Field of study: Finance Dissertation for obtaining the ... · Title: Valuing an Offshore Exploration Project Through Real Options Analysis Field of study: Finance Purpose: Dissertation

Title: Valuing an Offshore Exploration Project Through Real

Options Analysis

Field of study: Finance

Purpose: Dissertation for obtaining the Degree of Master in Business Administration (The Lisbon MBA International)

Author:

Pedro Santos

Thesis Supervisor:

Professor José Corrêa Guedes

Date:

May 2014

5

Abstract

This thesis applied real options analysis to the valuation of an offshore oil exploration

project, taking into consideration the several options typically faced by the management

team of these projects. The real options process is developed under technical and price

uncertainties, where it is considered that the mean reversion stochastic process is more

adequate to describe the movement of oil price through time. The valuation is realized to two

case scenarios, being the first a simplified approach to develop the intuition of the used

concepts, and the later a more complete case that is resolved using both the binomial and

trinomial processes to describe oil price movement.

Real options methodology demonstrated to be capable of assessing and valuing the projects

options, and of overcoming common capital budgeting methodologies flexibility limitation.

The added value of the application of real options is evident, but so is the method’s increased

complexity, which might adversely influence its widespread implementation.

Page i

Acknowledgements

I would like to thank my thesis supervisor, Professor José Corrêa Guedes, for his guidance

and advises, and whose support helped me achieve the completion of this thesis. I would

also like to thank Professors Gary Emery and Pedro Santa Clara for their recommendations,

and Galp Energia, Daniel Elias, and Catarina Ceitil for their help and accessibility in providing

the required project information and data.

Finally, I want to express my deep appreciation to my wife for her persistent motivation and

encouragement, and her kind patience throughout this period.

Page ii

Contents

Introduction .................................................................................................................... 1

1. Literature Review ....................................................................................................... 3

2. Data Sources and Methods Used to Collect Data ............................................................. 6

3. Oil and Gas Exploration Decision Taking Process ............................................................. 7

4. Real Options Analysis ............................................................................................... 13

5. Oil Price Stochastic Process ....................................................................................... 15

5.1. Estimating Mean Reversion Parameters .......................................................... 17

6. Approach to Project Resolution................................................................................... 19

7. Simplified Case ........................................................................................................ 22

8. Complete Case ........................................................................................................ 32

8.1. Sensitivity Analysis to Project Parameters ...................................................... 34

8.2. Options Value ............................................................................................ 39

Conclusions .................................................................................................................. 41

References ................................................................................................................... 42

Appendix A – Bayesian Analysis ..................................................................................... 48

Appendix B – Real Options Taxonomy ............................................................................. 49

Appendix C – Geometric Brownian Motion ....................................................................... 51

Appendix D – Trinomial Tree Building Procedure .............................................................. 52

Appendix E – Simplified Case Technological Uncertainty Project Data ................................ 56

Appendix F – Simplified Case Price Uncertainty Project Data ............................................. 57

Appendix G – Effect of New Information (Simplified Case) ................................................ 69

Appendix H – Simplified Case End Nodes Free Cash Flows Estimation ................................ 71

Appendix I - Simplified Case Hexanomial Tree Probabilities .............................................. 81

Appendix J– Simplified Case ROA Tree Evolution .............................................................. 85

Appendix K – Complete Case Technological Uncertainty Project Data ................................. 86

Appendix L – Complete Case Price Uncertainty Project Data ............................................. 88

Appendix M- Effect of New Information (Complete Case) .................................................. 94

Appendix N – Oil Price Evolution from End Nodes ............................................................. 96

Appendix O – Production Levels ..................................................................................... 98

Appendix P – Complete Case End Nodes Free Cash Flows Estimation (Trinomial) .............. 101

Appendix Q – Complete Case End Nodes Free Cash Flows Estimation (Binomial) .............. 124

Appendix R – Complete Case Hexanomial Tree Probabilities ............................................ 126

Appendix S – Complete Case Quadranomial Tree Probabilities ........................................ 133

Appendix T – Hexanomial Tree Mutually Exclusive NPVs ................................................. 135

Page iii

Appendix U – Quadranomial Tree Mutually Exclusive NPVs .............................................. 138

Appendix V – Complete Case Real Option Analysis ......................................................... 141

Appendix W – Effects of Varying Project Volatility .......................................................... 143

Appendix X – Real Options Analysis at the Absolute Certainty Level ................................ 144

Appendix Y – Real Options Analysis with DW2 Having a Cost of $50 Million ...................... 147

Appendix Z – Effects of Changes to the Initial Probabilities of the Site’s Quantity of Oil . 150

Appendix AA – Data for Initial Large Quantity of Oil Probability at Absolute Certainty Level157

Appendix BB – Trees for Each Option Value ................................................................... 159

Page iv

Nomenclature

DCF - Discounted Cash Flow .............................................................................................. 1

DW - Delineation Well ..................................................................................................... 22

GBM - Geometric Brownian Motion .................................................................................... 15

LP - Large Platform ........................................................................................................... 7

MAD - Market Asset Disclaimer ........................................................................................... 4

MRM - Mean Reversion Model ........................................................................................... 16

PV - Present Value .......................................................................................................... 24

ROA - Real Options Analysis ............................................................................................... 1

SEK - Standard Error for Kurtosis ..................................................................................... 60

SES - Standard Error for Skewness ................................................................................... 60

SP - Small Platform .......................................................................................................... 7

Page v

List of Figures

Figure 1 Oilfield Development Decision Tree .................................................................... 8

Figure 2 Oilfield Development Decision Tree with Computational Results ......................... 10

Figure 3 Sensitivity Analysis to Readapting Costs from a Small Platform to a Large Platform

................................................................................................................................... 11

Figure 4 Sensitivity Analysis to New Data Being Sufficient to Determine Quantity of Oil .... 11

Figure 5 Sensitivity Analysis to the Initial Probability of Having a Large Quantity of Oil ..... 12

Figure 6 Sensitivity Analysis to the Cost of Purchasing Additional Information ................. 12

Figure 7 Average Crude Oil Price Evolution (Data source: World Bank) ............................ 15

Figure 8 GBM and MRM Variance Evolution (Source: Dias, 2004) .................................... 16

Figure 9 Quadranomial Possible Outcomes ....................................................................... 20

Figure 10 Call Option Value ............................................................................................ 20

Figure 11 Hexanomial Tree Outcomes and Call Option Value ........................................... 21

Figure 12 Simple Case Oilfield Development Decision Tree ............................................. 22

Figure 13 Simple Case Hexanomial Event Tree .............................................................. 23

Figure 14 Acquiring Additional Imperfect Information NPV .............................................. 26

Figure 15 NPV for Setting a Large Platform at Year One ................................................. 27

Figure 16 NPV for Setting a Small Platform at Year One ................................................. 28

Figure 17 Real Options Analysis NPV ............................................................................. 29

Figure 18 Real Options Analysis Process........................................................................ 30

Figure 19 Complete Case Oilfield Development Decision Tree ......................................... 32

Figure 20 Sensitivity Analysis to Oil Price Volatility (Value of Flexibility) .......................... 34

Figure 21 Sensitivity Analysis to Oil Price Volatility (Project Value) ................................. 35

Figure 22 Sensitivity Analysis to the Sufficiency of DW2 Data ......................................... 35

Figure 23 Sensitivity Analysis to the Cost of Acquiring New Information .......................... 36

Figure 24 Sensitivity Analysis to the Initial Probability of Large Quantity of Oil ................ 37

Figure 25 Sensitivity Analysis to the Initial Probability of Small Quantity of Oil ................ 37

Figure 26 Sensitivity Analysis to the Decline of the Rate of Production ............................ 39

Figure 27 Trinomial Tree Branching Alternatives ............................................................ 53

Figure 28 Tree for X* in Hull-White Model (First Stage) .................................................. 54

Figure 29 Crude Oil Price Evolution ............................................................................... 58

Figure 30 Plot of Residuals versus X ............................................................................. 59

Figure 31 Plot of Residuals versus Predicted Y ............................................................... 59

Figure 32 Residuals Normal Probability Plot ................................................................... 61

Figure 33 Residuals Time Plot ...................................................................................... 61

Page vi

Figure 34 Price Evolution Trinomial Tree Nodes ............................................................. 65

Figure 35 Effect of New Information to Technological Uncertainty Decision Tree (Simplified

Case) ........................................................................................................................... 70

Figure 36 Real Options Analysis Process........................................................................ 85

Figure 37 Price Evolution Trinomial Tree Nodes ............................................................. 89

Figure 38 Effect of New Information to Technological Uncertainty Decision Tree (Complete

Case) ........................................................................................................................... 95

Figure 39 Price Evolution when Deciding to Set a Large or a Small Platform at Year Three 97

Figure 40 Price Evolution when Deciding to Set a Large or a Small Platform at Year Four .. 97

Figure 41 Production Levels for Set Large at Year Three ................................................. 98

Figure 42 Production Levels for Large Quantity of Oil ..................................................... 99

Figure 43 Production Levels for Small Quantity of Oil ................................................... 100

Figure 44 Evolution of Year Four Price Levels .............................................................. 124

Figure 45 Evolution of Year Five Price Levels ............................................................... 124

Figure 46 Complete Case Hexanomial Event Tree......................................................... 135

Figure 47 Acquiring Additional Imperfect Information NPV (Hexanomial) ....................... 136

Figure 48 NPV for Setting a Large Platform at Year Three (Hexanomial) ........................ 137

Figure 49 NPV for Setting a Small Platform at Year Three (Hexanomial) ........................ 137

Figure 50 Complete Case Quadranomial Event Tree ..................................................... 138

Figure 51 Acquiring Additional Imperfect Information NPV (Quadranomial) .................... 139

Figure 52 NPV for Setting a Large Platform at Year Three (Quadranomial) ..................... 140

Figure 53 NPV for Setting a Small Platform at Year Three (Quadranomial) ..................... 140

Figure 54 Hexanomial Tree Real Options Analysis ........................................................ 141

Figure 55 Quadranomial Tree Real Options Analysis ..................................................... 142





Figure 60 Hexanomial Tree Real Options Analysis (initial large oil probability at 40%) .... 150

Figure 61 Quadranomial Tree Real Options Analysis (initial large oil probability at 40%) . 151

Figure 62 Hexanomial Tree Real Options Analysis (initial large oil probability at 70%) .... 152


Figure 64 Hexanomial Tree Real Options Analysis (initial large oil probability at 100%) .. 154


Page vii

List of Tables

Table 1 Considered States of Nature ............................................................................... 9

Table 2 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil ..... 9

Table 3 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil ..... 9

Table 4 Joint Probabilities Addition ................................................................................ 10

Table 5 Effect of a value increase on the variables ......................................................... 14

Table 6 Best Option without Real Options Analysis ......................................................... 28

Table 7 Real Options Analysis Added Value ................................................................... 31

Table 8 Best Option without Real Options Analysis ......................................................... 33

Table 9 Best Option with Real Options Analysis ............................................................. 33

Table 10 Individual Option Value .................................................................................. 39

Table 11 Total Value of Used Options ............................................................................ 40

Table 12 Simplified Case Technological Uncertainty Project Data ..................................... 56

Table 13 Crude Oil Price (Source: World Bank) .............................................................. 57

Table 14 Used Data Set Regression Results ................................................................... 58

Table 15 Results of Kurtosis and Skew Statistical Tests .................................................. 60

Table 16 Results from the Durbin-Watson Test .............................................................. 62

Table 17 Estimation of Mean Reversion Parameters through Linear Regression................. 63

Table 18 Crude Oil Price Logarithmic Returns ................................................................ 63

Table 19 Volatility Estimation through Logarithmic Price Returns .................................... 64

Table 20 Input Parameters for the Construction of the Trinomial Tree ............................. 64

Table 21 Tree Modulation Parameters ........................................................................... 64

Table 22 j Tree ........................................................................................................... 65

Table 23 Table for X* and Nodes Probabilities ................................................................ 66

Table 24 Spot Average Crude Oil Futures Prices (Source: World Bank) ............................ 66

Table 25 Tree for Q ..................................................................................................... 67

Table 26 Q Values ....................................................................................................... 67

Table 27 αααα Values ....................................................................................................... 67

Table 28 Trinomial Tree for Oil Prices ........................................................................... 68

Table 29 Considered States of Nature ........................................................................... 69

Table 30 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil . 69

Table 31 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil . 69

Table 32 Joint Probabilities Addition .............................................................................. 69

Table 33 Oil Estimated Quantities and States of Nature Probabilities ............................... 71

Table 34 Set Large Platform Free Cash Flow Estimates ................................................... 71

Page viii

Table 35 Set Small Platform – Free Cash Flow Estimates for Large Amount of Oil ............. 72

Table 36 Set Small Platform – Free Cash Flow Estimates for Small Amount of Oil ............. 72

Table 37 Buy Additional Information, Data Indicates Large Quantity, Large Platform is

Established – Free Cash Flow Estimates for Large Amount of Oil ....................................... 73


Established – Free Cash Flow Estimates for Small Amount of Oil ....................................... 74

Table 39 Buy Additional Information, Data Indicates Large Quantity, Small Platform is




Table 41 Buy Additional Information, Data Indicates Small Quantity, Large Platform is




Table 43 Buy Additional Information, Data Indicates Small Quantity, Small Platform is




Table 45 Simplified Case Hexanomial Tree Nodes Probabilities ........................................ 81

Table 46 Complete Case Technological Uncertainty Project Data ..................................... 86

Table 47 Input Parameters for the Construction of the Trinomial Tree ............................. 88

Table 48 Tree Modulation Parameters ........................................................................... 88

Table 49 j Tree ........................................................................................................... 89

Table 50 Table for X* and Nodes Probabilities ............................................................... 90

Table 51 Spot Average Crude Oil Futures Prices (Source: World Bank) ............................ 91

Table 52 Tree for Q ..................................................................................................... 91

Table 53 Q Values ...................................................................................................... 92

Table 54 αααα Values ....................................................................................................... 92

Table 55 Trinomial Tree for Oil Prices ........................................................................... 93

Table 56 Input Parameters for the Construction of the Binomial Tree .............................. 93

Table 57 Calculated Parameters for the Construction of the Binomial Tree ....................... 93

Table 58 Binomial Tree for Oil Prices ............................................................................ 93

Table 59 Considered States of Nature ........................................................................... 94

Table 60 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil . 94

Table 61 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil . 94

Table 62 Joint Probabilities Addition .............................................................................. 94

Table 63 Prices Evolution when Deciding to Set a Large or a Small Platform at Year Three 96

Table 64 Prices Evolution when Deciding to Set a Large or a Small Platform at Year Four .. 96

Page ix

Table 65 Production Levels for Set Large at Year Three .................................................. 98

Table 66 Production Levels for Large Quantity of Oil ...................................................... 99

Table 67 Production Levels for Small Quantity of Oil .................................................... 100

Table 68 Oil Estimated Quantities and States of Nature Probabilities ............................. 101

Table 69 Set Large Platform at Year Three – Position s3L Q NPV Estimate ..................... 102

Table 70 Set Large Platform at Year Three End Nodes NPV Estimates ............................ 103

Table 71 Set Small Platform at Year Three – Position s3SO Q NPV Estimate ................... 104

Table 72 Set Small Platform at Year Three – Quantity is Large End Nodes NPV Estimates 105

Table 73 Set Small Platform at Year Three – Position s3S§ Q NPV Estimate ................... 106

Table 74 Set Small Platform at Year Three – Quantity is Small End Nodes NPV Estimates 107

Table 75 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set,

it is Large – Position s3b(D+)LO X NPV Estimate ........................................................... 108


Quantity is Large – End Nodes NPV Estimates ............................................................... 109


it is Small – Position s3b(D+)L§ X NPV Estimate ............................................................ 110


Quantity is Small – End Nodes NPV Estimates ............................................................... 111

Table 79 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set,

it is Large – Position s3b(D+)SO X NPV Estimate ........................................................... 112




it is Small – Position s3b(D+)S§ X NPV Estimate ........................................................... 114



Table 83 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set,

it is Large – Position s3b(D-)LO X NPV Estimate ............................................................ 116




it is Small – Position s3b(D-)L§ X NPV Estimate ............................................................. 118



Table 87 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set,

it is Large – Position s3b(D-)SO X NPV Estimate ............................................................ 120



Page x


it is Small – Position s3b(D-)SO X NPV Estimate ............................................................ 122



Table 91 Project Year Four NPVs ................................................................................ 125

Table 92 Project Year Five NPVs ................................................................................. 125

Table 93 Complete Case Hexanomial Tree Nodes Probabilities ...................................... 126

Table 94 Complete Case Quadranomial Tree Nodes Probabilities ................................... 133

Table 95 Project Results with Oil Price Standard Deviation at Ten Percent ..................... 143

Table 96 Project Results with Oil Price Standard Deviation at Twenty Percent ................ 143

Table 97 Project Results with Oil Price Standard Deviation at Fifty Percent .................... 143

Table 98 Best Option with Real Options Analysis .......................................................... 146

Table 99 Best Option with Real Options Analysis .......................................................... 149

Table 100 Best Option with Real Options Analysis (initial large oil probability at 40%) .... 156

Table 101 Best Option with Real Options Analysis (initial large oil probability at 70%) .... 156

Table 102 Best Option with Real Options Analysis (initial large oil probability at 100%) .. 156

Table 103 Considered States of Nature ....................................................................... 157

Table 104 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil

................................................................................................................................. 157

Table 105 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil

................................................................................................................................. 157

Table 106 Joint Probabilities Addition ........................................................................... 157

Table 107 Year Five to Year Four Probabilities if New Data Indicates Large Quantity ....... 158

Table 108 Year Five to Year Four Probabilities if New Data Indicates Small Quantity ....... 158

Table 109 Year Four to Year Three Set Large Platform Probabilities ............................... 158

Table 110 Year Four to Year Three Acquire Additional Imperfect Information Probabilities 158

Table 111 Tree with the Option to Set a Large Platform ............................................... 159

Table 112 Tree with the Option to Abandon ................................................................. 159

Table 113 Tree with the Option to Acquire Additional Imperfect Information .................. 159

Page xi

List of Equations

Equation 1 Mean Reversion Model (Schwartz, 1997) ...................................................... 16

Equation 2 Half-Life .................................................................................................... 17

Equation 3 Simple Mean Reverting Process Rewritten ..................................................... 17

Equation 4 Mean Reversion Speed ................................................................................ 17

Equation 5 Mean Reversion Long Run Mean ................................................................... 17

Equation 6 Linear Regression Volatility ......................................................................... 18

Equation 7 Technological Uncertainty Discount Rate Computation ................................... 20

Equation 8 Quadranomial Tree Risk-Neutral Probabilities ................................................ 20

Equation 9 Mean Reversion Model without Random Component (Schwartz, 1997) ............ 32

Equation 10 Bayes’ Rule .............................................................................................. 48

Equation 11 Geometric Brownian Motion Process ........................................................... 51

Equation 12 Geometric Brownian Motion Discrete Time Model ......................................... 51

Equation 13 Instantaneous Short Rate .......................................................................... 52

Equation 14 X* Process ................................................................................................ 52

Equation 15 Spacing Between the Underlying ................................................................ 52

Equation 16 X* Calculation ........................................................................................... 52

Equation 17 Trinomial Tree jmax .................................................................................... 53

Equation 18 Trinomial Tree jmin .................................................................................... 53

Equation 19 Branch Composed by Up One/Straight Along/Down One ............................... 53

Equation 20 Branch Composed by Straight Along/Down One/Down Two .......................... 53

Equation 21 Branch Composed by Up Two/Up One/Straight Along ................................... 54

Equation 22 Displacement of the Positions of the Nodes ................................................. 54

Equation 23 αααα1 Calculation ........................................................................................... 55

Equation 24 S Calculation ............................................................................................. 55

Equation 25 Price of a Zero-Coupon Bond ..................................................................... 55

Equation 26 ααααm Calculation .......................................................................................... 55

Equation 27 Qi,j Calculation .......................................................................................... 55

Equation 28 Standard Error for Skewness ..................................................................... 60

Equation 29 Standard Error for Kurtosis ........................................................................ 60

Equation 30 Durbin-Watson Test .................................................................................. 62

Equation 31 Equation of r ............................................................................................ 62

Page 1 of 159

Introduction

Traditional financial Discounted Cash Flow (DCF) methodology realises an estimation of the

cash flows that will occur during a project’s existence, and once these are established, it

assumes management has a passive attitude throughout the investment’s lifetime, being

irrevocably committed to the set strategy. This premise of future certainty, does not consider

possible strategic and operational options, and in this manner, it is not capable of capturing

management flexibility to adapt and revise later decisions.

These shortcomings of the DCF method, has brought attention to the application of option

pricing theory to the valuation of investments in non-financial assets, or “real assets”, as

indicated by Myers (1977). Real Options Analysis (ROA) valuation methodology is capable of

overcoming DCF limitations, and of capturing the investments flexibility, constituting a

financial and strategic tool to the project’s management team. As with their financial

counterpart, real options relevance increases with greater levels of uncertainty, being

particularly interesting to projects where uncertainty is significant.

Offshore oil and gas exploration is a dynamic activity, which is developed under challenging

harsh remote environments. Additionally to these constraints and difficulties, the required

heavy investments, accompanied with the inherent volatility of oil prices, results in larger

potential losses and higher degrees of uncertainty to be associated with these projects.

Predicted cash flows of such investments will probably differ from management’s

expectations, and new data will also be identified, which will possibility change the project’s

assumptions. Throughout this process the management team might face the option to change

the defined strategy, and real options analysis can provide the required framework to

financially and strategically value these projects.

Portuguese oil company Galp Energia develops offshore oil and gas projects, and its

managers face many options throughout the life cycle of a site’s exploration. Fundamental

decisions such as if a site should be explored, what potential resources exist and their

location, should an appraisal drill be carried out (appraisal drills are still the only way to

confirm findings and their extent), in which of the identified opportunities should the

exploration focus on, or for example, if at a certain point of the field’s exploration phase one

should pursue further findings or instead, stop exploring and start the field’s development

phase. The decision to move from exploration to the development phase, will bring closure to

the estimation of the volume of the findings, will enable the activities to proceed to the

dimensioning of the required infrastructures for the future production phase, and will define

the field’s future production capacity. In this manner, a future decision to alter the field’s

production designed scheme, although usually not technically impossible, it is certainly a

very expensive alternative.

Page 2 of 159

This thesis discusses the application of real options to the valuation of an offshore oil project,

which faces the above referred options. Guaranteeing data confidentiality, Galp Energia

provides typical figures for these projects, which the study uses to develop the considered

case scenarios. An introduction to the decision making process faced by the management

team of these projects is first realized, where the paths available for the development of the

site are considered, and an assessment of the interaction among the several components

that influence the course of action is also carried out.

Having established the technical decision framework, ROA is revised, and the particular

characteristics that distinct real options from their financial counterpart are also presented.

Oil price stochastic process is analysed next, in order to determine the model that best

describes the price movement of this commodity, being considered that the mean reversion

process better captures the behaviour of oil price movements. However, this process requires

the estimation of additional parameters, and the used methodology to achieve this purpose is

also presented.

Thus, the model developed for the ROA valuation assumes two sources of uncertainty, the

technological uncertainty and the oil price uncertainty. These uncertainties evolution through

time is distinctive, being therefore required that two separate trees are constructed to realize

the project’s valuation. Adopting Hull (2009) trinomial tree building procedure to describe oil

price mean reversion process, results on the combined tree to have a Hexanomial form.

Two case scenarios are studied, a simplified case that introduces the used methodologies,

and a complete case that is resolved using the binomial and trinomial processes to describe

oil price movement. Sensitivity analysis for various components that integrate the complete

case is also realized, being possible to assess how the project’s valuation is affect by these

variations.

Although computationally more elaborate, it is possible to conclude that ROA provides a more

complete valuation of this type of investments, also allowing for the intended strategic

analysis to be successfully achieved. Furthermore, the tighter mesh provided by the trinomial

model delivers a more detailed assessment, being capable of identifying paths not recognized

by the binomial approach. However, the trinomial methodology is far more complex, and the

benefits brought by its use have to be weighted against the required resources.

The study demonstrates that consideration of the available options can change a project’s

acceptance, confirming ROA financial and strategic capabilities, and making evident why the

methodology has been attracting increased interest. Nevertheless, the developed analysis

also exhibits that in comparison with the well-established DCF model, the more complex

procedures, and the several different ways in which the model can be applied, explain the

reasons behind ROA weak implementation as a valuation tool in today’s companies.

Page 3 of 159

1. Literature Review

Quantitative origin of real options methodology derives from the model developed by Fischer

Black and Myron Scholes, as modified by Robert Merton. Myers (1977) view that corporate

growth opportunities could be viewed as call options, introduced real options by referring

that option pricing theory could be used to value investment opportunities in non-financial

assets, or “real assets”. Cox, Ross, and Rubinstein (1979) binomial approach enabled a

simplified valuation of options in discrete time. Tourinho (1979) was the first to evaluate oil

reserves using option pricing techniques.

Real options relevance started partially as a reaction to the limitations of traditional capital

budgeting techniques. Hayes and Garvin (1982) acknowledged that discounted cash flow

criteria did not properly considered the investments flexibility, leading to eventual loss of

competitiveness. Myers (1987) recognizes that traditional capital budgeting techniques have

a limited response to investments with strategic and operating options, proposing that these

characteristics are better captured by option pricing methodology.

Conceptual real options framework are discussed by Mason and Merton (1985), or Trigeorgis

and Manson (1987). These last authors refer that traditional net present value is developed

in the premise of future certainty, and if investments uncertainty exists, then this capital

budgeting technique can not capture the investments flexibility.

Paddock et al. (1988) is a classical real options model for the oil and gas upstream industry,

where the authors develop a real options framework for the valuation of an offshore

petroleum lease. The model has been used for learning purposes, and as a first

approximation to the analysis of this type of projects. Ekern (1988) values a marginal

satellite oilfield. Bjerksund and Ekern (1990) demonstrated that for initial oilfield purposes

with an option to defer the investment, it is possible to ignore the options to abandon and

temporarily stop the investment.

Brealey and Myers (1992) consider that R&D opportunities give management the options to

continue or to abandon the project. If a R&D stage is unsuccessful, the project is

discontinued and the only loss is the realized initial investment. If the stage is successful,

then management has the option to continue, whose behaviour is identical to a call option.

In mid-nineties, real options analysis started to attract increased interest as a relevant tool

for the valuation of investments, principally in the oil and gas industry. Trigeorgis (1993)

developed seven categories of real options, namely, option to defer, time-to-build option

(staged investment), option to alter operating scale, option to abandon, option to switch,

growth options and multiple interacting options. Copeland et al. (1994) observe that option-

pricing combines the desirable features of both the NPV and DTA approaches.

Page 4 of 159

Shortcomings of discounted cash flow methodology in valuing projects with managerial

flexibility, as indicated by Dixit and Pindyck (1994), and Trigeorgis (1996) turned greater

focus to real options analysis. Dixit and Pindyck (1994) consider that conventional capital

budgeting approach assumes that management has a now or never opportunity to realize the

investment, and that this decision can not be deferred. Therefore, this approach fails to

recognize the value created by delaying the investment decisions, and possibly leading to

incorrect valuation of the project.

Ross (1995) also indicates that traditional net present value accept or reject criteria can lead

to erroneous investment decisions. A project that is rejected today may not be so at some

future time, as the investment’s uncertainty might alter the project’s future value, and

traditional capital budget methodology fails to recognise this property.

Dias (1997) assesses optimal timing for the exploratory drilling by combining real options

with game theory. Schwartz (1997) compares oil prices models and develops a mean

reversion model. Laughton (1998) indicates that in oil prospects, an increase in reserves

uncertainty anticipates exploration and delineation wells, and an increase in oil uncertainty

delays the exercise of all options, from exploration to decommissioning.

Cortazar and Schwartz (1998) apply Monte Carlo simulation to real options development of

an oilfield. Pindyck (1999) discusses the implications of oil prices long-term behaviour on real

options. Galli et al. (1999) analyse the application of real options, decision trees and Monte

Carlo simulation in petroleum applications.

Smith and Mccardle (1999) provide a tutorial introduction to option pricing methods, focusing

on how they relate to and can be integrated with decision analysis methods, and describe

some lessons learned in using these methods to evaluate some real oil and gas investments.

Amran and Kulatilaka (1999) directly applied option pricing theory to real investments,

providing several examples in various industries, inclusively one for the exploration of oil.

Chorn and Croft (2000) assess the value of reservoir information. Saito et al. (2001) consider

several oilfield development alternatives by combining real options with reservoir simulation.

Kenyon and Tompaidis (2001) study leasing contracts of offshore rigs. McCormack and Sick

(2001) analyse the valuation of undeveloped reserves.

Copeland and Antikarov (2001 and 2003) publish a real options practitioner’s guide that

assumes the Market Asset Disclaimer (MAD) approach, departing from standard option

pricing methodology of identifying a market replicated portfolio, which is considered to be

practically impossible to accomplish. Instead, it recommends the use of the present value of

the project itself, without flexibility, as the underlying risky asset of the used twin security,

and use it as the estimate of the price that the investment would have if it were a security

traded in the open market, considering that nothing is better correlated with the project than

the project itself.

Page 5 of 159

Cortazar et al. (2001) develop a real options model for valuing natural resource exploration

investments when there is joint price and geological-technical uncertainty. Zettl (2002)

applies option pricing theory to value exploration and production projects in the oil and gas

industry, where the binomial model is considered to be the preferred methodology to carry

out this type of analysis.

Real options raise the interest of other industries such as engineering, construction and

infrastructure investments, whose examples include Ho and Liang (2002), Ford et al. (2002),

and Cheah and Liu (2005).

Dias (2004) presents a set of selected real options models to evaluate investments in

petroleum exploration and production under market and technical uncertainties. Armstrong et

al. (2004) evaluate the option to acquire more information in using real options to value oil

projects. Copeland and Tufano (2004) develop the argument that the complexity of real

options can be eased through the use of a binomial valuation model.

Costa Lima et al. (2005) defend that oil and gas projects do not depend only on oil price

uncertainty, but also on other uncertainties such as fixed costs, production levels, and

investments magnitude. Triantis (2005) states that real options have clearly succeeded as a

way of thinking, but their application has been limited to companies in relatively few

industries, having thus, failed to meet the expectations created in the mid to late-nineties.

Borison (2005) indicates that real options can be modelled in many different ways, and this

characteristic introduces confusion to the application of the methodology. Costa Lima and

Suslick (2006) present an alternative numerical method based on present value of future

cash flows and Monte Carlo simulation to estimate the volatility of projects.

Hahn and Dyer (2011) develop an approach for modelling stochastic processes of variables,

such as commodities prices, in discrete time as two-dimensional binomial sequences. Baker

et al. (2011) develop a survey to assess the use of real options in Canadian firms,

determining that the methodology has not yet been adopted by most companies as a tool for

strategic decision making.

Page 6 of 159

2. Data Sources and Methods Used to Collect Data

The research methods consisted on:

• published literature about the topics in discussion;

• collection of data from Galp Energia;

• interviews with Galp Energia Exploration and Production management team;

• computer simulations to measure the value of oil and gas exploration options.

Page 7 of 159

3. Oil and Gas Exploration Decision Taking Process

Decisions in the oil and gas industry are made on the basis of uncertain information, and the

option to purchase additional imperfect information to better define the project value and the

involved uncertainties is often possible. In such cases, it is important to consider that by

purchasing new information, the decision maker is deferring his decision to a later time when

the new information becomes available. This makes the decision taken “today” dependent on

future sequential decisions, which will be made once the new information becomes known.

The fact that the purchased information is imperfect is a relevant characteristic of this

decision making process, as if it were perfect (i.e. the obtained information contained no

error), analysis and decisions would become much more straightforward. In this manner,

dealing with imperfect information makes the decision process considerably more complex,

but nevertheless, still following a consistent procedure.

To illustrate this procedure an offshore oil site that has been tested productive 1 is

considered, as are the options available to the project’s management team. At the assumed

point in time, management does not have robust information about the site, and faces the

decision to determine the size of the infrastructure to be set in place, which is dependent on

the extractable amount of oil. However, it is possible to improve the estimate about the

quantity of oil present in the geological structure by purchasing additional imperfect

information. As such, at the considered point in time, management has the options to set a

Large Platform (LP), to set a Small Platform (SP), to acquire additional imperfect information,

or to exit the project (option followed if the site were considered unproductive).

By establishing a LP, management will be following a more expensive solution, but a safer

one, as the set infrastructure will be capable of dealing with all estimated quantities of oil.

Nevertheless, if a small amount of oil is in fact found, considerable excessive resources will

have been allocated. If the pursued path is to build a SP, a much less costly structure will be

employed. This structure will deliver excellent results in the presence of a small quantity of

oil, but if it is later found that there is a large quantity of oil in the site, an additional

platform and further resources will have to be allocated, making the option significantly more

expensive than setting a LP in the first place. Management can thus, with respect to these

two options, follow a “safe” strategy by establishing a LP, or assume what can be considered

as a “gamble” strategy and setup a SP.

It is also possible to develop another delineation well and acquire additional imperfect

information, deferring the decision to a later stage when this new data becomes available. It

is important to note, that by acquiring additional information, and based on the exploration

results, the sequential decision to develop a LP or a SP is not a clear cut, as the new data is

not one hundred percent accurate. If the new data were one hundred percent reliable, such

1 The site has been previously surveyed and determined to be feasible for production.

Page 8 of 159

reasoning could be possible, but as it is not, the best decision might still be to develop a

large platform, even if the new data indicates the presence of a small amount of oil in the

geological structure (e.g. the downside of the potential losses in the case of a large amount

of oil could be so disastrous, which would justify the option to implement a LP). The decision

tree depicting all these options can be seen in the figure below, where the represented time

steps are annual, and the squares reflect decision nodes whereas circles indicate resolution

of exogenous uncertainty.

Figure 1 Oilfield Development Decision Tree

Considering all stated values are present values, a particular set of assumptions are

developed to help clarify the above decision process. The objective is to determine the option

that best minimizes expected costs, having access to the following data:

• it is currently judged, by the project geological experts, that there is a 65%

probability that a small quantity of oil is present in the field;

Page 9 of 159

• construction of a LP has an estimated cost of $90 million2;

• construction of a SP has an estimated cost of $30 million. However, if it is later found

that a large amount of oil is in fact the case, the installation of a second platform and

all associated costs represent an additional cost of $90 million. Thus, in this later

case, the total cost amounts to $120 million;

• drilling a second delineation well and deferring the decision has an estimated cost of

$5 million. The team considers that there is a 90% probability that the data collected

by this second well will be sufficient to determine the size of the discovery – there is

thus, a 10% probability that the collected data will not be sufficient (i.e. not perfect

information) to properly determine the size of the discovery.

Before introducing the above values to the developed decision tree, it is necessary to

compute the effect of new information on our current estimates. This procedure will be

achieved by using Bayes’ Rule (overviewed in Appendix A), which can be seen in the tables

below. The first table defines the possible states of nature, and the following three tables

determine the effect of the new data in the current estimates.

State of Nature Description

E1 Large quantity of oil

E2 Small quantity of oil

Table 1 Considered States of Nature

State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 0.35 0.90 0.315 0.8289

E2 0.65 0.10 0.065 0.1711

Total 1.00 1.00 0.38 1.00


State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 0.35 0.10 0.035 0.0565

E2 0.65 0.90 0.585 0.9435

Total 1.00 1.00 0.62 1.00


2 All monetary values are in US Dollars.

Page 10 of 159

Joint Probabilities

Table 2 result 0.38

Table 3 result 0.62

Total 1.00

Table 4 Joint Probabilities Addition

The calculations developed in the above tables permit the decision tree to be completed,

which is shown in the figure below.

Figure 2 Oilfield Development Decision Tree with Computational Results

In the above tree nodes (a) to (k) represent the end costs, nodes A to E and H represent

events of nature, and nodes F, G, and I, represent decision points. From the decision tree, it

is possible to see that the option that best minimizes expected cost is the option to defer the

decision in one year and acquire additional imperfect information.

Page 11 of 159

In order to consider the effect of changing key parameters a sensitivity analysis is

developed. The effects of changing the involved cost in the case of setting a SP and later

discovering that there is a large quantity of oil in the site, of changing the probability that

the acquired additional data will be sufficient to determine the quantity of oil present in the

site, of changing the initial probability that the case is a large quantity of oil, and of changing

the cost of acquiring additional information are analysed in the Figures 3, 4, 5, and 6.

Figure 3 Sensitivity Analysis to Readapting Costs from a Small Platform to a Large Platform

Figure 3 represents the expected required costs to readapt from a SP to a LP. The circled

points indicate the current estimated costs, namely $120 million – the ‘Set Small’ and ‘Buy

Additional Information’ points are superimposed on one another. It can be seen that setting a

small platform is the preferred decision until the level of expense overcomes roughly $118

million, point from which the option to acquire additional information is the one that best

minimizes expected costs. From around $1 billion onwards, the “Set Large” option is the path

that represents the choice with lowest expenditures.

The graph shown in Figure 4 illustrates the effect of changing the probability that the newly

acquired data will be sufficient to determine the amount of oil present in the geological

structure. The option to set a SP is the best option to follow until the confidence in the

sufficiency of the new data reaches 90%, and from this level onwards the best option is to

pursue the purchase of supplementary information.

Figure 4 Sensitivity Analysis to New Data Being Sufficient to Determine Quantity of Oil

$.M

$20.M

$40.M

$60.M

$80.M

$100.M

80M 90M 100M 110M 120M 130M 140M 150M 160M

Set Large Set Small Buy Additional Information

$.M

$30.M

$60.M

$90.M

$120.M

30% 40% 50% 60% 70% 80% 90% 100%


Page 12 of 159

The next analysis is made by altering the value of the initial estimate that the case at hand is

a large quantity of oil, which can be seen in Figure 5. ‘Set Small’ is the preferred alternative

until about 35%, point from which acquiring additional information becomes the best option.

This is so until roughly 65%, where from this point onwards the ‘Set Large’ alternative starts

to be the best path to follow.

Figure 5 Sensitivity Analysis to the Initial Probability of Having a Large Quantity of Oil

Lastly, in Figure 6, an investigation is developed to changing the price of additional

information. ‘Set Large’ and ‘Set Small’ options are unaffected by changing the cost of

acquiring new data, as this cost is only applied in the alternative to obtain supplementary

information. This study shows that purchasing new data is the best option to follow until the

cost of this data reaches around $5.5 million, and from this point onward the option that

minimizes expected costs is to set a SP.

Figure 6 Sensitivity Analysis to the Cost of Purchasing Additional Information

$.M

$30.M

$60.M

$90.M

$120.M

$150.M

5% 15% 25% 35% 45% 55% 65% 75% 85% 95%


$.M

$30.M

$60.M

$90.M

$120.M

1M 2M 3M 4M 5M 6M 7M 8M 9M 10.00


Page 13 of 159

4. Real Options Analysis

The traditional process in capital budgeting is the use of the Net Present Value (NPV)

approach, which uses the DCF technique to value the present values of all future cash flows.

These present values minus the initial investment give the NPV of the project, and the rule of

the methodology is to accept projects with positive NPV and reject those with negative NPV.

This approach implicitly assumes that once cash flows are established, management will have

a passive attitude throughout the project, being irrevocably committed to the set strategy.

Thus, NPV fails to consider and properly capture management’s flexibility to adapt and revise

later decisions, by not being capable of reviewing the set strategy.

In the real world, and particularly in offshore oil and gas exploration, uncertainty exists, and

cash flows will probably vary from management’s expectations. New data will also be

identified, which will most likely change the project’s assumptions, and throughout this

process the management team will be facing the option to possibly change the defined

strategy. Real options analysis valuation methodology brings the required financial flexibility

into the valuation of these projects, as the options of deferring, expanding, staging,

contracting, learning, or abandoning 3 the project throughout its life cycle are taken into

account, giving financial and strategic flexibility to the management team.

In this sense, a real option is thus, the right, but not the obligation, to take a certain action

at a predetermined cost within or at a specific period of time. Real options methodology is

built on their financial counterpart and on the model developed by Fischer Black and Myron

Scholes, as modified by Robert Merton. The term “Real Option” was attributed by Stewart

Myers in 1977, when it referred that option pricing theory could be used to value investment

opportunities in non-financial assets, or “real assets”.

Real options analysis is mainly characterized by the following six basic variables:

• Present value of expected cash flows – this is the present value of the expected cash

flows of the investment opportunity under analysis. It corresponds to the stock price

on which a conventional option is purchased.

• The exercise price – the required outlay to develop the investment opportunity.

Equivalently, it is the defined price for a financial option to be exercised.

• Uncertainty – uncertainty related to the project value. It is a measure of the standard

deviation of the present value of expected cash flows. On options theory, it is the

stock price volatility.

• Time to expiration of the option – period of time during which, or at which, the

investment option can be exercised.

3 Real options taxonomy is given in Appendix B.

Page 14 of 159

• The risk-free rate of interest – rate of a riskless security with the same maturity as

the period of existence of the option.

• Dividends – cash flows incurred during the life cycle of the project. Parallels with

dividends paid to stockholders in the option pricing model.

To analyse the behaviour of the above parameters, the effect of an increase in each of the

variables can be seen below in Table 5.

Increase in Variable Real Option Effect

Present Value of the Asset Increase

Exercise Price Decreases

Uncertainty Increases

Time to Expiration Increases

Risk-free Increases

Dividends Decreases

Table 5 Effect of a value increase on the variables

When compared to financial options, real options are however a more complex instrument.

This is the case for a number of characteristics, being the most fundamental one the fact that

real options underlying assets are non-tradable assets, making it harder to estimate some of

the above discussed parameters, as the “price” of these assets is not usually observable.

Another difference is that financial options are derivative securities (i.e. securities whose

price is derived from the prices of other securities), which are bought or written by agents

that do not have influence over the investment’s course of action, and no control over the

company’s share price. This is opposite to real options, where management has control over

the company and its investments, and whose actions directly influence the direction given to

the company and its investments.

Other feature is that financial options can never have a negative value, which is not true

about real options, where the underlying assets can assume negative values. There are other

differences between real and financial options, and the purpose is not to provide an

exhaustive list of these differences, but to note that the characteristics of these types of

options are distinct, which makes them to depart from one another, and leads to the

application of different resolution methods.

Page 15 of 159

5. Oil Price Stochastic Process

Black and Scholes option pricing methodology description of how assets price evolve through

time is based on the Geometric Brownian Motion (GBM)4 assumption. GBM is referred to in

financial theory as a random walk, where price movements are independent from one

another, and thus, past information cannot be used to predict future movements5.

However, energy commodities price behaviour is slightly different from GBM, as for example,

if oil prices had a significant increase, producers would increase the supply, which would

cause a fall in oil prices. Equally, if oil prices become very low, producers would reduce

production, resulting in oil prices to move up to a previous level. This movement is an

intrinsic characteristic of energy market prices, and a graphical representation of this

behaviour is shown in Figure 7, which shows crude oil price evolution from January 1985 to

December 1999. The figure’s price record is an equally weighted crude oil spot price average

of Brent, Dubai, and West Texas Intermediate crude oil monthly nominal prices, and

presented in US dollars.

Figure 7 Average Crude Oil Price Evolution (Data source: World Bank)

If a pure GBM methodology is used to model oil spot price, unrealistic price levels could be

observed, as if because of some abnormal market conditions, a peak price is reached,

instead of regressing to a previous mean price level, GBM would continue to move to

unrealistic levels.

4 Appendix C describes Geometric Brownian Motion process. 5 Assumption consistent with Efficient Market Hypothesis.

0.00

10.00

20.00

30.00

40.00

19

85

M0

1

19

86

M0

1

19

87

M0

1

19

88

M0

1

19

89

M0

1

19

90

M0

1

19

91

M0

1

19

92

M0

1

19

93

M0

1

19

94

M0

1

19

95

M0

1

19

96

M0

1

19

97

M0

1

19

98

M0

1

19

99

M0

1

Page 16 of 159

Mean Reversion Model (MRM) describes the type of movement realized by crude oil price, and

was first used by Oldrich Vasicek (1977) to model interest-rate dynamics. The method can be

thought as an adjustment to random walk, where price movements are not independent from

one another, but instead related. The mean reversion process can be described by the

following equation6:

Equation 1 Mean Reversion Model (Schwartz, 1997)

where S is the spot price, and α (taken to be strictly positive) is the speed at which the spot

price returns to the long term level, �̅ = ��. σ is the volatility of S, and dz is the Wiener7

process. In this model, if the spot price rises above the long term level, then the drift part of

the equation (i.e. α�μ − �� ) will become negative, and the price will tend to move back to

the long term level. The random component (i.e. σSdz) will then determine the size and

direction of the movement. Similarly, if the spot price is below the long term level, the drift

component will be positive, and the price will tend to move up to the long term level.

Although the distribution of futures prices is also lognormal as in GBM, MRM variance

increases until a future time, remaining constant after that point is reached. Figure 8

illustrates both processes, where GBM volatility increases with time, and where MRM

volatility grows until a certain point in time, after which it remains constant.

Figure 8 GBM and MRM Variance Evolution (Source: Dias, 2004)

An important property of mean reversion is the half-life concept, which is the time taken for

the price to move half way back from its current level to its long term level, assuming no

more random shocks occur. This is an average time (over a long period of time) that

provides a good sensitivity to the “velocity” of the mean reversion process, in alternative to

α, which is a value between 0 and 1 and not so intuitive. Mathematically, half-life is given by

the next equation.

6 This formulation is one of several possible equations that capture the same type of market price evolution. 7 Discussed in Appendix C.

SdzSdtSdS σµα +−= )ln(

Page 17 of 159

Equation 2 Half-Life

Oil price movement is thus, more accurately captured by the mean reverting model, ‘more

consistent with futures market, with long-term econometric tests and with microeconomic

theory’ (Dias, 2004), and as such, MRM will be the employed model to estimate oil price

evolution.

5.1. Estimating Mean Reversion Parameters

Unlike GBM models that have the advantage of input parameters being relatively easy to

estimate, and where volatility can be considered as the most complicated parameter to

evaluate, mean reversion models require the estimation of additional parameters. As referred

above, these are the long term level (�̅�, and the rate (α) at which the spot price reverts to �̅.

Mean reversion parameters can however be robustly estimated through linear regression. As

indicated in Shimko (2002), and Clewlow and Strickland (2000), the simple mean reverting

process, where µ represents the long run mean, can be rewritten as:

Equation 3 Simple Mean Reverting Process Rewritten

This is just like a regression with dependent variable (Xt+1-Xt) and independent variable Xt

with intercept αµ, and slope -α. If the estimated α is negative (the slope is positive), there is

no mean-reversion, and if α is positive (the slope is negative), there is indication that mean

reversion is present in the process. Statistical significance of α should then be tested by

looking at the parameter t-statistic (p-value can also be a good indicator), and being α

statistically significant, error homoscedasticity, normality, and independence tests should

also be carried out to test the validity of the hypothesis.

Concluding all statistical tests, the mean reversion speed is estimated by:

Equation 4 Mean Reversion Speed

and, the long run mean by:

Equation 5 Mean Reversion Long Run Mean

Volatility can be estimated using the regression standard error, in which case, as referred by

Clewlow and Strickland (2000), it is necessary to note that this standard error is expressed

in dollars, and not with no unit expression, like the volatility obtained from logarithmic price

α)2ln(

2/1 =t

11 ++ +−=− tttt XXX εααµ

αµ erceptint=

slope−=α

Page 18 of 159

returns. Thus, the volatility percentage obtained from linear regression will be estimated by

the following equation:

Equation 6 Linear Regression Volatility

In the development of the oil price analysis both methods of volatility estimation will be

carried out, and after assessment, one of these will be selected for the project development.

µσ ErrordardtanS=

Page 19 of 159

6. Approach to Project Resolution

In order to guarantee data confidentiality, the studied project represents a general case

hypothesis, where the used figures are typical industry values. The analysis is first developed

over a simplified case, which allows for the introduction of the used methodologies, being the

full exploration scenario developed at a later stage. In the later complete case, both binomial

and trinomial methodologies are considered, which correspond to the GBM and MRM

approaches, and a comparison between the obtained results is also realized.

The valuation of the project is addressed by defining two sources of uncertainty, namely,

price uncertainty and technological uncertainty. Price uncertainty represents market oil price

and its evolution through time, and technological uncertainty in the first stages of the

investigation process will constitute the uncertainty of the existence of oil in the surveyed

site, and at later stages, if the presence of oil is confirmed, technological uncertainty will

characterize the amount of oil that is present in the site.

These uncertainties have different “behaviours” through time, as price uncertainty is known

today and becomes more unclear as time evolves, and technological uncertainty reduces

through time as more information about the site’s geological structure becomes known.

Furthermore, technological uncertainty will not get resolved smoothly over time, as for

example in a Brownian motion process, being instead resolved at the moment new

information becomes available. Therefore, it is not adequate to produce an estimate for the

technological volatility and use it to generate the common binomial or trinomial lattice, which

assumes that uncertainty is resolved continuously through time.

It is thus, necessary to construct two separate trees that reflect the resolution of both price

and technological uncertainties, in order to correctly develop the ROA valuation. Following

the methodology presented in Copland and Antikarov (2003), and their introduction to the

Quadranomial Approach, in the case of a binomial lattice four outcomes will be possible at

the end of the first period. At this point in time, each uncertainty tree will have either moved

up or down, and the value of the project, V0, will be obtained by the combination of these

outcomes. This process is illustrated in Figure 9, where technological uncertainty up

movement is represented by S, depicting that the activity result has been successful, and the

down movement denoted by F, which indicates an unsuccessful outcome. Oil price up and

down movements are respectively represented by Pu and Pd.

Page 20 of 159

Figure 9 Quadranomial Possible Outcomes

Figure 10 Call Option Value

The quadranomial event lattice has four branches at every node, representing a

generalization of the binomial event lattice with two branches at every node, and Figure 10

expresses the valuation of a call option after one period.

As the existence, and possible quantity of oil present in the geological structure is not in any

manner influenced by developments of oil price in international markets, technological

uncertainty is considered to have a beta of zero. Equation 7 shows that with a �� = 0, the

appropriate discount rate is the risk free rate.

Equation 7 Technological Uncertainty Discount Rate Computation

The independence between the project’s two uncertainties, also has the result that the risk-

neutral probabilities of each branch of the quadranomial lattice, to be the product of the risk-

neutral probabilities of the same identical branch on the price and technological uncertainties

trees. Therefore, for each node, the probabilities will be:

Equation 8 Quadranomial Tree Risk-Neutral Probabilities

where π represents the quadranomial lattice risk-neutral probability, and p the individual

uncertainty risk-neutral probability. In addition, it is relevant to note that the assumption of

technological uncertainty being independent from market movements, also implies that this

uncertainty’s real and risk-neutral probabilities are equal.

The characterization of oil price movement, as refereed above, will be better captured by the

mean reverting model. For this purpose, Hull (2009) trinomial tree building procedure8 will be

the used methodology to describe oil price evolution through time. By combining this oil price

8 This procedure is discussed in Appendix D.

rf]rfr[rfr Mtectec =−+= β

dd

uu

dd

uu

PffP

PffP

PssP

PssP

pp

pp

pp

pp

×=

×=

×=

×=

ππππ

Page 21 of 159

trinomial tree with the technological uncertainty tree, a Hexanomial tree will be created, and

six outcomes will be possible at the end of one period. The hexanomial tree will be resolved

in a manner completely identical to the quadranomial tree, but having six branches at every

node. Figure 11 demonstrates this process, and as realized for the quadranomial process, the

right hand side of the figure also develops the valuation of a call option after one period.

Figure 11 Hexanomial Tree Outcomes and Call Option Value

Page 22 of 159

7. Simplified Case

The simplified case is based on the simple stylized example used earlier, motivating the

application of ROA. The case develops the scenario of an offshore site where a delineation

well (DW1) will be drilled, and in case the test is productive, management faces the decisions

discussed in point 3 of this thesis, which are the establishment of a LP, of a SP, or the

acquisition of additional imperfect information (DW2). As before, setting a LP can be

considered as a “safe” strategy, installing a SP as a “gamble” strategy, and the acquisition of

additional imperfect information as an alternative that will defer the decision for one year.

This process can be seen below in Figure 12, where the indicated time steps are also annual.

Figure 12 Simple Case Oilfield Development Decision Tree

Appendix E and Appendix F respectively show project technological and price uncertainties

data, constituting the data available to the management team at time zero. Price uncertainty

appendix also includes all necessary calculations to the construction of a trinomial tree, and

the effect of new information to technological uncertainty is exposed in Appendix G.

The result of the combination of technological and price uncertainties is showed next in

Figure 13, where for simplicity the end nodes valuations are a one-time free cash flow. The

used procedure to estimate these cash flows is price times quantity, minus OPEX, and their

calculation is shown in Appendix H.

Page 23 of 159

In year one, if DW1 is unsuccessful, the project is discontinued with no nodes emanating

from failure nodes. If DW1 is successful, management will face the discussed alternatives,

and will have to analyse the NPV of each mutually exclusive alternative. This is the base case

scenario, where without the consideration of ROA management would select the alternative

with best NPV.

0 1 2 3

0 1 2 3

PV s B sb(D+) E sb(D+)LO J

PV s B sb(D+) E $132,210,536.07

s C sb(D+) F sb(D+)LO K

s C sb(D+) F $91,186,975.28

s D sb(D+) G sb(D+)LO L

s D sb(D+) G $62,518,791.60

f B sb(D+) H sb(D+)LO M

f B sb(D+) H $42,484,822.35

f C sb(D+) I sb(D+)LO N

f C sb(D+) I $28,484,635.65

f D

sb(D+)LO O

f D

$18,700,991.42

sb(D+)LO P

$11,863,961.57

sb(D+)SO J

$126,210,536.07

sb(D+)SO K

$85,186,975.28

sb(D+)SO L

$56,518,791.60

sb(D+)SO M

$36,484,822.35

sb(D+)SO N

$22,484,635.65

sb(D+)SO O

$12,700,991.42

sb(D+)SO P

$5,863,961.57

sb(D-) E sb(D-)LO J

sb(D-) E $132,210,536.07

sb(D-) F sb(D-)LO K

sb(D-) F $91,186,975.28

sb(D-) G sb(D-)LO L

sb(D-) G $62,518,791.60

sb(D-) H sb(D-)LO M

sb(D-) H $42,484,822.35

sb(D-) I sb(D-)LO N

sb(D-) I $28,484,635.65

sb(D-)LO O

$18,700,991.42

sSO E sb(D-)LO P

$87,044,264.46 $11,863,961.57

sSO F sb(D-)SO J

$57,816,706.90 $126,210,536.07

sSO G sb(D-)SO K

$37,391,834.65 $85,186,975.28

sSO H sb(D-)SO L

$23,118,476.17 $56,518,791.60

sSO I sb(D-)SO M

$13,143,933.38 $36,484,822.35

sS§ E sb(D-)SO N

$46,022,132.23 $22,484,635.65

sS§ F sb(D-)SO O

$31,408,353.45 $12,700,991.42

sS§ G sb(D-)SO P

$21,195,917.33 $5,863,961.57

sS§ H

$14,059,238.09

sS§ I sb(D+)L§ J

$9,071,966.69 $66,105,268.04

sb(D+)L§ K

$45,593,487.64

sL E sb(D+)L§ L

$62,804,878.51 $31,259,395.80

sL F sb(D+)L§ M

$43,076,277.16 $21,242,411.18

sL G sb(D+)L§ N

$29,289,488.39 $14,242,317.83

sL H sb(D+)L§ O

$19,654,971.42 $9,350,495.71

sL I sb(D+)L§ P

$12,922,155.03 $5,931,980.78

sb(D+)S§ J

$65,605,268.04

sb(D+)S§ K

$45,093,487.64

sb(D+)S§ L

$30,759,395.80

sb(D+)S§ M

$20,742,411.18

sb(D+)S§ N

$13,742,317.83

sb(D+)S§ O

$8,850,495.71

sb(D+)S§ P

$5,431,980.78

sb(D-)L§ J

$66,105,268.04

sb(D-)L§ K

$45,593,487.64

sb(D-)L§ L

$31,259,395.80

sb(D-)L§ M

$21,242,411.18

sb(D-)L§ N

$14,242,317.83

sb(D-)L§ O

$9,350,495.71

sb(D-)L§ P

$5,931,980.78

sb(D-)S§ J

$65,605,268.04

sb(D-)S§ K

$45,093,487.64

sb(D-)S§ L

$30,759,395.80

sb(D-)S§ M

$20,742,411.18

sb(D-)S§ N

$13,742,317.83

sb(D-)S§ O

$8,850,495.71

sb(D-)S§ P

$5,431,980.78

Figure 13 Simple Case Hexanomial Event Tree

In the figure above, the code on the left hand side of each node describes technological

uncertainty path, and the letters at the node’s right hand side indicate the possible price

s – success

f – failure

b – buy info

S – set small

L – set Large

O – result is large

§ – result is Small

(D+) – data says it is large

(D–) – data says it is small

Technological uncertainty legend:

Colours Legend (Y2 and Y3):

Buy info; Result is (D+)

Data indicates (D+); Set LP

Data indicates (D+); Set SP

Buy info; Result is (D-)

Data indicates (D-); Set LP

Data indicates (D-); Set SP

Set LP at Y3

Set SP at Y3; It is large

Set SP at Y3; It is small

Abandon

Continue

Page 24 of 159

levels at that year. Blue and brown shaded cells represent the alternative of acquiring

additional information, where the blue cells characterize the case that the new data indicates

a large quantity of oil, and brown cells portray the case where a small quantity of oil is

determined by the obtained information. Year three blue sb(D+)L cells embody the path

where management decides to set a LP, with O representing the case that the site has in fact

a large quantity of oil, and § expressing the situation that the site has a small quantity of oil.

Similarly, blue sb(D+)S symbolize the case where management establishes a SP.

Identically, third year sb(D-)L brown cells indicate the path where management sets a LP,

with O being the case of a large quantity of oil, § the case of a small quantity, and sb(D-)S

depict the alternative route where management sets a SP. With a similar reasoning, year two

green cells depict the option where management sets a SP, and violet shaded cells represent

the alternative of setting a LP, being the reading of all these possibilities easily followed by

the figure’s legend.

Dependent on the followed option, at the end of the second or third year oil quantity

uncertainty will have been resolved, and a DCF model can be developed for each possible

result at each level of oil price. The values on the cells are the obtained results, and the cash

flow models for each of the end nodes can be found in the referred appendix.

The first alternative NPV to be computed is the option to acquire additional information,

where the tree’s end nodes NPVs are worked backward until year zero, being the project

Present Value (PV) obtained. In order to develop this process it is necessary to have each

node’s combined probabilities (i.e. π), which are showed in Appendix I. The risk-neutral

probabilities are then used to calculate the value at each node, and for example node sb(D+)

E, is the maximum value between the choice of either setting a large or a small platform.

Computationally, this is the maximum between (monetary values are expressed in millions):

and:

In the above, the value for the case of setting a LP (i.e. top equation) is obtained by

multiplying end nodes sb(D+)LO J, sb(D+)LO K, and sb(D+)LO L respectively by the

LO*(E)pu, LO*(E)pm, and LO*(E)pd risk–neutral probabilities, which are indicated in the Buy

info, data indicated large quantity, do large platform – To Point E section of the simplified

case trinomial tree nodes probabilities table. The one year risk-free discounted value

obtained by this multiplication, has to be reduced by the year two cost of installing a large

platform multiplied by the probability that a large quantity of oil is the case. The value

obtained by these computations is added to the value that although the new information

indicated a large quantity of oil to be present in the site, and a LP was set, the actual case is

that a small quantity is present in the geological structure.

171103031

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2163057530808508180126.$

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Page 25 of 159

Therefore, in an identical procedure, this last value is obtained by multiplying end nodes

sb(D+)L§ J, sb(D+)L§ K, and sb(D+)L§ L respectively by the L§*(E)pu, L§*(E)pm, and

L§*(E)pd risk–neutral probabilities, whose result is discounted to year two at the risk-free

rate. At year two, the investment of installing a large platform multiplied by the probability

that a small quantity of oil is the case is also reduced from the discounted value. The

addition of these two results will constitute the value of setting a LP when the new

information indicates a large quantity of oil.

It is necessary to refer that at the end of the computation of both possible outcomes, the

reduction of year two cost of setting up a LP was multiplied by each outcome probability. The

result would be the same, if the platform installation full cost was reduced at the end of the

equation, without multiplying it by any probability. Although this is the case in this possible

path, as it is showed next, this will not be the case in other possibilities, and thus, the

computation was constructed in this manner in order to maintain calculations uniformity.

The above result is for the option of setting a LP when the new data indicates a large

quantity of oil, but as referred, at this point in time (i.e. year two) management can also

decide to install a SP (the second equation), whose computation is constructed in a similar

manner to the calculations described above. Thus, this path result is achieved by multiplying

end nodes sb(D+)SO J, sb(D+)SO K, and sb(D+)SO L respectively by the SO*(E)pu,

SO*(E)pm, and SO*(E)pd risk–neutral probabilities, which are indicated in the Buy info, data

indicated large quantity, do small platform – To Point E section of the same simplified case

probabilities table. The one year risk-free discounted value obtained by this multiplication, is

reduced by the year two total infrastructures cost multiplied by the probability that a large

quantity of oil is the case. This infrastructures total cost includes the penalty costs of

installing a SP, and later finding that the site has a large quantity of oil. Hence, the

infrastructures total cost is composed by the cost of installing a small platform, plus the cost

of setting a second platform and readapting the extraction system.

As before, the obtained value is added to the result reached by the possibility that there is a

small quantity of oil in the site. This result is achieved by multiplying end nodes sb(D+)S§ J,

sb(D+)S§ K, and sb(D+)S§ L respectively by the S§*(E)pu, S§*(E)pm, and S§*(E)pd risk–

neutral probabilities, whose result is discounted to year two at the risk-free rate. At year

two, the investment of installing a SP, multiplied by the probability that a small quantity of

oil is the case, is reduced from the discounted value. The addition of these two results will

constitute the value of setting a SP when the new information indicates a large quantity of

oil. At this point, management will therefore select the path with maximum expected value,

between setting a large or small platform when the new information indicates that the site

has a large quantity of oil.

Page 26 of 159

In the figure below, year two cell colours will indicate which of the above options has a

maximum expected value by matching the alternative’s year three colour.

0 1 2 3

0 1 2 3

PV S B sb(D+) E sb(D+)LO J

$2,764,804.82 $29,236,380.28 $69,091,545.75 $132,210,536.07


$18,352,324.59 $46,188,176.77 $91,186,975.28


$10,309,300.57 $29,709,010.67 $62,518,791.60

F B sb(D+) H sb(D+)LO M

-$4,000,000.00 $17,851,424.63 $42,484,822.35

F C sb(D+) I sb(D+)LO N

-$4,000,000.00 $9,319,051.79 $28,484,635.65

f D

sb(D+)LO O

-$4,000,000.00

$18,700,991.42

sb(D+)LO P

$11,863,961.57

sb(D+)SO J

PV $2,764,804.82 $126,210,536.07

sb(D+)SO K

DW1 $4,000,000.00 $85,186,975.28

sb(D+)SO L

NPV -$1,235,195.18 $56,518,791.60

sb(D+)SO M

$36,484,822.35

sb(D+)SO N

$22,484,635.65

sb(D+)SO O

$12,700,991.42

sb(D+)SO P

$5,863,961.57

sb(D-) E sb(D-)LO J

$40,710,137.84 $132,210,536.07

sb(D-) F sb(D-)LO K

$27,506,946.61 $91,186,975.28

sb(D-) G sb(D-)LO L

$18,008,727.35 $62,518,791.60

sb(D-) H sb(D-)LO M

$11,175,275.03 $42,484,822.35

sb(D-) I sb(D-)LO N

$6,258,733.42 $28,484,635.65

sb(D-)LO O

$18,700,991.42

sb(D-)LO P

$11,863,961.57

sb(D-)SO J

$126,210,536.07

sb(D-)SO K

$85,186,975.28

sb(D-)SO L

$56,518,791.60

sb(D-)SO M

$36,484,822.35

sb(D-)SO N

$22,484,635.65

sb(D-)SO O

$12,700,991.42

sb(D-)SO P

$5,863,961.57

sb(D+)L§ J

$66,105,268.04

sb(D+)L§ K

$45,593,487.64

sb(D+)L§ L

$31,259,395.80

sb(D+)L§ M

$21,242,411.18

sb(D+)L§ N

$14,242,317.83

sb(D+)L§ O

$9,350,495.71

sb(D+)L§ P

$5,931,980.78

sb(D+)S§ J

$65,605,268.04

sb(D+)S§ K

$45,093,487.64

sb(D+)S§ L

$30,759,395.80

sb(D+)S§ M

$20,742,411.18

sb(D+)S§ N

$13,742,317.83

sb(D+)S§ O

$8,850,495.71

sb(D+)S§ P

$5,431,980.78

sb(D-)L§ J

$66,105,268.04

sb(D-)L§ K

$45,593,487.64

sb(D-)L§ L

$31,259,395.80

sb(D-)L§ M

$21,242,411.18

sb(D-)L§ N

$14,242,317.83

sb(D-)L§ O

$9,350,495.71

sb(D-)L§ P

$5,931,980.78

sb(D-)S§ J

$65,605,268.04

sb(D-)S§ K

$45,093,487.64

sb(D-)S§ L

$30,759,395.80

sb(D-)S§ M

$20,742,411.18

sb(D-)S§ N

$13,742,317.83

sb(D-)S§ O

$8,850,495.71

sb(D-)S§ P

$5,431,980.78

Figure 14 Acquiring Additional Imperfect Information NPV

At year one, the new data will either indicate that the quantity is large or small, being each

possibility multiplied by the possible price movements. Thus, node S B is obtained by

multiplying nodes sb(D+) E, sb(D+) F, sb(D+) G, sb(D-) E, sb(D-) F, and sb(D-) G

respectively by the b(D+)*(B)pu, b(D+)*(B)pm, b(D+)*(B)pd, b(D-)*(B)pu, b(D-)*(B)pm,

and b(D-)*(B)pd, risk–neutral probabilities, which are indicated in the Probabilities Y1 to Y2

Page 27 of 159

Buy Info – To Point B section of the above referred probabilities table. Discounting this value

one year, and subtracting the cost of acquiring additional information gives S B node value,

whose computations are showed below.

Similar arithmetic allows for the PV of the alternative to acquire additional imperfect

information to be computed:

Subtracting DW1 cost gives the alternative’s NPV of -$1,235,195.18.

The event tree for the mutually exclusive alternative of installing a LP can be seen below,

and this project’s PV estimation process is identical to the steps developed above.

Nevertheless, from year two to year one only price uncertainty exits, as by setting a LP a

fixed quantity is assumed – obtained by multiplying both oil estimated amounts by their

correspondent probabilities. Therefore, year one cell S B value is obtained by multiplying

cells sL E, sL F, and sL G respectively by Point B pu, Point B pm, and Point B pd indicated in

the probabilities table section Probabilities Y1 to Y2 Set Large:

Year zero PV is obtained by:

By reducing DW1 cost the NPV of -$4,091,196.15 is reached.

0 1 2

0 1 2

PV S B sL E

-$91,196.15 $32,482,529.69 $62,804,878.51

s C sL F

$20,108,285.14 $43,076,277.16

s D sL G

$11,205,688.99 $29,289,488.39

F B sL H

-$9,000,000.00 $19,654,971.42

F C sL I

-$9,000,000.00 $12,922,155.03

f D

-$9,000,000.00

PV -$91,196.15

DW1 $4,000,000.00

NPV -$4,091,196.15

Figure 15 NPV for Setting a Large Platform at Year One

The last alternative is to set a SP, and following this path cell S B value is obtained by

multiplying cells sSO E, sSO F, sSO G, sS§ E, sS§ F, and sS§ G respectively by L(B)*pu,

L(B)*pm, L(B)*pd, S(B)*pu, S(B)*pm, and S(B)*pd probabilities, which are indicated in the

Probabilities Y1 to Y2 Set Small – To Point B section of the probabilities table:

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Page 28 of 159

The result of this computation is seen in the figure below, and the platform’s estimated cost

of $6.150 million is obtained by multiplying the cost of installing a SP plus the cost of having

to install an additional platform and readapt the set extraction system, which mounts up to

$12 million, by the probability estimate that a large quantity is the case. This value is added

to the cost of $3 million multiplied by the probability that a small amount of oil is the

situation at hand. Numerically:

Following the same procedure of the other two mutually exclusive alternatives, a PV of

$1,990,055.61 is reached. Deducting DW1 cost gives a NPV of -$2,009,944.39.

0 1 2

0 1 2

PV S B sSO E

$1,990,055.61 $32,978,160.76 $87,044,264.46

s C sSO F

$20,603,916.20 $57,816,706.90

s D sSO G

$11,701,320.06 $37,391,834.65

F B sSO H

-$6,150,000.00 $23,118,476.17

F C sSO I

-$6,150,000.00 $13,143,933.38

f D sS§ E

-$6,150,000.00 $46,022,132.23

sS§ F

$31,408,353.45

sS§ G

$21,195,917.33

sS§ H

$14,059,238.09

sS§ I

$9,071,966.69

PV $1,990,055.61

DW1 $4,000,000.00

NPV -$2,009,944.39

Figure 16 NPV for Setting a Small Platform at Year One

As Table 6 shows, the best alternative would be to acquire additional imperfect information,

but as none of these alternatives has a positive NPV, all projects would be rejected.

Best Option without ROA

No ROA, with 2nd Drill -$1,235,195.18

No ROA, Set Large, no 2nd Drill -$4,091,196.15

No ROA, Set Small, no 2nd Drill -$2,009,944.39

Best Option -$1,235,195.18

Table 6 Best Option without Real Options Analysis

After these results, a ROA is developed in order to estimate the project’s value with

flexibility. Through this methodology, from year zero to year one management can exercise

the option to continue or to abandon the project. At year one, there are four options,

namely, to set a LP, to set a SP, to buy additional imperfect information, or to abandon. And

finally, in case the option to acquire additional information has been chosen, at year two, the

study result will have either been that a large or a small amount of oil is present in the site,

having management at these nodes the options to set a LP, to install a SP, or to abandon the

project.

The next figure illustrates the ROA process where these options are considered. The

introduction of the referred options at year one, determine that the best path to follow at

1506650335012 .$.$.$ =×+×

Page 29 of 159

nodes S B, S C, and S D is to set a SP. At nodes F B, F C, and F D, as management is no

longer irrevocably committed to the set strategy, the best option is to abandon the project.

0 1 2 3

0 1 2 3

PV S B sb(D+) E sb(D+)LO J

$6,169,667.26 $32,978,160.76 $69,091,545.75 $132,210,536.07


$20,603,916.20 $46,188,176.77 $91,186,975.28


$11,701,320.06 $29,709,010.67 $62,518,791.60

F B sb(D+) H sb(D+)LO M

$0.00 $17,851,424.63 $42,484,822.35

F C sb(D+) I sb(D+)LO N

$0.00 $9,319,051.79 $28,484,635.65

f D

sb(D+)LO O

$0.00

$18,700,991.42

sb(D+)LO P

$11,863,961.57

sb(D+)SO J

Y0 to Y1 legend:

$126,210,536.07

sb(D+)SO K

Buy Information $85,186,975.28

sb(D+)SO L

Set LP $56,518,791.60

sb(D+)SO M

Set SP

$36,484,822.35

sb(D+)SO N

Abandon

$22,484,635.65

sb(D+)SO O

Continue

$12,700,991.42

sb(D+)SO P

$5,863,961.57

sb(D-) E sb(D-)LO J

$40,710,137.84 $132,210,536.07

sb(D-) F sb(D-)LO K

$27,506,946.61 $91,186,975.28

sb(D-) G sb(D-)LO L

$18,008,727.35 $62,518,791.60

sb(D-) H sb(D-)LO M

$11,175,275.03 $42,484,822.35

sb(D-) I sb(D-)LO N

$6,258,733.42 $28,484,635.65

sb(D-)LO O

$18,700,991.42

sSO E sb(D-)LO P

PV $6,169,667.26 $87,044,264.46 $11,863,961.57

sSO F sb(D-)SO J

DW1 $4,000,000.00 $57,816,706.90 $126,210,536.07

sSO G sb(D-)SO K

NPV $2,169,667.26 $37,391,834.65 $85,186,975.28

sSO H sb(D-)SO L

$23,118,476.17 $56,518,791.60

sSO I sb(D-)SO M

$13,143,933.38 $36,484,822.35

sS§ E sb(D-)SO N

$46,022,132.23 $22,484,635.65

sS§ F sb(D-)SO O

$31,408,353.45 $12,700,991.42

sS§ G sb(D-)SO P

$21,195,917.33 $5,863,961.57

sS§ H

$14,059,238.09

sS§ I sb(D+)L§ J

$9,071,966.69 $66,105,268.04

sb(D+)L§ K

$45,593,487.64

sL E sb(D+)L§ L

$62,804,878.51 $31,259,395.80

sL F sb(D+)L§ M

$43,076,277.16 $21,242,411.18

sL G sb(D+)L§ N

$29,289,488.39 $14,242,317.83

sL H sb(D+)L§ O

$19,654,971.42 $19,654,971.42

sL I sb(D+)L§ P

$12,922,155.03 $5,931,980.78

sb(D+)S§ J

$65,605,268.04

sb(D+)S§ K

$45,093,487.64

sb(D+)S§ L

$30,759,395.80

sb(D+)S§ M

$20,742,411.18

sb(D+)S§ N

$13,742,317.83

sb(D+)S§ O

$8,850,495.71

sb(D+)S§ P

$5,431,980.78

sb(D-)L§ J

$66,105,268.04

sb(D-)L§ K

$45,593,487.64

sb(D-)L§ L

$31,259,395.80

sb(D-)L§ M

$21,242,411.18

sb(D-)L§ N

$14,242,317.83

sb(D-)L§ O

$9,350,495.71

sb(D-)L§ P

$5,931,980.78

sb(D-)S§ J

$65,605,268.04

sb(D-)S§ K

$45,093,487.64

sb(D-)S§ L

$30,759,395.80

sb(D-)S§ M

$20,742,411.18

sb(D-)S§ N

$13,742,317.83

sb(D-)S§ O

$8,850,495.71

sb(D-)S§ P

$5,431,980.78

Figure 17 Real Options Analysis NPV

Figure 18 illustrates the ROA process, where for a more clear illustration of the process, only

the evolution of the top nodes is realized. Nevertheless, the illustration of the process for all

nodes is shown in Appendix J.

Page 30 of 159

Figure 18 Real Options Analysis Process

s – success

f – failure

b – buy info

S – set small

L – set Large






Page 31 of 159

As the figure depicts, node S B is the maximum value among the options of setting a LP,

installing a SP, buying additional imperfect information, or abandoning the project. Using the

explained methodology, year one values are multiplied by their respective probabilities,

discounted to year zero at the risk-free rate, and the project PV is obtained. Subtracting DW1

cost results in a NPV of $2,169,667.26, which makes the project financially viable and

acceptable to the management team. The value of the project flexibility is obtained by the

difference between the ROA valuation and the best mutually exclusive alternative valuation,

which is also showed in the next table where the obtained results are summarized. Thus, the

total benefit of the introduction of flexibility to the project valuation is well illustrated in this

analysis, as is the influence that ROA methodology can exert on decision making.

Best Option with Flexibility

Best Option without ROA -$1,235,195.18

ROA value $2,169,667.26

Best Option $2,169,667.26

ROA Added Value $3,404,862.45

Table 7 Real Options Analysis Added Value

Page 32 of 159

8. Complete Case

This case is an extension to the simplified case, where two additional seismic activities exist

before the first delineation well is realized – 2D and 3D seismic surveys are preliminary

exploration activities. The next figure depicts the process, existing now three initial phases

with the option to continue or abandon the project, and at year three, management faces the

discussed options of installing a LP, of setting a SP, of acquiring additional imperfect

information (DW2), or of abandoning the project.

Figure 19 Complete Case Oilfield Development Decision Tree

As with the previous case, the data for technological and price uncertainties is respectively

shown in Appendix K and Appendix L, where price uncertainty appendix includes all

necessary calculations for the construction of the trinomial and binomial price trees. Also as

realized in the simplified case, the effect of new information to technological uncertainty is

indicated in Appendix M.

The well has a life expectancy of fifteen years, and in order to estimate the end nodes NPVs,

the reached trinomial tree price levels are expected to evolve towards the long run mean

value. To represent this price progression through time, Schwartz (1997) model is used

without the random component, using the formula presented below (this process and the

obtained prices are shown in Appendix N). The binomial model process is assumed to have a

drift of zero, maintaining therefore, the same price level during the well life expectancy.

Equation 9 Mean Reversion Model without Random Component (Schwartz, 1997)

Sdt)Sln(dS −= µα

Page 33 of 159

Production levels are dependent on the existing quantity of oil, being in this manner,

developed a production scenario for each possible outcome, which is shown in Appendix O.

Having defined these elements, it is possible to develop the estimation of the end nodes

NPVs, which are shown in Appendix P for the case of the trinomial price tree, and in Appendix

Q for the case of the binomial price tree.

The probabilities of the hexanomial and quadranomial trees are respectively shown in

Appendix R and Appendix S, which complete the required data for the computation of the

NPV of each mutually exclusive alternative, by each type of tree. These alternatives NPVs are

shown in Appendix T for the hexanomial tree, and in Appendix U for the quadranomial tree.

As showed in the table below, all obtained NPVs are negative, being all alternatives

consequently rejected by the management team.

Best Option without ROA

Hexanomial Quadranomial

No ROA, with 2nd Drill -$409,682,699.02 -$369,669,093.33

No ROA, Set Large, no 2nd Drill -$300,446,452.44 -$266,443,139.20

No ROA, Set Small, no 2nd Drill -$289,440,719.74 -$255,437,406.50

Best Option -$289,440,719.74 -$255,437,406.50

Table 8 Best Option without Real Options Analysis

The ROA is developed for both types of tree, and the result achieved by this methodology is

shown in the following table (the details of the ROA computations are shown in Appendix V).

Best Option with ROA

Hexanomial Quadranomial

Buy additional information -$409,682,699.02 -$369,669,093.33

Set Large, no 2nd Drill -$300,446,452.44 -$266,443,139.20

Set Small, no 2nd Drill -$289,440,719.74 -$255,437,406.50

Best option -$289,440,719.74 -$255,437,406.50

ROA $103,633,477.86 $137,636,791.10

ROA Added Value $393,074,197.60 $393,074,197.60

Table 9 Best Option with Real Options Analysis

Using the ROA approach, and taking into consideration the available options, brings the

project valuation to a positive level, which makes it acceptable by the management

structure. Interesting to note in the obtained results, is that by selecting the same options,

both methods correctly give the same valuation to flexibility, but the quadranomial tree

always presents better results than the hexanomial tree. This fact can be explained by the

binomial model not reflecting oil price mean reversion property, which allows prices to

wonder off, and therefore, results in an overestimation of the project’s value.

The strategic capability of ROA methodology is also well represented in the developed trees

(Appendix V), as it is possible to see the different paths indicated by the method at each

Page 34 of 159

$392.9M

$393.M

$393.1M

$393.2M

$393.3M

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

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σ

node’s position. The analysis establishes that, according to the registered oil price, year

three options to follow are either the setting of a LP or the abandonment of the project.

Furthermore, it is relevant to state that the trees detail can influence decision making and

the pursued path. This characteristic is discussed in the next section, where it can be seen

that at year three, with certain levels of the used parameters, the quadranomial tree only

indicates the installation of a LP or the abandonment of the project, and the hexanomial tree

greater detail identifies further alternatives. Dependent on the observed oil price, this later

tree will determine the setting of a LP, the acquisition of additional imperfect information

(deferring the decision for one year), or the abandonment of the project. Thus, the

hexanomial tree greater detail can identify alternative preferable paths, which naturally adds

financial and strategic value to the method.

Considering the process realized by the hexanomial tree analysis, the project is thus valued

at $103.6 million, and the application of the ROA approach, allowed the valuation process to

consider the existent decision making flexibility. In this case, project’s flexibility represents

an added value of $393 million, and the capabilities and potential of ROA are well illustrated,

as is the influence that the methodology can have on the decision making process.

8.1. Sensitivity Analysis to Project Parameters

Analysing the hexanomial tree (except if stated otherwise), it is also interesting and valuable

to assess how changes to key parameters influence flexibility valuation, and for this purpose,

a sensitivity analysis is realized to some of these elements. Oil price volatility is a crucial

factor on the developed analysis, and as such, the figure below reflects how changes to this

component affect the value of assessing the project’s flexibility. As it can be seen, and

expected, an increase in volatility will also result in an increase on the value of the

investment’s options, being the slope of this relationship more significant as volatility

progresses. An inverse relation exists with the project NPV, where Figure 21 shows that as

volatility increases the NPV of the project decreases.

Figure 20 Sensitivity Analysis to Oil Price Volatility (Value of Flexibility)

Page 35 of 159

Figure 21 Sensitivity Analysis to Oil Price Volatility (Project Value)

Also relevant to observe how the valuation differences between the hexanomial and

quadranomial trees behave as oil price volatility advances. Appendix W presents the project

results at the ten, twenty, and fifty percent volatility levels, being possible to confirm that

the difference between the two methods valuations increases with the growth of oil price

volatility. The cause of this behaviour is the methodologies different modelling of oil price

evolution.

In this particular study, unless there is absolute certainty about the reliability of the new

information, changes to the sufficiency of acquiring new data will not influence the end

results (see Figure 22). This occurs because the difference between large and small

quantities of oil is so significant, that the methodology consistently determines that it is more

advantageous to select the installation of a LP. Actually, this certain information is only

incorporated by the hexanomial tree, as the quadranomial tree lower detail does not have a

price level that absorbs the value of this information. Appendix X has the analysis of both

processes at the absolute certainty level, and this characteristic can be seen in the

hexanomial tree S3 P node, where the best option to follow is the acquisition of additional

information. The Appendix also shows a table with the valuation of the several processes

under this certainty assumption, and it is showed that the ROA added value of both

methodologies now differs, where the hexanomial tree higher flexibility value reflects the

incorporation of the referred option.

Figure 22 Sensitivity Analysis to the Sufficiency of DW2 Data

$393.072M

$393.074M

$393.076M

$393.078M

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Sufficiency of DW2 Data

$84.M

$90.M

$96.M

$102.M

$108.M

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Pro

ject

NP

V

σ

Page 36 of 159

The same inconsequence occurs with changes to the costs of altering the installed production

scheme from small quantity to large quantity, as the option of setting a SP is never selected

(i.e. by not selecting the setting of a SP at any node, such costs simply do not apply in the

valuation process). The difference between large and small quantity of oil is again the reason

behind this permanent selection for the establishment of the LP.

Altering the cost of new information has an impact until about $100 million, point from

which, the influence of these changes becomes residual, as Figure 23 illustrates. At the $50

million cost level, the hexanomial tree is once again the only method that recognizes the

advantage of acquiring information in one of its nodes. Appendix Y shows the hexanomial and

quadranomial assessments at this cost level, and also contains a table with the several

methods results. The hexanomial tree greater flexibility value is once more the result of the

tree’s increased detail, which allows it to capture the value of options not absorbed by the

quadranomial tree. Moreover, by defining DW2 cost at $50 million, the best mutually

exclusive alternative becomes the acquisition of additional imperfect information, which the

appendix’s table also shows.

Figure 23 Sensitivity Analysis to the Cost of Acquiring New Information

The assessment to determine the effect of changes to the initial probability that the site has

a large quantity of oil is developed next. Figure 24 depicts the behaviour of flexibility value

to these changes, being possible to observe that the value of flexibility has an interesting

growth until roughly 50%, suffering small changes beyond this level. This is an expected

evolution, as the options value will have smaller increases as the certainty of large quantity

of oil increases.

$370.M

$390.M

$410.M

$50.M $100.M $150.M $200.M $250.M $300.M $350.M $400.M

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Cost of Aquiring Additional Imperfect Information

Page 37 of 159

Figure 24 Sensitivity Analysis to the Initial Probability of Large Quantity of Oil

Naturally, this relationship is inversed when considering increases to the initial probability

that the site has a small quantity of oil, as the next figure demonstrates.

Figure 25 Sensitivity Analysis to the Initial Probability of Small Quantity of Oil

The effects of changes to the initial probabilities of the site’s quantity of oil in the hexanomial

and quadranomial trees are once again better captured by the hexanomial tree structure.

Appendix Z presents these trees at several probability levels, being possible to see that if the

initial probability of a large quantity of oil is set to forty percent, the hexanomial tree

immediately captures value, reflecting it in node S3 P. Setting this probability to seventy

percent, causes the hexanomial tree to incorporate the change in one more node, namely

node S3 O. Further increases from this point onwards will no longer affect the hexanomial

tree, and the quadranomial tree will only reflect changes from this parameter at the certainty

level, where it completely alters year three nodes selection from the installation of a LP to

the acquisition of new information. These distinct behaviours occur because of the different

oil price modulation by the trinomial and binomial trees, having the hexanomial tree more

price detail on its nodes and a smother reaction to this type of changes.

The same Appendix Z has in its last page tables that indicate the ROA added value at each of

the analysed levels, and it can be seen that the hexanomial tree value of flexibility is greater

at both the forty and seventy percent levels. At certainty level, the quadranomial tree

$340.M

$360.M

$380.M

$400.M

$420.M

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Initial Probability of the Site Having a Large Quantity of Oil

$340.M

$360.M

$380.M

$400.M

$420.M

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Initial Probability of the Site Having a Small Quantity of Oil

Page 38 of 159

flexibility value has a significant increase, which is a result of its year three option

modification. It is considered that the hexanomial tree has a more adequate representation

of the value of flexibility, and that the certainty level quadranomial tree valuation of

flexibility is an overestimation of this element. The tables also show that as the initial

probability of the site having a large quantity of oil increases, the best mutually exclusive

alternative becomes the installation of a LP.

Still regarding changes to the initial probability that the site has a large quantity of oil, and

considering the absolute certainty level, it is still necessary to explain why in some nodes (or

all in the case of the quadranomial tree) the preferred option is to acquire new information,

and defer the decision for one year, and not to immediately set a LP. Following the

quadranomial tree process, it is first necessary to recognize that from year five to year four

only the large quantity outcomes will have influence. Appendix AA has the required data for

this discussion, and there it can be seen that with the initial absolute certainty level, the

effect of new imperfect information results on only the large quantity events of nature being

considered (i.e. E1), which consequently influences the option valuation to increase. Year five

large quantity of oil events are brought to year four at the risk neutral probabilities (showed

in the data Appendix AA), as only nodes LO pu9 and LO pd10 apply. This is the process that

makes the option to acquire additional information more valuable at year four, and therefore

selected at year three by the methodology (i.e. both options have the same probabilities

from year four to year five – also in the appendix).

The hexanomial tree follows the exact same process, and what is considered to be of value to

the ROA is not the acquisition of additional information, as at the absolute certainty level

perfect information about the site’s oil quantity already exists, but instead, the selection of

the option to defer the decision for one year. For this reasoning, it is first required to note

that the option to pursue further information is actually composed by two simultaneous

options, where one is the acquisition of information, and the other is the deferral of the

decision for one year. These options could not coincide, as for example the acquisition of

information had immediate effects, which would be possible if the site had been previously

surveyed by a third party that would be willingly to sell the collected data. However, in this

case these the two options coincide, and only one of them will apply. Consequently, when

assessing the case of absolute certainty, what is considered to be of value by the

methodology is the option to defer the decision for one year, and not the option to acquire

additional imperfect information, being the cost to acquire the new data de option’s exercise

price.

Modifying the decline of the rate of production to ten and twenty five percent is also realized,

in order to assess the behaviour of flexibility value to this type of changes. The analysis

developed for this component assumes the current initial production levels, and truncates

9 Set large platform, quantity is large, and oil price moves up.

10 Set large platform, quantity is large, and oil price moves down.

Page 39 of 159

maximum production years at the used fifteen years level. Hence, with the application of this

approach, the reduction of the decline rate of production will result on the existent amount of

oil being extracted faster, and the increase of the parameter will have the consequence that

less quantity will be extracted from the well. As the next figure illustrates, the decrease of

this element will result in an increase of the value of flexibility.

Figure 26 Sensitivity Analysis to the Decline of the Rate of Production

8.2. Options Value

The assessment of each option value in the hexanomial tree is also developed, having the

analysis the objective of evaluating the influence of the several options on the final value of

flexibility. Being the option to install a SP the best mutually exclusive alternative, each option

will therefore be estimated in respect to this tree. Appendix BB shows the developed trees,

and the table below summarises the obtained results.

Options Value

Option to Set LP Option to Abandon

Option to Acquire Information

Original Set Small, no 2nd Drill NPV -$289,440,719.74 -$289,440,719.74 -$289,440,719.74

Valuation with ROA -$274,447,071.99 $88,639,830.12 -$282,976,579.97

ROA Added Value $14,993,647.74 $378,080,549.85 $6,464,139.76

Table 10 Individual Option Value

The complete ROA only used the options to install a large platform and to abandon the

project, and the option to acquire additional imperfect information was never used, seeing its

influence dominated by the other two options. Consequently, the simple sum of each option’s

added value does not represent the value of their combination, being the value of flexibility

instead determined by the sum of the used options, as is shown in the next table.

Nevertheless, as observed in the realized sensitivity analysis, it has to be regarded that small

changes to the project’s parameters may alter the ROA structure. This is for example, the

case of increasing by five percent the initial probability that the site has a large quantity of

oil.

$390.M

$391.5M

$393.M

$394.5M

0.1 0.2 0.25

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Decline of Rate of Production

Page 40 of 159

However, with the current set of parameters, the option to abandon the project is by far the

most relevant option, representing ninety six percent of ROA added value. The option to

abandon has this significant influence, because the several project stages and studies

represent substantial investments, and the NPV inflexible approach irrevocably commits

management to the established strategy, not reviewing the set path in case a stage’s result

does not develop according to expectations. This is not the case with ROA, which brings the

required flexibility assessment into the project valuation, permitting management to exit or

stop the project at a certain phase, in case the stage’s outcome is unsuccessful, not incurring

in this manner, in any further losses beyond the required investment to develop the stage’s

activities.

Total Value of Used Options

Option to Set LP Option to Abandon Total

ROA Added Value $14,993,647.74 $378,080,549.85 $393,074,197.60

Difference of the sum to the original ROA added value $0.00

Table 11 Total Value of Used Options

Page 41 of 159

Conclusions

The realized study exposed the characteristics of ROA, and the methodology financial and

strategic capabilities. The development of this valuation technique allowed the identification

and consideration of the project’s embedded options, turning an investment destined to

rejection into an interesting prospect.

The developed analysis confirmed that the trinomial tree is more consistent in representing

oil price evolution, as determined by the statistical analysis. This fact is observed in the

consequent hexanomial tree, which has greater detail and is a better expression of the

project’s options. The hexanomial tree response to changes in the project parameters also

presents consistent results, and with reliable sensitivity, capacities that are not so evident on

the quadranomial tree.

The ROA approach is therefore considered to be a more suitable valuation than the rigid DCF

methodology, which is a now or never approach, and incapable of assessing and valuing the

project’s flexibility. It is also considered that for this type of studies, where the modulation of

oil price is required, the hexanomial tree is the preferred solution.

ROA has numerous virtues, many of them evidenced in this work project, but the

methodology greater complexity is also well demonstrated throughout this dissertation. This

complexity is even more significant in the case of the developed trinomial tree, and the

consequent hexanomial tree, whose application has to be weighted against the demanded

resources. These ROA procedures, and the fact that the technique can be applied in several

different manners, are considered to introduce confusion about the method and its

application, and restrain the methodology acceptance. Nevertheless, being regarded that

ROA is financially and strategically more competent, and that computer and software

development may ease these processes, it is considered that ROA evident capabilities will

enable its future widespread implementation as a valuation and strategic management tool.

Page 42 of 159

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— Schwartz, E. and Trigeorgis, L. (2001), Real Options and Investment Under Uncertainty:

Classical Readings and Recent Contributions, The MIT Press, London, England.

— Shimko, D. C. (2002), Simulations of Prices, Rates and Cash Flows (A) and (B), Harvard

Business Review, Boston, USA.

— Skorodumov, B. (2008), Estimation of mean reversion in Oil and Gas Markets, Mitsui &

Co. Energy Risk Management.

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February.

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Philadelphia, USA.

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offshore petroleum production, Project Thesis, Norwegian University of Science and

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— Tabachnick, B. and Fidell, L. (2001), Using Multivariate Statistics, Fourth Edition, Allyn

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— Trigeorgis, L. and Mason, S. P. (1987), Valuing Managerial Flexibility, Midland Corporate

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theory, International Journal of Production Economics, no. 78, 109-116.

Page 48 of 159

Appendix A – Bayesian Analysis

Bayesian Analysis is a statistical method to revise probability estimates for a hypothesis with

the introduction of new information. The fundamental focus of the analysis is the theorem

developed by Reverend Thomas Bayes, which is called Bayes’ Rule.

E1, E2, …EN, are N mutually exclusive and collectively exhaustive outcomes of some event,

and A is an outcome of an information event or symptom related to E. The process requires

the estimate of the probability of the various events (Ei), and the conditional probabilities of

A given the various Ei.

A is believed to be correlated to event E, and the objective is to revise the probabilities for Ei

given new information that A is true or false. The revised probabilities are calculated using

the following equation:

Equation 10 Bayes’ Rule

• P(Ei) – probability of Ei before A has occurred (a priori probability).

• A – new data correlated with Ei.

• P(Ei|A) – probability of Ei given A is observed (a posterior probability).

• P(A|Ei) – probability of observing A given Ei.

P(Ei) terms are the original probability estimates, A is new data that can add supplemental

information on the validity of the original estimates, and the purpose is to revise the

estimates of P(Ei) given the new information A.

∑=

=N

j

jj

iii

EPEAP

EPEAPAEP

1

)()|(

)()|()|(

Page 49 of 159

Appendix B – Real Options Taxonomy

Deferral Option

It is an American call option, where the investor has the right to delay the project, or a stage

of the project. The exercise price is the amount of money to realize the project, or the stage

under analysis. This option gives the investor the opportunity to wait for further information,

to postpone the project until conditions become more favourable, or to abandon if

circumstances do not develop in the desired expectation.

Option to Expand

American call option, where, at a certain price (the exercise price), it is possible to scale up

the project. If market conditions are favourable, management can expand operations in order

to improve the project’s financial results.

Option to Contract

American put option, giving the capacity to scale back the project by selling part of it, or by a

fixed amount. If conditions are less favourable than expected, management may decide to

reduce the scale of the project, and in extreme cases production may be halted and restarted

at a later stage.

Option to Abandon

American put option, representing the right to abandon a project by selling it to a third party,

or by recovering its salvage value. If market conditions deteriorate, or events do not develop

in the expected format, management may decide to pursue this option.

Option to Switch

American call and put options, allowing their owner to switch, at a cost, between two modes

of operation. Can include the exchange of input or output parameter, process, volume, and

location, and is typically driven by price or demand changes.

Compound Options

These are options on options. It is a type of option that is dependent on the exercise of

previous options (phased investments are a typical example of these options). The value of

such an option is contingent on other options.

Page 50 of 159

Rainbow Options

Options that are driven by several sources of uncertainty (e.g. price and quantity). Most real

options fit under this category, as most real life projects are affected by multiple sources of

uncertainty.

Learning Options

Options to learn more about the conditions of the project and reduce uncertainty. Typically

present in phased investments decisions, where management has the flexibility to learn more

about the project before making further commitments to its development.

Page 51 of 159

Appendix C – Geometric Brownian Motion

Geometric Brownian Motion takes the name from Scottish botanist Robert Merton, and is

referred to in financial theory as a random walk, representing a process where price

movements are independent from one another, and thus, past information cannot be used to

predict future movements (current asset price fully reflects all information contained in past

prices). This process is consistent with the weak form of the efficient market hypothesis, and

is sometimes compared to the path of a drunkard leaving a bar, where it is not possible to

know the direction and distance of the drunkard’s next step.

GBM model is a continuous-time stochastic process, mathematically described by the

following stochastic differential equation:

Equation 11 Geometric Brownian Motion Process

where, µSdt constitutes the drift element, and σSdz is the random component. The asset

price is denoted by S, µ represents the constant growth rate, σ is the volatility, and dz the

increment of Wiener. Equation 11, is the most widely used model to describe stock price

behaviour, where the stock expected increase is µSΔt, being µ the stock’s expected return,

and σ the volatility of the stock price.

The discrete version of the model is:

∆� = ��∆ + ��√∆

Equation 12 Geometric Brownian Motion Discrete Time Model

where ϵ has a normal distribution with a mean of zero and a standard deviation of 1.

SdzSdtdS σµ +=

Page 52 of 159

Appendix D – Trinomial Tree Building Procedure

Hull and White proposed a consistent two-stage methodology for the construction of trinomial

trees for mean reverting one-factor models. This method is described below, which follows

the indications given in Hull (2009).

First Stage

The dynamic of the underlying is described by:

Equation 13 Instantaneous Short Rate

where:

• S – spot price;

• θ – mean price;

• a – constant mean reverting rate;

• σ – constant volatility.

The first step is to define variable X* that is initially zero and follows the process:

Equation 14 X* Process

The process is symmetrical about X* = 0. With Δt as the time step, the spacing between the

underlying on the tree, ΔX, is set as:

Equation 15 Spacing Between the Underlying

Define (i, j), as the node where t = iΔt, and:

Equation 16 X* Calculation

The variable i is a positive integer, and j is a positive or negative integer, and the node

probabilities on all three branches must be positive. Most of the time, branching in Figure

27(a) is adequate. When a>0, for a sufficiently large j, jmax, it is necessary to switch from

branching in Figure 27(a) to the branching depicted in Figure 27(b). Similarly, for a

[ ] dzdtSlna)t(Slnd σθ +−=

dzdtXadX ** σ+−=

tX ∆σ∆ 3=

XjX* ∆=

Page 53 of 159

sufficiently negative j, jmin, it is required to switch to the branching represented in Figure

27(c).

Figure 27 Trinomial Tree Branching Alternatives

jmax is defined as the smallest integer greater than:

Equation 17 Trinomial Tree jmax

and jmin as:

Equation 18 Trinomial Tree jmin

All probabilities are positive, and pu, pm, and pd are defined as the probabilities of the

highest, middle, and lowest branches emanating from the tree node, which must sum to

unity. This leads to three equations in the three probabilities, and for a node with the form of

Figure 27(a):

Equation 19 Branch Composed by Up One/Straight Along/Down One

For a node with the form of Figure 27(b):

Equation 20 Branch Composed by Straight Along/Down One/Down Two

)ta(

.jmax ∆

1840=

maxmin jj −=

)tjatja(p

tjap

)tjatja(p

d

m

u

∆∆

∆

∆∆

++=

−=

−+=

222

222

222

2

1

6

1

3

2

2

1

6

1

)tjatja(p

tjatjap

)tjatja(p

d

m

u

∆∆

∆∆

∆∆

−+=

+−−=

−+=

222

222

222

2

1

6

1

23

1

32

1

6

7

Page 54 of 159

And, for a node with the form of Figure 27(c):

Equation 21 Branch Composed by Up Two/Up One/Straight Along

Figure 28 illustrates the form of a possible trinomial tree for X* in the Hull-White model,

which concludes the required steps of the methodology’s first stage.

Figure 28 Tree for X* in Hull-White Model (First Stage)

Second Stage

The variable ln S follows the same process as X*, except for a time-dependent drift. The tree

for X* can be converted into a tree for ln S by displacing the positions of the nodes by α(t).

Equation 22 Displacement of the Positions of the Nodes

The α’s are calculated interactively so that the initial term structure is exactly matched. Qi,j is

defined as the present value of a security that pays $1 if node (i, j) is reached and nothing

otherwise. Both quantities are calculated using forward induction to match futures prices.

)tjatja(p

tjatjap

)tjatja(p

d

m

u

∆∆

∆∆

∆∆

32

1

6

7

23

1

2

1

6

1

222

222

222

++=

−−−=

++=

)t(X)t(Sln)t( *−=α

Page 55 of 159

Considering the displacement nodes at year one, the values of S are �� ,�∗

, �� ,#∗

, �� ,$�∗

.

Requiring that the expected value of S is equal to the futures price, the equation below is

developed, from which α1 can be computed.

Equation 23 α1 Calculation

Having α1:

Equation 24 S Calculation

A formal expression of these last steps is developed in Hull (2009), which characterizes the

same process for interest rates, and the conversion of the tree for R* into a tree for R.

Supposing Qi,j has been determined for i ≤ m (m≥0), it is first required to determine αm and

Qm, so that the tree correctly prices a zero-coupon bond maturing at time Δm. The interest

rate at node (m, j) is equal to αm+jΔR, so that the price of the referred zero-bond is:

Equation 25 Price of a Zero-Coupon Bond

where nm stands for the number of nodes on each side of the central node at time Δm. The

equation can be manipulated into:

Equation 26 αm Calculation

With αm, the Qi,j for i = m+1 can be computed by:

Equation 27 Qi,j Calculation

where q(k, j) expresses the probability of reaching node (m+1, j) when departing from node

(m, k).

1110111111011111

year

X

,

X

,

X

, icePrFutureseQeQeQ*,

*,

*, =×+×+× −+

−++ ααα

*)j,i(X

)j,i( eS+= 1α

[ ]∑

−=

+−+ =

m

m

m

n

nj

t)Rj(j,mm eQP ∆∆α

1

t

PlneQln m

m

n

nj mtRj

j,m

m ∆α

∆∆∑ −= +

− −=

1

[ ]∑

+−+ =

k

t)Rk(k,mj,m

me)j,k(qQQ ∆∆α1

Page 56 of 159

Appendix E – Simplified Case Technological Uncertainty Project Data

Table 12 Simplified Case Technological Uncertainty Project Data

Delineation Well 1 Success Probability

Probability of success of delineation well 1 30%

Probability of failure of delineation well 1 70%

Estimated Amount of Oil in Barrels

Maximum extractable amount of oil in barrels 500,000.00

Minimum extractable amount of oil in barrels 250,000.00

Large oil probability 35%

Small oil probability 65%

Expected amount of oil in barrels 337,500.00

Sufficiency of the Information Provided by Delineation Well 2

Probability delineation well 2 data is sufficient to determine existent amount of oil

40%

Probability delineation well 2 data is not sufficient to determine existent amount of oil

60%

Platform Structures CAPEX

Large platform $9,000,000.00

Small platform $3,000,000.00

Set 2nd extraction structure and readapt $9,000,000.00

Total cost with setting 2nd oil extraction structure and readapt $12,000,000.00

Cost of Setting Delineation Wells

Delineation well 1 $4,000,000.00

Delineation well 2 $4,000,000.00

OPEX

OPEX large oil platform (USD per bbl.) $8.00

OPEX small oil platform (USD per bbl.) $10.00

Page 57 of 159

Appendix F – Simplified Case Price Uncertainty Project Data

The raw data set presented below is composed of monthly spot prices, from January 2009 to

December 2013. These prices are equally weighted crude oil spot price average of Brent,

Dubai, and West Texas Intermediate crude oil nominal prices, and presented in US dollars.

Year & Month ($/bbl.) Year & Month ($/bbl.) Year & Month ($/bbl.)

2009M01 43.86 2010M09 76.12 2012M05 104.09

2009M02 41.84 2010M10 81.72 2012M06 90.73

2009M03 46.65 2010M11 84.53 2012M07 96.75

2009M04 50.28 2010M12 90.01 2012M08 105.27

2009M05 58.15 2011M01 92.69 2012M09 106.28

2009M06 69.15 2011M02 97.91 2012M10 103.41

2009M07 64.67 2011M03 108.65 2012M11 101.17

2009M08 71.63 2011M04 116.24 2012M12 101.19

2009M09 68.35 2011M05 108.07 2013M01 105.10

2009M10 74.08 2011M06 105.85 2013M02 107.64

2009M11 77.55 2011M07 107.92 2013M03 102.52

2009M12 74.88 2011M08 100.49 2013M04 98.85

2010M01 77.12 2011M09 100.82 2013M05 99.37

2010M02 74.76 2011M10 99.85 2013M06 99.74

2010M03 79.30 2011M11 105.41 2013M07 105.26

2010M04 84.18 2011M12 104.23 2013M08 108.16

2010M05 75.62 2012M01 107.07 2013M09 108.76

2010M06 74.73 2012M02 112.69 2013M10 105.43

2010M07 74.58 2012M03 117.79 2013M11 102.63

2010M08 75.83 2012M04 113.67 2013M12 105.48

Table 13 Crude Oil Price (Source: World Bank)

The above data range was selected to capture the last five years of historical prices, whose

evolution can be seen in the figure below.

Page 58 of 159

Figure 29 Crude Oil Price Evolution

The table below shows the regression results of this data set.

Table 14 Used Data Set Regression Results

Regression Statistics

Multiple R 0.310

R Square 0.096

Adjusted R Square 0.081

Standard Error 4.821

Observations 59

ANOVA

df SS MS F Significance F

Regression 1 141.347 141.347 6.081 0.017

Residual 57 1324.922 23.244

Total 58 1466.270

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 8.387 3.043 2.756 0.008 2.294 14.480

X Variable 1 -0.081 0.033 -2.466 0.017 -0.147 -0.015

0.00

40.00

80.00

120.00

160.00

2009M01 2010M01 2011M01 2012M01 2013M01

Page 59 of 159

Statistical Tests to the Used Data

The regression absolute t-statistic value is above 2, permitting to conclude that the null

hypothesis can be rejected, and that a linear relationship between X and Y exists. The

obtained p-value is below 0.05, which reinforces this conclusion.

Assessing homoscedasticity assumption, Figure 30 indicates that it does not appear to exist

any relationship between the magnitude of the residuals and the independent variable, X,

and the same can be said in relation to Figure 31, which is a plot of the residuals versus the

predicted value of Y. Based on the examination of these plots, it is considered not to exist

evidence of heteroscedasticity and that the variances of the error terms are uniform.

Figure 30 Plot of Residuals versus X

Figure 31 Plot of Residuals versus Predicted Y

-15

-10

-5

0

5

10

15

20 40 60 80 100 120 140

Re

sid

ua

ls

X Variable

Plot of Residuals vs X

-15

-10

-5

0

5

10

15

-2 -1 0 1 2 3 4 5 6

Re

sid

ua

ls

Predicted Y

Plot of Residuals vs Predicted Y

Page 60 of 159

To test error normality, residuals skewness and kurtosis have been computed, and their

result is shown in Table 15.

Kurtosis and Skew Statistical Tests

Skew -0.387

Kurtosis 0.120

Table 15 Results of Kurtosis and Skew Statistical Tests

Skewness test is approximately zero, which indicates an error distribution that is

approximately symmetric. Also, following Bulmer (1979), it can be stated that a distribution

is approximately symmetric if the skewness is between -0.5 and 0.5, which is the case.

Furthermore, Tabachnick and Fidell (2001) develop the following formula to approximately

obtain Standard Error for Skewness (SES):

Equation 28 Standard Error for Skewness

where N is the number of observations. The SES result is 0.319, and the obtained skewness

falls within two SES, which is further evidence that the distribution has no significant

skewness problem.

Kurtosis value is also approximately zero, similarly indicating normality. As with skewness,

Tabachnick and Fidell (2001) develop a formula that approximately expresses the Standard

Error for Kurtosis (SEK):

Equation 29 Standard Error for Kurtosis

SEK has a value of 0.638, and the obtained kurtosis result is thus, also within the statistic

expected range.

To conclude normality assumption analysis, the residuals normal probability plot is showed in

Figure 32. The residuals look linear and a good fit to the plotted line, providing further

evidence of residuals normality. Therefore, considering all these results, error normality

assumption is considered not to be violated.

NSES

6=

NSEK

24=

Page 61 of 159

Figure 32 Residuals Normal Probability Plot

To examine error independence assumption, first a residual time plot is developed and shown

in Figure 33. The plot does not show an apparent pattern in the progression through time,

and as such, it does not show evidence of autocorrelation.

Figure 33 Residuals Time Plot

A more formal autocorrelation test is the Durbin-Watson test, d, which is computed by

Formula 30. Following Newbold, Carlson and Thorn (2013), a first indication that errors are

not autocorrelated is if d is approximately 2, and r, the sample estimate of the population

correlation between adjacent errors, is approximately 0.

-15

-10

-5

0

5

10

15

-2.50 -1.50 -0.50 0.50 1.50 2.50

Re

sid

ua

ls

z-value

Normal Probability Plot

-15

-10

-5

0

5

10

15

0 20 40 60

Re

sid

ua

ls

Month

Residuals Time Plot

Page 62 of 159

Equation 30 Durbin-Watson Test

Equation 31 shows the formula for the computation of r:

Equation 31 Equation of r

The obtained value for d and r is 1.70 and 0.15 respectively, which indicates that errors are

not correlated. However, it is necessary to check d value against a table of critical values, in

order to determine if the obtained value deviates sufficiently from 2 as to reject the

hypothesis that no autocorrelation exists.

In the Durbin-Watson tables n represent the number of observations, and K the number of

regressors (i.e. number of independent variables). For several combinations of n11 and K, at

a certain level of significance, α, the table gives values of dL and dU. If d result is in between

dU and 4 – dU, the null hypothesis of no correlation is accepted, and as it can be seen in the

table below, this is the case for the computed Durbin-Watson test.

Durbin-Watson Test

d 1.70

α 0.05

n 55

K 1

dL 1.53

dU 1.60

4 - dU 2.40

Table 16 Results from the Durbin-Watson Test

With the above statistical tests, it is possible to conclude that the regression assumptions

hold, and that the obtained results are valid.

11 For values of n not represented in the table, the previous tabulated level of n is assumed.

∑

∑

=

=−−

=n

t

t

n

t

tt

e

)ee(

d

1

2

2

21

21

dr −=

Page 63 of 159

Estimation of Mean Reversion Parameters

Regression results allow for an estimation of the mean reversion parameters that are shown

in the next table, where it can be seen that the α value is positive (the slope is negative),

which indicates that mean reversion is present in the process.

Mean Reversion Parameters

α 0.081

µ $103.41

σ 0.05

Half-life (months) 8.55

Table 17 Estimation of Mean Reversion Parameters through Linear Regression

These parameters allow the development of the trinomial oil price tree, indicating that if no

more random shocks occur, the current oil price level takes sensibly eight and a half months

to move half way back to its long term level. However, the volatility term appears to be too

low, and not in accordance with the typically used values. Hull (2009) indicates crude oil

price standard deviation to be around 20%, which is also stated by Dias (2004) and others.

Therefore, logarithmic price returns are also computed and shown below, with the purpose of

estimating volatility through this methodology.

Year & Month

($/bbl.) Logarithmic

Return Year & Month


Return Year & Month


Return

2009M01 43.86 ln(St/St-1) 2010M09 76.12 0.004 2012M05 104.09 -0.088

2009M02 41.84 -0.047 2010M10 81.72 0.071 2012M06 90.73 -0.137

2009M03 46.65 0.109 2010M11 84.53 0.034 2012M07 96.75 0.064

2009M04 50.28 0.075 2010M12 90.01 0.063 2012M08 105.27 0.084

2009M05 58.15 0.146 2011M01 92.69 0.029 2012M09 106.28 0.010

2009M06 69.15 0.173 2011M02 97.91 0.055 2012M10 103.41 -0.027

2009M07 64.67 -0.067 2011M03 108.65 0.104 2012M11 101.17 -0.022

2009M08 71.63 0.102 2011M04 116.24 0.068 2012M12 101.19 0.000

2009M09 68.35 -0.047 2011M05 108.07 -0.073 2013M01 105.10 0.038

2009M10 74.08 0.081 2011M06 105.85 -0.021 2013M02 107.64 0.024

2009M11 77.55 0.046 2011M07 107.92 0.019 2013M03 102.52 -0.049

2009M12 74.88 -0.035 2011M08 100.49 -0.071 2013M04 98.85 -0.036

2010M01 77.12 0.029 2011M09 100.82 0.003 2013M05 99.37 0.005

2010M02 74.76 -0.031 2011M10 99.85 -0.010 2013M06 99.74 0.004

2010M03 79.30 0.059 2011M11 105.41 0.054 2013M07 105.26 0.054

2010M04 84.18 0.060 2011M12 104.23 -0.011 2013M08 108.16 0.027

2010M05 75.62 -0.107 2012M01 107.07 0.027 2013M09 108.76 0.006

2010M06 74.73 -0.012 2012M02 112.69 0.051 2013M10 105.43 -0.031

2010M07 74.58 -0.002 2012M03 117.79 0.044 2013M11 102.63 -0.027

2010M08 75.83 0.017 2012M04 113.67 -0.036 2013M12 105.48 0.027

Table 18 Crude Oil Price Logarithmic Returns

Page 64 of 159

And, the table below indicates the volatility computed by this method.

Volatility Estimation

Logarithmic return σ 0.06

Annualised σ (above value x √12) 21%

Table 19 Volatility Estimation through Logarithmic Price Returns

Logarithmic price returns estimated volatility is in compliance with Hull (2009) and Dias

(2004), and as such it will be the used value to develop the trinomial tree.

Trinomial Tree Construction

The trinomial tree construction strictly follows Hull (2009) process, as indicated in chapters

30 and 33. The input parameters for the development of the tree are:

Input Parameters

σ 0.21

α 0.08

No. Of steps per year (Δt) 1

Table 20 Input Parameters for the Construction of the Trinomial Tree

First Stage

With these parameters ΔX, jmax, and jmin can be computed, and their results are shown below.

Tree Parameters

ΔX 0.35836

jmax 3

jmin -3

Table 21 Tree Modulation Parameters

This results in a price evolution tree as shown in Figure 34, and in the development of the j

values tree, and the X* values and the nodes probabilities, which are respectively given in

Table 22 and Table 23.

Page 65 of 159

Figure 34 Price Evolution Trinomial Tree Nodes

3

3

2

2 2

1

1 1 1

j 0 0 0 0 0

-1

-1 -1 -1

-2

-2 -2

-3

-3

Year 0 1 2 3

Table 22 j Tree

Page 66 of 159

Year 0 1 2 3

Node: A B C D E F G H I J K L M N O P

X* 0.0000 0.3584 0.0000 -0.3584 0.7167 0.3584 0.0000 -0.3584 -0.7167 1.0751 0.7167 0.3584 0.0000 -0.3584 -0.7167 -1.0751

pu 0.1667 0.1294 0.1667 0.2105 0.0987 0.1294 0.1667 0.2105 0.2609

pm 0.6667 0.6601 0.6667 0.6601 0.6404 0.6601 0.6667 0.6601 0.6404

pd 0.1667 0.2105 0.1667 0.1294 0.2609 0.2105 0.1667 0.1294 0.0987

Table 23 Table for X* and Nodes Probabilities

Second Stage

The oil futures nominal price for the next three years futures of average crude oil prices are shown below in Table 24.

Oil Prices

Year Maturity Price

2014 Spot 103.50

2015 1 year 99.80

2016 2 year 98.60

2017 3 year 98.20

Table 24 Spot Average Crude Oil Futures Prices (Source: World Bank)

The reference tree for Q can be seen below in Table 25.

Page 67 of 159

3

Q(3,3)

2

Q(2,2) Q(3,2)

1

Q(1,1) Q(2,1) Q(3,1)

j 0 Q(0,0) Q(1,0) Q(2,0) Q(3,0)

-1

Q(1,-1) Q(2,-1) Q(3,-1)

-2

Q(2,-2) Q(3,-2)

-3

Q(3,-3)

Year 0 1 2 3

Table 25 Tree for Q

And, the next table shows Q values throughout the tree.

Node Q Value

B Q(1,1) 0.1667

C Q(1,0) 0.6667

D Q(1,-1) 0.1667

E Q(2,2) 0.0216

F Q(2,1) 0.2211

G Q(2,0) 0.5146

H Q(2,-1) 0.2211

I Q(2,-2) 0.0216

J Q(3,3) 0.0021

K Q(3,2) 0.0424

L Q(3,1) 0.2374

M Q(3,0) 0.4362

N Q(3,-1) 0.2374

O Q(3,-2) 0.0424

P Q(3,-3) 0.0021

Table 26 Q Values

With these it is possible to compute α values, shown in Table 27, and to conclude the

trinomial tree by obtaining the oil prices at each node of the tree, which are show in Table

28.

αααα’s

α0 0

α1 4.58

α2 4.55

α3 4.53

Table 27 α Values

Page 68 of 159

Year 1 2 3

3

272.42

2

194.09 190.37

1

139.79 135.63 133.04

j 0 103.50 97.69 94.78 92.97

-1

68.27 66.24 64.97

-2

46.29 45.40

-3

31.73

Table 28 Trinomial Tree for Oil Prices

Page 69 of 159

Appendix G – Effect of New Information (Simplified

Case)





State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 0.35 0.90 0.315 0.8289

E2 0.65 0.10 0.065 0.1711

Total 1.00 1.00 0.38 1.00


State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 0.35 0.10 0.035 0.0565

E2 0.65 0.90 0.585 0.9435

Total 1.00 1.00 0.62 1.00


Joint Probabilities

Table 30 result 0.38


Total 1.00


The effect of the new information to the technological uncertainty tree can be seen in Figure

35.

Page 70 of 159

Figure 35 Effect of New Information to Technological Uncertainty Decision Tree (Simplified

Case)

Page 71 of 159

Appendix H – Simplified Case End Nodes Free Cash Flows Estimation

The several tables presented below develop free cash flow estimates for the tree’s end

nodes. Table 33 presents the used oil quantity and states of nature probabilities.

Table 33 Oil Estimated Quantities and States of Nature Probabilities

Maximum amount of oil in barrels 500,000.00

Minimum amount of oil in barrels 250,000.00

State of Nature Probability

Large quantity of oil 0.35

Small quantity of oil 0.65

NPVs Set Large Platform

Considering a LP is the selected option, the used quantity is an expected amount, which is

computed by multiplying the possible amounts by their probabilities.

Table 34 Set Large Platform Free Cash Flow Estimates

Expected Amount of oil in Barrels 337,500.00

OPEX Large Oil Platform $8.00 USD per barrel

CF Year

2 2 2

Price sL E $194.09 sL F $135.63 sL G $94.78

Quantity

337,500.00 337,500.00 337,500.00

Revenues

$65,504,878.51 $45,776,277.16 $31,989,488.39

OPEX

$2,700,000.00 $2,700,000.00 $2,700,000.00

FCF

$62,804,878.51 $43,076,277.16 $29,289,488.39

CF Year 2 2

Price sL H $66.24 sL I $46.29

Quantity 337,500.00 337,500.00

Revenues $22,354,971.42 $15,622,155.03

OPEX $2,700,000.00 $2,700,000.00

FCF $19,654,971.42 $12,922,155.03

Page 72 of 159

NPVs Set Small Platform

For these NPVs if the quantity is large, it means that additional platform and resources need

to be allocated, and is assumed that this fact doubles OPEX. Two NPVs tables are developed,

one in case quantity is large and one in case quantity is small.

Table 35 Set Small Platform – Free Cash Flow Estimates for Large Amount of Oil

No 2nd Drill, Set Small, it is Large

Amount of Oil Present 500,000.00

OPEX Small – Oil Platform 1 $10.00 USD per barrel


Total OPEX $20.00 USD per barrel

CF Year 2 2 2

Price sSO E $194.09 sSO F $135.63 sSO G $94.78

Quantity 500,000.00 500,000.00 500,000.00

Revenues $97,044,264.46 $67,816,706.90 $47,391,834.65

OPEX $10,000,000.00 $10,000,000.00 $10,000,000.00

FCF $87,044,264.46 $57,816,706.90 $37,391,834.65

CF Year 2 2

Price sSO H $66.24 sSO I $46.29

Quantity 500,000.00 500,000.00

Revenues $33,118,476.17 $23,143,933.38

OPEX $10,000,000.00 $10,000,000.00

FCF $23,118,476.17 $13,143,933.38

Table 36 Set Small Platform – Free Cash Flow Estimates for Small Amount of Oil

No 2nd drill, set Small, it is Small


OPEX Small Oil Platform 1 $10.00 USD per barrel

CF Year 2 2 2

Price sS§ E $194.09 sS§ F $135.63 sS§ G $94.78

Quantity 250,000.00 250,000.00 250,000.00

Revenues $48,522,132.23 $33,908,353.45 $23,695,917.33

OPEX $2,500,000.00 $2,500,000.00 $2,500,000.00

FCF $46,022,132.23 $31,408,353.45 $21,195,917.33

CF Year 2 2

Price sS§ H $66.24 sS§ I $46.29

Quantity 250,000.00 250,000.00

Revenues $16,559,238.09 $11,571,966.69

OPEX $2,500,000.00 $2,500,000.00

FCF $14,059,238.09 $9,071,966.69

Page 73 of 159

NPVs Buy Additional Information, Large Quantity is Indicated, and a Large Platform

is Established

In this case, the option to acquire additional data is followed, and the result of the study

indicates that the site has a large quantity of oil. With this information management decides

to set a LP.


Established – Free Cash Flow Estimates for Large Amount of Oil

It is Large



CF Year 3 3 3

Price sb(D+)LO J $272.42 sb(D+)LO K $190.37 sb(D+)LO L $133.04

Quantity 500,000.00 500,000.00 500,000.00

Revenues $136,210,536.07 $95,186,975.28 $66,518,791.60

OPEX $4,000,000.00 $4,000,000.00 $4,000,000.00

FCF $132,210,536.07 $91,186,975.28 $62,518,791.60

CF Year 3 3 3

Price sb(D+)LO M $92.97 sb(D+)LO N $64.97 sb(D+)LO O $45.40

Quantity 500,000.00 500,000.00 500,000.00

Revenues $46,484,822.35 $32,484,635.65 $22,700,991.42

OPEX $4,000,000.00 $4,000,000.00 $4,000,000.00

FCF $42,484,822.35 $28,484,635.65 $18,700,991.42

CF Year

3

Price sb(D+)LO P $31.73

Quantity

500,000.00

Revenues

$15,863,961.57

OPEX

$4,000,000.00

FCF

$11,863,961.57

Page 74 of 159


Established – Free Cash Flow Estimates for Small Amount of Oil

It is Small



CF Year 3 3 3

Price sb(D+)L§ J $272.42 sb(D+)L§ K $190.37 sb(D-)L§ L $133.04

Quantity 250,000.00 250,000.00 250,000.00

Revenues $68,105,268.04 $47,593,487.64 $33,259,395.80

OPEX $2,000,000.00 $2,000,000.00 $2,000,000.00

FCF $66,105,268.04 $45,593,487.64 $31,259,395.80

CF Year 3 3 3

Price sb(D-)L§ M $92.97 sb(D-)L§ N $64.97 sb(D-)L§ O $45.40

Quantity 250,000.00 250,000.00 250,000.00

Revenues $23,242,411.18 $16,242,317.83 $11,350,495.71

OPEX $2,000,000.00 $2,000,000.00 $2,000,000.00

FCF $21,242,411.18 $14,242,317.83 $9,350,495.71

CF Year 3

Price sb(D-)L§ P $31.73

Quantity 250,000.00

Revenues $7,931,980.78

OPEX $2,000,000.00

FCF $5,931,980.78

Page 75 of 159

NPVs Buy Additional Information, Large Quantity is Indicated, and a Small Platform

is Established


indicates that the site has a large quantity of oil. With this information management decides

to set a SP. As previously, if the quantity is large, it means that additional platform and

resources need to be allocated, and is assumed that this fact doubles OPEX.



It is Large





CF Year 3 3 3

Price sb(D+)SO J $272.42 sb(D+)SO K $190.37 sb(D+)SO L $133.04

Quantity 500,000.00 500,000.00 500,000.00

Revenues $136,210,536.07 $95,186,975.28 $66,518,791.60

OPEX $10,000,000.00 $10,000,000.00 $10,000,000.00

FCF $126,210,536.07 $85,186,975.28 $56,518,791.60

CF Year 3 3 3

Price sb(D+)SO M $92.97 sb(D+)SO N $64.97 sb(D+)SO O $45.40

Quantity 500,000.00 500,000.00 500,000.00

Revenues $46,484,822.35 $32,484,635.65 $22,700,991.42

OPEX $10,000,000.00 $10,000,000.00 $10,000,000.00

FCF $36,484,822.35 $22,484,635.65 $12,700,991.42

CF Year 3

Price sb(D+)SO P $31.73

Quantity 500,000.00

Revenues $15,863,961.57

OPEX $10,000,000.00

FCF $5,863,961.57

Page 76 of 159



It tis Small


OPEX Small Oil Platform $10.00 USD per barrel

CF Year 3 3 3

Price sb(D+)S§ J $272.42 sb(D+)S§ K $190.37 sb(D+)S§ L $133.04

Quantity 250,000.00 250,000.00 250,000.00

Revenues $68,105,268.04 $47,593,487.64 $33,259,395.80

OPEX $2,500,000.00 $2,500,000.00 $2,500,000.00

FCF $65,605,268.04 $45,093,487.64 $30,759,395.80

CF Year 3 3 3

Price sb(D+)S§ M $92.97 sb(D+)S§ N $64.97 sb(D+)S§ O $45.40

Quantity 250,000.00 250,000.00 250,000.00

Revenues $23,242,411.18 $16,242,317.83 $11,350,495.71

OPEX $2,500,000.00 $2,500,000.00 $2,500,000.00

FCF $20,742,411.18 $13,742,317.83 $8,850,495.71

CF Year 3

Price sb(D+)S§ P $31.73

Quantity 250,000.00

Revenues $7,931,980.78

OPEX $2,500,000.00

FCF $5,431,980.78

Page 77 of 159

NPVs Buy Additional Information, Small Quantity is Indicated, and a Large Platform

is Established


indicates that the site has a small quantity of oil. With this information management decides

to set a LP.



It is Large



CF Year 3 3 3

Price sb(D-)LO J $272.42 sb(D-)LO K $190.37 sb(D-)LO L $133.04

Quantity 500,000.00 500,000.00 500,000.00

Revenues $136,210,536.07 $95,186,975.28 $66,518,791.60

OPEX $4,000,000.00 $4,000,000.00 $4,000,000.00

FCF $132,210,536.07 $91,186,975.28 $62,518,791.60

CF Year 3 3 3

Price sb(D-)LO M $92.97 sb(D-)LO N 64.97 sb(D-)LO O $45.40

Quantity 500,000.00 500,000.00 500,000.00

Revenues $46,484,822.35 $32,484,635.65 $22,700,991.42

OPEX $4,000,000.00 $4,000,000.00 $4,000,000.00

FCF $42,484,822.35 $28,484,635.65 $18,700,991.42

CF Year 3

Price sb(D-)LO P $31.73

Quantity 500,000.00

Revenues $15,863,961.57

OPEX $4,000,000.00

FCF $11,863,961.57

Page 78 of 159



It is Small



CF Year 3 3 3

Price sb(D-)L§ J $272.42 sb(D-)L§ K $190.37 sb(D-)L§ L $133.04

Quantity 250,000.00 250,000.00 250,000.00

Revenues $68,105,268.04 $47,593,487.64 $33,259,395.80

OPEX $2,000,000.00 $2,000,000.00 $2,000,000.00

FCF $66,105,268.04 $45,593,487.64 $31,259,395.80

CF Year 3 3 3

Price sb(D-)L§ M $92.97 sb(D-)L§ N $64.97 sb(D-)L§ O $45.40

Quantity 250,000.00 250,000.00 250,000.00

Revenues $23,242,411.18 $16,242,317.83 $11,350,495.71

OPEX $2,000,000.00 $2,000,000.00 $2,000,000.00

FCF $21,242,411.18 $14,242,317.83 $9,350,495.71

CF Year 3

Price sb(D-)L§ P $31.73

Quantity 250,000.00

Revenues $7,931,980.78

OPEX $2,000,000.00

FCF $5,931,980.78

Page 79 of 159

NPVs Buy Additional Information, Small Quantity is Indicated, and a Small Platform

is Established


indicates that the site has a small quantity of oil. With this information management decides

to set a SP. As previously, if the quantity is large, it means that additional platform and

resources need to be allocated, and is assumed that this fact doubles OPEX.



It is Large





CF Year 3 3 3

Price sb(D-)SO J $272.42 sb(D-)SO K $190.37 sb(D-)SO L $133.04

Quantity 500,000.00 500,000.00 500,000.00

Revenues $136,210,536.07 $95,186,975.28 $66,518,791.60

OPEX $10,000,000.00 $10,000,000.00 $10,000,000.00

FCF $126,210,536.07 $85,186,975.28 $56,518,791.60

CF Year 3 3 3

Price sb(D-)SO M $92.97 sb(D-)SO N $64.97 sb(D-)SO O $45.40

Quantity 500,000.00 500,000.00 500,000.00

Revenues $46,484,822.35 $32,484,635.65 $22,700,991.42

OPEX $10,000,000.00 $10,000,000.00 $10,000,000.00

FCF $36,484,822.35 $22,484,635.65 $12,700,991.42

CF Year 3

Price sb(D-)SO P $31.73

Quantity 500,000.00

Revenues $15,863,961.57

OPEX $10,000,000.00

FCF $5,863,961.57

Page 80 of 159



It is Small



CF Year 3 3 3

Price sb(D-)S§ J $272.42 sb(D-)S§ K $190.37 sb(D-)S§ L $133.04

Quantity 250,000.00 250,000.00 250,000.00

Revenues $68,105,268.04 $47,593,487.64 $33,259,395.80

OPEX $2,500,000.00 $2,500,000.00 $2,500,000.00

FCF $65,605,268.04 $45,093,487.64 $30,759,395.80

CF Year 3 3 3

Price sb(D-)S§ M $92.97 sb(D-)S§ N $64.97 sb(D-)S§ O $45.40

Quantity 250,000.00 250,000.00 250,000.00

Revenues $23,242,411.18 $16,242,317.83 $11,350,495.71

OPEX $2,500,000.00 $2,500,000.00 $2,500,000.00

FCF $20,742,411.18 $13,742,317.83 $8,850,495.71

CF Year 3

Price sb(D-)S§ P $31.73

Quantity 250,000.00

Revenues $7,931,980.78

OPEX $2,500,000.00

FCF $5,431,980.78

Page 81 of 159

Appendix I - Simplified Case Hexanomial Tree Probabilities

The table below continues in the right hand side of the page.

Table 45 Simplified Case Hexanomial Tree Nodes Probabilities

Probabilities Y0 to Y1 Price & Technological

Probability success DW1 0.3

Probability failure DW2 0.7

pu - to Point B 0.1667

pm - to Point C 0.6667

pd - to Point D 0.1667

spu (B) 0.0500

spm (C) 0.2000

spd (D) 0.0500

fpu (B) 0.1167

fpm (C) 0.4667

fpd (D) 0.1167

Total 1.00

Probabilities Y1 to Y2 Set Large

Quantity is fixed, and only price probability enters. Therefore, technological uncertainty assumes a probability of 1. 1.0000

Point B pu - to Point E 0.1294

Point B pm - to Point F 0.6601

Point B pd - to Point G 0.2105 1.00

Point C pu - to Point F 0.1667

Point C pm - to Point G 0.6667

Point C pd - to Point H 0.1667 1.00

Point D pu - to Point G 0.2105

Point D pm - to Point H 0.6601

Point D pd - to Point I 0.1294 1.00

Probabilities Y1 to Y2 Set Small

Large oil Probability 0.35

Small oil Probability 0.65










To Point B

L*(B)pu 0.0453

L*(B)pm 0.2310

L*(B)pm 0.0737

S*(B)pu 0.0841

S*(B)pm 0.4291

S*(B)pm 0.1368 1.00

To Point C

L*(C)pu 0.0583

L*(C)pm 0.2333

L*(C)pm 0.0583

S*(C)pu 0.1083

S*(C)pm 0.4333

S*(C)pm 0.1083 1.00

To Point D

L*(D)pu 0.0737

L*(D)pm 0.2310

L*(D)pm 0.0453

S*(D)pu 0.1368

S*(D)pm 0.4291

S*(D)pm 0.0841 1.00

Probabilities Y1 to Y2 Buy Info

Data indicates Large - b(D+) 38.00%

Data indicates Small - b(D-) 62.00% 1.00










To Point B

b(D+)*(B)pu 0.0492

b(D+)*(B)pm 0.2508

b(D+)*(B)pd 0.0800

b(D-)*(B)pu 0.0802

b(D-)*(B)pm 0.4093

b(D-)*(B)pd 0.1305 1.00

Page 82 of 159

To Point C

b(D+)*(C)pu 0.0633

b(D+)*(C)pm 0.2533

b(D+)*(C)pd 0.0633

b(D-)*(C)pu 0.1033

b(D-)*(C)pm 0.4133

b(D-)*(C)pd 0.1033 1.00

To Point D

b(D+)*(D)pu 0.0800

b(D+)*(D)pm 0.2508

b(D+)*(D)pd 0.0492

b(D-)*(D)pu 0.1305

b(D-)*(D)pm 0.4093

b(D-)*(D)pd 0.0802 1.00

Probabilities Y2 to Y3 - Buy info, Data indicates Large Quantity, do Large Platform

Probability Large - LO 82.89%

Probability Small - L§ 17.11% 1.00

Point E pu - to Point J 0.0987

Point E pm - to Point K 0.6404

Point E pd - to Point L 0.2609 1.00

Point F pu - to Point K 0.1294

Point F pm - to Point L 0.6601

Point F pd - to Point M 0.2105 1.00

Point G pu - to Point L 0.1667

Point G pm - to Point M 0.6667

Point G pd - to Point N 0.1667 1.00

Point H pu - to Point M 0.2105

Point H pm - to Point N 0.6601

Point H pd - to Point O 0.1294 1.00

Point I pu - to Point N 0.2609

Point I pm - to Point O 0.6404

Point I pd - to Point P 0.0987 1.00

To Point E

LO * (E)pu 0.0818

LO * (E)pm 0.5308

LO * (E)pd 0.2163

L§ * (E)pu 0.0169

L§ * (E)pm 0.1095

L§ * (E)pd 0.0446 1.00

To Point F

LO * (F)pu 0.1073

LO * (F)pm 0.5472

LO * (F)pd 0.1745

L§ * (F)pu 0.0221

L§ * (F)pm 0.1129

L§ * (F)pd 0.0360 1.00

To Point G

LO * (G)pu 0.1382

LO * (G)pm 0.5526

LO * (G)pd 0.1382

L§ * (G)pu 0.0285

L§ * (G)pm 0.1140

L§ * (G)pd 0.0285 1.00

To Point H

LO * (H)pu 0.1745

LO * (H)pm 0.5472

LO * (H)pd 0.1073

L§ * (H)pu 0.0360

L§ * (H)pm 0.1129

L§ * (H)pd 0.0221 1.00

To Point I

LO * (I)pu 0.2163

LO * (I)pm 0.5308

LO * (I)pd 0.0818

L§ * (H)pu 0.0446

L§ * (H)pm 0.1095

L§ * (H)pd 0.0169 1.00

Probabilities Y2 to Y3 - Buy info, Data indicates Large Quantity, do Small Platform

Probability Large 82.89%

Probability Small 17.11% 1.00
















To Point E

SO * (E)pu 0.0818

SO * (E)pm 0.5308

SO * (E)pd 0.2163

S§ * (E)pu 0.0169

S§ * (E)pm 0.1095

S§ * (E)pd 0.0446 1.00

Page 83 of 159

To Point F

SO * (F)pu 0.1073

SO * (F)pm 0.5472

SO * (F)pd 0.1745

S§ * (F)pu 0.0221

S§ * (F)pm 0.1129

S§ * (F)pd 0.0360 1.00

To Point G

SO * (G)pu 0.1382

SO * (G)pm 0.5526

SO * (G)pd 0.1382

S§ * (G)pu 0.0285

S§ * (G)pm 0.1140

S§ * (G)pd 0.0285 1.00

To Point H

SO * (H)pu 0.1745

SO * (H)pm 0.5472

SO * (H)pd 0.1073

S§ * (H)pu 0.0360

S§ * (H)pm 0.1129

S§ * (H)pd 0.0221 1.00

To Point I

SO * (I)pu 0.2163

SO * (I)pm 0.5308

SO * (I)pd 0.0818

S§ * (H)pu 0.0446

S§ * (H)pm 0.1095

S§ * (H)pd 0.0169 1.00

Probabilities Y2 to Y3 - Buy info, Data Indicates Small Quantity, do Large Platform


















To Point E

LO * (E)pu 0.0056

LO * (E)pm 0.0361

LO * (E)pd 0.0147

L§ * (E)pu 0.0931

L§ * (E)pm 0.6042

L§ * (E)pd 0.2462 1.00

To Point F

LO * (F)pu 0.0073

LO * (F)pm 0.0373

LO * (F)pd 0.0119

L§ * (F)pu 0.1221

L§ * (F)pm 0.6228

L§ * (F)pd 0.1986 1.00

To Point G

LO * (G)pu 0.0094

LO * (G)pm 0.0376

LO * (G)pd 0.0094

L§ * (G)pu 0.1573

L§ * (G)pm 0.6290

L§ * (G)pd 0.1573 1.00

To Point H LO * (H)pu 0.0119

LO * (H)pm 0.0373

LO * (H)pd 0.0073

L§ * (H)pu 0.1986

L§ * (H)pm 0.6228

L§ * (H)pd 0.1221 1.00

To Point I

LO * (I)pu 0.0147

LO * (I)pm 0.0361

LO * (I)pd 0.0056

L§ * (H)pu 0.2462

L§ * (H)pm 0.6042

L§ * (H)pd 0.0931 1.00

Page 84 of 159

Probabilities Y2 to Y3 - Buy Info, Data Indicates

Small Quantity, do Small Platform Probability Large 5.65%

















To Point E

SO * (E)pu 0.0056

SO * (E)pm 0.0361

SO * (E)pd 0.0147

S§ * (E)pu 0.0931

S§ * (E)pm 0.6042

S§ * (E)pd 0.2462 1.00

To Point F

SO * (F)pu 0.0073

SO * (F)pm 0.0373

SO * (F)pd 0.0119

S§ * (F)pu 0.1221

S§ * (F)pm 0.6228

S§ * (F)pd 0.1986 1.00

To Point G

SO * (G)pu 0.0094

SO * (G)pm 0.0376

SO * (G)pd 0.0094

S§ * (G)pu 0.1573

S§ * (G)pm 0.6290

S§ * (G)pd 0.1573 1.00

To Point H

SO * (H)pu 0.0119

SO * (H)pm 0.0373

SO * (H)pd 0.0073

S§ * (H)pu 0.1986

S§ * (H)pm 0.6228

S§ * (H)pd 0.1221 1.00

To Point I SO * (I)pu 0.0147

SO * (I)pm 0.0361

SO * (I)pd 0.0056

S§ * (H)pu 0.2462

S§ * (H)pm 0.6042

S§ * (H)pd 0.0931 1.00

Page 85 of 159

Appendix J– Simplified Case ROA Tree Evolution

Figure 36 Real Options Analysis Process

Page 86 of 159

Appendix K – Complete Case Technological Uncertainty Project Data

Table 46 Complete Case Technological Uncertainty Project Data

Input Parameters Technological Uncertainty

Probability of success of 2D seismic survey 7.00%

Probability of failure of 2D seismic survey 93.00%

Probability of success of 3D seismic survey 15.00%

Probability of failure of 3D seismic survey 85.00%

Probability of success of delineation well 1 30.00%

Probability of failure of delineation well 2 70.00%

Cumulative success probability of the initial 3 phases 0.32%

Estimated Amount of Oil in Barrels

Maximum extractable amount of oil in barrels 3,000,000,000.00

Minimum extractable amount of oil in barrels 1,000,000,000.00

Large oil probability 35.00%

Small oil probability 65.00%

Expected amount of oil in barrels 1,700,000,000.00

Sufficiency of the Information Provided by Delineation Well 2

Probability delineation well 2 data is sufficient to determine existent amount of oil

40.00%

Probability delineation well 2 data is not sufficient to determine existent amount of oil

60.00%

Well Life time

Life time of well (years) 15

Investment and Platform Structures CAPEX

2D Seismic Survey $50,000,000.00


Delineation Well 1 Activity $200,000,000.00

Delineation Well 2 Activity $200,000,000.00

Large platform $90,000,000.00

Small platform $30,000,000.00

Set 2nd extraction structure and readapt $90,000,000.00

Total cost with setting 2nd oil extraction structure and readapt $120,000,000.00

OPEX

OPEX large oil platform, quantity of oil is large (USD per bbl.) $8.00

OPEX large oil platform, quantity of oil is small (USD per bbl.) $12.00

OPEX small oil platform (USD per bbl.) $10.00

Depreciation of CAPEX Linear

Decommissioning (Liquidation) costs

Percentage of CAPEX Cost 18.00%

Decommissioning (Liquidation) costs Large Oil Platform $16,200,000.00

Decommissioning (Liquidation) costs Small Oil Platform $5,400,000.00

Decommissioning (Liquidation) costs Small Oil Platform with readapt for large quantity

$21,600,000.00

Page 87 of 159

(table continuation)

Tax and Risk-Free Rates

Tax 40.00%

Risk-free 3.00%

WACC Calculation

Debt/(Debt+Equity) Ratio 0.5

Equity/(Debt+Equity) Ratio 0.5

kl 0.18

kb 0.07

WACC 11.10%

Page 88 of 159

Appendix L – Complete Case Price Uncertainty Project Data

The complete case uses the same price data that was used by the simplified case. Just the

trinomial tree construction is extended for further periods. The binomial tree construction is

also realized in the last section of this appendix.

Trinomial Tree Construction

The input parameters for the development of the tree are:

Input Parameters

σ 0.21

α 0.08

No. Of steps per year (Δt) 1

Table 47 Input Parameters for the Construction of the Trinomial Tree

First Stage

With these parameters ΔX, jmax, and jmin can be computed, and their results are shown below.

Tree Parameters

ΔX 0.35836

jmax 3

jmin -3

Table 48 Tree Modulation Parameters

This results in a price evolution tree as shown in Figure 37, and in the development of the j

values tree, and the X* values and the nodes probabilities, which are respectively given in

Table 49 and Table 50.

Page 89 of 159

Figure 37 Price Evolution Trinomial Tree Nodes

3

3 3 3

2

2 2 2 2

1

1 1 1 1 1

j 0 0 0 0 0 0 0

-1

-1 -1 -1 -1 -1

-2

-2 -2 -2 -2

-3

-3 -3 -3

Year 0 1 2 3 4 5

Table 49 j Tree

Page 90 of 159

Table 50 Table for X* and Nodes Probabilities

Year 0 1 2 3

Node: A B C D E F G H I J K L M N O P

X* 0.0000 0.3584 0.0000 -0.3584 0.7167 0.3584 0.0000 -0.3584 -0.7167 1.0751 0.7167 0.3584 0.0000 -0.3584 -0.7167 -1.0751

pu 0.1667 0.1294 0.1667 0.2105 0.0987 0.1294 0.1667 0.2105 0.2609 0.8313 0.0987 0.1294 0.1667 0.2105 0.2609 0.0746

pm 0.6667 0.6601 0.6667 0.6601 0.6404 0.6601 0.6667 0.6601 0.6404 0.0941 0.6404 0.6601 0.6667 0.6601 0.6404 0.0941

pd 0.1667 0.2105 0.1667 0.1294 0.2609 0.2105 0.1667 0.1294 0.0987 0.0746 0.2609 0.2105 0.1667 0.1294 0.0987 0.8313

(table continuation)

Year 4 5

Node: Q R S T U V W X Y Z AA AB AC AD

X* 1.0751 0.7167 0.3584 0.0000 -0.3584 -0.7167 -1.0751 1.0751 0.7167 0.3584 0.0000 -0.3584 -0.7167 -1.0751

pu 0.8313 0.0987 0.1294 0.1667 0.2105 0.2609 0.0746

pm 0.0941 0.6404 0.6601 0.6667 0.6601 0.6404 0.0941

pd 0.0746 0.2609 0.2105 0.1667 0.1294 0.0987 0.8313

Page 91 of 159

Second Stage

The oil futures nominal price for the next five years futures of average crude oil prices are

shown below in Table 51.

Oil Prices

Year Maturity Price

2014 Spot 103.50

2015 1 year 99.80

2016 2 year 98.60

2017 3 year 98.20

2018 4 year 97.90

2019 5 year 97.60

Table 51 Spot Average Crude Oil Futures Prices (Source: World Bank)

The reference tree for Q can be seen below in Table 52.

3

Q(3,3) Q(4,3) Q(5,3)

2

Q(2,2) Q(3,2) Q(4,2) Q(5,2)

1

Q(1,1) Q(2,1) Q(3,1) Q(4,1) Q(5,1)

j 0 Q(0,0) Q(1,0) Q(2,0) Q(3,0) Q(4,0) Q(5,0)

-1

Q(1,-1) Q(2,-1) Q(3,-1) Q(4,-1) Q(5,-1)

-2

Q(2,-2) Q(3,-2) Q(4,-2) Q(5,-2)

-3

Q(3,-3) Q(4,-3) Q(5,-3)

Year 0 1 2 3 4 5

Table 52 Tree for Q

And, the next table shows Q values throughout the tree.

Page 92 of 159

Node Q Value

B Q(1,1) 0.1667

C Q(1,0) 0.6667

D Q(1,-1) 0.1667

E Q(2,2) 0.0216

F Q(2,1) 0.2211

G Q(2,0) 0.5146

H Q(2,-1) 0.2211

I Q(2,-2) 0.0216

J Q(3,3) 0.0021

K Q(3,2) 0.0424

L Q(3,1) 0.2374

M Q(3,0) 0.4362

N Q(3,-1) 0.2374

O Q(3,-2) 0.0424

P Q(3,-3) 0.0021

Q Q(4,3) 0.0060

R Q(4,2) 0.0581

S Q(4,1) 0.2406

T Q(4,0) 0.3907

U Q(4,-1) 0.2406

V Q(4,-2) 0.0581

W Q(4,-3) 0.0060

X Q(5,3) 0.0107

Y Q(5,2) 0.0689

Z Q(5,1) 0.2395

AA Q(5,0) 0.3618

AB Q(5,-1) 0.2395

AC Q(5,-2) 0.0689

AD Q(5,-3) 0.0107

Table 53 Q Values

With these it is possible to compute α values, shown in Table 54, and to conclude the

trinomial tree by obtaining the tree futures prices, which are show in Table 55.

αααα’s

α0 0

α1 4.58

α2 4.55

α3 4.53

α4 4.52

α5 4.50

Table 54 α Values

Page 93 of 159

Year 1 2 3 4 5

3

272.42 268.12 264.41

2

194.09 190.37 187.37 184.78

1

139.79 135.63 133.04 130.94 129.13

j 0 103.50 97.69 94.78 92.97 91.50 90.24

-1

68.27 66.24 64.97 63.94 63.06

-2

46.29 45.40 44.68 44.07

-3

31.73 31.23 30.80

Table 55 Trinomial Tree for Oil Prices

Binomial Tree Construction

The input parameters for the development of the tree are:

Input Parameters

Price Y0 $103.50

σ 21%

Life of Option (in years) 5

Annual risk-free 0.03

Number of steps per year 1

Table 56 Input Parameters for the Construction of the Binomial Tree

Calculated Parameters

u 1.2299

d 0.8131

up movement risk-neutral probability 0.5204

Down movement risk-neutral probability 0.4796

Table 57 Calculated Parameters for the Construction of the Binomial Tree

With these it is possible to develop the binomial price table, shown below, where a

movement to the right represents an up price movement, and a down movement indicates a

down movement of the oil price.

Year 0 1 2 3 4 5

$103.50 $127.29 $156.55 $192.53 $236.79 $291.22

$84.16 $103.50 $127.29 $156.55 $192.53

$68.43 $84.16 $103.50 $127.29

$55.64 $68.43 $84.16

$45.24 $55.64

$36.78

Table 58 Binomial Tree for Oil Prices

Page 94 of 159

Appendix M- Effect of New Information (Complete Case)





State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 0.35 0.40 0.14 0.2642

E2 0.65 0.60 0.39 0.7358

Total 1.00 1.00 0.53 1.00


State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 0.35 0.60 0.21 0.4468

E2 0.65 0.40 0.26 0.5532

Total 1.00 1.00 0.47 1.00


Joint Probabilities



Total 1.00


The effect of the new information to the technological uncertainty tree can be seen in Figure

38.

Page 95 of 159

Figure 38 Effect of New Information to Technological Uncertainty Decision Tree (Complete Case)

Page 96 of 159

Appendix N – Oil Price Evolution from End Nodes

Table 63 Prices Evolution when Deciding to Set a Large or a Small Platform at Year Three

Production Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Year 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Tri

nom

ial Pri

ce T

ree N

odes

Q

268.12 247.40 229.90 215.00 202.24 191.23 181.70 173.39 166.12 159.74 154.10 149.12 144.69 140.75 137.23 134.08

R

187.37 178.33 170.45 163.54 157.46 152.09 147.33 143.10 139.33 135.96 132.94 130.24 127.80 125.60 123.62 121.83

S

130.94 128.43 126.17 124.14 122.30 120.63 119.13 117.76 116.52 115.39 114.36 113.43 112.58 111.80 111.09 110.45

T

91.50 92.41 93.25 94.03 94.76 95.43 96.05 96.63 97.16 97.65 98.10 98.52 98.91 99.27 99.59 99.90

U

63.94 66.44 68.82 71.09 73.25 75.30 77.24 79.07 80.79 82.40 83.92 85.34 86.67 87.91 89.07 90.15

V

44.68 47.73 50.72 53.65 56.50 59.27 61.95 64.52 66.99 69.35 71.60 73.73 75.75 77.67 79.47 81.17

W

31.23 34.26 37.33 40.41 43.49 46.55 49.56 52.52 55.40 58.21 60.92 63.53 66.04 68.45 70.74 72.92

Note: production starts once the platform is installed, task that is assumed to run for one year. Therefore, in this table's case, the decision to set a large or small platform is done in year 3 (2017), platform constructed and installed in year 4 (2018), and first productive inflow or outflow is in year 5 (2019).

Table 64 Prices Evolution when Deciding to Set a Large or a Small Platform at Year Four

Production Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Year 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Tri

nom

ial Pri

ce T

ree N

odes

X

264.41 244.28 227.25 212.74 200.29 189.55 180.24 172.11 165.00 158.75 153.23 148.34 144.00 140.13 136.68 133.59

Y

184.78 176.08 168.48 161.81 155.93 150.74 146.13 142.03 138.38 135.11 132.18 129.55 127.18 125.04 123.12 121.38

Z

129.13 126.80 124.70 122.81 121.10 119.55 118.14 116.86 115.70 114.65 113.69 112.82 112.02 111.29 110.63 110.02

AA

90.24 91.23 92.16 93.02 93.82 94.56 95.25 95.88 96.47 97.01 97.51 97.98 98.41 98.80 99.17 99.50

AB

63.06 65.59 68.01 70.32 72.52 74.61 76.58 78.45 80.21 81.86 83.41 84.86 86.22 87.50 88.68 89.79

AC

44.07 47.12 50.12 53.06 55.93 58.72 61.42 64.01 66.50 68.88 71.15 73.31 75.36 77.29 79.11 80.83

AD

30.80 33.82 36.89 39.97 43.05 46.11 49.13 52.10 54.99 57.81 60.54 63.17 65.69 68.11 70.41 72.61

Note: production starts once the platform is installed, task that is assumed to run for one year. Therefore, in this table's case, the decision to set a large or small platform is done in year 4 (2018), platform constructed and installed in year 5 (2019), and first productive inflow or outflow is in year 6 (2020).

Page 97 of 159

Figure 39 Price Evolution when Deciding to Set a Large or a Small Platform at Year Three

Figure 40 Price Evolution when Deciding to Set a Large or a Small Platform at Year Four

0.00

50.00

100.00

150.00

200.00

250.00

300.00

20

18

20

19

20

20

20

21

20

22

20

23

20

24

20

25

20

26

20

27

20

28

20

29

20

30

20

31

20

32

20

33

Price Evolution

Q R S T U V W Long Term Mean

0.00

50.00

100.00

150.00

200.00

250.00

300.00

20

19

20

20

20

21

20

22

20

23

20

24

20

25

20

26

20

27

20

28

20

29

20

30

20

31

20

32

20

33

20

34

Price Evolution

X Y Z AA AB AC AD Long Term Mean

Page 98 of 159

Appendix O – Production Levels

Set large platform at year three

Expected Volume of Barrels 1,700,000,000.00

Year Produced Barrels % of total % Decrease

1 255,000,000.00 15.00%

2 306,000,000.00 18.00% -0.20

3 243,842,567.04 14.34% 0.20

4 194,311,102.95 11.43% 0.20

5 154,840,908.98 9.11% 0.20

6 123,388,250.75 7.26% 0.20

7 98,324,535.31 5.78% 0.20

8 78,351,983.97 4.61% 0.20

9 62,436,434.32 3.67% 0.20

10 49,753,792.23 2.93% 0.20

11 39,647,360.84 2.33% 0.20

12 31,593,837.40 1.86% 0.20

13 25,176,217.04 1.48% 0.20

14 20,062,200.63 1.18% 0.20

15 17,270,808.55 1.02% 0.14

Total 1,700,000,000.00 100.00%

Table 65 Production Levels for Set Large at Year Three

Figure 41 Production Levels for Set Large at Year Three

0.00

70,000,000.00

140,000,000.00

210,000,000.00

280,000,000.00

350,000,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Annual Rate of Production

Page 99 of 159

Set small platform at year three – quantity is large

Buy info, data indicates large, management sets large platform – quantity is large

Buy info, data indicates large, management sets small platform – quantity is large

Buy info, data indicates small, management sets large platform – quantity is large

Buy info, data indicates small, management sets small platform – quantity is large



1 450,000,000.00 15.00%

2 540,000,000.00 18.00% -0.20

3 430,310,412.43 14.34% 0.20

4 342,901,946.38 11.43% 0.20

5 273,248,662.90 9.11% 0.20

6 217,743,971.91 7.26% 0.20

7 173,513,885.84 5.78% 0.20

8 138,268,207.00 4.61% 0.20

9 110,181,942.92 3.67% 0.20

10 87,800,809.82 2.93% 0.20

11 69,965,930.90 2.33% 0.20

12 55,753,830.70 1.86% 0.20

13 44,428,618.30 1.48% 0.20

14 35,403,883.46 1.18% 0.20

15 30,477,897.45 1.02% 0.14

Total 3,000,000,000.00 100.00%

Table 66 Production Levels for Large Quantity of Oil

Figure 42 Production Levels for Large Quantity of Oil

0.00

200,000,000.00

400,000,000.00

600,000,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


Page 100 of 159

Set small platform at year three – quantity is small

Buy info, data indicates large, management sets large platform – quantity is small

Buy info, data indicates large, management sets small platform – quantity is small

Buy info, data indicates small, management sets large platform – quantity is small

Buy info, data indicates small, management sets small platform – quantity is small



1 150,000,000.00 15.00%

2 180,000,000.00 18.00% -0.20

3 143,436,804.14 14.34% 0.20

4 114,300,648.79 11.43% 0.20

5 91,082,887.63 9.11% 0.20

6 72,581,323.97 7.26% 0.20

7 57,837,961.95 5.78% 0.20

8 46,089,402.33 4.61% 0.20

9 36,727,314.31 3.67% 0.20

10 29,266,936.61 2.93% 0.20

11 23,321,976.97 2.33% 0.20

12 18,584,610.23 1.86% 0.20

13 14,809,539.43 1.48% 0.20

14 11,801,294.49 1.18% 0.20

15 10,159,299.15 1.02% 0.14

Total 1,000,000,000.00 100.00%

Table 67 Production Levels for Small Quantity of Oil

Figure 43 Production Levels for Small Quantity of Oil

0.00

50,000,000.00

100,000,000.00

150,000,000.00

200,000,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


Page 101 of 159

Appendix P – Complete Case End Nodes Free Cash Flows Estimation (Trinomial)

Table 68 Oil Estimated Quantities and States of Nature Probabilities

Maximum amount of oil in barrels 3,000,000,000.00

Minimum amount of oil in barrels 1,000,000,000.00

State of Nature Probability

Large quantity of oil 0.35

Small quantity of oil 0.65

Estimation of NPVs is show in the next pages, where in the cash flow models the letter M

signifies millions, and the letter B represents billions. For each type of possible outcome, the

full NPV model is only showed for the first price level, as the difference among the NPV

models for the same path outcome resides uniquely in the used price level.

Page 102 of 159

NPVs Set Large Platform at Year Three

Expected Amount of oil in Barrels 1,700,000,000.00


Table 69 Set Large Platform at Year Three – Position s3L Q NPV Estimate

Year (Project) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Year 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3L Q $247.40 $229.90 $215.00 $202.24 $191.23 $181.70 $173.39 $166.12 $159.74 $154.10 $149.12 $144.69 $140.75 $137.23 $134.08

Quantity

$255.M $306.M $243.843M $194.311M $154.841M $123.388M $98.325M $78.352M $62.436M $49.754M $39.647M $31.594M $25.176M $20.062M $17.271M

Revenues

$63.087B $70.348B $52.426B $39.297B $29.611B $22.419B $17.049B $13.016B $9.973B $7.667B $5.912B $4.571B $3.544B $2.753B $2.316B

OPEX

$2.04B $2.448B $1.951B $1.554B $1.239B $.987B $.787B $.627B $.499B $.398B $.317B $.253B $.201B $.16B $.138B

Decommissioning Costs

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $16.2M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX

$24.419B $27.16B $20.19B $15.097B $11.349B $8.573B $6.505B $4.956B $3.79B $2.908B $2.238B $1.727B $1.337B $1.037B $.865B

Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF


CAPEX (Fixed Assets)

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered


Discounted FCFU $0.00 $32.968B $33.006B $22.084B $14.864B $10.057B $6.838B $4.67B $3.202B $2.204B $1.522B $1.055B $.733B $.51B $.356B $.267B

PV $134,338,108,031.03

NPV $134,338,108,031.03

Page 103 of 159

Project Year 4

s3L R $101,250,267,383.14

s3L S $76,069,661,744.36

s3L T $56,898,653,738.89

s3L U $42,295,018,640.20

s3L V $31,163,143,816.88

s3L W $22,670,967,181.45

Table 70 Set Large Platform at Year Three End Nodes NPV Estimates

Page 104 of 159

NPVs Set Small Platform at Year Three

No 2nd Drill, Set Small, it is Large

Amount of Oil Present 3,000,000,000.00




Table 71 Set Small Platform at Year Three – Position s3SO Q NPV Estimate Year (Project) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Year 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3SO Q $247.40 $229.90 $215.00 $202.24 $191.23 $181.70 $173.39 $166.12 $159.74 $154.10 $149.12 $144.69 $140.75 $137.23 $134.08

Quantity


Revenues


OPEX

$9.B $10.8B $8.606B $6.858B $5.465B $4.355B $3.47B $2.765B $2.204B $1.756B $1.399B $1.115B $.889B $.708B $.61B


$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $10.8M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered


Discounted FCFU $0.00 $55.263B $55.096B $36.713B $24.609B $16.586B $11.234B $7.643B $5.223B $3.582B $2.466B $1.703B $1.179B $.819B $.57B $.429B

PV $223,115,556,481.47

NPV $223,115,556,481.47

Page 105 of 159

Project Year 4

s3SO R $164,725,249,455.78

s3SO S $120,288,886,563.81

s3SO T $86,457,695,965.93

s3SO U $60,686,575,203.53

s3SO V $41,042,090,221.21

s3SO W $26,055,896,158.68

Table 72 Set Small Platform at Year Three – Quantity is Large End Nodes NPV Estimates

Page 106 of 159

No 2nd drill, set Small, it is Small


OPEX Small Oil Platform 1 $10.00 USD per barrel

Table 73 Set Small Platform at Year Three – Position s3S§ Q NPV Estimate

Year (Project) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Year 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3S§ Q $247.40 $229.90 $215.00 $202.24 $191.23 $181.70 $173.39 $166.12 $159.74 $154.10 $149.12 $144.69 $140.75 $137.23 $134.08

Quantity


Revenues


OPEX

$1.5B $1.8B $1.434B $1.143B $.911B $.726B $.578B $.461B $.367B $.293B $.233B $.186B $.148B $.118B $.102B


$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $5.4M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX

$14.244B $15.832B $11.762B $8.789B $6.603B $4.985B $3.78B $2.878B $2.2B $1.687B $1.298B $1.001B $.775B $.601B $.502B

Net Income

$21.366B $23.749B $17.643B $13.184B $9.904B $7.477B $5.67B $4.317B $3.3B $2.53B $1.947B $1.502B $1.162B $.901B $.753B

Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered


Discounted FCFU $0.00 $19.231B $19.24B $12.865B $8.653B $5.851B $3.976B $2.714B $1.86B $1.28B $.883B $.612B $.425B $.296B $.206B $.155B

PV $78,247,711,060.88

NPV $78,247,711,060.88

Page 107 of 159

Project Year 4

s3S§ R $58,784,275,385.65

s3S§ S $43,972,154,421.66

s3S§ T $32,695,090,889.03

s3S§ U $24,104,717,301.56

s3S§ V $17,556,555,640.79

s3S§ W $12,561,157,619.95

Table 74 Set Small Platform at Year Three – Quantity is Small End Nodes NPV Estimates

Page 108 of 159

NPVs Buy Additional Information at Year Three, Large Quantity is Indicated, and a Large Platform is Established

It is Large



Table 75 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set, it is Large – Position s3b(D+)LO X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D+)LO X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX

$3.6B $4.32B $3.442B $2.743B $2.186B $1.742B $1.388B $1.106B $.881B $.702B $.56B $.446B $.355B $.283B $.244B


$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $16.2M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $234,491,395,523.84

NPV $234,491,395,523.84

Page 109 of 159

Project Year 5

s3b(D+)LO Y $176,717,322,701.87

s3b(D+)LO Z $132,749,325,569.35

s3b(D+)LO AA $99,274,090,372.08

s3b(D+)LO AB $73,773,515,156.90

s3b(D+)LO AC $54,334,704,386.16

s3b(D+)LO AD $39,504,922,909.92


Quantity is Large – End Nodes NPV Estimates

Page 110 of 159

It is Small



Table 77 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set, it is Small – Position s3b(D+)L§ X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D+)L§ X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $16.2M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX

$13.937B $15.498B $11.517B $8.609B $6.469B $4.884B $3.704B $2.821B $2.156B $1.653B $1.272B $.981B $.759B $.589B $.488B

Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $76,612,029,691.90

NPV $76,612,029,691.90

Page 111 of 159

Project Year 5

s3b(D+)L§ Y $57,354,005,417.91

s3b(D+)L§ Z $42,698,006,373.74

s3b(D+)L§ AA $31,539,594,641.31

s3b(D+)L§ AB $23,039,402,902.92

s3b(D+)L§ AC $16,559,799,312.67

s3b(D+)L§ AD $11,616,538,820.59


Quantity is Small – End Nodes NPV Estimates

Page 112 of 159

NPVs Buy Additional Information at Year Three, Large Quantity is Indicated, and a Small Platform is Established

It is Large





Table 79 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set, it is Large – Position s3b(D+)SO X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D+)SO X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $10.8M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $220,538,169,864.71

NPV $220,538,169,864.71

Page 113 of 159

Project Year 5

s3b(D+)SO Y $162,764,097,042.73

s3b(D+)SO Z $118,796,099,910.22

s3b(D+)SO AA $85,320,864,712.95

s3b(D+)SO AB $59,820,289,497.77

s3b(D+)SO AC $40,381,478,727.03

s3b(D+)SO AD $25,551,697,250.78



Page 114 of 159

It tis Small



Table 81 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set, it is Small – Position s3b(D+)S§ X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D+)S§ X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $5.4M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $77,388,582,188.62

NPV $77,388,582,188.62

Page 115 of 159

Project Year 5

s3b(D+)S§ Y $58,130,557,914.63

s3b(D+)S§ Z $43,474,558,870.46

s3b(D+)S§ AA $32,316,147,138.04

s3b(D+)S§ AB $23,815,955,399.64

s3b(D+)S§ AC $17,336,351,809.40

s3b(D+)S§ AD $12,393,091,317.31



Page 116 of 159

NPVs Buy Additional Information at Year Three, Small Quantity is Indicated, and a Large Platform is Established

It is Large



Table 83 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set, it is Large – Position s3b(D-)LO X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D-)LO X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX

$3.6B $4.32B $3.442B $2.743B $2.186B $1.742B $1.388B $1.106B $.881B $.702B $.56B $.446B $.355B $.283B $.244B


$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $16.2M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $234,491,395,523.84

NPV $234,491,395,523.84

Page 117 of 159

Project Year 5

s3b(D-)LO Y $176,717,322,701.87

s3b(D-)LO Z $132,749,325,569.35

s3b(D-)LO AA $99,274,090,372.08

s3b(D-)LO AB $73,773,515,156.90

s3b(D-)LO AC $54,334,704,386.16

s3b(D-)LO AD $39,504,922,909.92



Page 118 of 159

It is Small



Table 85 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set, it is Small – Position s3b(D-)L§ X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D-)L§ X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $16.2M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $76,612,029,691.90

NPV $76,612,029,691.90

Page 119 of 159

Project Year 5

s3b(D-)L§ Y $57,354,005,417.91

s3b(D-)L§ Z $42,698,006,373.74

s3b(D-)L§ AA $31,539,594,641.31

s3b(D-)L§ AB $23,039,402,902.92

s3b(D-)L§ AC $16,559,799,312.67

s3b(D-)L§ AD $11,616,538,820.59



Page 120 of 159

NPVs Buy Additional Information at Year Three, Small Quantity is Indicated, and a Small Platform is Established

It is Large





Table 87 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set, it is Large – Position s3b(D-)SO X NPV Estimate Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D-)SO X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $10.8M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $220,538,169,864.71

NPV $220,538,169,864.71

Page 121 of 159

Project Year 5

s3b(D-)SO Y $162,764,097,042.73

s3b(D-)SO Z $118,796,099,910.22

s3b(D-)SO AA $85,320,864,712.95

s3b(D-)SO AB $59,820,289,497.77

s3b(D-)SO AC $40,381,478,727.03

s3b(D-)SO AD $25,551,697,250.78



Page 122 of 159

It tis Small



Table 89 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set, it is Small – Position s3b(D-)SO X NPV Estimate

Year (Project) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034

Year (Production) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price s3b(D-)S§ X $244.28 $227.25 $212.74 $200.29 $189.55 $180.24 $172.11 $165.00 $158.75 $153.23 $148.34 $144.00 $140.13 $136.68 $133.59

Quantity


Revenues


OPEX



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $5.4M

EBITDA


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EBT


TAX


Net Income


Depreciation

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OCF



$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FCF Unlevered



PV $77,388,582,188.62

NPV $77,388,582,188.62

Page 123 of 159

Project Year 5

s3b(D-)S§ Y $58,130,557,914.63

s3b(D-)S§ Z $43,474,558,870.46

s3b(D-)S§ AA $32,316,147,138.04

s3b(D-)S§ AB $23,815,955,399.64

s3b(D-)S§ AC $17,336,351,809.40

s3b(D-)S§ AD $12,393,091,317.31



Page 124 of 159

Appendix Q – Complete Case End Nodes Free Cash Flows Estimation (Binomial)

Estimated end nodes NPVs for the quadranomial tree (i.e. combined tree constructed with the

use of the binomial price tree) are constructed in exactly the same manner as the NPVs for

the hexanomial tree (these NPVs are developed in the previous appendix), but the used oil

price, at each oil price level, is constant throughout the lifetime of the well, as it is assumed

that the binomial price model has a drift of zero, being thus, expected that next year’s oil

price is this year’s oil price. Both graphs in the figures below illustrate this price movement

for the estimated price levels at years four and five.

Figure 44 Evolution of Year Four Price Levels

Figure 45 Evolution of Year Five Price Levels

0.00

50.00

100.00

150.00

200.00

250.00

20

18

20

19

20

20

20

21

20

22

20

23

20

24

20

25

20

26

20

27

20

28

20

29

20

30

20

31

20

32

20

33

Price Evolution (Y4)

pu4 pu3d pu2pd2 pupd3 pd4

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

20

19

20

20

20

21

20

22

20

23

20

24

20

25

20

26

20

27

20

28

20

29

20

30

20

31

20

32

20

33

20

34

Price Evolution (Y5)

pu5 pu4pd pu3pd2 pu2pd3 pupd4 pd5

Page 125 of 159

Therefore, to avoid the replication of the tables exhibited in the previous appendix, the tables

below only show the end nodes NPVs.

Table 91 Project Year Four NPVs

Project Year 4

s3SO pu4 $252,085,109,978.02

s3SO pu3d $158,781,084,504.21

s3SO pu2d2 $97,094,507,817.94

s3SO pud3 $56,311,339,846.92

s3SO pd4 $29,348,151,433.79

s3S§ pu4 $87,904,228,893.06

s3S§ pu3d $56,802,887,068.46

s3S§ pu2d2 $36,240,694,839.70

s3S§ pud3 $22,646,305,516.03

s3S§ pd4 $13,658,576,044.98

s3L pu4 $150,754,188,345.74

s3L pu3d $97,881,907,243.91

s3L pu2d2 $62,926,180,455.03

s3L pud3 $39,815,718,604.78

s3L pd4 $24,536,578,504.01

Table 92 Project Year Five NPVs

Project Year 5

s3bD+LO pu5 $329,328,022,725.52

s3bD+LO pu4d $214,577,350,870.33

s3bD+LO pu3d2 $138,711,641,076.46

s3bD+LO pu2d3 $88,554,148,928.69

s3bD+LO pud4 $55,393,264,711.18

s3bD+LO pd5 $33,469,436,485.34

s3bD+SO pu5 $315,374,797,066.39

s3bD+SO pu4d $200,624,125,211.19

s3bD+SO pu3d2 $124,758,415,417.32

s3bD+SO pu2d3 $74,600,923,269.55

s3bD+SO pud4 $41,440,039,052.05

s3bD+SO pd5 $19,516,210,826.21

s3bD-LO pu5 $329,328,022,725.52

s3bD-LO pu4d $214,577,350,870.33

s3bD-LO pu3d2 $138,711,641,076.46

s3bD-LO pu2d3 $88,554,148,928.69

s3bD-LO pud4 $55,393,264,711.18

s3bD-LO pd5 $33,469,436,485.34

s3bD-SO pu5 $315,374,797,066.39

s3bD-SO pu4d $200,624,125,211.19

s3bD-SO pu3d2 $124,758,415,417.32

s3bD-SO pu2d3 $74,600,923,269.55

s3bD-SO pud4 $41,440,039,052.05

s3bD-SO pd5 $19,516,210,826.21

s3bD+L§ pu5 $108,224,238,759.13

s3bD+L§ pu4d $69,974,014,807.39

s3bD+L§ pu3d2 $44,685,444,876.10

s3bD+L§ pu2d3 $27,966,280,826.85

s3bD+L§ pud4 $16,912,652,754.35

s3bD+L§ pd5 $9,604,710,012.40

s3bD+S§ pu5 $109,000,791,255.85

s3bD+S§ pu4d $70,750,567,304.12

s3bD+S§ pu3d2 $45,461,997,372.83

s3bD+S§ pu2d3 $28,742,833,323.57

s3bD+S§ pud4 $17,689,205,251.07

s3bD+S§ pd5 $10,381,262,509.12

s3bD-L§ pu5 $108,224,238,759.13

s3bD-L§ pu4d $69,974,014,807.39

s3bD-L§ pu3d2 $44,685,444,876.10

s3bD-L§ pu2d3 $27,966,280,826.85

s3bD-L§ pud4 $16,912,652,754.35

s3bD-L§ pd5 $9,604,710,012.40

s3bD-S§ pu5 $109,000,791,255.85

s3bD-S§ pu4d $70,750,567,304.12

s3bD-S§ pu3d2 $45,461,997,372.83

s3bD-S§ pu2d3 $28,742,833,323.57

s3bD-S§ pud4 $17,689,205,251.07

s3bD-S§ pd5 $10,381,262,509.12

Page 126 of 159

Appendix R – Complete Case Hexanomial Tree Probabilities


Table 93 Complete Case Hexanomial Tree Nodes Probabilities


Probability success 2D seismic survey 0.07

Probability failure 2D seismic survey 0.93 1.00

pu - to Point B 0.1667

pm - to Point C 0.6667

pd - to Point D 0.1667 1.00

spu (B) 0.0117

spm (C) 0.0467

spd (D) 0.0117

fpu (B) 0.1550

fpm (C) 0.6200

fpd (D) 0.1550 1.00













To Point B

s*(B)pu 0.0194

s*(B)pm 0.0990

s*(B)pm 0.0316

f*(B)pu 0.1100

f*(B)pm 0.5611

f*(B)pm 0.1789 1.00

To Point C

s*(C)pu 0.0250

s*(C)pm 0.1000

s*(C)pm 0.0250

f*(C)pu 0.1417

f*(C)pm 0.5667

f*(C)pm 0.1417 1.00

To Point D

s*(D)pu 0.0316

s*(D)pm 0.0990

s*(D)pm 0.0194

f*(D)pu 0.1789

f*(D)pm 0.5611

f*(D)pm 0.1100 1.00



Probability failure DW1 0.7 1.00
















To Point E

s * (E)pu 0.0296

s * (E)pm 0.1921

s * (E)pd 0.0783

f * (E)pu 0.0691

f * (E)pm 0.4482

f * (E)pd 0.1826 1.00

To Point F

s * (F)pu 0.0388

s * (F)pm 0.1980

s * (F)pd 0.0632

f * (F)pu 0.0906

f * (F)pm 0.4621

f * (F)pd 0.1474 1.00

Page 127 of 159

To Point G

s * (G)pu 0.0500

s * (G)pm 0.2000

s * (G)pd 0.0500

f * (G)pu 0.1167

f * (G)pm 0.4667

f * (G)pd 0.1167 1.00

To Point H

s * (H)pu 0.0632

s * (H)pm 0.1980

s * (H)pd 0.0388

f * (H)pu 0.1474

f * (H)pm 0.4621

f * (H)pd 0.0906 1.00

To Point I

s * (I)pu 0.0783

s * (I)pm 0.1921

s * (I)pd 0.0296

f * (I)pu 0.1826

f * (I)pm 0.4482

f * (I)pd 0.0691 1.00


Quantity is fixed, and only price probability enters. Therefore, technological uncertainty assumes a probability of 1. 1.00

Point J pu - to Point Q 0.8313

Point J pm - to Point R 0.0941

Point J pd - to Point S 0.0746 1.00

Point K pu - to Point Q 0.0987

Point K pm - to Point R 0.6404

Point K pd - to Point S 0.2609 1.00

Point L pu - to Point R 0.1294

Point L pm - to Point S 0.6601

Point L pd - to Point T 0.2105 1.00

Point M pu - to Point S 0.1667

Point M pm - to Point T 0.6667

Point M pd - to Point U 0.1667 1.00

PoNnt N pu - to PoNnt T 0.2105

PoNnt N pm - to PoNnt U 0.6601

PoNnt N pd - to PoNnt V 0.1294 1.00

Point O pu - to Point U 0.2609

Point O pO - to Point V 0.6404

Point O pd - to Point W 0.0987 1.00

PoPPt P pu - to PoPPt U 0.0746

PoPPt P pm - to PoPPt V 0.0941

PoPPt P pd - to PoPPt W 0.8313 1.00


Large oil Probability (SO) 0.35

Small oil Probability (S§) 0.65 1.00






















To Point J

SO * (J)pu 0.2910

SO * (J)pm 0.0329

SO * (J)pd 0.0261

S§ * (J)pu 0.5403

S§ * (J)pm 0.0612

S§ * (J)pd 0.0485 1.00

To Point K

SO * (K)pu 0.0346

SO * (K)pm 0.2241

SO * (K)pd 0.0913

S§ * (K)pu 0.0642

S§ * (K)pm 0.4162

S§ * (Kpd 0.1696 1.00

To Point L

SO * (L)pu 0.0453

SO * (L)pm 0.2310

SO * (L)pd 0.0737

S§ * (L)pu 0.0841

S§ * (L)pm 0.4291

S§ * (L)pd 0.1368 1.00

Page 128 of 159

To Point M

SO * (M)pu 0.0583

SO * (M)pm 0.2333

SO * (M)pd 0.0583

S§ * (M)pu 0.1083

S§ * (M)pm 0.4333

S§ * (M)pd 0.1083 1.00

To Point N

SO * (N)pu 0.0737

SO * (N)pm 0.2310

SO * (N)pd 0.0453

S§ * (N)pu 0.1368

S§ * (N)pm 0.4291

S§ * (N)pd 0.0841 1.00

To Point O

SO * (O)pu 0.0913

SO * (O)pm 0.2241

SO * (O)pd 0.0346

S§ * (O)pu 0.1696

S§ * (O)pm 0.4162

S§ * (O)pd 0.0642 1.00

To Point P

SO * (P)pu 0.0261

SO * (P)pm 0.0329

SO * (P)pd 0.2910

S§ * (P)pu 0.0485

S§ * (P)pm 0.0612

S§ * (P)pd 0.5403 1.00


Data indicates Large - b(D+) 53.00%

Data indicates Small - b(D-) 47.00% 1.00






















To Point J

b(D+) * (J)pu 0.4406

b(D+) * (J)pm 0.0499

b(D+) * (J)pd 0.0395

b(D-) * (J)pu 0.3907

b(D-) * (J)pm 0.0442

b(D-) * (J)pd 0.0351 1.00

To Point K

b(D+) * (K)pu 0.0523

b(D+) * (K)pm 0.3394

b(D+) * (K)pd 0.1383

b(D-) * (K)pu 0.0464

b(D-) * (K)pm 0.3010

b(D-) * (K)pd 0.1226 1.00

To Point L

b(D+) * (L)pu 0.0686

b(D+) * (L)pm 0.3498

b(D+) * (L)pd 0.1116

b(D-) * (L)pu 0.0608

b(D-) * (L)pm 0.3102

b(D-) * (L)pd 0.0989 1.00

To Point M

b(D+) * (M)pu 0.0883

b(D+) * (M)pm 0.3533

b(D+) * (M)pd 0.0883

b(D-) * (M)pu 0.0783

b(D-) * (M)pm 0.3133

b(D-) * (M)pd 0.0783 1.00

To Point N

b(D+) * (N)pu 0.1116

b(D+) * (N)pm 0.3498

b(D+) * (N)pd 0.0686

b(D-) * (N)pu 0.0989

b(D-) * (N)pm 0.3102

b(D-) * (N)pd 0.0608 1.00

To Point O

b(D+) * (O)pu 0.1383

b(D+) * (O)pm 0.3394

b(D+) * (O)pd 0.0523

b(D-) * (O)pu 0.1226

b(D-) * (O)pm 0.3010

b(D-) * (O)pd 0.0464 1.00

Page 129 of 159

To Point P

b(D+) * (P)pu 0.0395 b(D+) * (P)pm 0.0499 b(D+) * (P)pd 0.4406 b(D-) * (P)pu 0.0351

b(D-) * (P)pm 0.0442

b(D-) * (P)pd 0.3907 1.00

Probabilities Y4 to Y5 - Buy info, data indicates large quantity, install large platform



Point Q pu - to Point X 0.8313

Point Q pm - to Point Y 0.0941

Point Q pd - to Point Z 0.0746 1.00

Point R pu - to Point X 0.0987

Point R pm - to Point Y 0.6404

Point R pd - to Point Z 0.2609 1.00

Point S pu - to Point Y 0.1294

Point S pm - to Point Z 0.6601

Point S pd - to Point AA 0.2105 1.00

Point T pu - to Point Z 0.1667

Point T pT - to Point AA 0.6667

Point T pd - to Point AB 0.1667 1.00

Point U pu - to Point AA 0.2105

Point U pm - to Point AB 0.6601

Point U pd - to Point AC 0.1294 1.00

Point V pu - to Point AB 0.2609

Point V pm - to Point AC 0.6404

Point V pd - to Point AD 0.0987 1.00

Point W pu - to Point AB 0.0746

Point W pm - to Point AC 0.0941

Point W pd - to Point AD 0.8313 1.00

To Point Q

LO * (Q)pu 0.2196

LO * (Q)pm 0.0249

LO * (Q)pd 0.0197

L§ * (Q)pu 0.6117

L§ * (Q)pm 0.0692

L§ * (Q)pd 0.0549 1.00

To Point R

LO * (R)pu 0.0261

LO * (R)pm 0.1692

LO * (R)pd 0.0689

L§ * (R)pu 0.0726

L§ * (R)pm 0.4712

L§ * (R)pd 0.1920 1.00

To Point S

LO * (S)pu 0.0342

LO * (S)pm 0.1744

LO * (S)pd 0.0556

L§ * (S)pu 0.0952

L§ * (S)pm 0.4857

L§ * (S)pd 0.1549 1.00

To Point T

LO * (T)pu 0.0440

LO * (T)pm 0.1761

LO * (T)pd 0.0440

L§ * (T)pu 0.1226

L§ * (T)pm 0.4906

L§ * (T)pd 0.1226 1.00

To Point U

LO * (U)pu 0.0556

LO * (U)pm 0.1744

LO * (U)pd 0.0342

L§ * (U)pu 0.1549

L§ * (U)pm 0.4857

L§ * (U)pd 0.0952 1.00

To Point V

LO * (V)pu 0.0689

LO * (V)pm 0.1692

LO * (V)pd 0.0261

L§ * (V)pu 0.1920

L§ * (V)pm 0.4712

L§ * (V)pd 0.0726 1.00

To Point W

LO * (W)pu 0.0197

LO * (W)pm 0.0249

LO * (W)pd 0.2196

L§ * (W)pu 0.0549

L§ * (W)pm 0.0692

L§ * (W)pd 0.6117 1.00

Probability Y4 to Y5 - Buy info, data indicates large quantity, install small platform















Page 130 of 159










To Point Q

LO * (Q)pu 0.2196

LO * (Q)pm 0.0249

LO * (Q)pd 0.0197

L§ * (Q)pu 0.6117

L§ * (Q)pm 0.0692

L§ * (Q)pd 0.0549 1.00

To Point R

LO * (R)pu 0.0261

LO * (R)pm 0.1692

LO * (R)pd 0.0689

L§ * (R)pu 0.0726

L§ * (R)pm 0.4712

L§ * (R)pd 0.1920 1.00

To Point S

LO * (S)pu 0.0342

LO * (S)pm 0.1744

LO * (S)pd 0.0556

L§ * (S)pu 0.0952

L§ * (S)pm 0.4857

L§ * (S)pd 0.1549 1.00

To Point T

LO * (T)pu 0.0440 LO * (T)pm 0.1761 LO * (T)pd 0.0440 L§ * (T)pu 0.1226 L§ * (T)pm 0.4906 L§ * (T)pd 0.1226 1.00

To Point U

LO * (U)pu 0.0556

LO * (U)pm 0.1744

LO * (U)pd 0.0342

L§ * (U)pu 0.1549

L§ * (U)pm 0.4857

L§ * (U)pd 0.0952 1.00

To Point V

LO * (V)pu 0.0689

LO * (V)pm 0.1692

LO * (V)pd 0.0261

L§ * (V)pu 0.1920

L§ * (V)pm 0.4712

L§ * (V)pd 0.0726 1.00

To Point W

LO * (W)pu 0.0197

LO * (W)pm 0.0249

LO * (W)pd 0.2196

L§ * (W)pu 0.0549

L§ * (W)pm 0.0692

L§ * (W)pd 0.6117 1.00

Probability Y4 to Y5 - Buy info, data indicates small quantity, install large platform
























To Point Q

LO * (Q)pu 0.3714

LO * (Q)pm 0.0420

LO * (Q)pd 0.0333

L§ * (Q)pu 0.4599

L§ * (Q)pm 0.0520

L§ * (Q)pd 0.0413 1.00

To Point R

LO * (R)pu 0.0441

LO * (R)pm 0.2861

LO * (R)pd 0.1166

L§ * (R)pu 0.0546

L§ * (R)pm 0.3542

L§ * (R)pd 0.1443 1.00

Page 131 of 159

To Point S

LO * (S)pu 0.0578

LO * (S)pm 0.2949

LO * (S)pd 0.0941

L§ * (S)pu 0.0716

L§ * (S)pm 0.3652

L§ * (S)pd 0.1165 1.00

To Point T

LO * (T)pu 0.0745

LO * (T)pm 0.2979

LO * (T)pd 0.0745

L§ * (T)pu 0.0922

L§ * (T)pm 0.3688

L§ * (T)pd 0.0922 1.00

To Point U

LO * (U)pu 0.0941

LO * (U)pm 0.2949

LO * (U)pd 0.0578

L§ * (U)pu 0.1165

L§ * (U)pm 0.3652

L§ * (U)pd 0.0716 1.00

To Point V

LO * (V)pu 0.1166

LO * (V)pm 0.2861

LO * (V)pd 0.0441

L§ * (V)pu 0.1443

L§ * (V)pm 0.3542

L§ * (V)pd 0.0546 1.00

To Point W

LO * (W)pu 0.0333

LO * (W)pm 0.0420

LO * (W)pd 0.3714

L§ * (W)pu 0.0413

L§ * (W)pm 0.0520

L§ * (W)pd 0.4599 1.00

Probability Y4 to Y5 - Buy info, data indicates small quantity, install small platform
























To Point Q

LO * (Q)pu 0.3714

LO * (Q)pm 0.0420

LO * (Q)pd 0.0333

L§ * (Q)pu 0.4599

L§ * (Q)pm 0.0520

L§ * (Q)pd 0.0413 1.00

To Point R

LO * (R)pu 0.0441

LO * (R)pm 0.2861

LO * (R)pd 0.1166

L§ * (R)pu 0.0546

L§ * (R)pm 0.3542

L§ * (R)pd 0.1443 1.00

To Point S

LO * (S)pu 0.0578

LO * (S)pm 0.2949

LO * (S)pd 0.0941

L§ * (S)pu 0.0716

L§ * (S)pm 0.3652

L§ * (S)pd 0.1165 1.00

To Point T

LO * (T)pu 0.0745

LO * (T)pm 0.2979

LO * (T)pd 0.0745

L§ * (T)pu 0.0922

L§ * (T)pm 0.3688

L§ * (T)pd 0.0922 1.00

To Point U

LO * (U)pu 0.0941

LO * (U)pm 0.2949

LO * (U)pd 0.0578

L§ * (U)pu 0.1165

L§ * (U)pm 0.3652

L§ * (U)pd 0.0716 1.00

To Point V

LO * (V)pu 0.1166

LO * (V)pm 0.2861

LO * (V)pd 0.0441

L§ * (V)pu 0.1443

L§ * (V)pm 0.3542

L§ * (V)pd 0.0546 1.00

Page 132 of 159

To Point W

LO * (W)pu 0.0333

LO * (W)pm 0.0420

LO * (W)pd 0.3714

L§ * (W)pu 0.0413

L§ * (W)pm 0.0520

L§ * (W)pd 0.4599 1.00

Page 133 of 159

Appendix S – Complete Case Quadranomial Tree Probabilities


Table 94 Complete Case Quadranomial Tree Nodes Probabilities




up risk-neutral probability (pu) 0.5204

down risk-neutral probability (pd) 0.4796 1.00

spu 0.0364

spd 0.0336

fpu 0.4840

fpd 0.4460 1.00






spu 0.0781

spd 0.0719

fpu 0.4424

fpd 0.4076 1.00



Probability failure DW1 0.7 1.00



spu 0.1561

spd 0.1439

fpu 0.3643

fpd 0.3357 1.00


Quantity is fixed, and only price probability enters. Therefore, technological uncertainty assumes a probability of 1.

1.00




Large oil Probability 0.35

Small oil Probability 0.65 1.00



SOpu 0.1822

SOpd 0.1678

S§pu 0.3383

S§pd 0.3117 1.00


Data says Large 53.00%

Data says Small 47.00% 1.00



D+pu 0.2758

D+pd 0.2542

D-pu 0.2446

D-pd 0.2254 1.00

Probabilities Y4 to Y5 - Buy info, data indicates large quantity, install large platform





LOpu 0.1375

LOpd 0.1267

L§pu 0.3830

L§pd 0.3529 1.00

Probability Y4 to Y5 - Buy info, data indicates large quantity, install small platform





SOpu 0.1375

SOpd 0.1267

S§pu 0.3830

S§pd 0.3529 1.00

Probability Y4 to Y5 - Buy info, data indicates small quantity, install large platform





Page 134 of 159

LOpu 0.2325

LOpd 0.2143

L§pu 0.2879

L§pd 0.2653 1.00

Probability Y4 to Y5 - Buy info, data indicates small quantity, install small platform





SOpu 0.2325

SOpd 0.2143

S§pu 0.2879

S§pd 0.2653 1.00

Page 135 of 159

Appendix T – Hexanomial Tree Mutually Exclusive NPVs

Using the methodology described in the simplified case, each mutually exclusive alternative

NPV is estimated. The figure below depicts the general process.

0 1 2 3 4 5

0 1 2 3 4 5

PV s B s2 E s3 J s3(D+) Q s3b(D+)LO X PV s B s2 E s3 J s3(D+) Q $234,491,395,523.84 s C s2 F s3 K s3(D+) R s3b(D+)LO Y s C s2 F s3 K s3(D+) R $176,717,322,701.87 s D s2 G s3 L s3(D+) S s3b(D+)LO Z s D s2 G s3 L s3(D+) S $132,749,325,569.35 F B s2 H s3 M s3(D+) T s3b(D+)LO AA F B s2 H s3 M s3(D+) T $99,274,090,372.08 F C s2 I s3 N s3(D+) U s3b(D+)LO AB F C s2 I s3 N s3(D+) U $73,773,515,156.90 f D sF E s3 O s3(D+) V s3b(D+)LO AC f D sF E s3 O s3(D+) V $54,334,704,386.16

sF F s3 P s3(D+) W s3b(D+)LO AD sF F s3 P s3(D+) W $39,504,922,909.92 sF G s2F J s3b(D+)SO X sF G s2F J $220,538,169,864.71 sF H s2F K s3b(D+)SO Y sF H s2F K $162,764,097,042.73 sF I s2F L s3b(D+)SO Z sF I s2F L $118,796,099,910.22

s2F M s3b(D+)SO AA s2F M $85,320,864,712.95 s2F N s3b(D+)SO AB s2F N $59,820,289,497.77 s2F O s3b(D+)SO AC s2F O $40,381,478,727.03 s2F P s3b(D+)SO AD s2F P $25,551,697,250.78

s3(D-) Q s3b(D-)LO X s3(D-) Q $234,491,395,523.84

s3(D-) R s3b(D-)LO Y s3(D-) R $176,717,322,701.87 s3(D-) S s3b(D-)LO Z s3(D-) S $132,749,325,569.35

s3(D-) T s3b(D-)LO AA s3(D-) T $99,274,090,372.08 s3(D-) U s3b(D-)LO AB s3(D-) U $73,773,515,156.90 s3(D-) V s3b(D-)LO AC s3(D-) V $54,334,704,386.16 s3(D-) W s3b(D-)LO AD s3(D-) W $39,504,922,909.92

s3b(D-)SO X $220,538,169,864.71 s3SO Q s3b(D-)SO Y $223,115,556,481.47 $162,764,097,042.73 s3SO R s3b(D-)SO Z $164,725,249,455.78 $118,796,099,910.22 s3SO S s3b(D-)SO AA $120,288,886,563.81 $85,320,864,712.95 s3SO T s3b(D-)SO AB $86,457,695,965.93 $59,820,289,497.77 s3SO U s3b(D-)SO AC $60,686,575,203.53 $40,381,478,727.03 s3SO V s3b(D-)SO AD $41,042,090,221.21 $25,551,697,250.78 s3SO W $26,055,896,158.68 s3S§ Q s3b(D+)L§ X $78,247,711,060.88 $76,612,029,691.90 s3S§ R s3b(D+)L§ Y $58,784,275,385.65 $57,354,005,417.91 s3S§ S s3b(D+)L§ Z $43,972,154,421.66 $42,698,006,373.74 s3S§ T s3b(D+)L§ AA $32,695,090,889.03 $31,539,594,641.31 s3S§ U s3b(D+)L§ AB $24,104,717,301.56 $23,039,402,902.92 s3S§ V s3b(D+)L§ AC $17,556,555,640.79 $16,559,799,312.67 s3S§ W s3b(D+)L§ AD $12,561,157,619.95 $11,616,538,820.59

s3b(D+)S§ X $77,388,582,188.62 s3L Q s3b(D+)S§ Y $134,338,108,031.03 $58,130,557,914.63 s3L R s3b(D+)S§ Z $101,250,267,383.14 $43,474,558,870.46 s3L S s3b(D+)S§ AA $76,069,661,744.36 $32,316,147,138.04 s3L T s3b(D+)S§ AB $56,898,653,738.89 $23,815,955,399.64 s3L U s3b(D+)S§ AC $42,295,018,640.20 $17,336,351,809.40 s3L V s3b(D+)S§ AD $31,163,143,816.88 $12,393,091,317.31 s3L W s3b(D-)L§ X $22,670,967,181.45 $76,612,029,691.90

s3b(D-)L§ Y $57,354,005,417.91 s3b(D-)L§ Z $42,698,006,373.74 s3b(D-)L§ AA $31,539,594,641.31 s3b(D-)L§ AB $23,039,402,902.92 s3b(D-)L§ AC $16,559,799,312.67 s3b(D-)L§ AD $11,616,538,820.59 s3b(D-)S§ X $77,388,582,188.62 s3b(D-)S§ Y $58,130,557,914.63 s3b(D-)S§ Z $43,474,558,870.46 s3b(D-)S§ AA $32,316,147,138.04 s3b(D-)S§ AB $23,815,955,399.64 s3b(D-)S§ AC $17,336,351,809.40 s3b(D-)S§ AD $12,393,091,317.31

Figure 46 Complete Case Hexanomial Event Tree

s – success

f – failure

b – buy info

S – set small

L – set Large












Set LP at Y3



Abandon

Continue


Page 136 of 159

Acquire Additional Imperfect Information

0 1 2 3

-$359,682,699.02 $2,308,711,804.43 $24,305,743,431.52 $110,925,938,317.32 $108,336,794,136.53 $234,491,395,523.84

$1,768,896,697.00 $19,322,546,522.09 $87,222,500,683.71 $83,351,738,141.75 $176,717,322,701.87

$1,324,174,269.06 $15,281,937,775.31 $68,215,554,055.82 $63,787,433,834.50 $132,749,325,569.35

-$532,693,939.11 $12,010,188,040.60 $53,104,245,989.13 $48,559,339,185.56 $99,274,090,372.08

-$532,693,939.11 $9,362,688,978.66 $41,095,380,158.98 $36,700,372,994.72 $73,773,515,156.90

-$532,693,939.11 -$394,174,757.28 $31,551,401,071.79 $27,459,687,454.52 $54,334,704,386.16

-$394,174,757.28 $24,023,813,398.42 $20,295,087,409.16 $39,504,922,909.92

-$394,174,757.28 -$200,000,000.00

$220,538,169,864.71

-$394,174,757.28 -$200,000,000.00

$162,764,097,042.73

-$394,174,757.28 -$200,000,000.00

$118,796,099,910.22

-$200,000,000.00

$85,320,864,712.95

-$200,000,000.00

$59,820,289,497.77

-$200,000,000.00

$40,381,478,727.03

-$200,000,000.00

$25,551,697,250.78

$134,794,596,339.96 $234,491,395,523.84

PV -$359,682,699.02

$103,837,278,470.92 $176,717,322,701.87


$79,596,452,776.86 $132,749,325,569.35

NPV -$409,682,699.02

$60,728,335,503.67 $99,274,090,372.08

$46,034,680,782.84 $73,773,515,156.90

$34,585,163,132.95 $54,334,704,386.16

$25,707,984,668.56 $39,504,922,909.92

$220,538,169,864.71

$162,764,097,042.73

$118,796,099,910.22

$85,320,864,712.95

$59,820,289,497.77

$40,381,478,727.03

$25,551,697,250.78

$76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31

$76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31

Figure 47 Acquiring Additional Imperfect Information NPV (Hexanomial)

Page 137 of 159

Install Large Platform at Year Three

0 1 2 3 4

-$250,446,452.44 $2,607,651,214.67 $26,545,893,081.54 $123,091,949,258.90 $134,338,108,031.03

$1,995,114,905.78 $20,783,083,736.31 $95,003,555,266.30 $101,250,267,383.14

$1,499,142,521.01 $16,201,484,603.83 $73,009,495,291.50 $76,069,661,744.36

-$429,008,389.10 $12,560,585,752.98 $55,890,468,501.64 $56,898,653,738.89

-$429,008,389.10 $9,667,067,784.29 $42,559,213,540.84 $42,295,018,640.20

-$429,008,389.10 -$287,378,640.78 $32,171,562,553.71 $31,163,143,816.88

-$287,378,640.78 $24,117,928,105.74 $22,670,967,181.45

-$287,378,640.78 -$90,000,000.00

-$287,378,640.78 -$90,000,000.00

-$287,378,640.78 -$90,000,000.00

-$90,000,000.00

-$90,000,000.00

PV -$250,446,452.44

-$90,000,000.00


-$90,000,000.00

NPV -$300,446,452.44

Figure 48 NPV for Setting a Large Platform at Year Three (Hexanomial)

Install Small Platform at Year Three

0 1 2 3 4

-$239,440,719.74 $2,412,685,502.02 $25,050,332,404.86 $117,890,690,935.65 $223,115,556,481.47

$1,800,149,193.14 $19,287,523,059.63 $89,802,296,943.05 $164,725,249,455.78

$1,304,176,808.36 $14,705,923,927.16 $67,808,236,968.25 $120,288,886,563.81

-$402,144,405.69 $11,065,025,076.30 $50,689,210,178.39 $86,457,695,965.93

-$402,144,405.69 $8,171,507,107.61 $37,357,955,217.59 $60,686,575,203.53

-$402,144,405.69 -$259,708,737.86 $26,970,304,230.46 $41,042,090,221.21

-$259,708,737.86 $18,916,669,782.49 $26,055,896,158.68

-$259,708,737.86 -$61,500,000.00 $78,247,711,060.88

-$259,708,737.86 -$61,500,000.00 $58,784,275,385.65

-$259,708,737.86 -$61,500,000.00 $43,972,154,421.66

-$61,500,000.00 $32,695,090,889.03

-$61,500,000.00 $24,104,717,301.56

PV -$239,440,719.74

-$61,500,000.00 $17,556,555,640.79 2D Seismic Survey $50,000,000.00

-$61,500,000.00 $12,561,157,619.95

NPV -$289,440,719.74

Figure 49 NPV for Setting a Small Platform at Year Three (Hexanomial)

Page 138 of 159

Appendix U – Quadranomial Tree Mutually Exclusive NPVs

Using the methodology described in the simplified case, each mutually exclusive alternative

NPV is estimated. The figure below depicts the general process.

0 1 2 3 4 5

0 1 2 3 4 5

PV S pu S2 pu2 s3 pu3 s3bD+ pu4 s3bD+LO pu5 PV S pu S2 pu2 s3 pu3 s3bD+ pu4 $329,328,022,725.52

s pd s2 pud s3 pu2d s3bD+ pu3d s3bD+LO pu4d s pd s2 pud s3 pu2d s3bD+ pu3d $214,577,350,870.33

f pu s2 pd2 s3 pud2 s3bD+ pu2d2 s3bD+LO pu3d2 f pu s2 pd2 s3 pud2 s3bD+ pu2d2 $138,711,641,076.46

f pd sf pu2 s3 pd3 s3bD+ pud3 s3bD+LO pu2d3 f pd sf pu2 s3 pd3 s3bD+ pud3 $88,554,148,928.69

sf pupd s2f pu3 s3bD+ pd4 s3bD+LO pud4 sf pupd s2f pu3 s3bD+ pd4 $55,393,264,711.18

sf pd2 s2f pu2d s3bD+LO pd5 sf pd2 s2f pu2d

$33,469,436,485.34

s2f pud2 s3bD+SO pu5 s2f pud2

$315,374,797,066.39

s2f pd3 s3bD+SO pu4d s2f pd3 $200,624,125,211.19

s3bD+SO pu3d2 $124,758,415,417.32

s3bD+SO pu2d3 $74,600,923,269.55

s3bD+SO pud4 $41,440,039,052.05

s3bD+SO pd5 $19,516,210,826.21

s3bD- pu4 s3bD-LO pu5 s3bD- pu4 $329,328,022,725.52

s3bD- pu3d s3bD-LO pu4d s3bD- pu3d $214,577,350,870.33

s3bD- pu2d2 s3bD-LO pu3d2 s3bD- pu2d2 $138,711,641,076.46

s3bD- pud3 s3bD-LO pu2d3 s3bD- pud3 $88,554,148,928.69

s3bD- pd4 s3bD-LO pud4 s3bD- pd4 $55,393,264,711.18

s3bD-LO pd5 $33,469,436,485.34

s3SO pu4 s3bD-SO pu5 $252,085,109,978.02 $315,374,797,066.39

s3SO pu3d s3bD-SO pu4d $158,781,084,504.21 $200,624,125,211.19

s3SO pu2d2 s3bD-SO pu3d2 $97,094,507,817.94 $124,758,415,417.32

s3SO pud3 s3bD-SO pu2d3 $56,311,339,846.92 $74,600,923,269.55

s3SO pd4 s3bD-SO pud4 $29,348,151,433.79 $41,440,039,052.05

s3S§ pu4 s3bD-SO pd5 $87,904,228,893.06 $19,516,210,826.21

s3S§ pu3d $56,802,887,068.46

s3S§ pu2d2 s3bD+L§ pu5 $36,240,694,839.70 $108,224,238,759.13

s3S§ pud3 s3bD+L§ pu4d $22,646,305,516.03 $69,974,014,807.39

s3S§ pd4 s3bD+L§ pu3d2 $13,658,576,044.98 $44,685,444,876.10

s3L pu4 s3bD+L§ pu2d3 $150,754,188,345.74 $27,966,280,826.85

s3L pu3d s3bD+L§ pud4 $97,881,907,243.91 $16,912,652,754.35

s3L pu2d2 s3bD+L§ pd5 $62,926,180,455.03 $9,604,710,012.40

s3L pud3 s3bD+S§ pu5 $39,815,718,604.78 $109,000,791,255.85

s3L pd4 s3bD+S§ pu4d $24,536,578,504.01 $70,750,567,304.12

s3bD+S§ pu3d2 $45,461,997,372.83

s3bD+S§ pu2d3 $28,742,833,323.57

s3bD+S§ pud4 $17,689,205,251.07

s3bD+S§ pd5 $10,381,262,509.12

s3bD-L§ pu5 $108,224,238,759.13

s3bD-L§ pu4d $69,974,014,807.39

s3bD-L§ pu3d2 $44,685,444,876.10

s3bD-L§ pu2d3 $27,966,280,826.85

s3bD-L§ pud4 $16,912,652,754.35

s3bD-L§ pd5 $9,604,710,012.40

s3bD-S§ pu5 $109,000,791,255.85

s3bD-S§ pu4d $70,750,567,304.12

s3bD-S§ pu3d2 $45,461,997,372.83

s3bD-S§ pu2d3 $28,742,833,323.57

s3bD-S§ pud4 $17,689,205,251.07

s3bD-S§ pd5 $10,381,262,509.12

Figure 50 Complete Case Quadranomial Event Tree

s – success

f – failure

b – buy info

S – set small

L – set Large












Set LP at Y3



Abandon

Continue


Page 139 of 159

Acquire Additional Imperfect Information

0 1 2 3 4 5

-$319,669,093.33 $2,986,877,211.99 $28,802,518,061.73 $120,658,373,604.81 $134,468,414,660.61 $329,328,022,725.52

$1,707,861,162.23 $18,315,800,025.07 $77,667,804,721.61 $86,936,175,268.29 $214,577,350,870.33

-$532,693,939.11 $11,382,661,469.99 $49,245,225,837.88 $55,510,938,088.49 $138,711,641,076.46

-$532,693,939.11 -$394,174,757.28 $30,454,058,114.62 $34,734,607,235.33 $88,554,148,928.69

-$394,174,757.28 -$200,000,000.00 $20,998,643,326.76 $55,393,264,711.18

-$394,174,757.28 -$200,000,000.00

$33,469,436,485.34

-$200,000,000.00

$315,374,797,066.39

-$200,000,000.00

$200,624,125,211.19

PV -$319,669,093.33

$124,758,415,417.32 2D Seismic Survey $50,000,000.00

$74,600,923,269.55

NPV -$369,669,093.33

$41,440,039,052.05

$19,516,210,826.21

$167,172,545,909.71 $329,328,022,725.52

$108,278,515,646.10 $214,577,350,870.33

$69,341,598,446.97 $138,711,641,076.46

$43,599,031,429.80 $88,554,148,928.69

$26,579,713,920.80 $55,393,264,711.18

$33,469,436,485.34

$315,374,797,066.39

$200,624,125,211.19

$124,758,415,417.32

$74,600,923,269.55

$41,440,039,052.05

$19,516,210,826.21

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

Figure 51 Acquiring Additional Imperfect Information NPV (Quadranomial)

Page 140 of 159

Install Large Platform at Year Three

0 1 2 3 4

-$216,443,139.20 $3,128,236,801.27 $29,168,009,247.91 $121,656,560,010.68 $150,754,188,345.74

$1,849,220,751.50 $18,681,291,211.25 $78,665,991,127.49 $97,881,907,243.91

-$429,008,389.10 $11,748,152,656.17 $50,243,412,243.75 $62,926,180,455.03

-$429,008,389.10 -$287,378,640.78 $31,452,244,520.50 $39,815,718,604.78

-$287,378,640.78 -$90,000,000.00 $24,536,578,504.01

-$287,378,640.78 -$90,000,000.00

-$90,000,000.00

-$90,000,000.00

PV -$216,443,139.20


NPV -$266,443,139.20

Figure 52 NPV for Setting a Large Platform at Year Three (Quadranomial)

Install Small Platform at Year Three

0 1 2 3 4

-$205,437,406.50 $2,933,271,088.63 $27,672,448,571.24 $116,455,301,687.43 $252,085,109,978.02

$1,654,255,038.86 $17,185,730,534.57 $73,464,732,804.24 $158,781,084,504.21

-$402,144,405.69 $10,252,591,979.50 $45,042,153,920.50 $97,094,507,817.94

-$402,144,405.69 -$259,708,737.86 $26,250,986,197.25 $56,311,339,846.92

-$259,708,737.86 -$61,500,000.00 $29,348,151,433.79

-$259,708,737.86 -$61,500,000.00 $87,904,228,893.06

-$61,500,000.00 $56,802,887,068.46

-$61,500,000.00 $36,240,694,839.70

PV -$205,437,406.50 $22,646,305,516.03

2D Seismic Survey $50,000,000.00 $13,658,576,044.98

NPV -$255,437,406.50

Figure 53 NPV for Setting a Small Platform at Year Three (Quadranomial)

Page 141 of 159

Appendix V – Complete Case Real Option Analysis

Hexanomial Tree Real Options Analysis

0 1 2 3 4 5

$153,633,477.86 $2,853,715,876.74 $26,607,058,130.08 $123,091,949,258.90 $108,336,794,136.53 $234,491,395,523.84

$2,241,179,567.86 $20,844,248,784.85 $95,003,555,266.30 $83,351,738,141.75 $176,717,322,701.87

$1,745,207,183.09 $16,262,649,652.37 $73,009,495,291.50 $63,787,433,834.50 $132,749,325,569.35

$0.00 $12,621,750,801.52 $55,890,468,501.64 $48,559,339,185.56 $99,274,090,372.08

$0.00 $9,728,232,832.83 $42,559,213,540.84 $36,700,372,994.72 $73,773,515,156.90

$0.00 $0.00 $32,171,562,553.71 $27,459,687,454.52 $54,334,704,386.16

$0.00 $24,117,928,105.74 $20,295,087,409.16 $39,504,922,909.92

$0.00 $0.00

$220,538,169,864.71

$0.00 $0.00

$162,764,097,042.73

$0.00 $0.00

$118,796,099,910.22

$0.00

$85,320,864,712.95

Y0 to Y3 legend:

$0.00

$59,820,289,497.77

Buy info

$0.00

$40,381,478,727.03

Set LP

$0.00

$25,551,697,250.78

Set SP

$134,794,596,339.96 $234,491,395,523.84

Abandon

$103,837,278,470.92 $176,717,322,701.87

Continue

$79,596,452,776.86 $132,749,325,569.35

$60,728,335,503.67 $99,274,090,372.08

$46,034,680,782.84 $73,773,515,156.90

$34,585,163,132.95 $54,334,704,386.16

PV $153,633,477.86

$25,707,984,668.56 $39,504,922,909.92


$220,538,169,864.71

NPV $103,633,477.86

$223,115,556,481.47 $162,764,097,042.73

$164,725,249,455.78 $118,796,099,910.22

$120,288,886,563.81 $85,320,864,712.95

$86,457,695,965.93 $59,820,289,497.77

$60,686,575,203.53 $40,381,478,727.03

$41,042,090,221.21 $25,551,697,250.78

$26,055,896,158.68

$78,247,711,060.88 $76,612,029,691.90

$58,784,275,385.65 $57,354,005,417.91

$43,972,154,421.66 $42,698,006,373.74

$32,695,090,889.03 $31,539,594,641.31

$24,104,717,301.56 $23,039,402,902.92

$17,556,555,640.79 $16,559,799,312.67

$12,561,157,619.95 $11,616,538,820.59

$77,388,582,188.62

$134,338,108,031.03 $58,130,557,914.63

$101,250,267,383.14 $43,474,558,870.46

$76,069,661,744.36 $32,316,147,138.04

$56,898,653,738.89 $23,815,955,399.64

$42,295,018,640.20 $17,336,351,809.40

$31,163,143,816.88 $12,393,091,317.31

$22,670,967,181.45 $76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31

Figure 54 Hexanomial Tree Real Options Analysis

Page 142 of 159

Quadranomial Tree Real Options Analysis

0 1 2 3 4 5

$187,636,791.10 $3,374,301,463.35 $29,229,174,296.46 $121,656,560,010.68 $134,468,414,660.61 $329,328,022,725.52

$2,095,285,413.58 $18,742,456,259.79 $78,665,991,127.49 $86,936,175,268.29 $214,577,350,870.33

$0.00 $11,809,317,704.72 $50,243,412,243.75 $55,510,938,088.49 $138,711,641,076.46

$0.00 $0.00 $31,452,244,520.50 $34,734,607,235.33 $88,554,148,928.69

$0.00 $0.00 $20,998,643,326.76 $55,393,264,711.18

$0.00 $0.00

$33,469,436,485.34

$0.00

$315,374,797,066.39

$0.00

$200,624,125,211.19

$124,758,415,417.32

Y0 to Y3 legend:

$74,600,923,269.55

Buy info

$41,440,039,052.05

Set LP

$19,516,210,826.21

Set SP

$167,172,545,909.71 $329,328,022,725.52

Abandon

$108,278,515,646.10 $214,577,350,870.33

Continue

$69,341,598,446.97 $138,711,641,076.46

$43,599,031,429.80 $88,554,148,928.69

$26,579,713,920.80 $55,393,264,711.18

$33,469,436,485.34

$252,085,109,978.02 $315,374,797,066.39

$158,781,084,504.21 $200,624,125,211.19

PV $187,636,791.10

$97,094,507,817.94 $124,758,415,417.32


$56,311,339,846.92 $74,600,923,269.55

NPV $137,636,791.10

$29,348,151,433.79 $41,440,039,052.05

$87,904,228,893.06 $19,516,210,826.21

$56,802,887,068.46

$36,240,694,839.70 $108,224,238,759.13

$22,646,305,516.03 $69,974,014,807.39

$13,658,576,044.98 $44,685,444,876.10

$150,754,188,345.74 $27,966,280,826.85

$97,881,907,243.91 $16,912,652,754.35

$62,926,180,455.03 $9,604,710,012.40

$39,815,718,604.78 $109,000,791,255.85

$24,536,578,504.01 $70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

Figure 55 Quadranomial Tree Real Options Analysis

Page 143 of 159

Appendix W – Effects of Varying Project Volatility

Trinomial Binomial Difference

Buy additional information -$407,782,210.39 -$369,669,093.33 $38,113,117.06

Set Large, no 2nd Drill -$298,752,436.09 -$266,443,139.20 $32,309,296.89

Set Small, no 2nd Drill -$287,746,703.38 -$255,437,406.50 $32,309,296.89

Best option -$287,746,703.38 -$255,437,406.50 $32,309,296.89

ROA $105,327,494.21 $137,636,791.10 $32,309,296.89

ROA Added Value $393,074,197.60 $393,074,197.60

Table 95 Project Results with Oil Price Standard Deviation at Ten Percent





Best option -$289,296,453.20 -$255,437,406.50 $33,859,046.71

ROA $103,777,744.39 $137,636,791.10 $33,859,046.71

ROA Added Value $393,074,197.60 $393,074,197.60

Table 96 Project Results with Oil Price Standard Deviation at Twenty Percent





Best option -$299,887,056.50 -$256,002,808.17 $43,884,248.34

ROA $93,359,089.53 $137,636,791.10 $44,277,701.57

ROA Added Value $393,246,146.03 $393,639,599.27

Table 97 Project Results with Oil Price Standard Deviation at Fifty Percent

Page 144 of 159

Appendix X – Real Options Analysis at the Absolute Certainty Level

0 1 2 3 4 5

$153,636,052.75 $2,853,715,876.74 $26,607,058,130.08 $123,091,949,258.90 $214,923,940,156.03 $234,491,395,523.84

$2,241,179,567.86 $20,844,248,784.85 $95,003,555,266.30 $165,879,200,610.71 $176,717,322,701.87

$1,745,434,508.98 $16,262,649,652.37 $73,009,495,291.50 $127,475,195,859.44 $132,749,325,569.35

$0.00 $12,621,750,801.52 $55,890,468,501.64 $97,583,010,067.08 $99,274,090,372.08

$0.00 $9,740,295,643.19 $42,559,213,540.84 $74,304,298,655.43 $73,773,515,156.90

$0.00 $0.00 $32,171,562,553.71 $56,165,175,187.63 $54,334,704,386.16

$0.00 $24,537,461,360.40 $42,101,330,654.16 $39,504,922,909.92

$0.00 $0.00

$220,538,169,864.71

$0.00 $0.00

$162,764,097,042.73

$0.00 $0.00

$118,796,099,910.22

$0.00

$85,320,864,712.95

Y0 to Y3 legend:

$0.00

$59,820,289,497.77

Buy info

$0.00

$40,381,478,727.03

Set LP

$0.00

$25,551,697,250.78

Set SP

$70,888,676,182.12 $234,491,395,523.84

Abandon

$54,540,429,667.01 $176,717,322,701.87

Continue

$41,739,094,749.92 $132,749,325,569.35

$31,775,032,819.13 $99,274,090,372.08

$24,015,462,348.58 $73,773,515,156.90

$17,969,087,859.32 $54,334,704,386.16

PV $153,636,052.75

$13,281,139,681.49 $39,504,922,909.92


$220,538,169,864.71

NPV $103,636,052.75

$223,115,556,481.47 $162,764,097,042.73

$164,725,249,455.78 $118,796,099,910.22

$120,288,886,563.81 $85,320,864,712.95

$86,457,695,965.93 $59,820,289,497.77

$60,686,575,203.53 $40,381,478,727.03

$41,042,090,221.21 $25,551,697,250.78

$26,055,896,158.68

$78,247,711,060.88 $76,612,029,691.90

$58,784,275,385.65 $57,354,005,417.91

$43,972,154,421.66 $42,698,006,373.74

$32,695,090,889.03 $31,539,594,641.31

$24,104,717,301.56 $23,039,402,902.92

$17,556,555,640.79 $16,559,799,312.67

$12,561,157,619.95 $11,616,538,820.59

$77,388,582,188.62

$134,338,108,031.03 $58,130,557,914.63

$101,250,267,383.14 $43,474,558,870.46

$76,069,661,744.36 $32,316,147,138.04

$56,898,653,738.89 $23,815,955,399.64

$42,295,018,640.20 $17,336,351,809.40

$31,163,143,816.88 $12,393,091,317.31

$22,670,967,181.45 $76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31


Page 145 of 159

0 1 2 3 4 5

$187,636,791.10 $3,374,301,463.35 $29,229,174,296.46 $121,656,560,010.68 $266,219,343,407.00 $329,328,022,725.52

$2,095,285,413.58 $18,742,456,259.79 $78,665,991,127.49 $172,915,317,933.18 $214,577,350,870.33

$0.00 $11,809,317,704.72 $50,243,412,243.75 $111,228,741,246.91 $138,711,641,076.46

$0.00 $0.00 $31,452,244,520.50 $70,445,573,275.89 $88,554,148,928.69

$0.00 $0.00 $43,482,384,862.77 $55,393,264,711.18

$0.00 $0.00

$33,469,436,485.34

$0.00

$315,374,797,066.39

$0.00

$200,624,125,211.19

$124,758,415,417.32

Y0 to Y3 legend:

$74,600,923,269.55

Buy info

$41,440,039,052.05

Set LP

$19,516,210,826.21

Set SP

$87,987,143,932.44 $329,328,022,725.52

Abandon

$56,885,802,107.83 $214,577,350,870.33

Continue

$36,323,609,879.08 $138,711,641,076.46

$22,729,220,555.40 $88,554,148,928.69

$13,741,491,084.36 $55,393,264,711.18

$33,469,436,485.34

$252,085,109,978.02 $315,374,797,066.39

$158,781,084,504.21 $200,624,125,211.19

PV $187,636,791.10

$97,094,507,817.94 $124,758,415,417.32


$56,311,339,846.92 $74,600,923,269.55

NPV $137,636,791.10

$29,348,151,433.79 $41,440,039,052.05

$87,904,228,893.06 $19,516,210,826.21

$56,802,887,068.46

$36,240,694,839.70 $108,224,238,759.13

$22,646,305,516.03 $69,974,014,807.39

$13,658,576,044.98 $44,685,444,876.10

$150,754,188,345.74 $27,966,280,826.85

$97,881,907,243.91 $16,912,652,754.35

$62,926,180,455.03 $9,604,710,012.40

$39,815,718,604.78 $109,000,791,255.85

$24,536,578,504.01 $70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12


Page 146 of 159


Trinomial Binomial




Best option -$289,440,719.74 -$255,437,406.50

ROA $103,636,052.75 $137,636,791.10

ROA Added Value $393,076,772.49 $393,074,197.60


Page 147 of 159

Appendix Y – Real Options Analysis with DW2 Having a Cost of $50 Million

0 1 2 3 4 5

$153,633,820.86 $2,853,715,876.74 $26,607,058,130.08 $123,091,949,258.90 $108,336,794,136.53 $234,491,395,523.84

$2,241,179,567.86 $20,844,248,784.85 $95,003,555,266.30 $83,351,738,141.75 $176,717,322,701.87

$1,745,237,464.77 $16,262,649,652.37 $73,009,495,291.50 $63,787,433,834.50 $132,749,325,569.35

$0.00 $12,621,750,801.52 $55,890,468,501.64 $48,559,339,185.56 $99,274,090,372.08

$0.00 $9,729,839,698.75 $42,559,213,540.84 $36,700,372,994.72 $73,773,515,156.90

$0.00 $0.00 $32,171,562,553.71 $27,459,687,454.52 $54,334,704,386.16

$0.00 $24,173,813,398.42 $20,295,087,409.16 $39,504,922,909.92

$0.00 $0.00 $220,538,169,864.71

$0.00 $0.00 $162,764,097,042.73

$0.00 $0.00 $118,796,099,910.22

$0.00 $85,320,864,712.95

Y0 to Y3 legend: $0.00 $59,820,289,497.77

Buy info $0.00 $40,381,478,727.03

Set LP $0.00 $25,551,697,250.78

Set SP $134,794,596,339.96 $234,491,395,523.84

Abandon $103,837,278,470.92 $176,717,322,701.87

Continue $79,596,452,776.86 $132,749,325,569.35

$60,728,335,503.67 $99,274,090,372.08

$46,034,680,782.84 $73,773,515,156.90

$34,585,163,132.95 $54,334,704,386.16

PV $153,633,820.86 $25,707,984,668.56 $39,504,922,909.92

2D Seismic Survey $50,000,000.00 $220,538,169,864.71

NPV $103,633,820.86 $223,115,556,481.47 $162,764,097,042.73

$164,725,249,455.78 $118,796,099,910.22

$120,288,886,563.81 $85,320,864,712.95

$86,457,695,965.93 $59,820,289,497.77

$60,686,575,203.53 $40,381,478,727.03

$41,042,090,221.21 $25,551,697,250.78

$26,055,896,158.68

$78,247,711,060.88 $76,612,029,691.90

$58,784,275,385.65 $57,354,005,417.91

$43,972,154,421.66 $42,698,006,373.74

$32,695,090,889.03 $31,539,594,641.31

$24,104,717,301.56 $23,039,402,902.92

$17,556,555,640.79 $16,559,799,312.67

$12,561,157,619.95 $11,616,538,820.59

$77,388,582,188.62

$134,338,108,031.03 $58,130,557,914.63

$101,250,267,383.14 $43,474,558,870.46

$76,069,661,744.36 $32,316,147,138.04

$56,898,653,738.89 $23,815,955,399.64

$42,295,018,640.20 $17,336,351,809.40

$31,163,143,816.88 $12,393,091,317.31

$22,670,967,181.45 $76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31


Page 148 of 159

0 1 2 3 4 5

$187,636,791.10 $3,374,301,463.35 $29,229,174,296.46 $121,656,560,010.68 $134,468,414,660.61 $329,328,022,725.52

$2,095,285,413.58 $18,742,456,259.79 $78,665,991,127.49 $86,936,175,268.29 $214,577,350,870.33

$0.00 $11,809,317,704.72 $50,243,412,243.75 $55,510,938,088.49 $138,711,641,076.46

$0.00 $0.00 $31,452,244,520.50 $34,734,607,235.33 $88,554,148,928.69

$0.00 $0.00 $20,998,643,326.76 $55,393,264,711.18

$0.00 $0.00 $33,469,436,485.34

$0.00 $315,374,797,066.39

$0.00 $200,624,125,211.19

$124,758,415,417.32

Y0 to Y3 legend: $74,600,923,269.55

Buy info $41,440,039,052.05

Set LP $19,516,210,826.21

Set SP $167,172,545,909.71 $329,328,022,725.52

Abandon $108,278,515,646.10 $214,577,350,870.33

Continue $69,341,598,446.97 $138,711,641,076.46

$43,599,031,429.80 $88,554,148,928.69

$26,579,713,920.80 $55,393,264,711.18

$33,469,436,485.34

$252,085,109,978.02 $315,374,797,066.39

$158,781,084,504.21 $200,624,125,211.19

PV $187,636,791.10 $97,094,507,817.94 $124,758,415,417.32

2D Seismic Survey $50,000,000.00 $56,311,339,846.92 $74,600,923,269.55

NPV $137,636,791.10 $29,348,151,433.79 $41,440,039,052.05

$87,904,228,893.06 $19,516,210,826.21

$56,802,887,068.46

$36,240,694,839.70 $108,224,238,759.13

$22,646,305,516.03 $69,974,014,807.39

$13,658,576,044.98 $44,685,444,876.10

$150,754,188,345.74 $27,966,280,826.85

$97,881,907,243.91 $16,912,652,754.35

$62,926,180,455.03 $9,604,710,012.40

$39,815,718,604.78 $109,000,791,255.85

$24,536,578,504.01 $70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12


Page 149 of 159


Trinomial Binomial




Best option -$272,411,450.11 -$232,397,844.43

ROA $103,633,820.86 $137,636,791.10

ROA Added Value $376,045,270.97 $370,034,635.53


Page 150 of 159

Appendix Z – Effects of Changes to the Initial Probabilities of the Site’s Quantity of Oil

Initial Probability of Large Quantity of Oil is Forty Percent

0 1 2 3 4 5

$163,402,679.28 $3,032,347,767.46 $28,185,519,217.51 $130,338,060,738.22 $114,643,725,853.66 $234,491,395,523.84

$2,383,779,911.00 $22,083,721,087.26 $100,597,408,275.46 $88,235,019,944.64 $176,717,322,701.87

$1,858,654,845.23 $17,232,616,123.46 $77,309,580,066.84 $67,555,940,463.19 $132,749,325,569.35

$0.00 $13,377,546,751.97 $59,183,551,701.11 $51,460,148,113.46 $99,274,090,372.08

$0.00 $10,314,998,015.41 $45,068,105,272.04 $38,925,457,353.34 $73,773,515,156.90

$0.00 $0.00 $34,069,415,991.54 $29,158,237,024.53 $54,334,704,386.16

$0.00 $25,582,944,483.48 $21,585,397,660.35 $39,504,922,909.92

$0.00 $0.00 $220,538,169,864.71

$0.00 $0.00 $162,764,097,042.73

$0.00 $0.00 $118,796,099,910.22

$0.00 $85,320,864,712.95

Y0 to Y3 legend: $0.00 $59,820,289,497.77

Buy info $0.00 $40,381,478,727.03

Set LP $0.00 $25,551,697,250.78

Set SP $142,499,340,937.66 $234,491,395,523.84

Abandon $109,802,847,907.44 $176,717,322,701.87

Continue $84,200,178,073.26 $132,749,325,569.35

$64,272,054,211.69 $99,274,090,372.08

$48,752,913,270.59 $73,773,515,156.90

$36,660,164,292.05 $54,334,704,386.16

PV $163,402,679.28 $27,284,267,936.41 $39,504,922,909.92

2D Seismic Survey $50,000,000.00 $220,538,169,864.71

NPV $113,402,679.28 $223,115,556,481.47 $162,764,097,042.73

$164,725,249,455.78 $118,796,099,910.22

$120,288,886,563.81 $85,320,864,712.95

$86,457,695,965.93 $59,820,289,497.77

$60,686,575,203.53 $40,381,478,727.03

$41,042,090,221.21 $25,551,697,250.78

$26,055,896,158.68

$78,247,711,060.88 $76,612,029,691.90

$58,784,275,385.65 $57,354,005,417.91

$43,972,154,421.66 $42,698,006,373.74

$32,695,090,889.03 $31,539,594,641.31

$24,104,717,301.56 $23,039,402,902.92

$17,556,555,640.79 $16,559,799,312.67

$12,561,157,619.95 $11,616,538,820.59

$77,388,582,188.62

$142,240,467,577.92 $58,130,557,914.63

$107,206,283,362.51 $43,474,558,870.46

$80,544,465,627.33 $32,316,147,138.04

$60,245,751,268.60 $23,815,955,399.64

$44,783,078,811.16 $17,336,351,809.40

$32,996,387,821.77 $12,393,091,317.31

$24,004,671,384.25 $76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31

Figure 60 Hexanomial Tree Real Options Analysis (initial large oil probability at 40%)

Page 151 of 159

0 1 2 3 4 5

$199,405,936.35 $3,583,556,035.63 $30,961,877,511.31 $128,818,236,828.34 $142,264,327,604.18 $329,328,022,725.52

$2,229,303,747.64 $19,858,293,707.79 $83,298,810,952.01 $92,023,698,502.90 $214,577,350,870.33

$0.00 $12,517,323,473.00 $53,204,315,663.35 $58,807,849,517.98 $138,711,641,076.46

$0.00 $0.00 $33,307,785,132.85 $36,847,682,148.97 $88,554,148,928.69

$0.00 $0.00 $22,329,042,234.21 $55,393,264,711.18

$0.00 $0.00 $33,469,436,485.34

$0.00 $315,374,797,066.39

$0.00 $200,624,125,211.19

$124,758,415,417.32

Y0 to Y3 legend: $74,600,923,269.55

Buy info $41,440,039,052.05

Set LP $19,516,210,826.21

Set SP $176,696,276,438.30 $329,328,022,725.52

Abandon $114,493,592,789.09 $214,577,350,870.33

Continue $73,369,208,331.58 $138,711,641,076.46

$46,180,429,684.23 $88,554,148,928.69

$28,204,970,742.15 $55,393,264,711.18

$33,469,436,485.34

$252,085,109,978.02 $315,374,797,066.39

$158,781,084,504.21 $200,624,125,211.19

PV $199,405,936.35 $97,094,507,817.94 $124,758,415,417.32

2D Seismic Survey $50,000,000.00 $56,311,339,846.92 $74,600,923,269.55

NPV $149,405,936.35 $29,348,151,433.79 $41,440,039,052.05

$87,904,228,893.06 $19,516,210,826.21

$56,802,887,068.46

$36,240,694,839.70 $108,224,238,759.13

$22,646,305,516.03 $69,974,014,807.39

$13,658,576,044.98 $44,685,444,876.10

$159,622,199,675.85 $27,966,280,826.85

$103,639,784,391.56 $16,912,652,754.35

$66,627,838,379.80 $9,604,710,012.40

$42,157,937,597.19 $109,000,791,255.85

$25,980,024,549.32 $70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

Figure 61 Quadranomial Tree Real Options Analysis (initial large oil probability at 40%)

Page 152 of 159

Initial Probability of Large Quantity of Oil is Seventy Percent

0 1 2 3 4 5

$222,034,607.98 $4,104,139,111.77 $37,656,285,742.06 $173,814,729,614.10 $158,243,819,028.61 $234,491,395,523.84

$3,239,481,114.67 $29,520,554,901.73 $134,160,526,330.42 $121,993,359,364.67 $176,717,322,701.87

$2,540,420,390.87 $23,052,414,950.00 $103,110,088,718.93 $93,607,790,635.48 $132,749,325,569.35

$0.00 $17,916,407,222.83 $78,942,050,897.96 $71,513,566,354.17 $99,274,090,372.08

$0.00 $13,872,039,075.61 $60,121,455,659.19 $54,307,562,267.29 $73,773,515,156.90

$0.00 $0.00 $45,564,913,591.57 $40,900,384,051.96 $54,334,704,386.16

$0.00 $34,937,730,993.86 $30,505,368,527.22 $39,504,922,909.92

$0.00 $0.00 $220,538,169,864.71

$0.00 $0.00 $162,764,097,042.73

$0.00 $0.00 $118,796,099,910.22

$0.00 $85,320,864,712.95

Y0 to Y3 legend: $0.00 $59,820,289,497.77

Buy info $0.00 $40,381,478,727.03

Set LP $0.00 $25,551,697,250.78

Set SP $182,735,229,392.31 $234,491,395,523.84

Abandon $140,956,377,187.04 $176,717,322,701.87

Continue $108,241,854,621.14 $132,749,325,569.35

$82,778,140,798.02 $99,274,090,372.08

$62,948,127,373.28 $73,773,515,156.90

$47,496,281,456.26 $54,334,704,386.16

PV $222,034,607.98 $35,515,969,446.27 $39,504,922,909.92

2D Seismic Survey $50,000,000.00 $220,538,169,864.71

NPV $172,034,607.98 $223,115,556,481.47 $162,764,097,042.73

$164,725,249,455.78 $118,796,099,910.22

$120,288,886,563.81 $85,320,864,712.95

$86,457,695,965.93 $59,820,289,497.77

$60,686,575,203.53 $40,381,478,727.03

$41,042,090,221.21 $25,551,697,250.78

$26,055,896,158.68

$78,247,711,060.88 $76,612,029,691.90

$58,784,275,385.65 $57,354,005,417.91

$43,972,154,421.66 $42,698,006,373.74

$32,695,090,889.03 $31,539,594,641.31

$24,104,717,301.56 $23,039,402,902.92

$17,556,555,640.79 $16,559,799,312.67

$12,561,157,619.95 $11,616,538,820.59

$77,388,582,188.62

$189,654,624,859.26 $58,130,557,914.63

$142,942,379,238.71 $43,474,558,870.46

$107,393,288,925.13 $32,316,147,138.04

$80,328,336,446.83 $23,815,955,399.64

$59,711,439,836.91 $17,336,351,809.40

$43,995,851,851.05 $12,393,091,317.31

$32,006,896,601.03 $76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31


Page 153 of 159

0 1 2 3 4 5

$270,020,807.88 $4,839,083,469.33 $41,358,096,800.47 $171,788,297,734.25 $196,157,812,735.84 $329,328,022,725.52

$3,033,413,752.01 $26,553,318,395.76 $111,095,729,899.16 $127,193,967,820.41 $214,577,350,870.33

$0.00 $16,765,358,082.72 $70,969,736,180.94 $81,599,541,574.04 $138,711,641,076.46

$0.00 $0.00 $44,441,028,806.94 $51,455,460,899.81 $88,554,148,928.69

$0.00 $0.00 $31,526,147,724.89 $55,393,264,711.18

$0.00 $0.00 $33,469,436,485.34

$0.00 $315,374,797,066.39

$0.00 $200,624,125,211.19

$124,758,415,417.32

Y0 to Y3 legend: $74,600,923,269.55

Buy info $41,440,039,052.05

Set LP $19,516,210,826.21

Set SP $226,431,313,643.13 $329,328,022,725.52

Abandon $146,950,106,758.03 $214,577,350,870.33

Continue $94,402,282,173.43 $138,711,641,076.46

$59,661,065,012.93 $88,554,148,928.69

$36,692,423,031.38 $55,393,264,711.18

$33,469,436,485.34

$252,085,109,978.02 $315,374,797,066.39

$158,781,084,504.21 $200,624,125,211.19

PV $270,020,807.88 $97,094,507,817.94 $124,758,415,417.32

2D Seismic Survey $50,000,000.00 $56,311,339,846.92 $74,600,923,269.55

NPV $220,020,807.88 $29,348,151,433.79 $41,440,039,052.05

$87,904,228,893.06 $19,516,210,826.21

$56,802,887,068.46

$36,240,694,839.70 $108,224,238,759.13

$22,646,305,516.03 $69,974,014,807.39

$13,658,576,044.98 $44,685,444,876.10

$212,830,267,656.50 $27,966,280,826.85

$138,187,047,277.45 $16,912,652,754.35

$88,837,785,928.44 $9,604,710,012.40

$56,211,251,551.62 $109,000,791,255.85

$34,640,700,821.12 $70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12


Page 154 of 159

Initial Probability of Large Quantity of Oil is One Hundred Percent

0 1 2 3 4 5

$280,729,653.28 $5,175,930,456.08 $47,127,052,266.60 $217,291,398,489.97 $214,923,940,156.03 $234,491,395,523.84

$4,095,654,440.14 $36,957,388,716.20 $167,723,644,385.38 $165,879,200,610.71 $176,717,322,701.87

$3,225,869,744.33 $28,872,213,776.53 $128,910,597,371.02 $127,475,195,859.44 $132,749,325,569.35

$0.00 $22,474,719,111.41 $98,700,550,094.80 $97,583,010,067.08 $99,274,090,372.08

$0.00 $17,525,335,704.42 $75,174,806,046.34 $74,304,298,655.43 $73,773,515,156.90

$0.00 $0.00 $57,576,495,751.37 $56,165,175,187.63 $54,334,704,386.16

$0.00 $44,292,517,504.25 $42,101,330,654.16 $39,504,922,909.92

$0.00 $0.00 $220,538,169,864.71

$0.00 $0.00 $162,764,097,042.73

$0.00 $0.00 $118,796,099,910.22

$0.00 $85,320,864,712.95

Y0 to Y3 legend: $0.00 $59,820,289,497.77

Buy info $0.00 $40,381,478,727.03

Set LP $0.00 $25,551,697,250.78

Set SP $214,923,940,156.03 $234,491,395,523.84

Abandon $165,879,200,610.71 $176,717,322,701.87

Continue $127,475,195,859.44 $132,749,325,569.35

$97,583,010,067.08 $99,274,090,372.08

$74,304,298,655.43 $73,773,515,156.90

$56,165,175,187.63 $54,334,704,386.16

PV $280,729,653.28 $42,101,330,654.16 $39,504,922,909.92

2D Seismic Survey $50,000,000.00 $220,538,169,864.71

NPV $230,729,653.28 $223,115,556,481.47 $162,764,097,042.73

$164,725,249,455.78 $118,796,099,910.22

$120,288,886,563.81 $85,320,864,712.95

$86,457,695,965.93 $59,820,289,497.77

$60,686,575,203.53 $40,381,478,727.03

$41,042,090,221.21 $25,551,697,250.78

$26,055,896,158.68

$78,247,711,060.88 $76,612,029,691.90

$58,784,275,385.65 $57,354,005,417.91

$43,972,154,421.66 $42,698,006,373.74

$32,695,090,889.03 $31,539,594,641.31

$24,104,717,301.56 $23,039,402,902.92

$17,556,555,640.79 $16,559,799,312.67

$12,561,157,619.95 $11,616,538,820.59

$77,388,582,188.62

$237,068,782,140.60 $58,130,557,914.63

$178,678,475,114.91 $43,474,558,870.46

$134,242,112,222.94 $32,316,147,138.04

$100,410,921,625.06 $23,815,955,399.64

$74,639,800,862.67 $17,336,351,809.40

$54,995,315,880.34 $12,393,091,317.31

$40,009,121,817.81 $76,612,029,691.90

$57,354,005,417.91

$42,698,006,373.74

$31,539,594,641.31

$23,039,402,902.92

$16,559,799,312.67

$11,616,538,820.59

$77,388,582,188.62

$58,130,557,914.63

$43,474,558,870.46

$32,316,147,138.04

$23,815,955,399.64

$17,336,351,809.40

$12,393,091,317.31


Page 155 of 159

0 1 2 3 4 5

$340,825,175.47 $6,097,399,202.07 $51,773,462,409.68 $214,824,094,339.05 $266,219,343,407.00 $329,328,022,725.52

$3,840,312,055.42 $33,267,489,403.80 $138,958,384,545.18 $172,915,317,933.18 $214,577,350,870.33

$0.00 $21,032,539,012.49 $88,800,892,397.41 $111,228,741,246.91 $138,711,641,076.46

$0.00 $0.00 $55,640,008,179.91 $70,445,573,275.89 $88,554,148,928.69

$0.00 $0.00 $43,482,384,862.77 $55,393,264,711.18

$0.00 $0.00 $33,469,436,485.34

$0.00 $315,374,797,066.39

$0.00 $200,624,125,211.19

$124,758,415,417.32

Y0 to Y3 legend: $74,600,923,269.55

Buy info $41,440,039,052.05

Set LP $19,516,210,826.21

Set SP $266,219,343,407.00 $329,328,022,725.52

Abandon $172,915,317,933.18 $214,577,350,870.33

Continue $111,228,741,246.91 $138,711,641,076.46

$70,445,573,275.89 $88,554,148,928.69

$43,482,384,862.77 $55,393,264,711.18

$33,469,436,485.34

$252,085,109,978.02 $315,374,797,066.39

$158,781,084,504.21 $200,624,125,211.19

PV $340,825,175.47 $97,094,507,817.94 $124,758,415,417.32

2D Seismic Survey $50,000,000.00 $56,311,339,846.92 $74,600,923,269.55

NPV $290,825,175.47 $29,348,151,433.79 $41,440,039,052.05

$87,904,228,893.06 $19,516,210,826.21

$56,802,887,068.46

$36,240,694,839.70 $108,224,238,759.13

$22,646,305,516.03 $69,974,014,807.39

$13,658,576,044.98 $44,685,444,876.10

$266,038,335,637.15 $27,966,280,826.85

$172,734,310,163.34 $16,912,652,754.35

$111,047,733,477.07 $9,604,710,012.40

$70,264,565,506.05 $109,000,791,255.85

$43,301,377,092.92 $70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12

$108,224,238,759.13

$69,974,014,807.39

$44,685,444,876.10

$27,966,280,826.85

$16,912,652,754.35

$9,604,710,012.40

$109,000,791,255.85

$70,750,567,304.12

$45,461,997,372.83

$28,742,833,323.57

$17,689,205,251.07

$10,381,262,509.12


Page 156 of 159

Effect of Changes on Valuation Results


Trinomial Binomial




Best option -$285,634,181.10 -$249,630,672.96

ROA $113,402,679.28 $149,405,936.35

ROA Added Value $399,036,860.38 $399,036,609.32

Table 100 Best Option with Real Options Analysis (initial large oil probability at 40%)


Trinomial Binomial




Best option -$232,063,799.93 -$184,059,122.42

ROA $172,034,607.98 $220,020,807.88

ROA Added Value $404,098,407.91 $404,079,930.30



Trinomial Binomial




Best option -$173,450,097.78 -$113,444,250.89

ROA $230,729,653.28 $290,825,175.47

ROA Added Value $404,179,751.06 $404,269,426.35


Page 157 of 159

Appendix AA – Data for Initial Large Quantity of Oil Probability at Absolute Certainty Level

Effect of New information





State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 1.00 0.40 0.40 1.00

E2 0.00 0.60 0.00 0.00

Total 1.00 1.00 0.40 1.00


State of

Nature

Original

Probabilities

Conditional

Probabilities

Joint

Probabilities

Revised

Probabilities

E1 1.00 0.60 0.60 1.00

E2 0.00 0.40 0.00 0.00

Total 1.00 1.00 0.60 1.00


Joint Probabilities



Total 1.00


Page 158 of 159

Year Five to Year Four Quadranomial Tree Probabilities

Probability Y5 to Y4 – Buy Info, data says Large, do Large


Probability Small 0.00%

up risk-neutral prob. (pu) 0.5204

down risk-neutral prob. (pd) 0.4796

LOpu 0.5204

LOpd 0.4796

L§pu 0.0000

L§pd 0.0000

Table 107 Year Five to Year Four Probabilities if New Data Indicates Large Quantity

Probability Y5 to Y4 – Buy Info, data says

Small, do Large


Probability Small 0.00%



LOpu 0.5204

LOpd 0.4796

L§pu 0.0000

L§pd 0.0000

Table 108 Year Five to Year Four Probabilities if New Data Indicates Small Quantity

Year Four to Year Three Quadranomial Tree Probabilities

Probabilities Y4 to Y3 – Set Large

Quantity is fixed, and only price probability enters. Therefore, technological uncertainty assumes a probability of 1.



Table 109 Year Four to Year Three Set Large Platform Probabilities

Probabilities Y4 to Y3 – Buy Info

Data says Large 40.00%

Data says Small 60.00%



D+pu 0.2082

D+pd 0.1918

D-pu 0.3123

D-pd 0.2877

Table 110 Year Four to Year Three Acquire Additional Imperfect Information Probabilities

Page 159 of 159

Appendix BB – Trees for Each Option Value

0 1 2 3 4

-$224,447,071.99 $2,633,306,318.82 $26,565,262,013.58 $123,091,949,258.90 $223,115,556,481.47

$2,020,770,009.94 $20,802,452,668.34 $95,003,555,266.30 $164,725,249,455.78

$1,524,797,625.16 $16,220,853,535.87 $73,009,495,291.50 $120,288,886,563.81

-$402,144,405.69 $12,579,954,685.01 $55,890,468,501.64 $86,457,695,965.93

-$402,144,405.69 $9,686,436,716.33 $42,559,213,540.84 $60,686,575,203.53

-$402,144,405.69 -$259,708,737.86 $32,171,562,553.71 $41,042,090,221.21

-$259,708,737.86 $24,117,928,105.74 $26,055,896,158.68

-$259,708,737.86 -$61,500,000.00 $78,247,711,060.88

-$259,708,737.86 -$61,500,000.00 $58,784,275,385.65

-$259,708,737.86 -$61,500,000.00 $43,972,154,421.66

-$61,500,000.00 $32,695,090,889.03

PV -$224,447,071.99

-$61,500,000.00 $24,104,717,301.56


-$61,500,000.00 $17,556,555,640.79

NPV -$274,447,071.99

-$61,500,000.00 $12,561,157,619.95

Table 111 Tree with the Option to Set a Large Platform

0 1 2 3 4

$138,639,830.12 $2,633,095,059.94 $25,092,128,521.37 $117,890,690,935.65 $223,115,556,481.47

$2,020,558,751.06 $19,329,319,176.14 $89,802,296,943.05 $164,725,249,455.78

$1,524,586,366.28 $14,747,720,043.66 $67,808,236,968.25 $120,288,886,563.81

$0.00 $11,106,821,192.81 $50,689,210,178.39 $86,457,695,965.93

$0.00 $8,213,303,224.12 $37,357,955,217.59 $60,686,575,203.53

$0.00 $0.00 $26,970,304,230.46 $41,042,090,221.21

$0.00 $18,916,669,782.49 $26,055,896,158.68

$0.00 $0.00 $78,247,711,060.88

$0.00 $0.00 $58,784,275,385.65

$0.00 $0.00 $43,972,154,421.66

$0.00 $32,695,090,889.03

PV $138,639,830.12

$0.00 $24,104,717,301.56


$0.00 $17,556,555,640.79

NPV $88,639,830.12

$0.00 $12,561,157,619.95

Table 112 Tree with the Option to Abandon

0 1 2 3 4

-$232,976,579.97 $2,455,575,056.78 $25,081,287,676.98 $117,890,690,935.65 $223,115,556,481.47

$1,895,931,537.19 $19,513,906,209.79 $89,802,296,943.05 $164,725,249,455.78

$1,448,849,073.47 $15,376,063,988.90 $68,215,554,055.82 $120,288,886,563.81

-$402,144,405.69 $12,104,314,254.19 $53,104,245,989.13 $86,457,695,965.93

-$402,144,405.69 $9,456,815,192.25 $41,095,380,158.98 $60,686,575,203.53

-$402,144,405.69 -$259,708,737.86 $31,551,401,071.79 $41,042,090,221.21

-$259,708,737.86 $24,023,813,398.42 $26,055,896,158.68

-$259,708,737.86 -$61,500,000.00 $78,247,711,060.88

-$259,708,737.86 -$61,500,000.00 $58,784,275,385.65

-$259,708,737.86 -$61,500,000.00 $43,972,154,421.66

-$61,500,000.00 $32,695,090,889.03

PV -$232,976,579.97

-$61,500,000.00 $24,104,717,301.56


-$61,500,000.00 $17,556,555,640.79

NPV -$282,976,579.97

-$61,500,000.00 $12,561,157,619.95

Table 113 Tree with the Option to Acquire Additional Imperfect Information

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Field of study: Finance Dissertation for obtaining the ... · Title: Valuing an Offshore Exploration Project Through Real Options Analysis Field of study: Finance Purpose: Dissertation