1. Real Options as Decision Tools:
Maximizing Value for Oil Field Investors
by Houston Hunter
Department of Industrial Engineering
University of Arkansas
INEG 4423: Advanced Engineering Economics
Term Paper
Dr. John A. White
Spring 2015
Abstract
This paper will assess the applicability and feasibility of the use of Real Option Analysis
(ROA) when making economic decisions as an oil field project moves forward from the
exploration period to the production period. This paper will serve as a quick tutorial on real
options as well as a brief economic analysis of a *fund’s recent investment into its drilling
company, ANEC. To illustrate and differentiate the use of real options from present worth
analysis using the discounted cash flow method, data has been provided from the fund’s recent
investment proposal into ANEC so that examples can be built to further explain the use of these
real options as strategic decision tools. ROA will introduce two variables that are not properly
accounted for in the discounted cash flow analysis, specifically the time to investment and the
expected return’s volatility. These can be used to not only better determine the ultimate value of
a project but as a decision tool that can be used when making flexible, forward looking,
economic decisions amid a future lined with uncertainty. The value of economic decisions, or
imbedded options for this paper’s purposes, may not be properly accounted for through use of
conventional present worth analysis. ROA better captures the value of these imbedded decisions
and communicates their worth to management. This paper requires basic knowledge of options,
fundamental engineering economic analysis, and a thorough understanding of the time value of
money.
*I am grateful for thecontent providedfromthe privatefundmanager’s investment proposal to investors.The proposal providedme with
sufficient data so that I couldconstruct a situation where the applicationof Real Options Analysis proves a valuable resource when making
strategic business decisions.

2. Introduction
In traditional finance, the discounted cash flow model serves as the basic framework for
most payback analysis. The discounted cash flow model is commonly used by firms to determine
the measure of return the firm can expect given its initial investment and expected cash flows.
With this fundamental analysis, a firm can expect a project with a positive net present value to
increase the firm’s wealth where a project with a negative net present value will yield the
opposite. However, the value the firm places on the equity it plans to acquire or project it wishes
to develop does not take into consideration future actions that may influence the cash flows of a
project such as the options to delay, expand or abandon a particular project. From a broader
view, the traditional value of equity may not reflect the financial flexibility of the option to
control various components that make up expected cash flows.
The first part of this paper is an introduction to options to help better understand the
mechanics and how these mechanics transfer to valuation of real options. Next, the Black-
Scholes option-pricing model will be discussed. Once a fundamental understanding of real
options is established, we will look at how managers can take advantage of these imbedded
decisions or real options to increase the value of the project for the fund’s investors.
Financial Option Basics
Financial options are financial contracts that state a price at which the contract holder
may buy or sell the underling equity at a designated price, the strike price. Option contracts are
not free however and there is a price at which you must pay to possess the contract or option.
These option prices are relatively cheap in financial markets when compared to the strike price
or the price of the underlying equity. A Call Option allows the holder to buy the underlying
asset, such as a stock or traded fund, at a predetermined price, the strike price. It can also be
noted that the option holder has the right but not the obligation to purchase the underlying. In
return, the seller of the option assumes the obligation to sell the underlying asset to the buyer at
the predestinated strike or exercise price. A Put Option allows the option holder to sell the
underlying asset at a predetermined price, also the strike price. Here, one must note that the
buyer obtains the right but not the obligation to sell the underlying asset. The seller of the put
option then assumes the obligation to purchase the underlying asset when at the strike price. The
buying power that results from a small purchase of an option is a type of leverage that can allow
the holder to net a disproportional gain in comparison to the option’s price. The price of the
option contract derives its value from the following factors: underlying asset’s price, strike price,
time to expiration, volatility, interest rates (assuming equity does not pay dividends), and option
type (American, European, Bermudan, Barrier, etc.)[7].
Real Options
Real options are identical to financial options in respect to they are options or agreements
to undergo a certain investment activity in the future. However, real options differ from financial
options in the following ways: There is not a securities market or market in general exists for real

3. options. Given this, pricing real options is much more complicated and less transparent as the
real option price is not a determinant of what a potential buyer or seller (more realistically the
market as a whole) is willing to ask or bid for the option. Without this market accessibility, the
supply and demand created in financial markets is not present so real options must be viewed as
inefficient entities where pricing discrepancies inherently exist. Also, real options reflect the
price of some physical asset rather that a financial asset like a stock or a traded fund. Lastly,
financial options are more tangible and recognizable since the parameters by which they are
priced to be more concrete and quantifiable. Real options are much less tangible allowing for
these parameters to be much more subjective and left up to the manager’s interpretation.
Several types or real options exist and can be compared to their financial counterparts.
The first type of option is the growth option or call option in financial markets. This type of
option can be used to expand production or develop new revenue streams in the future. Another
real option is the constriction option or put option in financial markets. It can be used to justify
the abandonment of a revenue stream or for a contraction in production. Switching options are
yet another type of real option commonly used. These can be used to switch between revenue
streams or switch between means of production. The last kind of real options is contractual real
options. These options can be used to place forward bets on future prices as well as establish
guaranteed salvage values for existing equipment [4].
In the Handbook of Modern Finance, Triantis describes five key option based strategies.
One, investment opportunities should never be identified as a now or never scenario. Two, there
does not need to be bias toward the most likely scenario, managers should create flexibility
allowing the project to be altered as business conditions govern. Third, managers should choose
to invest in stages rather than all at once. Fourth, managers should identify a broad set of future
alternatives when formulating their strategy. And fifth, creation of real options is most beneficial
when uncertainty is highest [9].
Black-Scholes Option Pricing
One of the best known continuous time pricing models was developed by Fischer Black,
Myron Scholes and Robert Merton during their research at MIT into stochastic pricing
techniques in 1973. This model, named the Black-Scholes Model (BSM), won the Nobel Peace
Prize in 1997 and is commonly used to price stock options paid to executives and board members
of corporations around the world [2].
In order to understand the BSM one must agree on the following assumptions: there are
no dividends, options are European, movements in the underlying cannot be predicted, no
commissions are paid out, no arbitrage opportunities are present, and finally the risk free rate and
the underlying’s volatility are said to be constant until maturity.
Although many variations of the original Black-Scholes model exist, this paper will use
the following adaptation made by Carlsson and Fuller [5]:
where and

4. In the first equation, C is the price of the call option, S is the share price, X is the strike or
exercise price of the stock, r is the risk free interest rate, T is the time until expiration, and σ is
standard deviation of the return of the stock.
Applying BSM to Real Options
As discussed in the section above, there are five parameters that affect the value of an
option (S, X, T, r, and σ ). These parameters are the same for financial options but how they are
interpreted differs. S is defined as the present worth of the investment’s future positive cash
flows (using the fund/firm’s hurdle rate or MARR) while X is the magnitude of the deferred
capital investment. T still represents the time until expiration or maturity, r still represents the
risk free rate, and σ represents the standard error of the cash flows generated by the future capital
investment [6]. Let’s look at an application of real options.
Real Options in Action
The unnamed fund’s most recent investment proposal into ANEC requires an investment
of approximately $20.66MM in order to pay the CAPEX cost of $16.6MM plus fees, facility
improvements, and leasehold requirements. This new infusion of capital into ANEC will then be
used to drill and complete nine new wells in a bayou in southern Louisiana. It is anticipated that
each well will take approximately one month to complete once the rig is in position. The rig will
move from drill site to drill site through a series of canals in the bayou and should take no more
than 8 hours to do so. Production from these wells is expected to yield 350 barrels per day net to
ANEC’s interest and should add an incremental $997,500.00 per month to existing revenue
(assuming oil is hedged at $95.00/BO). Individual well info is as follows:
Since these wells are unproved or new wells, we will use the primary reserve estimates
only by adjusting the planning horizon to three years, a reasonable time frame where only
primary reserves will be extracted. The expected value of a project usually depends upon two
variables, the price which the producer can expect to receive for each barrel of oil and the rate at
which oil is expected to be extracted. Since ANEC has expertly insured or “hedged” the price
during production to $95.00 per barrel throughout the planning horizon, our varying project
value metric will only be the rate at which oil is expected to be extracted.
Here we can define optimal oil extraction using real options. We model each well as an
individual real option where the call value of each well can be viewed as the value of a well if it
is drilled in a particular month. This ROA is used as a decision tool where we can determine the
WELL # PRI RESERVES (MBO) SEC RESERVES (MBO) WELL COST PRODUCTION/DAY(BO) PRODUCTION/MO(BO) REVENUE/MO
1 176 0 2,200,000.00$ 39.66 1189.90 113,040.57$
2 536 144 3,200,000.00$ 83.90 2516.86 239,101.80$
3 103 0 2,100,000.00$ 31.78 953.33 90,566.14$
4 150 71 1,500,000.00$ 29.85 895.52 85,074.46$
5 113 23 1,500,000.00$ 26.39 791.64 75,206.14$
6 77 77 1,500,000.00$ 23.02 690.57 65,604.54$
7 450 286 2,200,000.00$ 65.31 1959.15 186,119.45$
8 85 40 1,200,000.00$ 20.61 618.15 58,724.67$
9 180 60 1,200,000.00$ 29.50 884.87 84,062.24$
TOTALS = 1870 701 16,600,000.00$ 350 10500 997,500.00$

5. order of drilling that creates the maximum value for the project, hence “optimal oil extraction”.
Therefore, for each of the nine wells, we have nine different call prices where the well can be
drilled today, at the beginning of the second month and so forth until all wells are completed and
producing. So, for each period of drilling we will say that T = 0,1,2…8 for each of the nine
wells. We can then take the rate at which the oil is expected to be extracted to follow a normal
process assuming the fund manager actively continues his evaluation of 3D seismic surveys to
better understand this rate and how these estimates are subject to change. Therefore, we can
assume an implied volatility on the expected rate of oil extraction as it directly influences the
expected reserve value of each well. From industry data, typical implied volatility in reserve
value from exploration to production ranges from .142 to .25 [8]. Since the price is properly
hedged, we will use .15 for the implied volatility parameter, σ, as this is what can be expected as
the wells begin producing. Each well has an upfront investment cost that is stated to remain
constant so we will model this upfront cost as the strike price of the real option, X. We will
assume the hurdle rate or MARR of the fund is a continuous 1% per monthly period (equivalent
to a 12.75% nominal yearly rate). With this, our expected positive cash flow will be brought
back to the present using this 1% continuous compounding rate to find the present value of all
positive cash flows, S. We will also assume the risk free rate, r, to be 2% annually for practical
purposes.
Our use of ROA can then be used as a decision tool to determine the optimal order in
which the wells should be drilled to create the maximum value to ANEC’s project, thereby
creating the maximum value to the fund’s investors. We assume that the nine different wells can
be drilled in any order to maximize the project’s value where one well can only be drilled once
and one well can be drilled per month, creating (9
2
) or 36 possible drilling combinations. For
each of the 36 orders of drilling, we claim in the analysis that there is one route in particular that
yields the maximum value to the project. First a spreadsheet of all nine wells needs to be created
where each well has a different call value for month where is can be drilled therefore, creating
9x9 or 81 possible call values. The 81 call values are listed below:
One may notice that for some wells, the option price increases with additional time as
expected, but for other wells, option value degrades with time. I believe this is because the value
an option gains from an increased expiration can be overcome by the rate at which future cash
flows are discounted back to the present in some situations.
Since it is difficult to quickly calculate the sum of all nine call values for each of the 36
combinations of which drilling can be performed, we will use the linear optimization software,
cplex (coded in AMPL), to determine the optimum route. The objective function of the model
T CALL WELL 1 CALL WELL 2 CALL WELL 3 CALL WELL 4 CALL WELL 5 CALL WELL 6 CALL WELL 7 CALL WELL 8 CALL WELL 9
0 1,124,482.58$ 3,831,818.62$ 563,535.83$ 1,002,000.62$ 711,787.48$ 429,417.93$ 3,273,628.59$ 527,074.55$ 1,272,216.41$
1 1,095,343.77$ 3,766,954.69$ 550,038.40$ 979,527.44$ 692,662.33$ 418,192.50$ 3,222,673.95$ 512,438.59$ 1,249,531.43$
2 1,072,575.88$ 3,702,986.36$ 555,601.71$ 958,663.78$ 678,977.78$ 420,085.03$ 3,172,376.97$ 503,157.37$ 1,227,194.23$
3 1,057,434.19$ 3,640,210.23$ 564,982.38$ 941,212.90$ 670,766.85$ 425,357.69$ 3,122,679.46$ 498,358.05$ 1,205,499.32$
4 1,047,066.10$ 3,579,634.87$ 574,439.25$ 926,960.49$ 665,628.44$ 431,075.19$ 3,073,860.74$ 495,800.42$ 1,184,954.48$
5 1,039,465.61$ 3,521,999.98$ 583,126.00$ 915,096.81$ 662,138.60$ 436,475.87$ 3,026,312.75$ 494,339.39$ 1,165,784.85$
6 1,033,483.74$ 3,467,545.54$ 590,866.51$ 904,938.32$ 659,541.81$ 441,350.66$ 2,980,333.47$ 493,410.91$ 1,147,974.02$
7 1,028,458.09$ 3,416,187.01$ 597,673.04$ 895,996.55$ 657,424.31$ 445,661.01$ 2,936,070.14$ 492,722.49$ 1,131,398.71$
8 1,023,994.01$ 3,367,689.00$ 603,612.60$ 887,932.74$ 655,549.91$ 449,425.97$ 2,893,549.92$ 492,115.34$ 1,115,906.68$

6. maximizes the total call value and is subject to two constraints that state that only one well can
be drilled per month and each well can only be drilled once. The outputs of the software are
below:
Given this data, the optimal order of drilling going forward is {2, 7, 9, 4, 1, 5, 8, 6, 3}
creating a cumulative option value of $12,474,788.92. With the standard discounted cash flow
method, we can see that the total present worth, given the wells are drilled in this particular
order, is only $12,036,316.28. Not only did the application of ROA optimize drilling order, it
also created $438,472.64 in additional value for the oil project’s investors, given only a 3 year
planning horizon. This is just one example of how ROA can enhance and quantify business
strategy and add value to a project. With the traditional DCF method, this type of analysis is not
possible as the value of flexibility in waiting to pursue a particular investment is not properly
accounted for.
Conclusion
Oil exploration is not a risk adverse endeavor as information provided from third party
engineering firms about oil reserves is not always accurate and can lead to major discrepancies in
the expected return of a project, even when the price per barrel is certain. With the application of
real options analysis, risk can be quantified and used to the advantage of the project’s interest. In
this case, ROA is used to determine the exact order of drillings required to yield the maximum
value of the project during the drilling period. This type of analysis could not have been
accomplished with an otherwise rigid, discounted cash flow method. Regarding discounted flow
methods, Brealey notes [3], “When you use discounted cash flow to value a project, you
implicitly assume that the firm will hold the assets passively.” However, this is not the case as
managers are not compensated based upon how their investments are planned to preform but
rather on how they preform given that they are managed over time. In this paper, ROA is used as
a decision tool and as a means to calculate the present value of the project with a three year
planning horizon. We used only a three year planning horizon but any planning horizon can be
assumed to determine the optimum drilling strategy yet it is important to note the total value
created by ROA is subject to change as different planning horizons are assumed. It is also
important to note that there still exist other factors that can contribute an oil field’s decision
process such as safety, environmental circumstances, laws and regulations, and complex contract
terms [1].

7. The use of ROA does in fact add significantly more value to a project, both intrinsic and
tangible, since the time at which a decision takes place is properly accounted for as a value added
criterion. Overall, this paper has shown that managerial flexibility, especially in the face of
uncertainty or volatility, can provide a strategic advantage during project planning when ROA is
used as a decision tool and as a means to present the projects value. It is not recommended that
the discounted cash flow method be disbanded all together; however, more dynamic methods
may be required to make more sophisticated strategic decisions throughout the life of an
investment project.

8. References
[1] Babajide, A., De Neufville, R., & Hale, P. (2007). Real Options Analysis as a Decision Tool
in Oil Field Developments. Thesis, 55.
[2] Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of
Political Economy, 81(3), 637-654.
[3] Brealey, R., & Myers, S. (2014). Principles of Corporate Finance (11th ed.). New York, NY:
McGraw-Hill/Irwin
[4] Canada, J., Sullivan, W., White, J., & Kulonda, D. (2005). Capital Investment Analysis for
Engineering and Management (3rd ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
[5] Carlsson, C., & Fullér, R. (2001). A Fuzzy Approach to Real Option Valuation. Fuzzy Sets
and Systems, 297-312.
[6] Luehrman, T. (1995). Capital Projects as Real Options: An Introduction. Harvard Business
School.
[7] Preston, T., Kaufman, D., Sherrod, N., Ruffy, F., & Blackman, M. (2013). The Ultimate
Options Primer. In K. Lund (Ed.), How to Thinkorswim. T3 Publishing/SpeakMedia.
[8] Schwartz, E., & Trigeorgis, L. (2001). Option Valuation on Claims of Real Assets. In Real
Options and Investment Under Uncertainty: Classical Readings and Recent
Contributions (p. 794). MIT Press.
[9] Triantis, A. (2003). Real Options. Handbook of Modern Finance. New York, NY: Research
Institute of America.