Page 1
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
Page 2
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 3
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 4
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 5
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 6
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 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 8
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 56 Hexanomial Tree Real Options Analysis ........................................................ 144
Figure 57 Quadranomial Tree Real Options Analysis ..................................................... 145
Figure 58 Hexanomial Tree Real Options Analysis ........................................................ 147
Figure 59 Quadranomial Tree Real Options Analysis ..................................................... 148
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 63 Quadranomial Tree Real Options Analysis (initial large oil probability at 70%) . 153
Figure 64 Hexanomial Tree Real Options Analysis (initial large oil probability at 100%) .. 154
Figure 65 Quadranomial Tree Real Options Analysis (initial large oil probability at 70%) . 155
Page 9
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 10
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
Table 38 Buy Additional Information, Data Indicates Large Quantity, Large Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil ....................................... 74
Table 39 Buy Additional Information, Data Indicates Large Quantity, Small Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil ....................................... 75
Table 40 Buy Additional Information, Data Indicates Large Quantity, Small Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil ....................................... 76
Table 41 Buy Additional Information, Data Indicates Small Quantity, Large Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil ....................................... 77
Table 42 Buy Additional Information, Data Indicates Small Quantity, Large Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil ....................................... 78
Table 43 Buy Additional Information, Data Indicates Small Quantity, Small Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil ....................................... 79
Table 44 Buy Additional Information, Data Indicates Small Quantity, Small Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil ....................................... 80
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 11
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
Table 76 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set,
Quantity is Large – End Nodes NPV Estimates ............................................................... 109
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 ............................................................ 110
Table 78 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set,
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
Table 80 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set,
Quantity is Large – End Nodes NPV Estimates ............................................................... 113
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 ........................................................... 114
Table 82 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set,
Quantity is Small – End Nodes NPV Estimates ............................................................... 115
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
Table 84 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set,
Quantity is Large – End Nodes NPV Estimates ............................................................... 117
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 ............................................................. 118
Table 86 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set,
Quantity is Small – End Nodes NPV Estimates ............................................................... 119
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
Table 88 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set,
Quantity is Large – End Nodes NPV Estimates ............................................................... 121
Page 12
Page x
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 ............................................................ 122
Table 90 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set,
Quantity is Small – End Nodes NPV Estimates ............................................................... 123
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 13
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 14
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 15
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 16
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 17
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 18
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 19
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 20
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 21
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 22
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
Table 2 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil
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
Table 3 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil
2 All monetary values are in US Dollars.
Page 23
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 24
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%
Set Large Set Small Buy Additional Information
Page 25
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%
Set Large Set Small Buy Additional Information
$.M
$30.M
$60.M
$90.M
$120.M
1M 2M 3M 4M 5M 6M 7M 8M 9M 10.00
Set Large Set Small Buy Additional Information
Page 26
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 27
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 28
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 29
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 30
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 31
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 32
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 33
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 34
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 35
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 36
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 37
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
0446031109504501690668289012
031
2163057530808508180126.$
.
.$.$.$.$
.
.$.$.$ ×−×+×+×+×−×+×+×
171109031
044603110950460169066828909
031
2163063530809108180132.$
.
.$.$.$.$
.
.$.$.$ ×−×+×+×+×−×+×+×
Page 38
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 39
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
s C sb(D+) F sb(D+)LO K
$18,352,324.59 $46,188,176.77 $91,186,975.28
s D sb(D+) G sb(D+)LO L
$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 40
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 -$4,091,196.15
Figure 15 NPV for Setting a Large Platform at Year One
The last alternative is to set a SP, and following this path cell S B value is obtained by
multiplying cells sSO E, sSO F, sSO G, sS§ E, sS§ F, and sS§ G respectively by L(B)*pu,
L(B)*pm, L(B)*pd, S(B)*pu, S(B)*pm, and S(B)*pd probabilities, which are indicated in the
Probabilities Y1 to Y2 Set Small – To Point B section of the probabilities table:
4031
130501840930280802041080003025080460492069$
.
.$.$.$.$.$.$ −×+×+×+×+×+×
031
1167044667041167004050001020000180500029
.
.$.$..$.$.$.$ ×−×−×−×+×+×
9031
21053066010431294063$
.
$.$.$ −×+×+×
031
1167094667091167009050001120000200500032
.
.$.$..$.$.$.$ ×−×−×−×+×+×
6031
136802142910310841046073703723100580453087$
.
.$.$.$.$.$.$ −×+×+×+×+×+×
Page 41
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 42
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
s C sb(D+) F sb(D+)LO K
$20,603,916.20 $46,188,176.77 $91,186,975.28
s D sb(D+) G sb(D+)LO L
$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 43
Page 30 of 159
Figure 18 Real Options Analysis Process
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:
Page 44
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 45
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 46
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 47
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
RO
A A
dd
ed
Va
lue
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 48
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
RO
A A
dd
ed
Va
lue
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 49
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
RO
A A
dd
ed
Va
lue
Cost of Aquiring Additional Imperfect Information
Page 50
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
RO
A A
dd
ed
Va
lue
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
RO
A A
dd
ed
Va
lue
Initial Probability of the Site Having a Small Quantity of Oil
Page 51
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 52
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
RO
A A
dd
ed
Va
lue
Decline of Rate of Production
Page 53
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 54
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 55
Page 42 of 159
References
— Amram, M. and Kulatilaka, N. (1999), Real Options – Managing Strategic Investment in
an Uncertain World, Oxford University Press, USA.
— Armstrong, M., Galli, A., Bailey, W., and Couet, B. (2004), Incorporating technical
uncertainty in real option valuation of oil projects, Journal of Petroleum Science and
Engineering, no. 44, 67-82.
— Babajide, A. (2007), Real Options Analysis as a Decision Tool in Oilfields Developments,
Master Thesis, Massachusetts Institute of Technology, Boston, USA.
— Baker, H. K., Dutta, S., and Saadi, S. (2011), Management Views on Real Options in
Capital Budgeting, Journal of Applied Finance, no. 1.
— Benninga, S. and Tolkowsky, E. (2002), Real Options - An introduction and Application to
R&D Valuation, Volume 47, Number 2, The Engineering Economist.
— Bjerksund, P. and Ekern, S. (1990), Managing investment opportunities under price
uncertainty: from last chance to wait and see strategies, Financial Management 19 (3),
65– 83 (Autumn).
— Black, F. and Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, Journal
of Political Economy 81, May-June.
— Blanco, C., Choi, S., and Soronow, D. (2001), Energy Price Processes Used for Derivatives
Pricing & Risk Management, Three Articles Series, Energy Pricing, Financial Energy
Associates.
— Bodie, Z., Kane, A., and Marcus, A. (2011), Investments and Portfolio Management:
Global Edition, Ninth Edition, McGraw-Hill, New York, USA.
— Borison, A. (2005), Real Options Analysis: Where are the Emperor's Clothes?, Volume 12,
Number 2, Journal of Applied Corporate Finance.
— Brandão, L. E., Dyer, J. S. , and Hahn, W. J. (2005), Using Binomial Decision Trees to
Solve Real-Options Valuation Problems, Decision Analysis, Vol. 2, no. 2, 69-88.
— Brealey, R. A. and Myers, S. C. (1992), Principles of Corporate Finance, McGraw-Hill, New
York, USA.
— Bulmer, M. G. (1979), Principles of Statistics, Dover Publications, New York, USA.
— Burger-Helmchen, T. (2007), Justifying the Origin of Real Options and their Difficult
Evaluation in Strategic Management, October, Schmalenbach Business Review.
— Cheah, C.Y.J. and Liu, J. (2005), Real option evaluation of complex infrastructure
projects: the case of Dabhol power project in India. Journal of Financial Management of
Property and Construction, 10(1), 55–68.
— Chorn, L.G. and Croft, M. (2000), Resolving reservoir uncertainty to create value, Journal
of Petroleum Technology, 52– 59 (August).
Page 56
Page 43 of 159
— Clewlow, L. and Strickland, C. (2000), Energy Derivatives: Pricing and Risk Management,
Lacima Publications, London, UK.
— Clewlow, L., Strickland, C., and Kaminski, V., Making the most of mean reversion –
adapting and estimating a version of the mean-reversion model for energy markets,
Energy Pricing.
— Copeland, T and Tufano, P. (2004), A Real-World Way to Manage Real Options, March,
Harvard Business Review, Boston, USA.
— Copeland, T, and Antikarov, V. (2003), Real options: A Practitioner’s Guide, Texere, New
York, USA.
— Copeland, T., Koller, T., and Murrin, J. (1994), Valuation: Measuring and Managing the
Value of Companies, 2nd Edition, John Wiley and Sons, New York, USA.
— Cortazar, G. and Schwartz, E. (1998), Monte Carlo evaluation model of an undeveloped
oil field, Journal of Energy Finance and Development 3 (1), 73–84.
— Cortazar, G. and Schwartz, E. (2003), Implementing a stochastic model for oil futures
prices, Energy Economics, no. 25, 215-238.
— Cortazar, G., Schwartz, E., Casassus, J. (2001), Optimal exploration investments under
price and geological-technical uncertainty: a real options model, R&D Management, no.
31.
— Costa Lima, G. A. and Suslick, S. B. (2006), Estimation of Volatility of Selected Oil
Production Projects, Journal of Petroleum Science and Engineering, no. 54 129-139.
— Costa Lima, G. A., Suslick, S. B., and Bordieri, C. A. (2005) A quantitative method for
estimation of volatility of oil production projects, Society of Petroleum Engineers,
Hydrocarbon Economics and Evaluation Symposium, Dallas, U.S.A.
— Couet, W. B. B., Bhandari, A., Faiz, S., Srinivasan, S., and Weeds, H. (2003), Unlocking
the Value of Real Options, Oilfield Review.
— Cox, J. and Ross, S. (1976), The Valuation of Options for Alternative Stochastic
Processes, Journal of Financial Economics, no. 3, 145-166.
— Cox, J., Ross, S., and Rubinstein, M. (1979), Option Pricing: A Simplified Approach,
Journal of Financial Economics, North-Holland Publishing Company, Berkeley, USA.
— Denison, A. C., Farrel, A. M., and Jackson, K. E. (2012), Managers' Incorporation of the
Value of Real Options into Their Long-Term Investment Decisions: An Experimental
Investigation, Volume 29, Number 2, Contemporary Accounting Research, Canada.
— Dias, M. (1997), The timing of investment in E&P: uncertainty, irreversibility, learning,
and strategic consideration, Society of Petroleum paper no. 37949, pp. 135-148,
Proceedings of SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, USA.
— Dias, M. A. G. (2004), Valuation of exploration and production assets: an overview of real
options models, Journal of Petroleum Science and Engineering, no. 44, 93-114.
Page 57
Page 44 of 159
— Dinicã, M. (2011), The Real Options Attached to an Investment Project, Volume 14, Issue
2, Economia Seria Management.
— Dixit A.K. and Pindyck R.S. (1994), Investment under Uncertainty, Princeton University
Press, Princeton, NJ, USA.
— Dzyuma, U. (2012), Real Options Compared to Traditional Company Valuation Methods:
Possibilities and Constraints in their Use, Volume 8, Number 2, eFinance - Finance
Internet Quarterly, University of Information Technology and Management, Rzeszów,
Poland.
— Ekern, S. (1988), An option pricing approach to evaluating petroleum projects, Energy
Economics, 91–99 (April).
— Ford, D., Lander, D., and Voyer, J. (2002), A real option approach to valuing strategic
flexibility in uncertain construction projects. Construction Management and Economics,
20(4), 343–51
— Galli, A., Armstrong, M., and Jehl, B. (1999), Comparison of three methods for evaluating
oil projects, Journal of Petroleum Technology, 44– 49 (October).
— Gibson, R. and Schwartz, E. (1990), Stochastic Convenience Yield and the Pricing of Oil
Contingent Claims, The Journal of Finance, Vol. XLV, no. 3.
— Hahn, W. J. (2005), A Discrete-Time Approach for Valuing Real Options with Underlying
Mean-Reverting Stochastic Processes, Dissertation, University of Texas at Austin, USA.
— Hahn, W. J. and Dyer, J. S. (2011), A discrete time Approach for Modelling Two-factor
Mean Reverting Stochastic Processes, Decision Analyses, Vol. 8, No. 3, 220-232.
— Hayes, R. and Garvin, D. (1982), Managing as if Tomorrow Mattered, Harvard Business
Review 60, no. 3: 71-79.
— He, Y. (2007), Real Options in the Energy Markets – Dissertation, University of Twente.
— Hillier, D., Grinblatt, M. and Titman, S. (2011), Financial Markets and Corporate Strategy,
Second European Edition, McGraw-Hill Higher Education, London, UK.
— http://pt.wikipedia.org/wiki/Black-Scholes, 26/03/2014, 22:11.
— http://www.retailenergy.com/archives/shimko2.htm, 06/06/204, 19:50.
— Hull, J. and White, A. (1996), Using Hull-White Interest-Rate Trees, University of Toronto,
Canada.
— Hull, J. C. (2009), Options, Futures, and other derivatives, Seventh Edition, Pearson
International Edition, Pearson Prentice Hall, New Jersey, USA.
— Jiao, Y., Du, J., and Jiao, J. (2007), A financial model of flexible manufacturing systems
planning under uncertainty: identification, valuation and applications of real options,
Volume 45, Number 15, International Journal of Production Research, Vol. 45, No. 6,
March 2007.
Page 58
Page 45 of 159
— Karami, M. and Farsani, F. A. (2011), Real Option Method and Escalation of Commitment
in the Evaluation of Investment Projects, No. 3, American Journal of Economics and
Business Administration.
— Kenyon, C.M. and Tompaidis, S. (2001), Real options in leasing: the effect of idle time,
Operations Research 49 (5), 675–689.
— Kulatilaka, N. and Marcus, A. (1988), A General Formulation of Corporate Operating
Options, Research in Finance, Vol. 7, ed. Andrew Chen, JAI Press, (Spring 1988), 183-
199.
— Kulatilaka, N. and Marcus, A. (1992), Project Valuation under Uncertainty: When does
DCF Fail?, Journal of Applied Corporate Finance, Vol. 5 (Fall, 1992), pp. 92-100.
— Kvalevag, T. (2009), How do discounted cash flow analysis and real options differ as a
basis for decision making about oil and gas field developments?, Master Thesis,
Copenhagen Business School, Denmark.
— Lander, D.M. and Pinches, G.E. (1998), Challenges to practical implementation of
modelling and valuing real options, Quarterly Review of Economics and Finance, 38(4),
537–67.
— Laughton, D. (1998), The management of flexibility in the upstream petroleum industry,
Energy Journal 19 (1), 83– 114 (January).
— Laughton, D., Guerrero, R., and Lessard, D. (2008), Real Asset Valuation: A Back-to-
basics Approach, Volume 20, Number 2, Journal of Applied Corporate Finance.
— Leslie, K. J. and Michaels, M. P. (1997), The real power of real options, The Mckinsey
Quarterly, no. 3.
— Lund, M. W., Real Options in Offshore Oil Field Development Projects, Statoil, Stavanger,
Norway.
— Mason, S.P. and Merton, R.C. (1985), The Role of Contingent Claims Analysis in Corporate
Finance Recent Advances in Corporate Finance, Homewood, IL: Richard D. Irwin, pp.7-54.
— Mattar, M. H. and Cheah, C. Y. J. (2006), Valuing large engineering projects under
uncertainty: private risk effects and real options, Construction Management and
Economics, no. 24, 847-860.
— McCormack, J. and Sick, G. (2001), Valuing PUD reserves: a practical application of real
options techniques, Journal of Applied Corporate Finance 13 (4), 110– 115.
— Mello, A. S. and Triantis, A. (1992), An Integrated Model of Multinational Flexibility and
Financial Hedging, December, Banco de Portugal, WP 23-92, Lisbon, Portugal.
— Mello, S. and Pyo, U. (2003), Real Options with Market Risks and Private Risks, Journal of
Applied Corporate Finance, Vol. 15, no. 2, 89-101.
— Merton, R. C. (1973), Theory of Rational Option Pricing, Bell Journal of Economics and
Management Science 4, Spring.
Page 59
Page 46 of 159
— Morgan, D. G., Abdallah, S. B. and Lasserre, P. (2008), A Real Options Approach to
Forest-Management Decision Making to Protect Caribou under the Threat of Extinction,
Volume 13, Number 1, Ecology and Sociology.
— Mun, J. (2002), Real Options Analysis - Tools and Techniques for Valuing Strategic
Investments and Decisions, John Wiley & Sons, New Jersey, USA.
— Myers, S. C. (1977), Determinants of Corporate Borrowing, Journal of Financial Economy
no. 5: 147-175, North-Holland Publishing Company, Massachusetts, USA.
— Myers, S. C. (1987), Finance Theory and Financial Strategy, Midland Corporate Finance
Journal 5, no. 1: 6-13.
— Newbold, P., Carlson, W., and Thorne, B. (2013), Statistics for Business and Economics,
Eighth Edition, Pearson Education Limited, Essex, UK.
— Newendorp, P. and Schuyler, J. (2000), Decision Analysis for Petroleum Exploration,
Second Edition, Planning Press, Aurora, Colorado, USA.
— Owusu-Ansah, I. (2008), Financial decision making about found oil and gas in Ghana:
Real Options vs Traditional Methods, Master Thesis, Michigan Technological University.
— Paddock, J.L., Siegel, D.R. and Smith, J.L. (1988), Option valuation of claims on real
assets: the case of offshore petroleum leases, Quarterly Journal of Economics, 479– 508
(August).
— Pedersen, E. (2011), Evaluating the effect of the oil prices' uncertainty on the optimal
timing of transition from oil to gas production using Real Option techniques, Master
Thesis, Universitete i Stavanger, Norway.
— Pindyck, R.S. (1999), The long-run evolution of energy prices, Energy Journal 20 (2), 1–
27.
— Pires, D. D. G. (2010), Mathematical Methods in Finance: Real Options on Mean-Reverting
Cash Flow Processes, Instituti de Matemática Pura e Aplicada.
— Ross, S. A. (1978), A Simple Approach to the Valuation of Risky Income Streams, Journal
of Business, Vol. 51, No. 3, 1978, pp. 453-475.
— Ross, S. A. (1995), Uses, Abuses, and Alternatives to the Net-Present-Value Rule,
Financial Management, Vol. 24, No. 3, 1995, pp. 96-102.
— Roveanin, A. (2005), Investments as Real Options.
— Saito, R., de Castro, G. N., Mezzomo, C. and Schiozer, D. J. (2001), Value assessment for
reservoir recovery optimization, Journal of Petroleum Science and Engineering 32, 151–
158.
— Schwartz, E. (1997), The Stochastic Behaviour of Commodity Prices: Implications for
Valuation and Hedging, The Journal of Finance, Vol. 52, No. 3, American Finance
Association, USA.
Page 60
Page 47 of 159
— Schwartz, E. and Smith, J. E. (2000), Short-Term Variations and Long-Term Dynamics in
Commodity Prices, Management Science, Vol. 46, no. 7, 893-911.
— 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.
— Smith, J. E. and Mccardle, K. F. (1999), Options in the Real World: Lessons Learned in
Evaluating Oil and Gas Investments, Operations Research, Vol. 47, No. 1, January-
February.
— Song, S. R. (2006), Real Option Approach to R&D Project Valuation, Dissertation.
— Strata, S. R. (2002), Risk Neutral Valuation, Montgomery Investment Technology,
Philadelphia, USA.
— Svendsen, A. (2009), Real option valuation of expansion and abandonment options in
offshore petroleum production, Project Thesis, Norwegian University of Science and
Technology, Norway.
— Tabachnick, B. and Fidell, L. (2001), Using Multivariate Statistics, Fourth Edition, Allyn
and Bacon, Boston, USA.
— Tourinho, O.A.F. (1979), The Valuation of Reserves of Natural Resources: An Option
Pricing Approach. University of California, Berkeley, PhD Dissertation.
— Triantis, A. (2003), Real Options, Handbook of Modern Finance, Research Institute of
America, New York, USA.
— Triantis, A. (2005), Realizing the Potential of Real Options: Does Theory Meet Practice?,
Volume 17, Number 2, Journal of Applied Corporate Finance.
— Triantis, A. and Borison, A. (2001), Real Options: State of Practice, Journal of Applied
Corporate Finance, Vol. 14, no. 2, 8-24.
— Trigeorgis, L. (1997), Real Options - Managerial Flexibility and Strategy in Resource
Allocation, The MIT Press, London, England.
— Trigeorgis, L. and Mason, S. P. (1987), Valuing Managerial Flexibility, Midland Corporate
Finance Journal 5, 1 (Spring), pp. 14-21.
— Vasicek, O. (1977), An Equilibrium Characterization of the Term Structure, Journal of
Financial Economics No. 5, North-Holland Publishing Company, Berkeley, USA.
— Zeng, S. and Zhang, S. (2011), Real Options Literature Review, Number 3, Scientific
Research.
— Zettl, M. (2001), Valuing exploration and production projects by mean of option pricing
theory, International Journal of Production Economics, no. 78, 109-116.
Page 61
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 62
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 63
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 64
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 65
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 66
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 67
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 $1 if node (i, j) is reached and nothing
otherwise. Both quantities are calculated using forward induction to match futures prices.
)tjatja(p
tjatjap
)tjatja(p
d
m
u
∆∆
∆∆
∆∆
32
1
6
7
23
1
2
1
6
1
222
222
222
++=
−−−=
++=
)t(X)t(Sln)t( *−=α
Page 68
Page 55 of 159
Considering the displacement nodes at year one, the values of S are ���� �,�∗
, ���� �,#∗
, ���� �,$�∗
.
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 69
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.) $10.00
Page 70
Page 57 of 159
Appendix F – Simplified Case Price Uncertainty Project Data
The raw data set presented below is composed of monthly spot prices, from January 2009 to
December 2013. These prices are equally weighted crude oil spot price average of Brent,
Dubai, and West Texas Intermediate crude oil nominal prices, and presented in US dollars.
Year & Month ($/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 71
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 72
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 73
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 74
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 75
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 76
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
($/bbl.) Logarithmic
Return Year & Month
($/bbl.) Logarithmic
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 77
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 78
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 79
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 80
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 81
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 82
Page 69 of 159
Appendix G – Effect of New Information (Simplified
Case)
State of Nature Description
E1 Large quantity of oil
E2 Small quantity of oil
Table 29 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
Table 30 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil
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
Table 31 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil
Joint Probabilities
Table 30 result 0.38
Table 31 result 0.62
Total 1.00
Table 32 Joint Probabilities Addition
The effect of the new information to the technological uncertainty tree can be seen in Figure
35.
Page 83
Page 70 of 159
Figure 35 Effect of New Information to Technological Uncertainty Decision Tree (Simplified
Case)
Page 84
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 85
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
OPEX Small – Oil Platform 2 $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
Amount of Oil Present 250,000.00
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 86
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.
Table 37 Buy Additional Information, Data Indicates Large Quantity, Large Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil
It is Large
Amount of Oil Present 500,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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 87
Page 74 of 159
Table 38 Buy Additional Information, Data Indicates Large Quantity, Large Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil
It is Small
Amount of Oil Present 250,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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 88
Page 75 of 159
NPVs Buy Additional Information, Large Quantity is Indicated, and a Small 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 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.
Table 39 Buy Additional Information, Data Indicates Large Quantity, Small Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil
It is Large
Amount of Oil Present 500,000.00
OPEX Small – Oil Platform 1 $10.00 USD per barrel
OPEX Small – Oil Platform 2 $10.00 USD per barrel
Total OPEX $20.00 USD per barrel
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 89
Page 76 of 159
Table 40 Buy Additional Information, Data Indicates Large Quantity, Small Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil
It tis Small
Amount of Oil Present 250,000.00
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 90
Page 77 of 159
NPVs Buy Additional Information, Small 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 small quantity of oil. With this information management decides
to set a LP.
Table 41 Buy Additional Information, Data Indicates Small Quantity, Large Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil
It is Large
Amount of Oil Present 500,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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 91
Page 78 of 159
Table 42 Buy Additional Information, Data Indicates Small Quantity, Large Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil
It is Small
Amount of Oil Present 250,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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 92
Page 79 of 159
NPVs Buy Additional Information, Small Quantity is Indicated, and a Small 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 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.
Table 43 Buy Additional Information, Data Indicates Small Quantity, Small Platform is
Established – Free Cash Flow Estimates for Large Amount of Oil
It is Large
Amount of Oil Present 500,000.00
OPEX Small – Oil Platform 1 $10.00 USD per barrel
OPEX Small – Oil Platform 2 $10.00 USD per barrel
Total OPEX $20.00 USD per barrel
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 93
Page 80 of 159
Table 44 Buy Additional Information, Data Indicates Small Quantity, Small Platform is
Established – Free Cash Flow Estimates for Small Amount of Oil
It is Small
Amount of Oil Present 250,000.00
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 94
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
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
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
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
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 95
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
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
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 96
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
Probability Large 5.65%
Probability Small 94.35% 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 0.0056
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 97
Page 84 of 159
Probabilities Y2 to Y3 - Buy Info, Data Indicates
Small Quantity, do Small Platform Probability Large 5.65%
Probability Small 94.35% 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
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 98
Page 85 of 159
Appendix J– Simplified Case ROA Tree Evolution
Figure 36 Real Options Analysis Process
Page 99
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
3D Seismic Survey $150,000,000.00
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 100
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 101
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 102
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 103
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 104
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 105
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 106
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 107
Page 94 of 159
Appendix M- Effect of New Information (Complete Case)
State of Nature Description
E1 Large quantity of oil
E2 Small quantity of oil
Table 59 Considered States of Nature
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
Table 60 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil
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
Table 61 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil
Joint Probabilities
Table 60 result 0.53
Table 61 result 0.47
Total 1.00
Table 62 Joint Probabilities Addition
The effect of the new information to the technological uncertainty tree can be seen in Figure
38.
Page 108
Page 95 of 159
Figure 38 Effect of New Information to Technological Uncertainty Decision Tree (Complete Case)
Page 109
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 110
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 111
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 112
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
Expected Volume of Barrels 3,000,000,000.00
Year Produced Barrels % of total % Decrease
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
Annual Rate of Production
Page 113
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
Expected Volume of Barrels 1,000,000,000.00
Year Produced Barrels % of total % Decrease
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
Annual Rate of Production
Page 114
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 115
Page 102 of 159
NPVs Set Large Platform at Year Three
Expected Amount of oil in Barrels 1,700,000,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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
$61.047B $67.9B $50.475B $37.742B $28.372B $21.432B $16.262B $12.389B $9.474B $7.269B $5.595B $4.319B $3.342B $2.593B $2.161B
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
$61.047B $67.9B $50.475B $37.742B $28.372B $21.432B $16.262B $12.389B $9.474B $7.269B $5.595B $4.319B $3.342B $2.593B $2.161B
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
$36.628B $40.74B $30.285B $22.645B $17.023B $12.859B $9.757B $7.434B $5.684B $4.362B $3.357B $2.591B $2.005B $1.556B $1.297B
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
$36.628B $40.74B $30.285B $22.645B $17.023B $12.859B $9.757B $7.434B $5.684B $4.362B $3.357B $2.591B $2.005B $1.556B $1.297B
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
$36.628B $40.74B $30.285B $22.645B $17.023B $12.859B $9.757B $7.434B $5.684B $4.362B $3.357B $2.591B $2.005B $1.556B $1.297B
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 116
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 117
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
OPEX Small – Oil Platform 1 $10.00 USD per barrel
OPEX Small – Oil Platform 2 $10.00 USD per barrel
Total OPEX $20.00 USD per barrel
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
$450.M $540.M $430.31M $342.902M $273.249M $217.744M $173.514M $138.268M $110.182M $87.801M $69.966M $55.754M $44.429M $35.404M $30.478M
Revenues
$111.329B $124.143B $92.516B $69.347B $52.254B $39.564B $30.086B $22.97B $17.6B $13.53B $10.433B $8.067B $6.253B $4.858B $4.086B
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
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 $10.8M
EBITDA
$102.329B $113.343B $83.91B $62.489B $46.789B $35.209B $26.616B $20.204B $15.396B $11.774B $9.034B $6.952B $5.365B $4.15B $3.466B
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
$102.329B $113.343B $83.91B $62.489B $46.789B $35.209B $26.616B $20.204B $15.396B $11.774B $9.034B $6.952B $5.365B $4.15B $3.466B
TAX
$40.932B $45.337B $33.564B $24.996B $18.716B $14.084B $10.646B $8.082B $6.159B $4.71B $3.614B $2.781B $2.146B $1.66B $1.386B
Net Income
$61.398B $68.006B $50.346B $37.493B $28.074B $21.125B $15.969B $12.123B $9.238B $7.065B $5.42B $4.171B $3.219B $2.49B $2.08B
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
$61.398B $68.006B $50.346B $37.493B $28.074B $21.125B $15.969B $12.123B $9.238B $7.065B $5.42B $4.171B $3.219B $2.49B $2.08B
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
$61.398B $68.006B $50.346B $37.493B $28.074B $21.125B $15.969B $12.123B $9.238B $7.065B $5.42B $4.171B $3.219B $2.49B $2.08B
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 118
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 119
Page 106 of 159
No 2nd drill, set Small, it is Small
Amount of Oil Present 1,000,000,000.00
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
$150.M $180.M $143.437M $114.301M $91.083M $72.581M $57.838M $46.089M $36.727M $29.267M $23.322M $18.585M $14.81M $11.801M $10.159M
Revenues
$37.11B $41.381B $30.839B $23.116B $17.418B $13.188B $10.029B $7.657B $5.867B $4.51B $3.478B $2.689B $2.084B $1.619B $1.362B
OPEX
$1.5B $1.8B $1.434B $1.143B $.911B $.726B $.578B $.461B $.367B $.293B $.233B $.186B $.148B $.118B $.102B
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 $5.4M
EBITDA
$35.61B $39.581B $29.404B $21.973B $16.507B $12.462B $9.45B $7.196B $5.499B $4.217B $3.244B $2.503B $1.936B $1.501B $1.255B
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
$35.61B $39.581B $29.404B $21.973B $16.507B $12.462B $9.45B $7.196B $5.499B $4.217B $3.244B $2.503B $1.936B $1.501B $1.255B
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
$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
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
$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
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 120
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 121
Page 108 of 159
NPVs Buy Additional Information at Year Three, Large Quantity is Indicated, and a Large Platform is Established
It is Large
Amount of Oil Present 3,000,000,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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
$450.M $540.M $430.31M $342.902M $273.249M $217.744M $173.514M $138.268M $110.182M $87.801M $69.966M $55.754M $44.429M $35.404M $30.478M
Revenues
$109.925B $122.714B $91.542B $68.68B $51.795B $39.245B $29.864B $22.815B $17.491B $13.454B $10.379B $8.029B $6.226B $4.839B $4.071B
OPEX
$3.6B $4.32B $3.442B $2.743B $2.186B $1.742B $1.388B $1.106B $.881B $.702B $.56B $.446B $.355B $.283B $.244B
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
$106.325B $118.394B $88.1B $65.936B $49.609B $37.503B $28.476B $21.708B $16.61B $12.751B $9.819B $7.583B $5.871B $4.556B $3.811B
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
$106.325B $118.394B $88.1B $65.936B $49.609B $37.503B $28.476B $21.708B $16.61B $12.751B $9.819B $7.583B $5.871B $4.556B $3.811B
TAX
$42.53B $47.357B $35.24B $26.375B $19.843B $15.001B $11.39B $8.683B $6.644B $5.101B $3.928B $3.033B $2.348B $1.822B $1.525B
Net Income
$63.795B $71.036B $52.86B $39.562B $29.765B $22.502B $17.086B $13.025B $9.966B $7.651B $5.892B $4.55B $3.522B $2.733B $2.287B
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
$63.795B $71.036B $52.86B $39.562B $29.765B $22.502B $17.086B $13.025B $9.966B $7.651B $5.892B $4.55B $3.522B $2.733B $2.287B
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
$63.795B $71.036B $52.86B $39.562B $29.765B $22.502B $17.086B $13.025B $9.966B $7.651B $5.892B $4.55B $3.522B $2.733B $2.287B
Discounted FCFU $0.00 $57.421B $57.551B $38.546B $25.967B $17.585B $11.966B $8.178B $5.611B $3.864B $2.67B $1.851B $1.286B $.896B $.626B $.472B
PV $234,491,395,523.84
NPV $234,491,395,523.84
Page 122
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
Table 76 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set,
Quantity is Large – End Nodes NPV Estimates
Page 123
Page 110 of 159
It is Small
Amount of Oil Present 1,000,000,000.00
OPEX Large Oil Platform $12.00 USD per barrel
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
$150.M $180.M $143.437M $114.301M $91.083M $72.581M $57.838M $46.089M $36.727M $29.267M $23.322M $18.585M $14.81M $11.801M $10.159M
Revenues
$36.642B $40.905B $30.514B $22.893B $17.265B $13.082B $9.955B $7.605B $5.83B $4.485B $3.46B $2.676B $2.075B $1.613B $1.357B
OPEX
$1.8B $2.16B $1.721B $1.372B $1.093B $.871B $.694B $.553B $.441B $.351B $.28B $.223B $.178B $.142B $.122B
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
$34.842B $38.745B $28.793B $21.522B $16.172B $12.211B $9.261B $7.052B $5.39B $4.133B $3.18B $2.453B $1.898B $1.471B $1.219B
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
$34.842B $38.745B $28.793B $21.522B $16.172B $12.211B $9.261B $7.052B $5.39B $4.133B $3.18B $2.453B $1.898B $1.471B $1.219B
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
$20.905B $23.247B $17.276B $12.913B $9.703B $7.326B $5.556B $4.231B $3.234B $2.48B $1.908B $1.472B $1.139B $.883B $.731B
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
$20.905B $23.247B $17.276B $12.913B $9.703B $7.326B $5.556B $4.231B $3.234B $2.48B $1.908B $1.472B $1.139B $.883B $.731B
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
$20.905B $23.247B $17.276B $12.913B $9.703B $7.326B $5.556B $4.231B $3.234B $2.48B $1.908B $1.472B $1.139B $.883B $.731B
Discounted FCFU $0.00 $18.816B $18.834B $12.598B $8.476B $5.732B $3.896B $2.659B $1.823B $1.254B $.866B $.599B $.416B $.29B $.202B $.151B
PV $76,612,029,691.90
NPV $76,612,029,691.90
Page 124
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
Table 78 Buy information at Year Three, Large Quantity is Indicated, Large Platform is Set,
Quantity is Small – End Nodes NPV Estimates
Page 125
Page 112 of 159
NPVs Buy Additional Information at Year Three, Large Quantity is Indicated, and a Small Platform is Established
It is Large
Amount of Oil Present 3,000,000,000.00
OPEX Small – Oil Platform 1 $10.00 USD per barrel
OPEX Small – Oil Platform 2 $10.00 USD per barrel
Total OPEX $20.00 USD per barrel
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
$450.M $540.M $430.31M $342.902M $273.249M $217.744M $173.514M $138.268M $110.182M $87.801M $69.966M $55.754M $44.429M $35.404M $30.478M
Revenues
$109.925B $122.714B $91.542B $68.68B $51.795B $39.245B $29.864B $22.815B $17.491B $13.454B $10.379B $8.029B $6.226B $4.839B $4.071B
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
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 $10.8M
EBITDA
$100.925B $111.914B $82.936B $61.822B $46.33B $34.89B $26.394B $20.049B $15.288B $11.698B $8.98B $6.914B $5.337B $4.131B $3.451B
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
$100.925B $111.914B $82.936B $61.822B $46.33B $34.89B $26.394B $20.049B $15.288B $11.698B $8.98B $6.914B $5.337B $4.131B $3.451B
TAX
$40.37B $44.765B $33.175B $24.729B $18.532B $13.956B $10.558B $8.02B $6.115B $4.679B $3.592B $2.765B $2.135B $1.652B $1.38B
Net Income
$60.555B $67.148B $49.762B $37.093B $27.798B $20.934B $15.836B $12.03B $9.173B $7.019B $5.388B $4.148B $3.202B $2.479B $2.071B
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
$60.555B $67.148B $49.762B $37.093B $27.798B $20.934B $15.836B $12.03B $9.173B $7.019B $5.388B $4.148B $3.202B $2.479B $2.071B
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
$60.555B $67.148B $49.762B $37.093B $27.798B $20.934B $15.836B $12.03B $9.173B $7.019B $5.388B $4.148B $3.202B $2.479B $2.071B
Discounted FCFU $0.00 $54.505B $54.401B $36.287B $24.346B $16.422B $11.132B $7.58B $5.182B $3.557B $2.45B $1.693B $1.173B $.815B $.568B $.427B
PV $220,538,169,864.71
NPV $220,538,169,864.71
Page 126
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
Table 80 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set,
Quantity is Large – End Nodes NPV Estimates
Page 127
Page 114 of 159
It tis Small
Amount of Oil Present 1,000,000,000.00
OPEX Small Oil Platform $10.00 USD per barrel
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
$150.M $180.M $143.437M $114.301M $91.083M $72.581M $57.838M $46.089M $36.727M $29.267M $23.322M $18.585M $14.81M $11.801M $10.159M
Revenues
$36.642B $40.905B $30.514B $22.893B $17.265B $13.082B $9.955B $7.605B $5.83B $4.485B $3.46B $2.676B $2.075B $1.613B $1.357B
OPEX
$1.5B $1.8B $1.434B $1.143B $.911B $.726B $.578B $.461B $.367B $.293B $.233B $.186B $.148B $.118B $.102B
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 $5.4M
EBITDA
$35.142B $39.105B $29.08B $21.75B $16.354B $12.356B $9.376B $7.144B $5.463B $4.192B $3.226B $2.49B $1.927B $1.495B $1.25B
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
$35.142B $39.105B $29.08B $21.75B $16.354B $12.356B $9.376B $7.144B $5.463B $4.192B $3.226B $2.49B $1.927B $1.495B $1.25B
TAX
$14.057B $15.642B $11.632B $8.7B $6.542B $4.942B $3.751B $2.858B $2.185B $1.677B $1.291B $.996B $.771B $.598B $.5B
Net Income
$21.085B $23.463B $17.448B $13.05B $9.812B $7.414B $5.626B $4.286B $3.278B $2.515B $1.936B $1.494B $1.156B $.897B $.75B
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
$21.085B $23.463B $17.448B $13.05B $9.812B $7.414B $5.626B $4.286B $3.278B $2.515B $1.936B $1.494B $1.156B $.897B $.75B
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
$21.085B $23.463B $17.448B $13.05B $9.812B $7.414B $5.626B $4.286B $3.278B $2.515B $1.936B $1.494B $1.156B $.897B $.75B
Discounted FCFU $0.00 $18.978B $19.009B $12.723B $8.566B $5.797B $3.942B $2.693B $1.847B $1.271B $.878B $.608B $.423B $.294B $.205B $.155B
PV $77,388,582,188.62
NPV $77,388,582,188.62
Page 128
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
Table 82 Buy information at Year Three, Large Quantity is Indicated, Small Platform is Set,
Quantity is Small – End Nodes NPV Estimates
Page 129
Page 116 of 159
NPVs Buy Additional Information at Year Three, Small Quantity is Indicated, and a Large Platform is Established
It is Large
Amount of Oil Present 3,000,000,000.00
OPEX Large Oil Platform $8.00 USD per barrel
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
$450.M $540.M $430.31M $342.902M $273.249M $217.744M $173.514M $138.268M $110.182M $87.801M $69.966M $55.754M $44.429M $35.404M $30.478M
Revenues
$109.925B $122.714B $91.542B $68.68B $51.795B $39.245B $29.864B $22.815B $17.491B $13.454B $10.379B $8.029B $6.226B $4.839B $4.071B
OPEX
$3.6B $4.32B $3.442B $2.743B $2.186B $1.742B $1.388B $1.106B $.881B $.702B $.56B $.446B $.355B $.283B $.244B
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
$106.325B $118.394B $88.1B $65.936B $49.609B $37.503B $28.476B $21.708B $16.61B $12.751B $9.819B $7.583B $5.871B $4.556B $3.811B
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
$106.325B $118.394B $88.1B $65.936B $49.609B $37.503B $28.476B $21.708B $16.61B $12.751B $9.819B $7.583B $5.871B $4.556B $3.811B
TAX
$42.53B $47.357B $35.24B $26.375B $19.843B $15.001B $11.39B $8.683B $6.644B $5.101B $3.928B $3.033B $2.348B $1.822B $1.525B
Net Income
$63.795B $71.036B $52.86B $39.562B $29.765B $22.502B $17.086B $13.025B $9.966B $7.651B $5.892B $4.55B $3.522B $2.733B $2.287B
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
$63.795B $71.036B $52.86B $39.562B $29.765B $22.502B $17.086B $13.025B $9.966B $7.651B $5.892B $4.55B $3.522B $2.733B $2.287B
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
$63.795B $71.036B $52.86B $39.562B $29.765B $22.502B $17.086B $13.025B $9.966B $7.651B $5.892B $4.55B $3.522B $2.733B $2.287B
Discounted FCFU $0.00 $57.421B $57.551B $38.546B $25.967B $17.585B $11.966B $8.178B $5.611B $3.864B $2.67B $1.851B $1.286B $.896B $.626B $.472B
PV $234,491,395,523.84
NPV $234,491,395,523.84
Page 130
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
Table 84 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set,
Quantity is Large – End Nodes NPV Estimates
Page 131
Page 118 of 159
It is Small
Amount of Oil Present 1,000,000,000.00
OPEX Large Oil Platform $12.00 USD per barrel
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
$150.M $180.M $143.437M $114.301M $91.083M $72.581M $57.838M $46.089M $36.727M $29.267M $23.322M $18.585M $14.81M $11.801M $10.159M
Revenues
$36.642B $40.905B $30.514B $22.893B $17.265B $13.082B $9.955B $7.605B $5.83B $4.485B $3.46B $2.676B $2.075B $1.613B $1.357B
OPEX
$1.8B $2.16B $1.721B $1.372B $1.093B $.871B $.694B $.553B $.441B $.351B $.28B $.223B $.178B $.142B $.122B
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
$34.842B $38.745B $28.793B $21.522B $16.172B $12.211B $9.261B $7.052B $5.39B $4.133B $3.18B $2.453B $1.898B $1.471B $1.219B
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
$34.842B $38.745B $28.793B $21.522B $16.172B $12.211B $9.261B $7.052B $5.39B $4.133B $3.18B $2.453B $1.898B $1.471B $1.219B
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
$20.905B $23.247B $17.276B $12.913B $9.703B $7.326B $5.556B $4.231B $3.234B $2.48B $1.908B $1.472B $1.139B $.883B $.731B
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
$20.905B $23.247B $17.276B $12.913B $9.703B $7.326B $5.556B $4.231B $3.234B $2.48B $1.908B $1.472B $1.139B $.883B $.731B
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
$20.905B $23.247B $17.276B $12.913B $9.703B $7.326B $5.556B $4.231B $3.234B $2.48B $1.908B $1.472B $1.139B $.883B $.731B
Discounted FCFU $0.00 $18.816B $18.834B $12.598B $8.476B $5.732B $3.896B $2.659B $1.823B $1.254B $.866B $.599B $.416B $.29B $.202B $.151B
PV $76,612,029,691.90
NPV $76,612,029,691.90
Page 132
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
Table 86 Buy information at Year Three, Small Quantity is Indicated, Large Platform is Set,
Quantity is Small – End Nodes NPV Estimates
Page 133
Page 120 of 159
NPVs Buy Additional Information at Year Three, Small Quantity is Indicated, and a Small Platform is Established
It is Large
Amount of Oil Present 3,000,000,000.00
OPEX Small – Oil Platform 1 $10.00 USD per barrel
OPEX Small – Oil Platform 2 $10.00 USD per barrel
Total OPEX $20.00 USD per barrel
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
$450.M $540.M $430.31M $342.902M $273.249M $217.744M $173.514M $138.268M $110.182M $87.801M $69.966M $55.754M $44.429M $35.404M $30.478M
Revenues
$109.925B $122.714B $91.542B $68.68B $51.795B $39.245B $29.864B $22.815B $17.491B $13.454B $10.379B $8.029B $6.226B $4.839B $4.071B
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
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 $10.8M
EBITDA
$100.925B $111.914B $82.936B $61.822B $46.33B $34.89B $26.394B $20.049B $15.288B $11.698B $8.98B $6.914B $5.337B $4.131B $3.451B
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
$100.925B $111.914B $82.936B $61.822B $46.33B $34.89B $26.394B $20.049B $15.288B $11.698B $8.98B $6.914B $5.337B $4.131B $3.451B
TAX
$40.37B $44.765B $33.175B $24.729B $18.532B $13.956B $10.558B $8.02B $6.115B $4.679B $3.592B $2.765B $2.135B $1.652B $1.38B
Net Income
$60.555B $67.148B $49.762B $37.093B $27.798B $20.934B $15.836B $12.03B $9.173B $7.019B $5.388B $4.148B $3.202B $2.479B $2.071B
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
$60.555B $67.148B $49.762B $37.093B $27.798B $20.934B $15.836B $12.03B $9.173B $7.019B $5.388B $4.148B $3.202B $2.479B $2.071B
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
$60.555B $67.148B $49.762B $37.093B $27.798B $20.934B $15.836B $12.03B $9.173B $7.019B $5.388B $4.148B $3.202B $2.479B $2.071B
Discounted FCFU $0.00 $54.505B $54.401B $36.287B $24.346B $16.422B $11.132B $7.58B $5.182B $3.557B $2.45B $1.693B $1.173B $.815B $.568B $.427B
PV $220,538,169,864.71
NPV $220,538,169,864.71
Page 134
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
Table 88 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set,
Quantity is Large – End Nodes NPV Estimates
Page 135
Page 122 of 159
It tis Small
Amount of Oil Present 1,000,000,000.00
OPEX Small Oil Platform $10.00 USD per barrel
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
$150.M $180.M $143.437M $114.301M $91.083M $72.581M $57.838M $46.089M $36.727M $29.267M $23.322M $18.585M $14.81M $11.801M $10.159M
Revenues
$36.642B $40.905B $30.514B $22.893B $17.265B $13.082B $9.955B $7.605B $5.83B $4.485B $3.46B $2.676B $2.075B $1.613B $1.357B
OPEX
$1.5B $1.8B $1.434B $1.143B $.911B $.726B $.578B $.461B $.367B $.293B $.233B $.186B $.148B $.118B $.102B
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 $5.4M
EBITDA
$35.142B $39.105B $29.08B $21.75B $16.354B $12.356B $9.376B $7.144B $5.463B $4.192B $3.226B $2.49B $1.927B $1.495B $1.25B
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
$35.142B $39.105B $29.08B $21.75B $16.354B $12.356B $9.376B $7.144B $5.463B $4.192B $3.226B $2.49B $1.927B $1.495B $1.25B
TAX
$14.057B $15.642B $11.632B $8.7B $6.542B $4.942B $3.751B $2.858B $2.185B $1.677B $1.291B $.996B $.771B $.598B $.5B
Net Income
$21.085B $23.463B $17.448B $13.05B $9.812B $7.414B $5.626B $4.286B $3.278B $2.515B $1.936B $1.494B $1.156B $.897B $.75B
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
$21.085B $23.463B $17.448B $13.05B $9.812B $7.414B $5.626B $4.286B $3.278B $2.515B $1.936B $1.494B $1.156B $.897B $.75B
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
$21.085B $23.463B $17.448B $13.05B $9.812B $7.414B $5.626B $4.286B $3.278B $2.515B $1.936B $1.494B $1.156B $.897B $.75B
Discounted FCFU $0.00 $18.978B $19.009B $12.723B $8.566B $5.797B $3.942B $2.693B $1.847B $1.271B $.878B $.608B $.423B $.294B $.205B $.155B
PV $77,388,582,188.62
NPV $77,388,582,188.62
Page 136
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
Table 90 Buy information at Year Three, Small Quantity is Indicated, Small Platform is Set,
Quantity is Small – End Nodes NPV Estimates
Page 137
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 138
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 139
Page 126 of 159
Appendix R – Complete Case Hexanomial Tree Probabilities
The table below continues in the right hand side of the page.
Table 93 Complete Case Hexanomial Tree Nodes Probabilities
Probabilities Y0 to Y1 Price & Technological
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
Probabilities Y1 to Y2 Price & Technological
Probability success 3D seismic survey 0.15
Probability failure 3D seismic survey 0.85 1.00
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
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
Probabilities Y2 to Y3 Price & Technological
Probability success DW1 0.3
Probability failure DW1 0.7 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
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 140
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
Probabilities Y3 to Y4 Set Large
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
Probabilities Y3 to Y4 Set Small
Large oil Probability (SO) 0.35
Small oil Probability (S§) 0.65 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
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 141
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
Probabilities Y3 to Y4 Buy Info
Data indicates Large - b(D+) 53.00%
Data indicates Small - b(D-) 47.00% 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
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 142
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
Probability Large - LO 26.42%
Probability Small - L§ 73.58% 1.00
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
Probability Large - LO 26.42%
Probability Small - L§ 73.58% 1.00
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
Page 143
Page 130 of 159
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 small quantity, install large platform
Probability Large - LO 44.68%
Probability Small - L§ 55.32% 1.00
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 0.3714
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 144
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
Probability Large - LO 44.68%
Probability Small - L§ 55.32% 1.00
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 0.3714
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 145
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 146
Page 133 of 159
Appendix S – Complete Case Quadranomial Tree Probabilities
The table below continues in the right hand side of the page.
Table 94 Complete Case Quadranomial Tree Nodes Probabilities
Probabilities Y0 to Y1 Price & Technological
Probability success 2D seismic survey 0.0700
Probability failure 2D seismic survey 0.9300 1.00
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
Probabilities Y1 to Y2 Price & Technological
Probability success 3D seismic survey 0.15
Probability failure 3D seismic survey 0.85 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
spu 0.0781
spd 0.0719
fpu 0.4424
fpd 0.4076 1.00
Probabilities Y2 to Y3 Price & Technological
Probability success DW1 0.3
Probability failure DW1 0.7 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
spu 0.1561
spd 0.1439
fpu 0.3643
fpd 0.3357 1.00
Probabilities Y3 to Y4 Set Large
Quantity is fixed, and only price probability enters. Therefore, technological uncertainty assumes a probability of 1.
1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
Probabilities Y3 to Y4 Set Small
Large oil Probability 0.35
Small oil Probability 0.65 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
SOpu 0.1822
SOpd 0.1678
S§pu 0.3383
S§pd 0.3117 1.00
Probabilities Y4 to Y3 Buy Info
Data says Large 53.00%
Data says Small 47.00% 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 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
Probability Large 26.42%
Probability Small 73.58% 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
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
Probability Large 26.42%
Probability Small 73.58% 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
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
Probability Large 44.68%
Probability Small 55.32% 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
Page 147
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
Probability Large 44.68%
Probability Small 55.32% 1.00
up risk-neutral probability (pu) 0.5204
down risk-neutral probability (pd) 0.4796 1.00
SOpu 0.2325
SOpd 0.2143
S§pu 0.2879
S§pd 0.2653 1.00
Page 148
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
O – result is large
§ – result is Small
(D+) – data says it is large
(D–) – data says it is small
Colours Legend (Y4 and Y5):
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
Technological uncertainty legend:
Page 149
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
2D Seismic Survey $50,000,000.00
$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 150
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
2D Seismic Survey $50,000,000.00
-$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 151
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
O – result is large
§ – result is Small
(D+) – data says it is large
(D–) – data says it is small
Colours Legend (Y4 and Y5):
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
Technological uncertainty legend:
Page 152
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 153
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
2D Seismic Survey $50,000,000.00
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 154
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
2D Seismic Survey $50,000,000.00
$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 155
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
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
Figure 55 Quadranomial Tree Real Options Analysis
Page 156
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
Trinomial Binomial Difference
Buy additional information -$409,521,073.44 -$369,669,093.33 $39,851,980.11
Set Large, no 2nd Drill -$300,302,185.91 -$266,443,139.20 $33,859,046.71
Set Small, no 2nd Drill -$289,296,453.20 -$255,437,406.50 $33,859,046.71
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
Trinomial Binomial Difference
Buy additional information -$421,104,809.29 -$369,787,215.57 $51,317,593.72
Set Large, no 2nd Drill -$310,740,291.58 -$266,443,139.20 $44,297,152.37
Set Small, no 2nd Drill -$299,887,056.50 -$256,002,808.17 $43,884,248.34
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 157
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
2D Seismic Survey $50,000,000.00
$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
Figure 56 Hexanomial Tree Real Options Analysis
Page 158
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
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
Figure 57 Quadranomial Tree Real Options Analysis
Page 159
Page 146 of 159
Best Option with ROA
Trinomial Binomial
Buy additional information -$408,202,007.97 -$368,188,402.29
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 $103,636,052.75 $137,636,791.10
ROA Added Value $393,076,772.49 $393,074,197.60
Table 98 Best Option with Real Options Analysis
Page 160
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
Figure 58 Hexanomial Tree Real Options Analysis
Page 161
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
Figure 59 Quadranomial Tree Real Options Analysis
Page 162
Page 149 of 159
Best Option with ROA
Trinomial Binomial
Buy additional information -$272,411,450.11 -$232,397,844.43
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 -$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
Table 99 Best Option with Real Options Analysis
Page 163
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 164
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 165
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
Figure 62 Hexanomial Tree Real Options Analysis (initial large oil probability at 70%)
Page 166
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
Figure 63 Quadranomial Tree Real Options Analysis (initial large oil probability at 70%)
Page 167
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
Figure 64 Hexanomial Tree Real Options Analysis (initial large oil probability at 100%)
Page 168
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
Figure 65 Quadranomial Tree Real Options Analysis (initial large oil probability at 70%)
Page 169
Page 156 of 159
Effect of Changes on Valuation Results
Best Option with ROA
Trinomial Binomial
Buy additional information -$400,031,374.95 -$357,664,027.75
Set Large, no 2nd Drill -$290,677,502.08 -$254,673,993.95
Set Small, no 2nd Drill -$285,634,181.10 -$249,630,672.96
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%)
Best Option with ROA
Trinomial Binomial
Buy additional information -$342,123,430.53 -$285,633,634.27
Set Large, no 2nd Drill -$232,063,799.93 -$184,059,122.42
Set Small, no 2nd Drill -$262,794,949.26 -$214,790,271.75
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
Table 101 Best Option with Real Options Analysis (initial large oil probability at 70%)
Best Option with ROA
Trinomial Binomial
Buy additional information -$284,215,486.10 -$213,603,240.78
Set Large, no 2nd Drill -$173,450,097.78 -$113,444,250.89
Set Small, no 2nd Drill -$239,955,717.42 -$179,949,870.53
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
Table 102 Best Option with Real Options Analysis (initial large oil probability at 100%)
Page 170
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 Description
E1 Large quantity of oil
E2 Small quantity of oil
Table 103 Considered States of Nature
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
Table 104 Probabilities in Case New Data Indicates the Presence of a Large Amount of Oil
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
Table 105 Probabilities in Case New Data Indicates the Presence of a Small Amount of Oil
Joint Probabilities
Table 104 result 0.40
Table 105 result 0.60
Total 1.00
Table 106 Joint Probabilities Addition
Page 171
Page 158 of 159
Year Five to Year Four Quadranomial Tree Probabilities
Probability Y5 to Y4 – Buy Info, data says Large, do Large
Probability Large 100.00%
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 Large 100.00%
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 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.
up risk-neutral prob. (pu) 0.5204
down risk-neutral prob. (pd) 0.4796
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%
up risk-neutral prob. (pu) 0.5204
down risk-neutral prob. (pd) 0.4796
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 172
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
2D Seismic Survey $50,000,000.00
-$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
2D Seismic Survey $50,000,000.00
$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
2D Seismic Survey $50,000,000.00
-$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