R,T) ; 

i.e., R* = 17.0%, and F IRR (0.10, 0.30) ~ F IRR (0.17, 0.20). Similarly, for F defined by 

R*= 12.5% and T*, 

 

IRR(R*,T*) = 32.8 − 30.7T* = 24.7 = IRR(R,T) ; 

i.e., T* = 26.3%, and F IRR (0.10, 0.30) ~ F IRR (0.125, 0.263). ■

The fiscal regime F ) (R,T forms a class of φ(f)-equivalent systems, {F φ (R,T)} , 

defined by (R,T) through the linear functional φ(f) as follows: 

{F} φ= {(R,T) |φ(R,T) = φ(R*,T*) }. 

For a properly specified system, three of the four system variables, R, T, R*, T*, must be 

known. If a fiscal regime is defined such that R* > R (R* < R), then to maintain φ(f)-

equivalency it is clear that T* < T (T* > T). 

1.8.2. Feasibility Constraints: For an operator to consider an investment opportunity 

feasible, certain minimum economic criteria must be satisfied. For example, if the fiscal 

regime of government is so constraining as to make development projects uneconomic, or 

if the fiscal marksmanship of a country is unrealistic and leaves production unprofitable, 

or if a contractor’s expectation of return is unrealistically high, then the fiscal regime in 

the “eye” of the contractor would be considered infeasible since viable projects will 

either be abandoned prematurely or not developed. 

The relationship of a fiscal system to operator constraints determines various “feasible” 

regions. A feasibility constraint is defined for a specific field and fiscal regime, and is 

determined by the functional φ(f) and the selection of a user-defined parameter ε > 0. 

Definition. The (φ(f), ε)-constraint Π(φ( f ),ε ) (R,T) = {) (R,T | φ(f) > ε} for field f defines 

the set of fiscal parameters (R,T) that satisfy the design constraint φ(f) > ε. ■

Example. For (Po

, c D , g D ) = (20, 0.15, 0.10), the rate of return functional is defined by 

 

IRR(R,T) = 38.3 − 44.1R − 30.7T.

 

If the operator considers an acceptable rate of return for the investment to be 10%, then 

the operator’s rate of return feasibility constraint is defined by 
20 

Π(IRR,10) (R = ,T) {(R, T)| 44.1R + 30.7T < 28.3}; 

e.g., (R, T) = (0.2, 0.2) satisfies the operator criteria while (R, T)= (0.4, 0.4) does not. ■

Example. For Po = $20/bbl, c D = 15%, and g D = 10%, the present value of field f is 

computed as 

PV(R,T) = 132.7 −129.2R − 99.1T. 

If the operator considers a present value of $50M the minimum acceptable return relative 

to the risk of the project, the initial capital required, and other investment opportunities 

available, then the present value feasibility constraint would be defined by the half-space: 

Π(PV ,50) (R = ,T) {(R, T)| 129.2R + 99.1T < 82.7}. ■

1.8.3. Feasible Domain: The collection of feasibility constraints and the logic operator 

“AND” defines the operator’s “feasible” domain, the region that will simultaneously 

satisfy all the economic requirements of the operator. 

Definition. The feasible domain of the operator, ΣO (R,T) , is defined as the intersection 

of the set of all feasibility constraints, Π(φ( f ),ε ) : 

ΣO (R,T) = Ι

( ( ), )

( ( ), )

φ ε

φ ε

f

Π f . ■

Since the intersection of all collection of convex sets is itself convex, it is not difficult to 

show the following theorem. 

Theorem. ΣO (R,T) is a convex domain. 

 

Example. For the parameter specification (Po, c D , g D ) = (20, 0.15, 0.10) and feasibility 

constraints defined by (IRR,10) and (PV,50), the operator’s feasible domain ΣO (R,T) is 

defined as 

Σ (R,T) = {(R,T) | 44.1R + 30.7T ≤ 28.3;129.2R + 99.1T ≤ 82.7; R,T ≥ 0}. O

 ■

Analogous to the operator’s feasible domain, the host government also maintains a 

feasible domain with respect to its own expectations on take, rate of return, present value 

and other socioeconomic objectives. In this case, if the economic and system functionals 

are denoted ψ(f) and δ > 0 represent the level curve parameters, then the host 

government’s feasible domain is defined as follows. 

Definition. The feasible domain of the host government, ΣHG (R,T) , is defined as 

 
21 

ΣHG (R,T) = Ι

( ( ), )

( ( ), )

φ δ

φ δ

f

Π f , 

where } {( , ) | ( ) Π(ψ ( f ),δ ) = R T ψ f > δ for field f, system functional ψ(f), and constraint 

parameter δ . ■

The definition of the operator and host governments feasible domains allows a simple 

(geometric) characterization of a “deal.” Agreement can be reached between the operator 

and host government on the terms of the contract for a specific field if the intersection of 

the respective feasible domains is non-empty. More formally, 

Theorem. If ΣO (R,T) Σ (R,T) = HG Ι {}, then no deal is possible. If 

ΣO (R,T) Σ (R,T) ≠ HG Ι {}, then a deal may be achieved. 

 

1.8.4. Progressive Fiscal Regimes: The notion of “progressive” and “regressive” fiscal 

regimes are widely discussed in the trade press. Fiscal regimes that tax profitable projects 

heavily and marginal projects lightly are referred to as progressive, while fiscal regimes 

that taxes marginal fields heavily relative to profitable projects are called regressive. A 

progressive regime is usually defined by the absence of royalties, bonuses, and other 

types of payment based on gross production, while emphasizing profit-based mechanisms 

such as taxation and sliding-scale terms. A progressive fiscal regime usually encourages 

the development of marginal prospects since the government take is at its lowest when oil 

company profitability is low; and as the profitability of a field increases, the government 

will extract more take. 

 

Two definitions of a progressive fiscal regime are provided. The first definition refers to 

the time history of one field, while the second definition refers to a collection of fields {f} 

evaluated at a point in time. The relationship between government take and rate of return 

is used to define the fiscal regime. 

Definition. A fiscal regime F ) (R,T is said to be progressive (regressive) with respect to 

the field f if ( f , g τ F) and IRR(f, F) are positively (negatively) correlated. ■

Definition. A fiscal regime F ) (R,T is said to be progressive (regressive) with respect to 

the collection of fields {f} if ( f , g τ F) is an increasing (decreasing) function of IRR(f, F); 

i.e., 

( f , g τ F) = α + β IRR(f, F), 

where β > 0 (β < 0). ■

Example. Consider fields {f1, f2,..., fk} evaluated under the parameter specification 

(P, c D , g D ) and defined by the empirical relations: 

( ,i

g τ f F) = Ai +BiR + CiT, i = 1, ..., k, 

 IRR(fi, F) = Di +EiR + FiT, i = 1, ..., k, 
22 

where the values Ai Fi ,..., are specific to field fi, i = 1, ..., k. For a given value of ) (R,T , 

evaluate , ( i

g τ f F) and IRR(fi, F), i = 1, ..., k, and estimate the relation 

( f , g τ F) = α (R,T) + β (R,T) IRR(f, F). 

If β (R > ,T) 0 the value ) (R,T is said to determine a progressive fiscal regime. ■

Definition. The progressive fiscal domain } Π { f }(R,T) = {(R,T) | (R,T) > 0 p β defines the 

fiscal parameters that lead to a positive correlation between government take and 

contractor rate of return. ■

1.9. Deepwater Gulf of Mexico Case Study: Na Kika 

1.9.1. Na Kika Deepwater Development: The Na Kika deepwater development is 

located approximately 140 miles southeast of New Orleans in water depths ranging from 

1,800m (5,800 ft) to 2,100m (7,000 ft). See Appendix Figure A.1. The project is a subsea 

development of five independent fields – Kepler, Ariel, Fourier, Herschel, and East 

Anstey – tied back to a centrally located, permanently-moored floating development and 

production host facility situated on Mississippi Canyon Block 474 (Gallun et al., 2001). 

A sixth field, Coulomb, is in water depth of approximately 2,300m (7,600 ft) and will be 

tied back to the host facility as production capacity becomes available. 

Shell and BP each hold a 50% interest in the host facility and the Kepler, Ariel, Fourier, 

and Herschel fields. In East Anstey, Shell has a 37.5% interest with BP holding the 

remaining 62.5%, and in the Coulomb field, Shell has a 100% interest. 

The host is a semisubmersible-shaped hull with topside facilities for fluid processing and 

pipelines for oil and gas export to shore. See Appendix Figure A.2. The fields will flow 

production from 12 satellite subsea wells equipped to handle 425 MMcf/day of gas, 

110,000 bbl/day of oil, and 7,000 bbl/day of water. The Kepler, Ariel, and Herschel fields 

are primarily oil, while the Fourier and East Anstey fields are primarily gas. The API 

gravity of the fields range from 25o (Herschel) to 29o (Fourier). The first phase of 

production from 10 wells in Kepler, Ariel, Fourier, East Anstey, and Herschel is due 

onstream during 4Q 2003. Coulomb is slated to begin in 2004 from two subsea wells. 

1.9.2. Development Scenario: The development scenario for Na Kika is based on an 

estimated gross ultimate recovery of roughly 300 MMBOE. Proved reserves are currently 

estimated at 189 MMbbl of oil and 728 Bcf of gas. The cash flow projection is shown in 

Appendix Table A.3. 

Total project cost is approximately $1.26B, excluding leasing costs of $20M 

(www.countonshell.com). Approximately 50% of the costs are associated with the 

fabrication and installation of the host facility and pipeline, 25% of the costs are 

associated with the fabrication and installation of the subsea components, and 25% are 
23 

associated with the drilling and completion of the wells. The life cycle capital 

expenditures are estimated as $3.73/bbl with operating cost estimated at $1.20/bbl. OPEX 

is forecast to increase steadily from less than $1/bbl early in the production cycle to over 

$8/bbl near the end of the life of the field. 

1.9.3. Deepwater Royalty Relief: For leases acquired between November 28, 1995 and 

November 28, 2000, the OCS Deepwater Royalty Relief Act (DWRRA; 43 U.S.C. 

§1337) provided economic incentives for operators to develop fields in water depths 

greater than 200 m (656 ft). The incentives provide for the automatic suspension of 

royalty payments on the initial 17.5 MMBOE produced from a field in 200-400 m (656-

1,312 ft) of water, 52.5 MMBOE for a field in 400-800 m (1,312-2,624 ft) of water, and 

87.5 MMBOE for a field in greater than 800 m (2,624 ft) of water (Baud et al., 2002). 

The impact of royalty relief is to make marginal fields economic, enhance the 

return/profitability of intermediate fields, and reduce the risk associated with some 

projects. The DWRRA expired on November 28, 2000, but leases acquired during the 

time royalty relief was active retain the incentives until their expiration. Reduction of 

royalty payments is also available through an application process for deepwater fields 

leased prior to the DWRRA but which had not yet gone on production. Provisions 

effective in 2001 are specified for each lease sale, are granted to individual leases (not 

fields as in the DWRRA), and are subject to change with each lease sale as economic 

conditions warrant. 

 

If Qt denotes the annual hydrocarbon production from field f in year t, d(f) the (average) 

water depth of the field, and Q(f) the volume of production for which royalty is 

suspended, then deepwater royalty rates are determined as follows: 

R(DWRR) 











>

≤

=

∑

∑

t

t

t

t

Q Q f

Q Q f

16.67%, if ( ).

0, if ( )

If the lease on which the field is located was acquired between November 28, 1995 and 

November 28, 2000, then 

Q(f) 











≥

≤ ≤

≤ ≤

=

87.5 MMBOE, if ( ) 800 m.

52.5 MMBOE, if 400 m ( ) 799 m

17.5 MMBOE, if 200 m ( ) 399 m

d f

d f

d f

For lease sales held after November 28, 2000, the water depth categories and value of 

Q(f) is specific to the lease sale. 

1.9.4. Regression Model Results: The design space for the four models under 

consideration is shown in Appendix Table A.4. In Model I the system parameters are 

selected uniformly from each design interval, and in Model II, the design intervals are 

more narrowly defined and the hydrocarbon prices assumed Lognormally distributed. 
24 

Model III employs the same parameter intervals as in Model II but the oil and gas price is 

assumed to vary over each year of the production cycle; i.e., o P ~ t LN(25, 5), g P ~ t

LN(3.5, 1.5) for t = 1,..., 12. In Model IV, the Model III parameters are applied with an 

annual tax rate selected from a triangular distribution; i.e., T ~ t TR(0.38, 0.44, 0.50) for t 

= 1,..., 12. 

 

The results of the regression models for ( f ,Q) c τ , PV(f, Q) and IRR(f, Q) are shown in 

Appendix Table A.5. The model coefficients all have the expected signs, the fits are 

robust, and all the coefficients – except the government discount factor – are highly 

significant. For any value of (Po, Pg, R, Q, T, c D , g D ) within the design space, the 

regression model can be used to evaluate and compare parameter selections. For Model I, 

the results of the meta-model yield 

( f ) = c τ 80.0 + 0.2 Po

+0.5 Pg – 53.0R + 0.04Q – 79.1T – 84.3 c D + 86.2 ,

g D 

PV(f)=10,460.7+38.2Po

+131.5Pg–1,259.8R+1.1Q–1,856.1T–3,699.4 c D +79.8 ,

g D 

IRR(f) = 63.4 + 2.6 Po+8.6 Pg – 58.9R + 0.1Q – 126.2T – 131.5 c D + 2.2 g D .

A quick glance at the regression coefficients of the functionals indicates some of the 

characteristics of royalty relief specific to the Na Kika development. First, the absolute 

magnitude of the tax coefficients exceeds the royalty rate. This is not entirely unexpected 

since a royalty suspension has been granted on the first Q(f) MMBOE production thereby 

dampening its impact. Under royalty relief, the government foregoes royalty for a period 

of time, but its tax collection will increase (since the operators revenue will increase with 

suspended royalties). 

 The contractor and government discount factors are approximately equal in the take 

computation, but a significant difference exists in the present value and rate of return 

measures. If c D and g D are required to satisfy c D = g D = D, the new model coefficients 

for D is nearly the same as c D and the rest of the model coefficients do not change 

appreciably. 

In Model II, the hydrocarbon prices are assumed Lognormally distributed and the design 

intervals are more narrowly defined. The impact of these changes to the regression 

models is shown in Appendix Table A.5. The mean, P5, and P95 estimates11 of the 

computed measures are shown in Appendix Table A.6. These values bound the expected 

range of each measure for the design space and model specification. Observe that as the 

design specification becomes more narrowly defined, the range defined by P95 – P5

generally shrinks, while the variability introduced through o Pt and g Pt do not noticeably 

affect the range. 

 

11 The P5 and P95 measures indicate that 5% of the time the estimated value is expected to be less than P5 or 

greater than P95. 
25 

The inclusion of structural variability in Model III and Model IV, where the hydrocarbon 

prices and tax rates are now assumed to vary annually, negatively impacts the robustness 

of the model fits, but the impact on the regression coefficients is relatively minor in most 

instances. 

The ratio δ/γ for each regression model provides an estimate of the correspondence 

between royalty relief volume suspensions and the royalty rate. For the present value 

functional, for instance, a 1 MMBOE change in royalty suspension is equivalent to 

0.087% ≈ 0.1% change in the royalty rate. Or in other words, a 10 MMBOE increase in 

the value of Q(f) is roughly equivalent to a 1% decrease in the royalty rate with respect to 

its impact on the present value of the field. Similar observations follow for the take and 

rate of return measure. 

1.9.5. The Impact of Royalty Relief: The design parameters of royalty relief include the 

royalty rate R, 0 ≤ R ≤ 1, and level of the suspension volume, Q(f). Intuitively, it is clear 

that decreasing the value of R and/or increasing Q(f) will act in favor of the contractor, 

but the exact manner of the impact can only be determined through empirical modeling. 

If Po

 = $25/bbl, Pg = $3.5/Mcf, R = 16.67%, T = 40%, and c D = 20%, g D = 10%, then 

based on the functional constructed for Model I, 

( f ) = c τ 38.0 + 0.04Q, 

PV(f) =1,192 + 1.1Q, 

IRR(f) = 71.9 + 0.1Q. 

For Q = 0 (no royalty relief), the take, present value, and rate of return of the investment 

is estimated at 38%, $1.192B, and 71.9%, while with Q = 87.5 MMBOE (royalty relief), 

( f ) c τ = 41.5%, PV(f) = $1.288B, and IRR(f) = 80.7%. As Q(f) increases, royalty is 

suspended on the initial Q(f) MMBOE production, and both the contractor take and 

economic measures of the field increase. 

The value of royalty relief to the operator as a percentage of the present value is 

estimated as 

VPV (f, Q) ( ,0)

( , ) ( ,0)

PV f

PV f Q − PV f = = Q Q 0.092

1192

1.1 = ; 

so that for Q = 17.5 MMBOE, V(f, Q) = 1.6%; Q = 52.5 MMBOE, V(f, Q) = 4.8%; and 

Q = 87.5 MMBOE, V(f, Q) = 8.1%. 

In terms of the contractor take, the percentage variation of ( f ) c τ as a function of Q 

relative to the baseline case of no relief is also readily computed: 
26 

V c ( f ,Q) τ ( ,0)

( , ) ( ,0)

f

f Q f c

c c

τ

τ −τ = = Q Q 0.00105

38.0

0.04 = ; 

so that for Q = 17.5 MMBOE, ) V c ( f ,Q τ = 0.018%; Q = 52.5 MMBOE, ) V c ( f ,Q τ =

0.055%; and Q = 87.5 MMBOE, ) V c ( f ,Q τ = 0.092%. 

1.10. Conclusions 

The weaknesses and uncertainty associated with the application of take have not been 

properly addressed in the literature, and so the first task of the paper was to delineate the 

shortcomings of this statistic and to offer a fresh perspective on interpretation. 

To understand the economic and system measures associated with a royalty/tax fiscal 

regime a meta-model was developed. In the meta-evaluation procedure, a cash flow 

model specific to a given fiscal regime is used to generate meta data that describes the 

influence of various system variables. Meta-modeling is not a new idea, but as applied to 

fiscal system analysis and contract valuation, is new, novel, and useful. Modeling take 

and economic measures in this manner is especially useful for contract negotiation 

strategies and plays a central role in understanding the intricate mechanics of fiscal 

system analysis. 

A constructive approach to fiscal system analysis was developed to isolate variable 

interaction and determine the manner in which private and market uncertainty impact 

take and the economic measures associated with a field. Functional relations were 

developed by computing the component measures for parameter vectors selected within a 

given design space. The relative impact of the parameters and the manner in which the 

variables are correlated was also established in a general manner. The methodology was 

illustrated on a hypothetical oil field and a case study for the deepwater Na Kika 

development was considered. The impact of royalty relief on the field economics of Na 

Kika was also examined. 
27 

CHAPTER 2: CONTRACTUAL SYSTEMS 

2.1. Introduction 

Most governments in the world want oil and gas companies to explore for and develop 

the hydrocarbon resources of their country since development and production activities 

provide foreign direct investment, new jobs and infrastructure creation, revenue for the 

government, and improved conditions for its citizenry. The extent to which revenues 

accruing from natural resources generate wealth for an economy is a lively and much 

debated subject. For a recent review of the literature in this area, see (Stevens, 2003). 

Governments encourage exploration and development activity through their license 

rounds and fiscal terms. 

Exploration and development is a high risk capital intensive business. Finding oil and 

natural gas throughout most of the world is difficult, costly, and uncertain. The cost of 

obtaining leases and conducting exploratory work requires a significant investment 

before reserves are found and economic viability ensured. Investment, in its most basic 

form, is paying now for the promise of a reward later, and particularly in oil and gas 

ventures, there are risks of various kinds that need to be considered. Does oil exist in the 

region? If reserves are found are they smaller than expected or decline faster than 

geologic conditions suggest? Can the project be brought on line on time and under 

budget? Will oil prices remain strong or nose-dive? How will inflation rates behave? Will 

the government try to renegotiate the terms of the contract at a later date? 

 

The first objective of an exploration project is to satisfy the economic criteria established 

by the company. The project must achieve the goals from which the corporation can 

profit in the form of monetary gain, enhanced knowledge, or strategic opportunity. The 

government’s perspective is more broadly defined since its desire is to provide a fair 

return to the state while maximizing the wealth from its natural resources. If balance 

between these two competing interests can be reached, then a deal can be struck. 

The purpose of this Chapter is to develop an analytic framework to quantify the influence 

of private and market uncertainty on the economic and system measures associated with a 

field under a Production Sharing Agreement (PSA). The impact of changes in system 

parameters is usually presented as a series of graphs or tables that depict the present 

value, rate of return, or take (or whatever measure is under consideration) as a function of 

one or more variables under a “high” and “low” case scenario; e.g., (Smith, 1993; Wood, 

1993). While useful, this approach is generally piecemeal and the results are anchored to 

the initial conditions employed. A more general and concise approach to fiscal system 

analysis, previously applied to a royalty/tax system, is developed in this paper. 

The outline of the Chapter is as follows. In Chapter 2.2, the licensing and negotiation 

process involved in exploration and development activities is formalized, and in Chapter 

2.3, the basic features of concessionary and contractual systems are outlined. In Chapter 

2.4, the cash flow analysis of a generic PSA is developed, and in Chapter 2.5, the 

economic and system measures associated with a field are defined. In Chapter 2.6, the 
28 

meta-modeling approach is presented in terms of a generalized fiscal system analysis. A 

hypothetical oil field is used to illustrate the analytic approach in Chapter 2.7, and in 

Chapter 2.8, the Angolan deepwater field development Girassol is presented as a case 

study. In Chapter 2.9, conclusions complete the Chapter. 

2.2. The Licensing and Negotiation Process 

Parties to a potential contract must be able to agree to the terms of the contract if a “deal” 

is to be made. The “deal” in oil and gas industry lore is the stuff of legend, and the 

wheeling, dealing, rough, and romantic industry of black gold does not necessarily lend 

itself to a sequence of precise and explicitly-enumerated stages, but categorizing, 

decomposing, and specifying the licensing and negotiation process is nonetheless a useful 

exercise even if it is ultimately flawed. 

Signing a “bad deal” is the basic fear for both the contractor and host government, 

although the meaning of a “bad deal” varies with each party. Signing an unprofitable deal 

is the basic fear of the contractor, and contractors hedge against this outcome by 

involving multiple partners, maintaining a diverse portfolio of projects, and by paying 

particularly close attention to the risk-reward indicators estimated for each project. The 

economic measures – present value, rate of return, and profitability index – serve as a 

primary gauge for a contractor’s negotiating strategies. 

The objective of a host government is to acquire and maximize the wealth from its 

natural resources by encouraging appropriate levels of exploration and development 

activity. Since oil is a non-renewable resource, the benefits producers receive should be 

as owners of the oil, and not a rent. Oil is a commodity that is dispensed. The host 

government wants oil and gas companies interested in exploration to create healthy 

competition and market efficiency, and in the high pressure environment in which 

government representatives work, negotiations occur on a stage that is scrutinized and 

politicized by many government agencies, officials, and the press. The host government 

is primarily interested in the division of profits with the contractor12, as well as various 

economic and socioeconomic indicators. 

The basic stages of licensing and negotiation are presented in the following stylized 

framework. For a more comprehensive review of each stage, see (Bunter, 2002; 

Dur,1993). Refer to Appendix Figure B.1 for a schematic of the basic process. The 

timetable associated with each stage depends upon many factors, such as the economic 

conditions and political uncertainty that exist at the time of the licensing and/or 

negotiation, the level of interest of foreign participants, the experience of the host 

government and level of bureaucracy, the commitment and interest of the personnel 

involved, the frequency and timing of competitive prospects, etc. The basic stages follow. 

 

12 This is not always the case and depends upon conditions specific to the country. For example, in Saudi 

Arabia’s first bidding round for onshore natural gas exploration, one Saudi official commented: “The key 

factors in successful bidding would be neither signature bonuses nor the amount of government take. Our 

objective is not the cash. The minimum work program will primarily be the main bidding parameter.” 

(Husari, 2003) 
29 

Stage 1. The host government (HG) divides prospective exploration areas into 

concession areas or blocks B = { ,..., } B1 Bk . Data packages are prepared for each 

block Bi, i = 1,..., k, and the form (or a draft) of the model contract Γ and fiscal terms 

F to be used as the basis for bid preparation is specified. The license round is 

advertised, and government officials may make a promotional tour to increase the 

awareness and interest in the sale. 

Stage 2. For each block Bi a data package is purchased by the foreign oil company 

(FOC). FOCs submit details of proposed consortia and comment on the (draft) model 

contract and fiscal terms. Companies may need to be “pre-qualified” to form 

consortia. 

Stage 3. The HG may meet with pre-qualified operators for clarification of the 

process, the bidding parameters, the fiscal systems, the model contract, etc. The HG 

may also emphasize the main bidding parameters, volume of production desired, 

expected time frame for development, etc. 

 

Stage 4. The FOC evaluates exploration and development scenarios for individual 

blocks based on public and proprietary information. Technical and commercial bids 

are prepared consistent with the geologic prospectivity, strategic objectives, and 

capital budget of the firm. 

a. Technical bids provide a work commitment schedule W describing the 

seismic work (in kilometers) and the number of wells to be drilled (by type – 

exploratory, delineation, etc. and total footage) to be performed on each block 

Bi. 

b. Commercial bids specify the fiscal terms F and biddable parameters which 

will govern the block if exploratory activities find commercial quantities of 

resource. 

Stage 5. The HG receives the bids for each block Bi and evaluates the work 

commitment and fiscal terms offered. Work commitment is a certain13 event, while 

the proposed fiscal terms only hold if commercial quantities of oil/gas are discovered. 

a. Technical bids are evaluated14 on the work commitment proposed; the 

technical standing, experience, capabilities, past business practices, and 

financial position (credit worthiness/financial strength) of the FOC; and 

previous experience and success in exploration in the area or similar areas. 

The present value of the work commitment, PV(W), represents the expected 

cost of the work program to drill X wells and shoot Y miles of seismic. The 

 

13 Unless optionality agreements are written into the contract. Penalty terms for noncompliance are usually 

specified. 

14 Technical bids are typically evaluated by engineers, geologists, and management personnel within the 

exploration department of the National Oil Company or Oil Ministry. Commercial bids are evaluated by 

economist, financial personnel, and lawyers in the legal/financial division. 
30 

value of the total work requirement is important in determining the winning 

bid but is not necessarily an overriding factor. 

b. Commercial bids are evaluated to test the fiscal terms proposed by each 

contactor. The evaluation of fiscal terms are more complicated and time 

consuming than the evaluation of the work commitment since it is based on a 

number of conditions that are uncertain (such as discovery, commerciality, 

reserve size, and field characteristics). Take and economic indicators 

associated with the development plan are the primary measures computed by 

the HG. 

Stage 6. The HG compares the bids received to determine which terms are the “most 

favorable.” The FOC(s) with the most favorable terms are short listed for further 

negotiation. In some cases, after the selection of the short list contractor(s), only 

“fine-tuning” of the contract is required. In other cases, additional more difficult 

negotiations will be required to “hammer out” an agreement. 

Stage 7. The HG and FOC negotiate the final terms of the contract such that the 

economic, development, and socioeconomic objectives of each party are satisfied. 

 

a. (FOC Perspective) The FOC concentrates primarily, but not exclusively, on 

profitability measures associated with the contract15. The common economic 

measures include 

PV(Bi, F) = Present value of block Bi under fiscal system F, 

IRR(Bi, F) = Internal rate of return of block Bi under fiscal system F. 

b. (HG Perspective) The HG focus is more broadly defined since it wants to 

provide a fair return to the state, create healthy competition and market 

efficiency, and maximize the wealth from its natural resources. The HG 

considers the division of profits defined by the take statistic, 

( ,i

c τ B F) = Contractor take for block Bi under fiscal system F, 

the economic measures PV(Bi, F) and IRR(Bi, F), and socioeconomic 

measures, 

U(Bi) = Socioeconomic measures for block Bi. 

Stage 8. Terms of the fiscal regime F which are negotiable are suggested by the 

contractor to enhance their objective functions. These terms are then evaluated by the 

host government. The process is continued until either a mutually agreeable set of 

terms is determined, in which case a deal is made, or agreement cannot be reached 

 

15 The Royal Dutch/Shell statement of general business principles is standard:

“Profitability ... is essential for the proper allocation of corporate resources and necessary to 

support the continuing investment required to develop and produce future energy supplies... The 

criteria for investment decisions are essentially economic, but also take into account social and 

environmental considerations and an appraisal of the security of the investment.” 
31 

and the deal is dead or negotiation resumes16 at a later date. The negotiation process is 

specified as follows: 

a. (FOC Perspective) The fiscal terms are negotiated to maintain company criteria 

on the expected economic and system measures for the risk capital invested: 

E[PV(Bi, F)] ≥ Ai, 

E[IRR(Bi, F)] ≥ Bi, 

where the values Ai and Bi are usually “known,” at least approximately, for the 

block under consideration. 

b. (HG Perspective) The fiscal terms are negotiated to maintain government 

criteria on providing a fair return to the state, attracting foreign investment, 

and maximizing the wealth from its natural resources: 

E[PV(Bi, F)] ≤ Di, 

E[IRR(Bi, F)] ≤ Ei, 

E[τ

c

(Bi, F)] ≤ Fi, 

where the values of Di, Ei, and Fi are again known17 approximately. The HG 

also has development and socioeconomic objectives that are specified in 

generalized functional form U (Bi), 

 U (Bi) ≥ Gi. 

Stage 9. The outcome of negotiation either results in a deal or no-deal. 

a. (Deal) If the fiscal terms F can be negotiated such that the functional values 

satisfy the FOC and HG constraints, 

Ai ≤ PV(Bi, F) ≤ Di, 

Bi ≤ IRR(Bi, F) ≤ Ei, 

τ

c

(Bi, F) ≤ Fi,

U (Bi) ≥ Gi, 

then an agreement can be reached and terms of the contract can be signed. 

b. (No Deal) If fiscal terms cannot be agreed upon, the deal is dead. 

 

16 These are very real concerns as the failed $25B Saudi Gas Initiative illustrates. From the beginning of 

talks with Saudi Aramco, ExxonMobil steadfastly demanded a 15%-18% rate of return on its investment, 

while the Saudis offered only 8%-10%. It is not surprising that the deal, after several years of talks, died. 

17The degree to which the threshold limits are known for each functional depend in large measure on the 

host government’s experience in licensing, the perceived geologic prospectivity and political risk in the 

region, the financial strength of the host government and desire for foreign capital, and the economic 

conditions that exist at the time. 
32 

Stage 10. The FOC submits final negotiated terms to the HG and then proceeds with 

activity as specified in the work commitment schedule. 

2.3. Background Information 

2.3.1. Contractual Systems: In most countries of the world, the government owns all 

the mineral resources, but will offer to foreign oil companies blocks to explore and 

develop. Contractual systems derive from the Napoleonic era and are based on the French 

legal concept that mineral resources should be owned by the state for the benefit of all 

citizens (Allen and Seba, 1993; Johnston, 1994b). The host government gives the oil 

company the right to receive a share of the production (or revenue) in accord with a PSA 

or Service Contract. The basic terms of a contractual system is usually determined 

through legislation, but many aspects may be negotiated. The terms of model contracts 

are frequently put forward by the host government as a basis for bidding and represent 

the start of negotiation between the contractor and government. The terms of model 

contracts are also frequently subject to renegotiation as political and economic conditions 

change, or as additional information becomes available. 

2.3.2. Fiscal Components of Contractual Systems: In a production sharing agreement, 

exploration is performed by the operating company at its own risk. The risk is similar to 

the risk associated with exploration under a contractual system, but significant 

differences arise in how the expenditures are recovered if commercial reserves are found 

and the manner reserves are split between the host country and the company. 

In its most basic form, a PSA has four components: 

1. Royalty, 

2. Cost Recovery, 

3. Profit Oil, and 

4. Tax. 

The royalty is computed as a percentage of the gross revenues of the sale of 

hydrocarbons, and like many elements in a PSA, may be determined on a sliding scale 

the terms of which may be negotiable or biddable. The oil company pays royalty to the 

government and is then entitled to a pre-specified share of production for cost recovery. 

The remainder of the production is split between the government and the oil company at 

a stipulated (often negotiated) rate. The oil company normally has to pay income tax on 

its share of profit oil, although in some instances the National Oil Company may pay a 

portion of the amount. 

2.4. Cash Flow Analysis of a Production Sharing Agreement 

The terms and conditions of PSAs vary widely and change frequently, and are often 

subject to negotiations (and renegotiations) which are unobservable and uncertain. 

Production sharing agreements are known for their diversity and complexity of terms, 

and so it should come as no surprise that PSAs need to be analyzed and treated on an 
33 

individual basis. The intent of the following discussion is to provide a general analytic 

framework to describe the fiscal terms common to most PSAs. 

 

2.4.1. After-Tax Net Cash Flow Vector: The net cash flow vector of an investment is 

the cash received less the cash spent during a given period, usually taken as one year, 

over the life of the project. The after tax net cash flow associated with field f in year t 

generally takes the form 

/ , NCFt = GRt − ROYt − CAPEXt − OPEXt − BONUSt − PO Gt −TAXt − OTHERt

where, 

NCFt = After-tax net cash flow in year t, 

GRt = Gross revenues in year t, 

ROYt = Total royalties paid in year t, 

CAPEXt = Total capital expenditures in year t, 

OPEXt = Total operating expenditures in year t, 

BONUSt = Bonus paid in year t, 

PO/Gt = Government profit oil in year t, 

TAXt = Total taxes paid in year t, 

OTHERt = Other costs paid in year t. 

The after tax net cash flow vector associated with field f is denoted as 

( ) ( , ,..., ) NCF1 NCF2 NCFk NCF f = , 

and is assumed to begin in year one (t = 1) and run through field abandonment (or 

divestment) at t = k. The after-tax net cash flow vector serves as the basic element in the 

computation of all system measures associated with the field. 

2.4.2. Cash Flow Components: The gross revenues in year t due to the sale of 

hydrocarbons is defined as 

GRt = gt

o

 Pt

o

 Qt

o +gtg

 Pt

g

 Qt

g

, 

where, 

gt

o

, gt

g

 = Conversion factor of oil (o), gas (g) in year t, 

Pt

o

, Pt

g

 = Average oil, gas wellhead price in year t, 

Qt

o

, Qt

g

 = Total oil, gas production in year t. 

The conversion factor depends primarily on the API gravity and the sulfur content of oil, 

and the amount of impurities, condensate, and hydrogen sulfide of natural gas (Hyne, 

1995). Conversion factors are both time and field dependent. The hydrocarbon price is 

based on a reference benchmark expressed as a time average over a given horizon. 
34 

The gross revenues adjusted for the cost of transportation and basic processing form the 

base of the royalty payment, 

ROYt = R(ψ)(GRt – ALLOWt), 

where the total allowance cost is denoted by ALLOWt and the royalty rate R(ψ) depends 

upon the location and time the tract was leased and the incentive schemes, if any, in 

effect. The royalty rate R(ψ), 0 ≤ R(ψ) ≤ 1, may be fixed or a sliding scale may be 

employed. The terms of the royalty rate, like many other PSA factors, may be negotiable 

or biddable. 

The capital and operating expenditures, CAPEXt and OPEXt, are estimated relative to the 

expected reserves and development plan. Capital expenditures (CAPEX) are the 

expenditures incurred early in the life of a project, often several years before any revenue 

is generated, to develop and produce hydrocarbons. CAPEX typically consist of 

geological and geophysical costs; drilling costs; and facility costs. Capital costs may also 

occur over the life of a project, such as when recompleting wells into another formation, 

upgrading existing facilities, etc. Operating expenditures (OPEX) represent the money 

required to operate and maintain the facilities; to lift the oil and gas to the surface; and to 

gather, treat, and transport the hydrocarbons. In many fiscal systems, no distinction is 

made between operating costs and intangible capital costs, and both are expensed. 

Various types of bonus payments may be required in a PSA. Signature bonuses are 

sometimes paid upon finalization of negotiations and contract signing, while discovery 

bonuses are paid in cash or equipment upon discovery of oil/gas. Signature and discovery 

bonuses are normally one-time fees, while production bonuses are paid when production 

reaches one or more specified levels. Bonus payments are not normally considered for 

cost recovery. 

The profit oil is the portion of production or revenue that the government shares with the 

contractor after royalties and cost oil (COt ) is recovered from the gross revenue: 

POt = GRt − ROYt − COt . 

The profit oil is split between the contractor and government: 

 

POt = PO / , Ct + / PO Gt

where, 

PO /Ct = PO(ψ)POt =Contractor profit oil in year t, 

PO /Gt = (1− PO(ψ))POt = Government profit oil in year t, 

PO = (ψ) Profit oil split, 0 ≤ ) PO(ψ ≤ 1. 

The cost recovery scheme determines how the cost oil is computed. Many variations of 

cost recovery exist, and in its most basic form is computed as 
35 

t t t t t t t DECOMt CR = U + CAPEX / , I + OPEX + DEP + INT + INV +

where, 

CRt =Cost recovery in year t, 

Ut = Unrecovered cost carried over from year t – 1, 

CAPEX / Intangible capital expenditures in year It = t, 

DEPt =Depreciation in year t, 

INTt = Interest on financing in year t, 

INVt = Investment credits and uplift in year t, 

DECOMt = Decommissioning cost recovery fund apportionment in year t. 

Unrecovered costs carried over from previous years may include tax loss carry forward, 

unrecovered depreciation balance, unrecovered amortization balance, and cost recovery 

carry forward. Some contracts allow capital expenditures to be expensed in the year 

incurred and recovered from the cost recovery, while in other cases, these costs have to 

be amortized and only the amortized amount is allowed for recovery. Depreciation 

schedules are normally legislated, and in nearly half of PSAs worldwide, are not 

permitted for cost recovery. Investment credits and uplifts are incentives that allow the 

contractor to recover an additional percentage of capital costs through cost recovery. The 

anticipated cost of abandonment may be accumulated through a sinking fund that matures 

at the time of abandonment. 

The amount of revenues the contractor can claim for cost recovery is normally bound 

from above by the so-called “cost recovery ceiling,” and in some cases, a time limitation 

for full cost recovery may also be imposed. Cost oil is constrained in value through a 

functional relation such as 

COt = min(CRt, ( CR ψ)GRt), 

where the value of ) CR(ψ , 0 ≤ ) CR(ψ ≤ 1, may be constant or based on a sliding scale18. 

It is generally agreed that operators must be allowed to recover their costs for a venture to 

be profitable, but the manner in which the costs are recovered and the impact of cost 

ceilings on the economic measures of the field are not well understood. 

Taxable income is determined as a percentage of the contractor profit oil and tax loss 

carry forward, if applicable. Tax rates are denoted by the value T(ψ), 0 ≤ T(ψ) ≤ 1, and

may be fixed or based on a sliding scale: 

 

18 Note that when GRt = 0, COt = 0; or in words, the operator can only begin to recover cost after 

production begins. 
36 







− − ≤

− − − > = 0, / 0,

( )( / ), / 0

t t t

t t t t t

t PO C BONUS CF

T PO C CF PO C BONUS CF

TAX ψ 

where CFt represents the tax loss carry forward in year t. 

A number of elements commonly employed in PSAs, such as commerciality 

requirements, government participation, domestic market obligations, ringfencing, and 

reinvestment obligations impact the net cash flow position of the contractor. These terms 

are referred to and denoted as OTHERt in the cash flow equation. In some instances, the 

impact of these conditions may be quantifiable; at other times, it may not be possible to 

incorporate the terms in the analysis. In all cases the terms are field, contract, and 

operator specific. The reader is referred to (Allen and Seba, 1993; Johnston, 1994b; 

Thompson and Wright, 1984) for further description of these elements. 

2.4.3. Sliding Scales: Sliding scales are one of the most common and distinctive features 

of PSAs. The idea of a sliding scale is to create a fiscal arrangement that adjusts to the 

private and market uncertainties that occur over the life cycle of a project and impact the 

contractor or host government. Sliding scales represent a mechanism intended to control 

(or dampen) volatility and bound uncertainty. The principal is to adjust the terms of a 

contract to the profitability of the field, so that as production rates and/or oil prices 

increase, or reach a given threshold level, the contractor should be willing to accept a 

smaller amount of cost recovery, to take a smaller share of profit oil, to pay a larger tax 

rate, etc. Similarly, as production rates and/or oil prices decrease, the government should 

be willing to reduce tax levels, to accept a smaller share of profit oil, etc. The idea is to 

try to achieve balance within a dynamic and volatile market environment. 

Production bonuses, royalty rates, cost recovery, profit oil splits, and tax rates are 

typically based on sliding scales that are a function of one or more variables. The 

variables that are typically used include the average daily production, cumulative 

production, crude oil price, or “R-Factor19”; parameters such as the age or depth of 

reservoirs, field location, crude oil quality, water depth, and rate of return factors may 

also be employed. The variables are frequently negotiable. 

 

2.5. Economic and System Measures 

2.5.1. Economic Indicators: The purpose of economic evaluation is to assess if the 

revenues generated by the project cover the expenditures and capital investment, and the 

 

19 The R-Factor (RF) can be defined in various ways, but in its most basic form, is computed as the ratio of 

the contractor’s cumulative revenue after taxes and royalty to the contractor’s cumulative cost: 

∑

∑ − −

=

=

= x

t

t

x

t

t t t

x

TC

GR ROY TAX

RF

1

1

( )

, 

where TCt = EXPt+ CAPEXt+ OPEXt+ OTHERt. The terms may be inflation adjusted. 
37 

return on capital is consistent with the risk associated with the project and the strategic 

objectives of the corporation. The primary analytic techniques utilize a time value of 

money approach (Brealey and Myers, 1991), and several popular measures such as the 

present value, internal rate of return, and investment efficiency ratio are frequently 

employed in analysis. 

For field f and the fiscal regime denoted by F, the present value and internal rate of return 

of the cash flow vector NCF(f) is computed as 

 

PV(f, F) ∑=

− + =

k

t

t

t

D

NCF

1

1 (1 ) , 

IRR(f, F) = {D | PV ( f , F) = 0}. 

A profitability index, or investment efficiency ratio, normalizes the value of the project 

relative to the total investment and is calculated as 

PI(f, F) PV(TC)

PV(f,F) = . 

The present value provides an evaluation of the project’s net worth to the contractor in 

absolute terms, while the rate of return and profitability index are relative measures that 

are used to establish which projects should be selected to optimize the use of capital 

funds. A combination of indicators is usually necessary to adequately evaluate a 

contract’s economic performance. 

2.5.2. Government and Contractor Annual Take: The division of profit between 

contractor and government determines take. The total profit in year t is determined as, 

TPt = GRt −TCt , 

where, 

TPt = Total profit in year t, 

TCt = CAPEXt + OPEXt = Total cost in year t. 

The contractor and government take is computed as, 

CTt = TPt − BONUSt − ROYt − PO / Contractor take in year Gt − TAXt = t, 

GTt = BONUSt + ROYt + PO/ Government take in year Gt + TAXt = t. 

The contractor and government take in year t, expressed in percentage terms, is 

defined as 
38 

t

t c

t TP

CT

τ = , 

t

t g

t TP

GT

τ = . 

2.5.3. Government and Contractor Discounted Take: Take varies as a function of 

time over the life history of a field and is best computed on a discounted cumulative basis 

to account for the distribution of the cash flow and the distinct manner in which the 

contractor and government value money. The contractor and government take computed 

on a cumulative discounted basis in year x, x = 1,..., k, is written 

, ( ) ( )

( ) ( )

, ( ) ( )

( ) ( )

PV CT PV GT

PV GT PV

PV CT PV GT

PV CT PV

x x

g x

x

x x

c x

x

+ =

+ =

τ

τ

 

where, 

PVx(CT) = = + ∑=

−

x

t

c t

t

D

CT

1

1 (1 ) Present value of contractor take through year x, x = 1,..., k, 

PVx(GT) = = + ∑=

−

x

t

g t

t

D

GT

1

1 (1 ) Present value of government take through year x, x = 1,..., k, 

c D = Discount factor for contractor, 

g D = Discount factor for government. 

It is common practice to report take without discounting20, and this case is easy to handle 

by setting c D = g D = 0 in the above relation. Discounted take is computed by assuming c D = g D ≠ 0, or by considering c D and g D as decision parameters which range over 

specified design intervals. 

2.6. Generalized Fiscal System Analysis 

2.6.1. Terms of a Contract: The basic terms of a contract Γ are set forth by the 

legislative and regulatory requirements of the host government. The primary terms of a 

PSA include 

 

20 Undiscounted take is considered somewhat perverse, however, and failure to discount will significantly 

bias the statistic. One reason why take is frequently not discounted may be due to the requirement that the 

user select the “appropriate” value of c D and g D , but the default condition is itself a selection (and not a 

very good one): c D = g D = 0. See also footnote 7.
39 

• Duration (exploration, production), 

• Relinquishment, 

• Exploration obligations, 

• Bonuses (signature, discovery, production), 

• Royalty rate, 

• Cost recovery schedule, 

• Depreciation, 

• Profit oil split, 

• Taxation, 

• Ringfencing, 

• Domestic market obligations, 

• Investment uplift, and 

• State participation. 

Tax rates, depreciation schedules, government participation, investment credits, domestic 

obligation, and ringfencing are normally legislated and thus provide no opportunity for 

negotiation, while relinquishment requirements, bonus payments, cost recovery, and 

profit sharing can be subject to negotiation. Generally speaking, the more aspects of a 

contract that are subject to negotiation the better, since flexibility is often required to 

offset differences between basins, regions, and license areas within a country (Johnston, 

1994b). 

2.6.2. System Functionals: A contract is written for the block Bi, and if exploratory 

efforts on the block are successful, one or more fields will be discovered. The terms of 

the contract that were negotiated before exploratory activities were undertaken now hold 

for the commercial activity on the block. If the field discoveries are “significantly 

different” than the assumptions used in the negotiation process (either on the upside or 

downside), or if economic or political conditions change dramatically, then renegotiation 

of the terms of the contract may be initiated by the contractor or host government. 

A field is described by its expected reserves X(f), development plan D(f), cost structure

C(f), and production profile Q(f): 

f ↔ { X(f), C(f), D(f), Q(f)}. 

Contract Γ is a function of the fiscal terms negotiated for the block, and it is impossible, 

except under the very simplest contracts, to quantify all aspects of the PSA21. 

Fortunately, the terms of a contract most relevant from an economic perspective can 

usually be quantified without regard to the complexity and sophistication of the fiscal 

conditions, and if a condition can be specified its “impact” can usually be assessed. 

 

21 For instance, how does one quantify the impact of dispute resolution agreements, procurement 

guidelines, government involvement, sovereign immunity waivers, management commitments, 

relinquishment requirements, or license duration on the economic and system measurements? 
40 

The fiscal terms of a contract are written in terms of functionals described through the 

parameters of the fiscal regime: 

F (ψ) = (F 1(ψ), ..., F m(ψ)), 

where F i(ψ) are functions of the variable set ψ. A partial representation of ψ includes 

elements such as qt = Qt/365, CQt, Pt, RFt,... The primary fiscal terms of a contract 

include 

B(ψ) = Bonus payment, 

R(ψ) = Royalty rate, 

CR(ψ) = Cost recovery schedule, 

PO(ψ) = Profit oil split, and 

T(ψ) = Taxation structure. 

The functionals can be constant; i.e., F i(ψ) = α, α ≥ 0, but more often than not, the 

functions are based on one or more sliding scales, the terms of which are often 

negotiable. 

The economic and system measures of a field are written in general as φi(f, F), and 

denoted in vector form as 

Φ(f, Γ) = (φ1(f, F), ..., φl(f, F)). 

 A variety of system measures are employed, and as previously defined, include 

τ

c

(f, F) = Contractor take, 

τ

g

(f, F) = Government take, 

PV(f, F) = Present value, 

IRR (f, F) = Internal rate of return, and 

PI(f, F) = Profitability index. 

2.6.3. Meta-Modeling Methodology: The manner in which the system functionals PV(f, 

F), τ

c

(f, F), and IRR(f,F) depend upon the fiscal terms F(ψ) is of considerable significance 

since contract negotiation determines in large part the profitability of the project and the 

revenues received by the host government. There are many ways to analyze a fiscal 

system, and the standard approach is a variation on one basic theme. For field f and fiscal 

regime F, 

1. Specify a baseline case through the variable set ψ and compute φ(f, F (ψ)). 

2. Change the variable set ψ one (or more) factors at a time ψi → ψi' , ψ' = (ψ1, ..., 

ψi', ..., ψn), and compute φ(f, F(ψ')). 
41 

3. Infer results of the change in factor ψi through the difference ∆φ(ψ, ψ')= ∆φ(F(ψ), 

F(ψ'))= φ(f, F(ψ'))– φ(f, F(ψ)). 

4. Employ the graphical relations ∆φ(F(ψ), F(ψ')) in fiscal system analysis. 

Although useful and commonly employed in fiscal system analysis, there are also 

significant limitations associated with this approach. The methodology is piecemeal and 

the results are only valid relative to the initial conditions specified. The analysis does not 

readily describe how the variables interact or the relative significance of the parameters. 

The amount of work involved to generate and present the model results is nontrivial, and 

the restrictions associated with geometric and tabular presentations of multidimensional 

data is significant; e.g., on a planar graph at most three or four variables can be examined 

simultaneously. Fiscal system analysis is more often confusing rather than illuminating 

because of the limitations associated with the solution approach. 

A more general and concise approach to fiscal system analysis, previously applied to a 

royalty/tax fiscal regime, is now described. A meta-modeling approach is developed to 

construct functional relations that describe how the system variables interact and impact 

the system measures. A cash flow model of the system is first constructed, and then 

parameters of the system are defined and bound through specified design intervals. The 

parameters of the system are sampled from the design space and evaluated in the cash 

flow model. The results of the model and system parameters are then analyzed and linear 

models constructed from the generated data. The general approach is as follows. 

1. Specify the variable set ψ and determine the design interval , l u ,i 1,...,n i ≤ψ i ≤ i =

for each parameter of interest. Denote the design space as Ω: 

Ω = { } ( ,..., ) | l u ,i 1..., n ψ = ψ1 ψn i ≤ ψi ≤ i = . 

2. Form ψ* ( *,..., *) = ψ1 ψn , where ψi* is sampled uniformly from the design 

interval, [ , ] i i U l u , , i = 1,...,n and compute φ(f, F(ψ*)). 

3. Based on the data sets {ψ*} and {φ(f, F(ψ*))}, estimate for each measure φ the 

functional relation 

φ(f, F(ψ)) = i

n

i

∑αi φ ψ =1

( ) , 

where the coefficients αi (φ) are determined through regression modeling. 

4. Employ the functional relations φ(f, F(ψ)) in fiscal system analysis and design. 
42 

2.7. A Functional Analytic Approach to System Evaluation 

2.7.1. Development Scenario: The development scenario outlined is for a hypothetical 

40 MMbbl field with a projected 11-year life depicted in Appendix Table B.1. The 

projected production, capital expenditures, and operating expenditures are extracted from 

Johnston (Johnston, 1994b) under a base case development scenario specified for P50

reserves. 

 

Total capital costs are estimated at $60M and distributed as 28% intangibles (services) 

and 72% tangibles (facilities, equipment, etc.). The tangible capital costs are depreciated 

using a 5-year straight line schedule. Estimated operating costs during the life of the 

project is $117M representing on average a $3/bbl full cycle cost. OPEX is initially stable 

at $2.5/bbl but increases significantly near the end of the life of the field. 

The royalty rate is calculated as a percentage R(ψ), 0 ≤ R(ψ) ≤ 1, of gross revenues, and 

the income tax is calculated as a percentage T(ψ), 0 ≤ T(ψ) ≤ 1, of taxable income. Tax 

losses are carried forward from a previous year if negative. The cost oil COt is computed 

as: 

COt = min(CRt, CR(ψ)GRt), 

for 0 ≤ CR(ψ) ≤ 1, and the profit oil split PO(ψ) is assumed constant throughout the life 

of the field. 

 

Cash flows are presented in nominal terms, and the oil price Pt and the contractor and 

government discount factors, 0 ≤ c D , g D ≤ 1, are assumed constant. The conversion 

factor gt is assumed to be unity and the allowance term ALLOWt is set equal to zero. 

There is no government participation or domestic market obligations associated with the 

contract. 

2.7.2. Regression Modeling Results: The design space for the two models considered 

are specified in Appendix Table B.2. In Model I, the PSA is developed with no sliding 

scale parameters, and in Model II, a sliding scale profit oil schedule is examined. 

Regression models are constructed for τ

c

(f, F), PV(f, F), and IRR(f, F) for 500 points 

selected uniformly from the design space interval. The regression coefficients quickly 

stabilize with the sample rate and the 500 data point simulation is considered 

representative. The regression results for Model I are shown in Appendix Table B.3: 

( ) 14.1 0.1 18.4 40.8 27.3 54.7 61.6 , c c g τ f = + P − R + PO − T − D + D =2 R 0.95, 

( ) 25.3 3.7 24.0 118.2 80.8 204.1 ,

c PV f = − + P + CR + PO − T − D =2 R 0.87, 

( ) 1.0 12.2 9.1 36.4 21.2 42.0 ,

c IRR f = P − R + CR + PO − T − D =2 R 0.31. 

All the coefficients have the expected signs and the model fits are fairly robust. For any 

value of (P, R, CR, PO, T, c D , g D ) within the design space shown in Appendix Table 
43 

B.2, the regression models can be used to evaluate and compare the impact of userspecified parameters. 

Contractor take increases with an increase in commodity price and profit oil and falls 

with the royalty and tax rate. As the contractors discount factor is increased, or the 

government discount factor is decreased, take declines. For (P, R, T, c D , g D ) = (20, 

0.15, 0.35, 0.20, 0.10), 

( f , c τ F) , = 4.5 + 40.8PO

indicating that for PO = 10%, a 1% increase in PO will increase f c τ ( , F) by 0.5%, while 

if PO = 60%, a 1% increase in PO will increase ( f , c τ F) by 2.8%. It is clear that as the 

component vector varies within the design space, so too will the functional relation 

between take and profit oil. For instance, for (P, R, T, c D , g D ) = (25, 0.125, 0.50, 0.15, 

0.10), 

( f , c τ F) = −1.4 + 40.8PO , 

and in this case, a 1% increase in the profit oil will increase take 1.5% (at PO = 10%) and 

1.1% (at PO = 60%). 

The present value functional increases with price, cost oil and profit oil, and decreases 

with the tax rate and corporate discount factor. An increase in commodity price will 

increase the value of the venture, and as cost oil is increased, the contractor can recover a 

greater percentage of its cost earlier in the life of the field. Similarly, as profit oil is 

increased, a greater share of the profit is received by the contractor sooner, further 

increasing the value of the project. The present value functional evaluated at P = $20/bbl, 

T = 35%, and c D = 10% yields 

PV(f, F) = 50.6 + 24.0CR + 118.2PO. 

Under very tough fiscal terms; e.g., CO = PO = 10%, the field remains profitable, but 

whether the field satisfies the rate of return criteria of the operator is another matter. For 

(P, R, T, c D ) = (20, 0.15, 0.35, 0.10), 

IRR (f, F) = 6.6 + 9.1CR + 36.4PO, 

and at CR = PO = 10%, IRR(f, F) = 11%. 

The value of the profit oil split is apparently a more significant parameter than the 

selection of cost recovery (about four-to-five times more significant), and so the 

contractor would be well served to focus attention on negotiating the best terms for this 

factor. For example, if CR = 40% and PO = 50%, then every one percentage point 

increase in the cost recovery (profit oil) will lead to a 0.2% (1.0%) increase in the present 

value of the project, or in absolute dollar terms, every one percentage point differential is 

worth $240,000 ($1.2M). 
44 

 

For a given component specification, such as (P, CR, T, c D ) = (20, 0.6, 0.35, 0.10), it is 

easy to express take in terms of the present value or rate of return measure through 

regression: 

PV(f, F) 9 = 52 + 2. ( f , c τ F). 

More generally, the correlation between c τ and PV is ( ,PV) = c ρ τ 0.76, and 

( ,IRR) = c ρ τ 0.46, ρ(PV,IRR) = 0.61. 

The expected value and standard deviation of the system measures are shown in the last 

two rows of Appendix Table B.3. The expected value and standard deviation of the 

system measures, E[φ(f, F)] and σ[φ(f, F)], is a function of the design space Ω and the 

value of σ[φ(f, F)] is dependent on the “volume” of Ω, so that for instance if tighter 

bounds on the intervals are selected; e.g., P ~ U(20, 25), R ~ U(0.125, 0.167), CR ~ 

U(0.40, 0.60), etc. a reduction in the value of σ[φ(f, F)] is expected. 

 

2.7.3. Profit Oil Sliding Scale: After the base model is constructed, it is relatively easy 

to develop more sophisticated sliding scale mechanisms for one or more fiscal parameters 

of the PSA. Complexity can be added a layer at a time and the impact of the specification 

analyzed sequentially for each component term. In Model II, a two-tranche sliding scale 

profit oil schedule is illustrated. 

A profit oil sliding scale is defined in terms of cumulative production as follows: 









>

≤ =

∑

∑

- 2, ( ),

-1, ( ), ( ) PO Q Q fPO Q Q f PO

t

t

ψ

where the variables PO-1 and PO-2 are bound in the design intervals: 

PO-1 ~ U(0.40, 0.60), 

PO-2 ~ U(0.30, 0.40), 

and the factor Q(f) serves to trigger the application of PO-2. The value of Q(f) is 

described in terms of MMBOE and is selected uniformly from the interval 5 MMBOE ≤

Q(f) ≤ 35 MMBOE: 

Q(f) ~ U(5, 35). 

 The results of the regression model are depicted in Table 4. 

The present value functional is computed as, 

PV + ( f ) = −17.1 2.7P + 17.0CR– 58.1T – 176.8 c D + 5.5PO-1+ 106.4PO-2 + 0.1Q, 
45 

and with the exception of PO-1 and Q(f), all the coefficients are highly significant. The 

present value of the project increases with the price, cost oil and profit oil, and decreases 

with the tax rate and corporate discount factor. The model coefficients for PO-1 and PO2 suggest that the value of PO-2 is considerably more significant to the profitability of 

the field than PO-1. Insights derived from the regression modeling are a quick and 

convenient way to evaluate and direct negotiation strategies. 

2.8. Deepwater Angola Case Study: Girassol 

2.8.1. The Angola Play: The West Africa play runs along the Nigeria-Angola axis and 

includes the countries Nigeria, Cameroon, Equatorial Guinea, Sao Tome and Principe, 

Gabon, and Angola. Refer to Appendix Figure B.2. When the continents were spreading 

millions of years ago, a large volcanic ridge extended across the South Atlantic which 

closed off and restricted the northern oceanic waters, which eventually evaporated into 

salt basins along the north of the ridge (Shirley, 2000). The result is that the West Africa 

region has extremely rich source rocks in salt basins characterized by faulting – adding 

up to large structures with good migration paths. South of Angola (and the ridge), the 

geology changes dramatically and so do the prospects. More than 30 deepwater fields in 

West Africa are planned to come on stream by 2007, with the majority of these located in 

Angola and Nigeria (Deluca, 2002). Within 10 years the West Africa region has the 

potential to mature to a scale that will rival the North Sea at its peak (Edwardes, 2000). 

Oil production started in Angola in 1955, and since 1975, has been the principal export, 

contributing between 75% and 90% of all government revenue through signature 

bonuses, equity profit oil shares, additional contract deals, taxes, and duties. The 

petroleum industry accounts for about 50% of Angola’s GDP (Clarke, 2000). In 2002, oil 

production averaged 920,000 BOPD and plans are to achieve 1.5 MMBOPD by 2006 

(Angola, 2003). Current proved and probable reserves are estimated at 20 Bbbl of oil and 

7-8 Tcf of gas (Angola, 2003). The USGS petroleum assessment for undiscovered

resources is estimated at 15 Bbbl oil and 42 Tcf gas. To date, 34 offshore blocks have 

been delineated, and the major operators ChevronTexaco, ExxonMobil, TotalFinaElf, and 

BP have assembled enough field developments that the government now has a queue. 

Angola is expected to challenge Nigeria in the years ahead as Africa’s leading crude oil 

producer. 

2.8.2. Angolan Production Sharing Agreements: Angola adapted a PSA in 1979 for 

shallow waters, and later modified the contract with fiscal incentives applied to 

demarcated deepwater zones. The fiscal system in Angola has been characterized 

variously as “tough” and “very tough” over the years, and estimates of government take 

range between 81%-88% (see Bindemann, 1999; Johnston, 1994b; Van Meurs and Seck, 

1997). Sonangol is the National Oil Company and the business arm of the government. 

Sonangol’s main function is to oversee the petroleum operations of foreign companies, 

and under Angolan law, has exclusive rights to make concessions in the form of PSAs 

(www.mbendi.co.za). 
46 

Angolan PSAs typically have no royalty requirements and the 50% tax rate may be paid 

in lieu by Sonangol. Cost recovery is usually fixed at 50% but this can be increased under 

certain circumstances. A negotiable uplift on development cost (40% ceiling) and a (3-5)-

year straightline depreciation schedule hold for most contracts written since 1984. 

Exploration cost is expensed and ringfencing is required for cost recovery around the 

license (for exploration) and around a field (for development). 

 

The profit oil split in contracts written before 1990 tended to be on a volume-basis, but 

today, the value of PO(ψ) is based on R-Factors that are negotiable. Before 1991, 

contract duration for exploration was typically 3 years plus two 1-year extensions. After 

1991, exploration was defined as 3 years plus three 1-year extensions for shallow water, 

and 4 years plus one 2-year extension for deepwater. The terms of production currently 

extend for 20-25 years. The work requirements to be performed are specified in the 

exploration obligations, which is block specific and biddable; e.g., Conoco (1986) spent 

$60M on 4,000km seismic and 6 wells; Total (1989) spent $9M on seismic and 2 wells. 

Signature bonuses22 vary with the block, operator, lease sale, and other factors; e.g., 

blocks 31-33 brought in $300M in signature bonus from BP, TotalFinaElf, and 

ExxonMobil in 1999; while block 21 ($40M, BHP), block 24 ($69M, ESSO) and block 

25 ($85M, Agip) also held significant interest (Shirley, 2001a; Shirley, 2001b). 

Prior to 1991, there were no domestic market obligations, but at the request of Sonangol 

there is now a prorate option with rights up to 40% of production and the contractor 

responsible for marketing local sales. A price cap fee of 100% is paid to Sonangol on all 

revenue generated by oil prices in excess of the price cap which is currently set above 

$30/bbl. A training contribution of $200,000 per year per block is set during the 

exploration phase, and $0.15/bbl once production starts. A number of other factors also 

impact the bottom line. Customs duties and fees include a stamp duty of 0.5% on customs 

clearance documents for imports and exports; a statistical tax of 0.1%, and fees for 

services rendered by state agencies. Foreign oil companies are subject to special foreign 

exchange terms to retain outside the country, and to dispose of, the proceeds derived from 

oil sales. Special legislation and regulatory measures protect foreign companies from the 

local currency’s devaluation. 

2.8.3. Block 17 Deepwater Development: The Girassol deepwater development in 

block 17 was one of the first commercial deepwater fields in Angola and is by far the 

most spectacular in Angola’s deep water province (Cottrill, 2001). Girassol was 

discovered in 1996 approximately 150km off the Angolan coast in 1,350m water depth. 

Elf Exploration Angola, an affiliate of the French company TotalFinaElf, formed a 

project team for Girassol and took it to sanction in July 1998. TotalFinaElf serves as 

operator with a 40% interest along with its partners ExxonMobil (20%), BP (16.67%), 

Statoil (13.33%), and Norsk Hydro (10%). The initial development of Girassol 

experienced delays, and three and a half years after the decision to proceed with the 

development was taken, first oil flowed in December 2001. Girassol is estimated to have 

recoverable oil reserves between 725 MMBOE and 1 BBOE. 

 

22 In Angolan bidding rounds, companies bid for the operatorships as well as for the rights to non-operating 

equity, and at both times, a signature bonus is required. 
47 

The development plan was scheduled in two phases. In phase I, approximately 75% of 

the $2.7B budget was used to construct and install a Floating Production Storage 

Offloading (FPSO) vessel23 and drill 24 wells. In phase II, 15 additional wells will be 

completed. The complete subsea system will have 23 producers out of a total of 39 wells 

feeding in pairs to daisychains of manifolds. Fourteen water injectors and 2 gas injectors 

are planned. The subsea installations consist of 70 km of infield pipelines linked to 

insulated flowline bundles and 3 riser towers carrying production to an FPSO to process 

200,000 BOPD, treat 180,000 BPD and inject 390,000 BPD of water. See Appendix 

Figure B.3 and Appendix Figure B.4. By mid-2002, production from Girassol reached a 

plateau output of roughly 200,000 BOPD. 

A number of additional discoveries have been made on block 17, and at the end of 2002, 

15 oil discoveries now exist: Girassol, Dalia, Rosa, Lirio, Cravo, Orchidea, Camelia, 

Tuplia, Jasmim, Perpetua, Violletta, Anturio, Zinia, Acasia, and Hortensia. Jasmim is 

being developed as a satellite tied back to Girassol, and is due to start production in 3Q 

2003. Project sanction for Rosa will take place in 2003 at the earliest, and a decision to 

develop Cravo and Lirio will be taken later. It is likely that Rosa, Cravo, and Lirio will be 

developed as satellites to Girassol. Calls for tender have been launched for Dalia’s $3B 

development scheme scheduled to start in 2006 (Beckman, 2003). 

2.8.4. Development Scenario: The development scenario for Girassol is based on an 

estimated gross ultimate recovery of 725 MMBOE. The projected production, capital 

expenditures, and operating expenditures are shown in Appendix Table B.5 based on 

publicly available sources of information. Total project cost is estimated at $2.7B. 

Approximately 40% of the costs are associated with the fabrication and installation of the 

FPSO; 20% to the underwater network of flowlines, risers, and umbilicals which form the 

links between wellhead and floater; 20% to the subsea system; and 20% to the drilling 

and completion of the wells. Life cycle capital expenditures are estimated at $1.94/bbl, 

with operating cost estimated at $2.25/bbl. 

2.8.5. The Design Space: The design space for the three models under consideration is 

shown in Appendix Table B.6. The contract parameters for the “model” Angolan PSA are 

specified in Model I, while the basic elements of fiscal design are explored in Model II 

and Model III. In Model II, the impact of a change in the depreciation schedule is 

examined, and in Model III, the profit oil split is generalized so that we may determine 

what an incremental change in the profit oil split functional is worth. 

The model PSA has no royalty requirements and tax is paid in lieu by Sonangol, and so 

the contract parameters are specified to reflect small variations in these parameters; i.e., R 

~ U(0.00, 0.10), T ~ U(0.00, 0.20). Exploration costs are expensed and development costs 

are depreciated according to a 5-year straight line schedule. The profit oil split is 

specified in Appendix Table B.7, and since the production stream is specified under a 

fixed development scenario, it is clear that the profit oil percentage terms are determined 

by the value of qt = Qt/365 shown in Appendix Table B.5. 

 

23 The FPSO has a storage capacity of 2 MMbbl. 
48 

Cost oil is defined in terms of the cost recovery scheme as follows: 

COt = min(CRt, CR(ψ)GRt), 

where CR(ψ) is determined through a Uniform distribution, CR(ψ) ~ U(0.25, 0.75), and 

unrecovered cost in year t – 1 is carried forward and recovered in a subsequent period. If 

CR(ψ)GRt > CRt, then CRt will be selected through the minimization operator “min” in 

the cost oil, and there will not be any unrecovered cost. On the other hand, if CR(ψ)GRt < 

CRt, then the selection of CR(ψ)GRt will prevent full cost recovery, and the difference 

between these two quantities, or 

Ut = CRt – CR(ψ)GRt, 

determines the unrecovered cost which is passed through to the next year. 

Uplift is a fiscal incentive which allows the contractor to recover an additional percentage 

of the development costs associated with placing a discovery into production24. Uplift 

follows the Uniform distribution, UP ~ U(0.30, 0.50), and acts as a multiplier on all 

tangible and intangible capital expenditures as follows: 

(1+ UP)CAPEX/Tt ,

(1+ UP)CAPEX/It . 

The contractor and government discount factors are assumed to range as follows: 

Dc ~ U(0.05, 0.20), 

D g ~ U(0.00, 0.10). 

Domestic market obligations and government participation are not considered, and since 

the range of the oil price is assumed to fall below $30/bbl, the price cap fee does not play 

a role in the analysis. 

In Model II and Model III the depreciation schedule and profit oil split are considered 

design variables. Depreciation schedules are an accounting convention designed to 

emulate the cost associated with a reduction in the value of a tangible asset. Although 

different assets normally have different depreciation horizons, most PSAs in the world 

use a 5-year straight line depreciation schedule, and Angola is no exception with most 

contracts written since 1984 using a 3-5 year straight line schedule. Dd denotes a d-year 

straight line depreciation schedule, and the value of d is assumed to be integer-valued, d 

= 3, d= 5, or d = 7. In Model III the profit oil split schedule is generalized in terms of a 

variable tranche Yi and percentage value Z j as shown in Appendix Table B.8. The values 

 

24 For example, if a contractor spent $100M on development costs (drilling, production facilities, 

transportation costs) and the government allowed a 40% uplift, then the contractor is allowed to recover 

$100(1+0.4)M = $140M. 
49 

of Yi , i = 1,..., 4 and Z j , j = 1,..., 4 are selected from the distributions shown in 

Appendix Table B.6. 

2.8.6. Regression Model Results: The results of the regression models for τ

c

(f, F), PV(f, 

F), and IRR(f, F) for Models I-III are shown in Appendix Tables B.9-B.11. 

In Model I, the coefficients αi of the linear model 

φ(f, F) i

i

∑ iX =

=

7

1

α

for parameter vector ( ) ,..., ) ( , , , , , , 1 7

c g X X = P R CR UP T D D and φ(f, F) = {PV(f, F), 

c τ (f, F), IRR(f, F)} are estimated using standard least squares regression. For the most 

part, the model coefficients maintain the expected signs, the fits are generally very robust, 

and the coefficients are statistically significant. Coefficients that do not exhibit the 

expected signs are usually not statistically significant. 

The present value functional of the field development is estimated as 

PV(f, F) 8 = −724. + 54.5P–28.7R+731.4CR+278.0UP –514.7T – 4639.1 c g D −120.7D , 

so that at ( , , , , , , ) = c g P R CR UP T D D (25, 0, 0.5, 0.4, 0, 0.15, 0.05), 

 

PV(f, F) = $412.7M. 

The regression coefficients for take and rate of return are shown in Appendix Table B.9, 

and when evaluated at the above parameter specification yields 

c τ (f, F) = 6.8%, 

IRR(f, F) = 7.1%. 

In Model II, separate regression models are constructed for the depreciation 

schedules Dd , d = 3 and d = 7: 

φ(f, F) ,

7

1

i

i

∑ ijX =

= α j = 3, 7. 

To model the impact of a change in depreciation schedule, it is necessary to dynamically 

link the requirements of depreciation with the uplift parameter and the unrecovered cost. 

The uplift parameter is a Uniform random variable which impacts the amount of tangible 

capital expenditures that can be depreciated, subsequently impacting the cost recovery 

schedule and the amount of unrecovered cost. The results of Model II are shown25 in 

Appendix Table B.10. 

 

25 The results of the regression models could also be combined into one relation, 
50 

In Model IIa, a 3-year depreciation schedule is applied, while in Model IIc, a 7-year 

depreciation schedule is used (Model IIb = Model I, a 5-year depreciation schedule). For 

comparison we evaluate each model at ( , , , , , , ) = c g P R CR UP T D D (25, 0, 0.5, 0.4, 0, 

0.15, 0.05). The results in this case, 

PV(f, D3) = $387.9M, 

PV(f, D5) = $412.7M, 

PV(f, D7) = $382.5M, 

are inclusive since the expected relation PV(f, D3) >PV(f, D5) > PV(f, D7) does not hold 

across the three depreciation schedules. 

In Model III, the profit oil split schedule depicted in Appendix Table B.7 is considered 

the “design” variable. As a casual examination of Appendix Table B.7 reveals, the 

variable selected to drive the model (q), the number of tranches (4), the tranche 

thresholds (25, 50, 100), and the value of the profit oil split percentages (55, 30, 20, 10) 

specify the Angolan profit oil split. In total, ignoring the selection of the driver variable 

and number of tranches, 3 threshold levels denoted Yi, i = 1,2,3, and 4 profit oil split 

percentage values Zi, i = 1,...,4, determine a 7-dimensional structure. 

There are various system and preference constraints associated with the profit oil 

functional shown in Appendix Table B.8 that must be incorporated in the design 

structure, most notably, Y1 < Y2 < Y3 (system constraint) and Z1 > Z2 > Z3 > Z4 (preference 

constraint). Thus, in the selection of the sample intervals, if Yi ~ U(ai, bi), then 

1 2 2 3 b ≤ a and b ≤ a is required to prevent the occurrence of spurious relationships. The 

preference constraint is not as strictly defined and in principle it is possible (although not 

likely) that mixed relations such as Z1 < Z2 > Z3 < Z4 will be designed. In the selection of 

design intervals for Zi some overlap in the sampling is therefore permitted. 

The regression model for the profit oil structure is presented in generalized form as 

φ(f, F) ∑ ∑ ∑ = = == + +

4

1

3

1

7

0 k

k k

j

i j

i

αiX β Y γ Z 

 

φ(f, F) 2 1 2 1

3

1

7

1

∑ + + = ∑ + = = i

Xi j D j

i j

α β , 





 = 0, otherwise.

1, depreciation schedule used j

j

D

D

Under a standard royalty/tax fiscal regime we would expect 3 5 7 β > β > β since a quicker depreciation 

schedule means that the operator can recover their cost more quickly, but in a PSA regime with cost 

recovery schemes, the cost ceiling controls the degree to which depreciation schedules impact the cash 

flow. If cost recovery schemes are dominant, then the impact of advanced depreciation may not be 

detectable. 
51 

to delineate the system parameters (Xi) from the design parameters (Yj, Zk). Since the 

structure of the regression model has changed by the addition of 7 new variables, it is 

clear that the coefficients αi will change relative to Model I, and to ensure the stability of 

the model results, additional iterations should be performed. The signs of the coefficients 

αi , i =1, ...,7 should be the same as Model I, while the signs for β j , j =1, 2, 3 and k γ , k 

=1, ...,4 are expected to be positive since an increase in the tranche level or profit oil 

split percentage will increase the profitability of the field, and subsequently, the take, 

present value, and internal rate of return measures. 

The results of Model III are shown in Appendix Table B.11. The αi coefficients change 

while the β j coefficients are identically zero, indicating that the selection of threshold 

levels does not noticeably impact the present value of the field. This apparently 

anomalous relation is explained by closer examination of the field’s production profile. 

From Appendix Table B.6, observe that Girassol flows in excess of 100 MBOPD for the 

first 9 years of production, and since Y3 ~ U(50, 100), it is clear that Z4 will be the only 

percentage value used in the first 9 years of production. Further, since Y3 ~ U(50, 100), 

anywhere between 1-4 years of production may be added at the profit oil split percentage

Z4 depending on the sample value selected for Y3. Thus, since the profile is fixed and the 

tranche levels are restricted through process constraints, variability in the Y3-tranche 

levels cannot effectively be felt. The first 9-13 years of production will be maintained at 

profit oil split percentages determined by Z4 and Z3 . 

The coefficients γk are positive and statistically significant with magnitudes γ1 < γ2 < γ3 < 

γ4 as expected. Girassol is expected to flow in excess of Y3 for nearly a decade, and so the 

value selected (negotiated) for Z4 is the most significant term of the profit oil schedule. 

The regression model also allows us to infer the value of each of these terms. In brief, 

every percentage point increase negotiated in Zi translates to a 0.01γi increase in the 

present value of the field; i.e., a percentage point increase in Z4 is worth $38M, $9M for 

Z3, $4M for Z2, and $1M for Z1. Observe also that the impact of the choice of Z4 (as well 

as Z3) dominates the choice of the cost recovery factor CR and uplift UP. The coefficients 

for take can be interpreted similarly. Every 1% point increase in Zi translates to a 0.01Yi

increase in the contractor take; i.e., a 1% increase in Z4 equates to a 0.4 percentage point 

addition in take. 

For ( , , , , , , ) = c g P R CR UP T D D (25, 0, 0.5, 0.4, 0, 0.15, 0.05), 

PV(f, F) = -523.2 + 90.2Z1 +403.9Z2 + 869.6Z3 +3771.7Z4

c τ (f, F) = -1.3+0.8 Z1 + 3.8Z2 +4.9Z3+ 40.0 Z4 

and so at (Z1, Z2, Z3, Z4) =(0.50, 0.40, 0.25, 0.10),

PV(f, F) = $278.0M c τ (f, F) = 5.8%. 

A number of additional insights follow from a more detailed examination and comparison 

of the model functionals. 
52 

2.9. Conclusions 

To understand the economic and system measures associated with a contractual fiscal 

regime a meta-model was developed. In the meta-evaluation procedure, a cash flow 

model specific to a given fiscal regime is coupled with a simulation strategy to 

investigate the influence of various system variables. Meta-modeling is not a new idea, 

but as applied to fiscal system analysis and contract valuation, is new, novel, and useful. 

A constructive approach to fiscal system analysis was developed to isolate variable 

interaction and determine the manner in which private and market uncertainty impact 

take and the economic measures associated with a field. Functional relations were 

developed by computing the component measures for parameter vectors selected within a 

given design space. The relative impact of the parameters and the manner in which the 

variables are correlated was also established in a general manner. The methodology was 

illustrated on a hypothetical oil field and a case study for the Angolan deepwater Girassol 

development was considered. The impact of fiscal design on the field economics of 

Girassol was also examined. 
53 

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57 

APPENDIX A 

CONCESSIONARY SYSTEMS FIGURES AND TABLES
59 

Source:Shell (www.shell.com) 

Figure A.1: The Na Kika Field Development. 

Source: Shell (www.shell.com) 

Figure A.2: The Na Kika Host Platform and Subsea Well Configuration. 
60 

Table A.1 

 Projected Production, Capital Expenditures, and Operating Expenditures for a 

Hypothetical 40 MMbbl Field 

 Oil Production CAPEX/I CAPEX/T OPEX 

Year (MMbbl) ($M) ($M) ($M) 

1994 0 10 10 0 

1995 0 5 8 0 

1996 0 3 40 0 

1997 4.500 0 25 11.5 

1998 7.000 0 0 14.0 

1999 5.600 0 0 12.6 

2000 4.760 0 0 11.8 

2001 4.046 0 0 11.0 

2002 3.439 0 0 10.4 

2003 2.923 0 0 9.9 

2004 2.485 0 0 9.5 

2005 2.087 0 0 9.1 

2006 1.732 0 0 8.7 

2007 1.427 0 0 8.4 

2008 0 0 0 0 

Total 40.000 18 83 117.0 

 Source: Johnston, 1994b; Table 3-2. 

Table A.2 

Regression Models for Contractor Take, Present Value, and Internal Rate of Return 

for a Hypothetical 40 MMbbl Field 

φ(f) φ(f) = k +αP + βR + γT + δDc

 + εDg

Iterations 

k α β γ δ ε

R2

c τ (f) 100 44.5(2) 3.1(7) -72.6(-2) -89.1(-2) -216.3(-6) -6(*) 0.70 

500 36.1(7) 2.8(30) -84.5(-10) -71.7(-8) -163.4(-21) 43.1(3) 0.75 

1,000 28.8(6) 2.9(34) -77.1(-9) -51.0(-6) -174.1(-26) 21.7(1) 0.65 

5,000 29.1(10) 2.8(56) -81.2(-17) -56.6(-11) -165.2(-41) 50.0(5) 0.73 

PV(f) 100 76.7(4) 5.3(16) -132.8(-5) -111.7(-3) -331.1(-13) 64.3(1) 0.93 

500 74.3(16) 5.2(61) -129.2(-16) -99.1(-12) -318.1(-46) 21.0(1) 0.93 

 1,000 76.2(21) 5.4(86) -146.5(-22) -98.5(-15) -325.4(-65) -0.3(*) 0.93 

5,000 74.6(47) 5.4(95) -135.0(-49) -101.1(-37) -316.0(-145) 1.7(*) 0.93 

IRR(f) 100 18.1(13) 1.8(73) -40.7(-15) -30.5(-14) -89.1(-47) 2.3(1) 0.98 

500 16.9(26) 1.7(153) -44.1(-40) -30.7(-28) -85.3(-90) 2.3(1) 0.98 

 1,000 17.9(37) 1.8(218) -43.7(-52) -31.3(-38) -87.4(-139) -0.5(*) 0.99 

5,000 18.2(54) 1.8(311) -44.3(-79) -31.7(-55) -86.2(-189) -0.6(*) 0.99 

Footnote: t-statistics are in parenthesis, (*): t-statistic < 1 
61 

Table A.3 

Projected Production, Capital Expenditures, and Operating Expenditures 

for the Na Kika Field Development 

Year Oil Production 

(bbl/day) 

Gas Production 

(MMcf/day) 

CAPEX/T 

($M) 

CAPEX/I 

($M) 

OPEX 

($M) 

2001 0.0 0.0 52.83 0.00 0.00 

2002 0.0 0.0 350.13 19.24 0.00 

2003 100,000.0 325.0 475.33 263.98 5.66 

2004 95,177.5 312.0 0.00 0.00 25.30 

2005 95,177.5 312.0 0.00 0.00 30.09 

2006 82,002.8 304.2 0.00 0.00 30.09 

2007 55,538.0 235.5 0.00 0.00 30.09 

2008 37,514.4 171.9 0.00 0.00 30.09 

2009 25,279.5 125.2 0.00 0.00 37.28 

2010 16,683.1 91.5 0.00 0.00 37.28 

2011 11,694.0 66.8 0.00 0.00 37.28 

2012 0.0 48.8 0.00 0.00 106.47 

Total 878.29 283.22 369.65 

Source: Data provided by Thierno Sow of the MMS. 
62 

Table A.4 

The Design Space of the Na Kika System Parameters 

Parameter (unit) Model I a Model IIb Model III Model IV

Po($/bbl) U(20, 30) LN(25, 5) LN(25, 5)c LN(25, 5)c

Pg ($/Mcf) U(2, 5) LN(3.5, 1.5) LN(3.5, 1.5)c LN(3.5, 1.5)c

R (%) U(0.10, 0.20) U(0.15, 0.18) U(0.15, 0.18) U(0.15, 0.18) 

Q (MMBOE) U(0, 100) U(0, 100) U(0, 100) U(0, 100) 

T (%) U(0.35, 0.50) U(0.40, 0.50) U(0.40, 0.50) TR(0.38, 0.44, 0.50)d

Dc (%) U(0.15, 0.40) U(0.05, 0.15) U(0.05, 0.15) U(0.05, 0.15) 

Dg (%) U(0.05, 0.15) U(0.00, 0.05) U(0.00, 0.05) U(0.00, 0.05) 

 Footnote: (a) U(a, b) denotes a Uniform probability distribution with endpoints (a, b). 

 (b) LN(c, d) represents a Lognormal probability distribution with mean c and standard deviation 

d. 

(c) Po

 and Pg are assumed to vary on an annual basis; i.e., Po =Pt

o

 ~ LN(25, 5) and Pg = Pt

g ~ 

LN(3.5, 1.5) for t= 1, ..., 12. 

(d) TR(e, f, g) represents a Triangular probability distribution with minimum e, most likely f,

and maximum g. T is assumed to vary on an annual basis; i.e., T= Tt ~ TR(0.38, 0.44, 

0.50) for t= 1, ..., 12. 

Table A.5 

The Impact of Royalty Relief on Contractor Take, Present Value, and Internal Rate 

of Return for the Na Kika Field Development 

φ(f) φ(f) = k + αPo

 + βPg + γR + δQ + εT + θDc + λDg

R2

Model k α β γ δ ε θ λ

c τ (f) I 80.0(161) 0.2(18) 0.5(13) -53.0(-50) 0.04(42) -79.1(-112) -84.3(-198) 86.2(78) 0.99 

II 86.7(369) 0.2(26) 0.1(21) -54.1(-51) 0.04(121) -77.4(-243) -108.6(-337) 107.9(164) 0.99 

III 86.8(123) 0.1(4) 0.1(2) -53.3(-21) 0.03(50) -78.6(-99) -107.9(-145) 107.0(70) 0.98 

IV 86.7(30) 0.1(1) 0.1(*) -54.6(-12) 0.04(30) -76.0(12) -108.9(-81) 106.8(40) 0.95 

PV(f) I 1460.7(33) 38.2(40) 131.5(42) -1259.8(79) 1.1(12) -1856.1(-30) -3699.4(-99) 79.8(1) 0.97 

II 2113.6(29) 56.9(98) 232.0(119) -2200.6(-7) 1.8(17) -3404.8(-35) -8294.5(-83) 27.6(*) 0.98 

III 2252.5(12) 52.6(12) 226.5(14) -1957.1(-3) 1.2(6) -3414.2(-17) -8086.6(-42) 609.8(2) 0.84 

IV 2088.8(4) 74.2(14) 212.9(13) -3285.9(-4) 2.2(9) -3632.6(-3) -8407.1(34) -212.1(*) 0.75 

IRR(f) I 63.4(54) 2.6(145) 8.6(103) -58.9(-24) 0.1(49) -126.2(-76) -131.5(-131) 2.2(1) 0.99 

II 72.9(40) 2.8(185) 5.6(196) -68.4(-8) 0.2(50) -150.0(-61) -171.5(-65) 2.2(*) 0.99 

III 82.8(6) 2.9(9) 8.4(7) -68.5(-1) 0.1(7) -167.2(-10) -160.0(-11) 1.6(*) 0.44 

IV 83.9(2) 3.4(8) 7.71(6) -169.1 (-3) 0.2(9) -152.1(-2) -186.8(-9) 19.8(-2) 0.34 

Footnote: t-statistics are in parenthesis, (*): t-statistic < 1 
63 

Table A.6 

Statistical Data for the Na Kika Regression Models 

Functional (unit) Model P5 Mean P95

c τ (f) (%) I 

II 

III 

IV 

15.1 

31.8 

31.4 

33.3 

31.6 

38.6 

38.4 

39.4 

53.4 

45.7 

46.2 

45.9 

PV(f) ($M) I 

II 

III 

IV 

483 

1,178 

1,321 

1,339 

939 

1,809 

1,756 

1,818 

1,540 

2,745 

2,324 

2,331 

IRR(f) (%) I 

II 

III 

IV 

42.1 

64.8 

69.9 

70.9 

62.7 

89.7 

87.7 

90.8 

95.2 

125.6 

112.7 

120.7 
65 

APPENDIX B 

CONTRACTUAL SYSTEMS FIGURES AND TABLES
67 

Figure B.1: Typical Bid Evaluation and Negotiation Process in Licensing Agreements. 
68 

Figure B.2: Angola Oil License Blocks. 
69 

Source: Stolt Offshore (www.stoltoffshore.com) 

Figure B.3: The Girassol FPSO. 
70 

Source: Total (www.total.com) 

Figure B.4: The Girassol Development Plan. 
71 

Table B.1 

Projected Production, Capital Expenditures, and Operating Expenditures for a 

Hypothetical 40 MMbbl Field 

 Oil Production CAPEX/I CAPEX/T OPEX 

Year (MMbbl) ($M) ($M) ($M) 

1994 0 0 10.0 0 

1995 0 0 8.0 0 

1996 0 0 15.0 0 

1997 4.500 15.0 10.0 11.5 

1998 7.000 2.0 0 14.0 

1999 5.600 0 0 12.6 

2000 4.760 0 0 11.8 

2001 4.046 0 0 11.0 

2002 3.439 0 0 10.4 

2003 2.923 0 0 9.9 

2004 2.485 0 0 9.5 

2005 2.087 0 0 9.1 

2006 1.732 0 0 8.7 

2007 1.427 0 0 8.4 

2008 0 0 0 0 

Total 40.000 17.0 43.0 117.0 

Source: Johnston, 1994b; Table 4-3. 

 

 

Table B.2 

The Design Space of the System Parameters 

 Parameter (unit) Model Ia Model II 

Po ($/bbl) U(10, 30) U(10, 30) 

R (%) U(0.10, 0.30) U(0.10, 0.30) 

CR (%) U(0.10, 0.75) U(0.10, 0.75) 

PO (%) U(0.10, 0.75) U(0.10, 0.75) 

T (%) U(0.20, 0.40) U(0.20, 0.40) 

Dc (%) U(0.15, 0.40) U(0.15, 0.40) 

Dg (%) U(0.10, 0.20) U(0.10, 0.20) 

Q (MMBOE) U(5, 35) 

PO-1(%) U(0.40, 0.60) 

PO-2 (%) U(0.30, 0.40) 

Footnote: (a) U(a, b) denotes a Uniform probability distribution with endpoints (a, b). 
72 

Table B.3 

Contractor Take, Present Value, and Internal Rate of Return for a Hypothetical 40 

MMbbl Field – Model I Results

φ(f, F)= α0+ α1P+ α2R+ α3CR+ α4PO+ α5T+ α6Dc+ α7Dg

Model Coefficient c τ (f, F) 

 (%) 

PV(f, F) 

($M) 

IRR(f, F) 

(%)

α0 14.1 (14) -25.3 (-4) 2.5 (*) 

α1 0.1 (7) 3.7 (34) 1.0 (9) 

α2 -18.4 (-11) 0.7 (*) -12.2 (-2) 

α3 -1.9 (-1) 24.0 (7) 9.1 (3) 

α4 40.8 (75) 118.2 (35) 36.4 (10) 

α5 -27.3 (-15) -80.8 (-7) -21.2 (-2) 

α6 -54.7 (-40) -204.1(-24) -204.1 (-24) 

α7 61.6 (18) -23 (-1) -23 (-1) 

R2 0.95 0.87 0.31 

E[φ(f, F)] 15.5% $24.7M 14.8% 

σ[φ(f, F)] 9.2% $36.4M 12.8% 

Footnote: t-statistics are in parenthesis, (*): t-statistic < 1 
73 

Table B.4 

Contractor Take, Present Value, and Internal Rate of Return for a Hypothetical 40 

MMbbl Field – Model II Results 

φ(f, F)= α0 + α1P + α2R + α3CR + α4T + α5Dc + α6Dg + 

β1PO-1 + β2PO-2 + γQ 

Model Coefficient c τ (f, F) 

 (%) 

PV(f, F) 

($M) 

IRR(f, F) 

(%)

α0 8.8(13) -17.1(-3) 16.9(-9) 

α1 0.0(15) 2.7(53) 1.7(91) 

α2 -12.4 (-20) -0.7 (*) 2.3 (1) 

α3 -0.8 (-4) 17.0 (-2) 12.2 (21) 

α4 19.5 (31) -58.1(-12) -32.1 (-18) 

α5 -46.0 (-95) -176.8 (-45) -88.6 (-63) 

α6 50.9 (42) -4.3 (*) -3.8 (-1) 

β1 1.4 (2) 5.5 (1) 2.6 (2) 

β2 40.2 (32) 106.4 (10) 58.6 (16) 

γ 0.1(1) 0.1 (2) 0.2 (1) 

R2 0.97 0.91 0.96 

E[φ(f, F)] 14.9% $15.3M 10.2% 

σ[φ(f, F)] 14.1% $22.5M 11.7% 

Footnote: t-statistics are in parenthesis, (*): t-statistic < 1 
74 

Table B.5 

Projected Production, Capital Expenditures, and Operating Expenditures for the 

Girassol Field Development 

Year Production 

(bbl/day) 

CAPEX/T 

($M) 

CAPEX/I 

($M) 

OPEX 

($M) 

1999 0.0 32.31 0.00 0.00 

2000 0.0 204.77 252.35 4.92 

2001 0.0 337.12 316.02 5.91 

2002 192,000.0 98.07 168.02 31.43 

2003 192,000.0 0.00 0.00 64.33 

2004 192,000.0 0.00 0.00 64.33 

2005 192,000.0 0.00 0.00 64.33 

2006 192,000.0 0.00 0.00 64.33 

2007 184,856.0 0.00 0.00 95.60 

2008 156,249.0 0.00 0.00 95.25 

2009 130,373.8 0.00 0.00 94.94 

2010 108,782.9 0.00 0.00 94.68 

2011 83,553.0 0.00 0.00 137.69 

2012 76,930.7 0.00 0.00 94.30 

2013 64,190.5 0.00 0.00 94.14 

2014 53,560.1 0.00 0.00 94.02 

2015 44,690.1 0.00 0.00 93.91 

2016 37,289.1 0.00 0.00 93.82 

2017 31,113.8 0.00 0.00 93.75 

2018 25,961.1 0.00 0.00 93.68 

2019 21,661.8 0.00 0.00 93.63 

2020 19,464.8 0.00 0.00 65.31 

Total 672.28 736.38 1634.31 

Source: Data provided by Thierno Sow of the MMS. 
75 

Table B.6 

The Design Space for the Girassol Field Development 

 Parameter (unit) Model Ia Model II Model III 

Po ($/bbl) U(10, 30) U(10, 30) U(10, 30) 

R (%) U(0.00, 0.10) U(0.00, 0.10) U(0.00, 0.10) 

CR (ψ) (%) U(0.25, 0.75) U(0.25, 0.75) U(0.25, 0.75) 

UP (%) U(0.30, 0.50) U(0.30, 0.50) U(0.30, 0.50) 

T (%) U(0.00, 0.20) U(0.00, 0.20) U(0.00, 0.20) 

Dc (%) U(0.05, 0.20) U(0.05, 0.20) U(0.05, 0.20) 

Dg (%) U(0.00, 0.10) U(0.00, 0.10) U(0.00, 0.10) 

Dd (yr) d= 5 d = 3, 7 d = 5

Y1 (MBOPD) U(0, 25) 

Y2 (MBOPD) U(25, 50) 

Y3 (MBOPD) U(50, 100) 

Z1 (%) U(0.30, 0.75) 

Z2 (%) U(0.20, 0.40) 

Z3 (%) U(0.10, 0.30) 

Z4 (%) U(0.00, 0.20) 

 Footnote: (a) U(a, b) denotes a Uniform probability distribution with endpoints (a, b). 

Table B.7 

 Angolan Profit Oil Split (1990) 

q PO(q)

(MBOPD) (%)

< 25 55 

25-50 30 

50-100 20 

> 100 10 

 
76 

Table B.8 

A Generalized Profit Oil Split Functional 

q 

(MBOPD) 

PO (q) 

(%) 

< Y1 Z1

Y1– Y2 Z2

Y2– Y3 Z3

 ≥ Y3 Z4

Table B.9 

Girassol Regression Model I Results 

φ(f, F)= α0+ α1P+ α2R+ α3CR+ α4UP+ α5T+ α6Dc+ α7Dg

Model Coefficient c τ (f, F) 

 (%) 

PV(f, F) 

($M) 

IRR(f, F) 

(%)

α0 11.2 (75) -724.8 (-25) -18.9 (-37) 

α1 0.01 (3) 54.5 (103) 1.1 (115) 

α2 -7.5 (-14) -28.7 (*) -2.6 (-2) 

α3 -0.5 (-5) 731.4 (36) 17.4 (49) 

α4 -0.3 (-1) 278.0 (5) 7.9 (9) 

α5 -7.3 (-28) -514.7 (-10) -11.2 (-13) 

α6 -43.1 (-121) -4639.1 (-67) -86.7 (-14) 

α7 43.5 (81) -120.7 (-1) -2.4 (-1) 

R2 0.96 0.94 0.96 

P5 3.5 -364 -5.6 

Mean 6.7 195 5.0 

P95 11.2 957 17.2 

 Footnote: t-statistics are in parenthesis, (*): t-statistic < 1

 
77 

Table B.10 

Girassol Regression Model II Results 

φ(f, F)= α0+ α1P+ α2R+ α3CR+ α4UP+ α5T+ α6Dc+ α7Dg

Model IIa (d=3) c τ (f, F) 

 (%) 

PV(f, F) 

($M) 

IRR(f, F) 

(%)

α0 11.2 (79) -922.1 (-33) -18.5 (-26) 

α1 0.01 (5) 56.5 (110) 1.1 (52) 

α2 -8.1 (-16) -164.1 (-2) -2.6 (-1) 

α3 0.4 (4) 881.9 (42) 15.6 (41) 

α4 -0.6 (-2) 270.7 (5) 7.4 (10) 

α5 -7.3 (-27) -607.6 (-12) -11.3 (-11) 

α6 -43.0 (-120) -4368.0 (-62) -86.6 (-25) 

α7 43.2 (82) 69.7 (*) -2.5 (*) 

R2 0.96 0.95 0.94 

P5 3.5 -460 -6.2 

Mean 6.6 160 5.6 

P95 11.1 915 18.9 

Model IIc (d=7) 

α0 11.0 (54) -586.8 (-15) -14.6 (-15) 

α1 0.01 (3) 50.3 (68) 1.0 (88) 

α2 -8.8 (-12) -252 (-2) -2.6 (-1) 

α3 0.3 (2) 672.6 (24) 14.9 (37) 

α4 -0.2 (*) 320.7 (4) 7.1 (7) 

α5 -7.2 (-19) -531.1 (-7) -11.8 (-12) 

α6 -42.4 (-88) -4988.6 (-53) -88.6 (-68) 

α7 43.5 (57) -85.1 (*) -2.5 (-1) 

R2 0.96 0.94 0.96 

P5 3.4 -374 -5.3 

Mean 6.7 195 4.6 

P95 11.3 897 15.4 

 Footnote: t-statistics are in parenthesis, (*): t-statistic < 1

 
78 

Table B.11 

Girassol Regression Model III Results 

φ(f, F)= j k k

j

i j iiX Y Z

k

∑ + ∑ + ∑ = = =

3 4

1

7

0 1

α β γ

Model Coefficient c τ (f, F) 

 (%) 

PV(f, F) 

($M) 

α0 1.2 (3) -1666.1 (-15) 

α1 0.01 (4) 47.4 (48) 

α2 -4.8 (-6) -214.2 (-1) 

α3 -0.5 (-3) 869.4 (22) 

α4 -0.4 (-1) 216.9 (2) 

α5 -4.5 (-11) -408.2 (-4) 

α6 -30.5 (-57) -3793.4 (-29) 

α7 28.3 (18) 9.9 (*) 

β1 0 (0) 0 (*) 

β2 0 (5) 0 (1) 

β3 0 (9) 0 (4) 

γ1 0.8 (2) 90.2 (1) 

γ2 3.8 (9) 403.9 (4) 

γ3 4.9 (6) 869.6 (4) 

γ4 40.0 (50) 3771.7 (20) 

R2 0.94 0.92 

P5 1.4 -533 

Mean 4.0 180 

P95 7.7 738 

 Footnote: t-statistics are in parenthesis, (*): t-statistic < 1
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for most of our nationally owned public lands and natural resources. This includes fostering 

sound use of our land and water resources; protecting our fish, wildlife, and biological diversity; 

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and for people who live in island territories under U.S. administration. 

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primary responsibilities are to manage the mineral resources located on the Nation's Outer 

Continental Shelf (OCS), collect revenue from the Federal OCS and onshore Federal and Indian 

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Moreover, in working to meet its responsibilities, the Offshore Minerals Management Program 

administers the OCS competitive leasing program and oversees the safe and environmentally 

sound exploration and production of our Nation's offshore natural gas, oil and other mineral 

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The MMS strives to fulfill its responsibilities through the general guiding principles of: (1) being 

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