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HOW CAN REAL OPTIONS APPROACHES
VALUE UNCERTAINTY AND FLEXIBILITY
IN OIL AND GAS INVESTMENTS?
David C. Wilde
29thJanuary, 2011.
ABSTRACT: Investment projects in the oil and gas industry are typically
characterised by a large degree of uncertainty and managerial flexibility. Accurate
evaluation of such investment projects requires sophisticated appraisal methods
beyond the traditional net present value approach. In this paper, currently used real
options approaches are categorised and discussed with regards to their theoretical
and conceptual strengths and weaknesses. The analysis shows that proposed real
options approaches differ significantly in the underlying assumptions, the modelling of
project uncertainty, required data and analytical complexity. Based on these results,
recommendations for valuing oil and gas investments can be made.
.
The author is currently an MSc Candidate in Energy Studies and LLM Candidate in Energy Law andPolicy at the Univeristy of Dundee. He earlier graduated from the Univeristy of Cologne, Germany
where he studied Business Administration with specialisation in Energy Economics, Business Finance
and Banking Business. He is worked at Haarmann Hemmelrath, Ernst & Young AG, RWE AG, RWEPower AG and the Energy Institute at the University of Cologne (EWI).
Email:[email protected] in CEPMLP Annual Review - CAR Volume 15 (2013) Editor-in-Chief: Dramani Bukari
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TABLE OF CONTENTS
Table of Contents .................................................................................................... II
Abbreviations and Formula Symbols .................................................................... III
1 Introduction ........................................................................................................ 1
2 Replicating portfolio approach (RPA) ............................................................... 3
2.1 Application ................................................................................................ 5
2.2 Critical assessment .................................................................................... 6
2.3 Subjective Replication Portfolio Approach .............................................. 7
3 The Marketed Asset Disclaimer Approach (MAD) ........................................... 8
3.1 Application ................................................................................................ 9
3.2 Critical assessment .................................................................................. 11
4 The Hybrid Real Options Approach (HROA) ................................................. 13
4.1 Application .............................................................................................. 13
4.2 Critical Assessment ................................................................................. 17
5 Conclusion ....................................................................................................... 18
Bibliography .......................................................................................................... 19
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ABBREVIATIONS AND FORMULA SYMBOLS
Annual volatility
C Call option
COFf Fixed cash outflow
cofv Variable cash outflow
d Down factor
HROA Hybrid real options approach
I Investment cost
L Liquidation value
M Market capitalisation
MAD Marketed asset disclaimer
MV Market value
NPV Net present value
OC Oil company
OP Oil price
prn Risk-neutral probability
R Proved reserves
rf Risk-free rate
t Time index
T Time to expiration
u Up factor
V Value of undeveloped oil field
WACC Weighted average cost of capital
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1 Introduction
The financial evaluation of projects is at the centre of every firms investment
decision. In the oil and gas industry, investment projects typically share three
characteristics:1
Property 1: Various uncertaintiescan be identified ex-antethat influence the value of
the project. In the development stage of an oil or natural gas field, for example, these
uncertainties refer to future commodity prices, the size of the business, technical
aspects of the development, investment costs and regulatory uncertainty.
Property 2: By investing, the firm is able to learnmore about the project and gather
additional information regarding the associated uncertainties as they resolve over the
course of time. After acquiring development rights, the firm can, for example, gain
more information about flow rates and production profiles by testing the field before
drilling.
Property 3: During the investment process, management has theflexibilityto adapt its
strategy to the new information. In the case that field tests turn out to be disappointing,
management can decide to abandon the project before spending money for drilling.
Similarly, management can decide to wait with production and observe oil prices
before making the final decision to produce. In this sense, management is typically
faced with severalsequentialinvestment decisions rather than a single decision at the
beginning of the project.2
In analogy to financial options, the managerial flexibilities inherent in investment
projects can be termed real options. Real options in a broad sense provide
opportunities for management to consider new information regarding project
uncertainties, adapt the investment process and thereby actively influence the cash
1Smith, J. E., McCardle, K. F., (1998), p. 198.
2Mun, J., (2002), p.17.
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flow pattern of the project.3The conceptual analogy between financial and real options
can be demonstrated by the example of an oil company acquiring development rights
for an undeveloped field. The acquisition of these rights offers the firm the opportunity
but not the obligation to enter into the production phase. Once the uncertainty
regarding the size of the field has been resolved and management decides to produce,
the option is exercised. Alternatively, management could decide to keep the option
alive and wait for increasing oil prices before investing in production.
Real options, i.e. managerial flexibility, can add significant value to an investment
project, particularly when uncertainty regarding the project value is high.4 The
evaluation of such projects requires sophisticated appraisal methods beyond the
traditional net present value (NPV) approach.5Although the theoretical strengths of the
real options methodology are widely accepted it has not become the standard in project
evaluation in practice.6 Besides the conceptual and mathematical complexity of real
options valuation, problems arise from the fact that the underlyingof a real option is
not a standardised traded commodity like a stock or currency but an investment project
with unique features, such as construction lags, regulatory uncertainty and complex tax
and royalty structures.7
Over the past 30 years, a variety of different, case-based real options approaches has
been developed and applied in the academic literature. The approaches differ
significantly in their underlying assumptions, applicability and mechanics.8This paper
aims at categorising currently used approaches and discussing their application to the
evaluation of oil and gas investment projects. In the following chapters, the three
dominant types of real options approaches in the literature are described and critically
3Dixit, A. K., Pindyck, R. S., (1994), p. 6.
4Amram, M., Kulatilaka, N., (1999), p.8.
5
Dixit, A. K., Pindyck, R. S., (1994), p. 7.6Borison, A., (2005a), p. 17.7Smith, J. E., McCardle, K. F., (1999), p. 2.
8Borison, A., (2005a), p. 18.
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assessed with regards to their theoretical and conceptual strengths and weaknesses. In
order to illustrate the mechanics of real options valuation, each approach is applied to
the following case study:
Canadian Oil is evaluating an investment opportunity in an undeveloped oil field in
Western Canada. The size of the field is uncertain but exploration activities estimated
proved reserves to be RWC (in million barrels). Future oil prices represent the second
uncertainty. The firm can either buy and develop the field today for I0or purchase an
option Cwhich gives the firm the right to buy the field in three years from now (T) for
I3. The option allows Canadian Oil to learn more about the project and the associated
uncertainties through test drilling and market observations before making the final
decision in T to exercise the option and develop the field or to reject further
investment. The option premium C (call option) can be interpreted as a development
right which has to be purchased from the Canadian government. Alternatively, the firm
can decide not to invest at all.
2 Replicating portfolio approach (RPA)
Under the RPA, real options are valued by directly applying pricing formulas used to
value financial options, such as the Black-Scholes or the Cox-Ross-Rubinstein
models.9 A development right which offers the opportunity to invest in field
development and production is therefore seen as completely analogous to a call option
on a stock. The option is valuable if the value of the underlying oil field is volatile due
to project uncertainties and if there is considerable time until the expiration date of the
option.10A rational investor would exercise the option on expiration date Tonly, if the
value of the field (V) in Texceeds the price I3 to be paid for the field. The resulting
payoff in T is max[V-I3 ; -C]. Because the RPA as applied in Amram and Kulatilaka
9This real options approach is used in: Amram, M., Kulatilaka, N., (1999); Brennan, M., Schwartz, E.,
(1985), Trigeorgis, L., Mason, P., (1987); Trigeorgis, L., (1999)10
Mun, J., (2002), p. 101.
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(1999) uses the Black-Scholes pricing formula for valuing real option, the value of the
underlying oil field (V) is assumed to behave according to a Geometric Brownian
motion.
The calculated real option value represents financial market value, i.e. the price that
would be paid for the investment in the capital markets.11 Regardless of subjective
beliefs and preferences, all risk-averse decision makers can agree on the project value
and the investment strategy.12
The main assumption of the RPA is that the returns of the real option in question can
be perfectly replicated in a dynamic manner by constructing a portfolio of market
traded securities. Capital markets are thus assumed to be complete. According to no-
arbitrage arguments in efficient markets, this portfolio (or single asset) must then have
the same value as the real option. Brennan and Schwartz (1985), for example, suggest
forming this replicating portfolio by trading in oil futures.13Alternatively, one could
try to find a stock of a publicly traded oil firm that is analogous to the investment
project.
The possibility to dynamically replicate the value of the undeveloped oil field allows
for the creation of a hedge position consisting of the replicating portfolio and the real
option which earns a risk-free rate of return.14The real option value does therefore not
depend on the required rate of return on the undeveloped field or investors risk
preferences so that a risk-neutral world can be assumed for valuation purposes. In such
as risk-neutral world, the estimation of a risk premium is not required.
11
Borison, A., (2005a), p. 18.12Smith, J. E., McCardle, K. F., (1998), p. 199.13
Brennan, M., Schwartz, E., (1985), p. 154.14
Amram, M., Kulatilaka, N., (1999), p. 112.
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2.1 Application
In order to evaluate the investment opportunities and find the value maximising
strategy according to the RPA, the firm has to estimate the following option
parameters:
Table 1: Option parameters to be estimated under the RPA
Parameter Real Option (European type)
V Current (market) value of undeveloped field
I3 Cost of investment (exercise price)
rf Risk-free rate of return
T (= 3) Time to expiration
Volatility of value of undeveloped field
Source: Author based on Amram, M., Kulatil aka, N., (1999), p. 121.
One way of estimating the current market value of the field under consideration (V) is
to identify the market capitalisation (MOC) of a publicly traded oil company (OC)
whose assets (reserves =ROC) exactly replicate the cash flows of the field. The size of
the investment relative to the replicating portfolio is given by the ratio of proved
reserves RWC/ROC. The market value of the field can then be calculated as:
V = (RWC/ROC)MOC.
If short-term and long-term options on the OC-stock are available, the implied
volatility can be calculated to obtain .As suggested by Amram and Kulatilaka (1999),
the Black-Scholes formula can be used to calculate the market value of a call option on
the undeveloped field (CMV):15
CMV= N(d1)VN(d2)I3-rT, with (1)
d1= [ln(V/I3) + (rf+ 0.52)T] / T0.5and (2)
d2= d1T0.5. (3)
15
The RPA does not rely on option pricing based on the Black-Scholes model. Alternatively, otherclosed-form solutions or binomial approaches can be used to value American type options or options on
a dividend paying underlying. All the potential pricing formulas under the RPA, however, rely on the
no-arbitrage condition.
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Because the no-arbitrage condition implies that the replicating portfolio offers exactly
the same return as the undeveloped oil field in all states of the world, shareholder value
is only created if I0V. Analogously, purchasing the development right only creates
shareholder value if C CMV. The investment decision is thus made as follows:
If (V I0) max[CMV C;0] 0, invest in field development today to maximise
shareholder value. In this case, the current market value of the undeveloped field (V)
exceeds the investment costs (I0) by more than the difference between the market value
of the call option (CMV) and the option premium (C).
If (CMVC)max[VI0;0] 0, invest in call option on the field (development right)
to maximise shareholder value. In this case, purchasing the call option is more valuable
than investing in field development today.
If (C CMV 0) and (I0 V 0), do not invest at all because the option and the
investment project are overpriced and shareholder value is destroyed.
2.2
Critical assessmentA critical shortcoming of the RPA is the lack of generality. 16Single projects are not
traded on capital markets and information regarding covariances between financial and
real assets is generally not available.17 Therefore, portfolios consisting of traded
securities that perfectly replicate the cash flows of single oil or natural gas investments
are unlikely to be found.
If oil futures are used in order to replicate the project, as suggested by Brennan and
Schwartz (1985) or Siegel, Smith and Paddock (1987), only price risks can be hedged.
Project specific risks, however, such as production rate risks cannot be perfectly
replicated by this approach. Publicly traded companies, on the other hand, usually hold
portfolios of numerous projects of different types and in different stages in order to
16Smith, J. E., McCardle, K. F., (1998), p. 199.
17Borison, A., (2005a), p. 19.
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mitigate risks. It cannot be expected that securities of such companies are highly
correlated with single real assets.
In the case that a required replicating portfolio cannot be found, the use of financial
option formulas, such as Black-Scholes, is generally inappropriate.18
All these
formulas implicitly discount the projects cash flows at the risk-free rate (rf) based on
the no-arbitrage condition. If the risk of a project cannot be fully hedged because
capital markets are incomplete, the value of the real option to wait depends on the
firms expectations regarding future cash flows and discounting this expected value at
the risk-free rate results in inaccuracy. Furthermore, a correct calculation of the annual
volatility () of the underlying which highly influences the option value becomes
difficult. Amram and Kulatilaka (1999) who use the RPA point out that the attempt to
dynamically replicate real assets can result in tracking errorsbut they do not provide
a quantitative estimation of the resulting inaccuracy.19 Overall, using option pricing
methods that rely on no-arbitrage conditions and the law of one price seems
inappropriate in many real option applications.
2.3 Subjective Replication Portfolio Approach
A variation of the RPA described above which can be termed subjective RPA is used
in some applications.20Under this approach, standard option pricing formulas are used
to value real options without identifying a market based replicate portfolio.21Although
the valuation relies on the same assumptions as the Black-Scholes methodology, the
option input parameters are not determined based on objective market information but
on subjective estimates.
18Dixit, A. K., Pindyck, R. S., (1994), p. 137.
19
Amram, M., Kulatilaka, N., (1999), pp. 52-54.20Luehrman, T., (1998a); Luehrman, T., (1998b); Luehrman, T., (1997); Howell, S., Stark, A., Newton,
D., Paxon, D., Cavus, M., Pereira, J., Patel, K., (2001)21
Borison, A., (2005a), p. 20.
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Referring back to the example in chapter 2.1, option parameters such as the current
market value of the undeveloped field (V) and its volatility () could simply be
estimated by using average values of the Canadian oil industry as comparables.22The
option (market) value would then be calculated by applying the standard Black-
Scholes formula. Using financial option formulas to value real options without making
an attempt to identify a replicating portfolio cannot lead to reliable valuation results.
Because of its conceptual inconsistency, this approach fails at serving as a reliable
investment decision support.
3
The Marketed Asset Disclaimer Approach (MAD)
As described in chapter 2, identifying a replicating portfolio in order to determine the
parameters of options on real assets (V, ) and valuing these options using standard
option pricing formulas can be a very difficult task. To overcome this problem,
Copeland and Antikarov (2003) propose the MAD approach which does not require a
traded replicating portfolio. Rather the replicating portfolio is represented by the net
present value (NPV) of the projects expected cash flows without managerial
flexibility.23
According to the MAD approach, a project could theoretically be traded as a security
in capital markets and the NPV of a project without flexibility can therefore be used as
a proxi for its market price. In the same way that the fundamental value of traded
equities, i.e. the present value of its future cash flows, can be used as an estimate of its
spot price, the NPV represents an estimate of the projectscurrent market value (V).
According to MAD, the NPV of a project without flexibility is the best estimate of a
replicating portfolio because in most cases, it unlikely to find securities in capital
markets that have a higher correlation with the cash flows of a real asset than the asset
22Borison, A., (2005a), p. 21.
23Copeland, T., Antikarov, V., (2003), p. 94. See also Brando, L. E., Dyer, J. S., Hahn, W. J., (2005)
for a similar approach.
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itself.24 Following this argumentation, a real option on a projects NPV is the best
estimate of the market value of that option.25
The underlying reasoning for the assumptions made in real options valuation under
MAD refers to the fact that similar assumptions are made in standard discounted cash
flow valuations (DCF) of corporate investments. As stated by Brealey and Myers
(2006), any investment project is valued under the DCF approach as if it were a firm
whose shares can be traded in capital markets.26 The required rate of return on a
project and the appropriate discount rate are thereby determined based on the risk
characteristics (beta) and expected returns of publicly traded securities. Accordingly,
the value of a real option on the NPV should be a good estimate of the market value of
the flexible project if it were traded.27 The application of the MAD approach is
illustrated in the next section.
3.1
Application
As a first step, the projects NPV is calculated in order to determine the current market
value of the undeveloped field (V). Vrepresents the market value of the project without
any flexibility. The NPV calculation is based on a single deterministic scenario
regarding oil reserves, the start of production, production rates, oil prices and
production costs. For the assessment of future oil prices, Copeland and Antikarov
(2003) suggest using either historical data or subjective, forward-looking estimates by
management.28The costs of acquiring the option are not considered. As an appropriate
discount rate, the weighted average costs of capital (WACC) of oil firms, mainly
investing in Canada, could be used.
24Copeland, T., Antikarov, V., (2003), p. 133.
25
Borison, A., (2005a), p. 22.26Brealey, R., Myers, S., (2006), p. 622.27
Borison, A., (2005a), p. 22.28
Copeland, T., Antikarov, V., (2003), p. 215.
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NPV = V = - I0+ T
t=1((Ptcofvt) xtCOFft) q-t+ L qT where (4)
t= time index; T= last year of project; I0= initial investment outlay; P= sales price;
cofv= variable cash outflows per unit; x= sales volume; COFf= fixed cash outflows;
q= 1/(1+WACC) = discount factor; L = liquidation value.29
After having calculated V, probability distributions for the key uncertainties, such as
reserves and oil prices, can be defined and a simulation program be used to determine
the volatility of project cash flows (). The call option, i.e. the flexible part of the
investment project, can now either be valued using the standard Black-Scholes formula
or, as suggested by Copeland and Antikarov (2003), using a risk-neutral binomial
valuation model. The valuation process is summarised in Figure 1.30
Figure 1: Option valuation in the binomial model
Source: Author
At first, the value development of the underlying and the NPV of the project is
modelled. After the first year, the current value can either increase to V0uor decrease
29Gtze, U., Northcott, D., Schuster, P., (2008), p. 56.
30For a detailed description of the binomial valuation model see Brealey, R., Myers, S., (2006).
V0u
V0d
V0u2
V0ud
V0u2
t0 t1 t3
C1 = max[V0u3-I3;0]
C2 = max[V0u2d-I3;0]
C3 = max[V0ud -I3;0]
C4 = max[V0d -I3;0]
V0
CMV
2,2
CMV
2,1
CMV
2,0
CMV
1,1
CMV
1,0
CMV
0
t2 t0t1t2
1. Modelling the
underlying (NPV)2. Option value
at expirry
3. Recursive determi-
nation of option value
Vj = V0ujd
n-j
Ci = {prnCut+1 + (1-prn)C
dt+1}(1+rf)
-1
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to V0d, with ued nT
/1/
.
(4)
The up- and down-factors reflect a value process that follows the Geometric Brownian
motion.31On the date of expiration T, the call option is exercised if the value of the
NPV (V) is greater than the cost for investing (I3). In order to determine the current
option value (CMV) the binomial tree is solved in a recursive manner using risk-neutral
probabilities (prnand 1-prn) and discounting at the risk-free rate (rf), with
prn= (erfT/nd) / (ud). (5)
In analogy to the RPA, the goal of real options valuation under the MAD approach is
to maximise shareholder value and its output reflects the value created for the firms
diversified investors.32The investment decision results in:
If (V0 I0) max[CMV,0 C;0] 0, invest in field development today to maximise
shareholder value.
If (CMV,0C) max[V0 I0; 0] 0, invest in call option on the field (development
right) to maximise shareholder value.
If (C CMV 0) and (I0 V 0), do not invest at all because the option and the
investment project are overpriced and shareholder value is destroyed.
3.2 Critical assessment
The description of the MAD approach in the previous section shows that, in contrast to
the RPA, the resulting market values are not based on a traded replicating portfolio.
The NPV as the current market value of the underlying (V0) as well as the option value
(CMV,0) are not purely determined by objective market data but are largely dependent
on subjective estimates of future cash flows. Market data is only used to calculate the
31The same process in assumed in the Black-Scholes model. Alternatively, a different process could be
defined.32
Borison, A., (2005b), p. 53.
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equilibrium discount rate in the NPV model.33 V0 as the fundamental value of the
undeveloped oil field can be interpreted as an estimate of its current equilibrium value.
Although the correlation between the fundamental value and the fields capitalisation
on the market might generally be high, the degree of correlation depends on a market
premium which can be highly variable due to changing market sentiments.34
Compared to the subjective RPA, the oil field investment and the development right
are priced consistently so that the non-arbitrage condition between the investment and
the option may be met. However, the MAD approach does not ensure that the
investment and option are priced correctly relative to the market.35Therefore, arbitrage
opportunities between the investment project under consideration and related traded
investments may exist. The values of oil and gas investments are particularly sensitive
to future commodity prices. Liquid commodity markets, in which oil and natural gas
products are traded with different time horizons, provide information regarding these
markets risks which could be incorporated into the option valuation process in order to
avoid arbitrage opportunities. If market and subjective expectations regarding future
commodity prices deviate, arbitrage opportunities are introduced.
The values of the undeveloped oil field and the development right under the MAD
approach are also highly dependent on the assumed value process of the underlying
investment (V). The Geometric Brownian motion within the binomial valuation model
may not accurately reflect the true development of the project value. Rather, the value
could be driven by specific events at specific points in time, such as the discovery of
larger reserves than expected or higher discovery factors than anticipated.36 The
assumed price process should account for such an evolution of value.
33
Borison, A., (2005a), p. 24.34Guj, P., (2010), p. 2.35
Borison, A., (2005b), p. 53.36
Borison, A., (2005a), p. 24.
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4 The Hybrid Real Options Approach (HROA)
The HROA explicitly distinguishes between two types of risks associated with most
investment projects: Public risks (market risks), such as price risk, and private risks,
i.e. project specific risks.37
In comparison to the RPA, the HROA does not assume that
capital markets are complete and a replicating portfolio can be found which perfectly
hedges all project risks. Rather, financial markets are assumed to be partially
complete.38Whereas public risks associated with an investment project can be hedged
in any state of the world by trading in existing securities, private risks cannot be
hedged by trading and have to be assessed by subjective judgement. In that sense,
option pricing methods are used to value public risks and decision analysis methods
are used to value private risks.39
It becomes obvious that under the HROA, real options valuation differs considerably
from financial options valuation and standard option pricing formulas cannot be
applied. Investment projects which are characterised by managerial flexibility are
valued using a risk-adjusted decision tree. Such a decision tree incorporates decision
analysis and option pricing approaches.
4.1 Application
The risk adjusted decision tree shown in Figure 2 indicates the logic of the HROA. In
t=0, the firm is faced with three decision alternatives. The undeveloped oil field can
either be bought and the field be developed. The resulting value of the investment
project depends on two uncertainties which is the price and the amount of oil.
Alternatively, the firm can decide to purchase the development right and wait for the
uncertainties to resolve over time. The uncertainty regarding the amount of oil resolves
after year one, whereas the price of oil evolves incrementally over the time to
37
The HROA is described and applied in Smith, J. E., McCardle, K. F., (1998); Smith, J. E., McCardle,K. F., (1999) and Smith, J. E., Nau, R. F., (1995).38
Smith, J. E., McCardle, K. F., (1999), p. 199.39
Borison, A., (2005a), p. 27.
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expiration of the call option. In year T=3, the firm must decide to either exercise the
option to purchase and develop the oil field or let the option expire and the third option
is not to invest at all.
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Figure 2: Risk-adjusted decision tree in HROA
Source: Author
Decision node Amount of oil Price of oil End node
No
No
Exercise option
Exercise option
No
Exercise option
Down
Down
Up
Up
Up
High
Down
Down
Up
Up
Up
Down
No
Exercise option
Low
Buy option
Up
Low
High
Up
No investment
Up
Down
Down
Base
Base
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
Down
Up
Up
Buy oil field
Down
Up
Up
DownDown
Up
Down
Down
Down
t = 0 t = 1 t = 2 T = 3
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
NPV(rf)
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For the application of the HROA, the uncertainties associated with the undeveloped oil
field have to be defined as public and private risks. The oil price can be defined as a
public risk and the size of the reservoir is defined as a private risk. The private risk is
by definition not correlated with any individual investment or portfolio of investments
in financial markets.40For the private risk, a beta of zero can therefore be assumed. For
the amount of gas, three scenarios are defined and subjective probabilities are assigned
for each scenario. These subjective probabilities can be determined based on
geological experiences.
The public risk which can be replicated in capital markets is treated differently.41The
price risk is modelled using a discrete binomial model in which the oil price can either
make an up-movement with a risk-neutral probability of prnor a down-movement with
1-prnin each time period (Figure 3). The binomial model is constructed using market
information regarding annual volatilities and convenience yields from traded oil price
options and futures.
Figure 3: Binomial oil price model within HROA
Source: Author
At each end node of the risk-adjusted decision tree, a spreadsheet cash-flow model is
used to calculate state-contingent NPVs depending on the amount of oil in the field
40Borison, A., (2005a), p. 26.
41Smith, J. E., McCardle, K. F., (1998), p. 201.
OP1 u
OP0
OP1 d
OP2 uu
OP2 ud
OP2 dd
OP3 uuu
OP3 uud
OP3 udd
OP3 ddd
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and incorporating expectations of capital markets regarding the development of future
oil prices. From the perspective of diversified shareholders, the cash flows can be
discounted using the risk-free rate (rf) because public risks can be perfectly hedged and
private risks are not correlated with traded securities (beta = 0).
The values of the undeveloped oil field (VHROA) and the development right (CHROA) are
finally found by applying the roll-back method to solve the decision tree. Starting at
T=3, the value maximising decisions are made and the state contingent NPVs are
multiplied with the respective risk-neutral or subjective probabilities and discounted at
the risk-free rate. As under the approaches in chapters 2 and 3, the following
investment decisions are made:
If (VHROAI0)max[CHROAC;0] 0, invest in field development today to maximise
shareholder value.
If (CHROAC)max[VHROAI0; 0] 0, invest in call option on the field (development
right) to maximise shareholder value.
If (CCHROA0) and (I0VHROA0), do not invest at all because the option and the
investment project are overpriced and shareholder value is destroyed.
4.2 Critical Assessment
The HROA explicitly decomposes the uncertainty associated with investment projects
and addresses market risks and private risks separately. The assumption that oil and
gas investment projects are characterised by risks that can be hedged in capital markets
and risks that cannot be replicated seems realistic and allows the HROA to be applied
in a very broad range of corporate investments. In particular, it enables decision
makers to overcome the problem of finding a perfectly replicating portfolio and
applying standard option pricing formulas when capital markets are assumed to be
incomplete. By incorporating available market information, the valuation process also
mitigates the problem of introducing arbitrage opportunities.
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From a practical perspective, the HROA can be problematic due to its high degree of
complexity. When several uncertainties and time periods are incorporated into the
project valuation, structuring the problem can be difficult and the resulting decision
tree quickly becomes very large with several thousand end nodes.42
5 Conclusion
In this paper, real option approaches currently used to value oil and gas investment
projects are categorised and described with regard to the assumptions made, the
treatment of project uncertainty and the necessary calculations. The analysis reveals
significant differences between the various approaches.
Applying the RPA and using standard option pricing formulas is only justified if
capital markets are complete and the underlying investment project can be perfectly
replicated. With regard to real-world investment projects, the assumptions made under
the RPA are restrictive and limit its applicability.
The subjective RPA as well as the MAD approach also use standard option pricing
formulas to value real options. Both approaches, however, do not attempt to identify a
replicating portfolio of securities traded in capital markets. Rather, the approaches
heavily rely on subjective estimates which do not ensure consistent and arbitrage-free
valuation results.
The HROA incorporates option pricing and decision analysis in order to meet the
assumption that capital markets are only partially complete. Due to its less restrictive
assumptions, the approach is applicable in a broader range of investment cases. The
valuation process is, however, more complex than under the above approaches which
can be a trade-off for decision makers.
42Smith, J. E., McCardle, K. F., (1999), p. 3.
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