1. finance
2. investing
3. options

October 2009
grand award grand award
Volume 26
Number 3
The MONTHLY journal for Producers, Marketers, Pipelines, Distributors, and End-Users
How to Value Energy Assets Using Real
Options
R. Kenneth Skinner
S
ince the early studies of the 1980s, much has been written about real-option valuation. Led by the seminal work of
Brennan and Schwartz,1 who solve for the value of a natural
resource investment, these studies sought to build upon the
financial-option work of Black and Scholes2 and others. Nevertheless, today there remains a real skepticism among many
capital asset valuation professionals as to the role of real-option valuation techniques. The skepticism is driven in part by
misconceptions and in part by valid concerns. In this article,
I briefly describe the real-option valuation method, discuss
the misconceptions and concerns, and take a look at four examples of how the real-option technique can effectively value
capital asset projects. The empirical methods are referred to
but not explicitly stated.
Real-option valuation is often perceived as an alternative
or competing method to discounted cash flow (DCF) techniques. It seems at times that economists and statisticians
align themselves in one corner and engineers align themselves
in the other corner and then proceed to debate the virtues
of the two methods. But in fact, the real-option technique
relies on the DCF method and does not change the DCF
calculations at all. As we will see, the DCF techniques provide
R. Kenneth Skinner (kenneth.skinner@integralanalytics.com,
[513] 762-7621) is vice president and chief operating officer of
Integral Analytics.
Other Features
Risk Management
The Art and Science of Risk
Management Reporting
Julia Ryan.............................................. 9
Taxation and Finance
Financing T&D Systems the “REIT” Way
David A. Miller and W. Kirk Baker....... 14
Renewables
PV Pulling Ahead, but Why Pay
Transmission Costs?
Bill Powers........................................... 19
Smart Grid
NAESB Electric Demand-Response
Standards Break New Ground
Rae McQuade..................................... 23
FERC Regulation—Natural Gas
Today’s Array of Pricing Schemes
Yields Optimal Pipeline-Construction
Financing
Bruce E. Warner.................................. 28
Published online in Wiley InterScience (www.interscience.wiley.com).
DOI: 10.1002/gas.10098 © 2009 Wiley Pe­ri­od­i­cals, Inc.
Natural Gas & Electricity
Associate Publisher: Robert E. Willett
Executive Editor: Isabelle Cohen-DeAngelis
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Editorial Advisory Board
2
Kenneth L. Beckman, President
International Gas Consulting, Inc.
Houston
Keith Martin, Esq.
Chadbourne & Parke
Washington, D.C.
Christine Hansen, Executive Director
Interstate Oil and Gas, Compact
Commission
Oklahoma City
Rae McQuade, Executive Director
North American Energy Standard
Board
Houston
James J. Hoecker, Senior Counsel
Husch Blackwell Sanders LLP
Washington, D.C.
and Principal,
Hoecker Energy Law & Policy, PLLC
Markham, VA
Former Chairman, Federal Energy
Regulatory Commission
Robert C. Means, President
USI Inc.
Arlington, VA
John E. Olson, Managing Director,
Houston Energy Partners, and
Chief Investment Officer,
SMH Capital, Houston
R. Skip Horvath, President
Natural Gas Supply Association
Washington, D.C.
Brian D. O’Neill, Esq.
LeBoeuf, Lamb, Greene & MacRae
Washington, D.C.
Jonathan A. Lesser, President
Continental Economics, Inc.
Albuquerque, NM
David N. Parker, President / CEO
American Gas Association
Washington, D.C.
© 2009 Wiley Periodicals, Inc. / DOI 10.1002/gas
Cynthia L. Quarterman, Esq.
Steptoe & Johnson, formerly
Director,
Minerals Management Service
Washington, D.C.
Donald F. Santa Jr., President
Interstate Natural Gas
Association of America
Washington, D.C.
Benjamin Schlesinger, President
Schlesinger and Associates, Inc.
Bethesda, MD
John Shelk, President
Electric Supply Power Association
Washington, D.C.
Richard G. Smead, Director
Navigant Consulting, Inc.,
Houston
William H. Smith Jr., Executive
Director
Organization of MISO States
Des Moines, IA
Natural Gas & electricity
october 2009
us with a very important result—the expected
value of the project.
However, the result provides very little information about the riskiness of the project. There
is no discussion about “contingent decisions,”
meaning how the project will be managed as
more information is received. There is little effort given to improving the odds of success and
reducing the chance of failure. And, most importantly, the DCF technique does not value
the potential payoff of proactively managing the
asset. In many cases, the proactive management
is simply another way of describing the inherent
operation of the asset.
For example, the operator of a peaking power
plant knows to generate when the spark spread
exceeds a certain threshold and shut the plant
down when prices fall below that point. The operator proactively manages the asset like a real
option on the spark spread. The peaking plant
may only operate a few hours every year. But
because of the uncertainty of those few hours,
the DCF method alone has been shown to be
a very unreliable estimate of value for this type
of asset.
Real-Option Approach
The real-option approach is generally considered an extension of financial option theory
applied to investment options on real (nonfinancial) assets. While financial options are detailed in contracts, real options are embedded
in strategic investment projects and can have
a substantial impact on the final project value.
Because of the explicit valuation of investment
opportunities, the real-option approach requires
a shift in thinking that helps managers to better
plan and manage strategic investments.
The real-option thinking follows a three-step
process.3 First, strategic investment options are
identified and valued using financial engineering methods. Options are contingent decisions.
An option is an opportunity to make a decision
after you see how events unfold. The first step
then is to recognize the possible outcomes and
the choices that will exist given these different
outcomes. Second, the investment decision is
redesigned to better take advantage of positive
developments and to avoid negative outcomes.
Third, real-option thinking is then used to proactively manage the investment through the options created.
october 2009
Natural Gas & electricity
Exhibit 1. Long Call-Option Payoff Diagram
The real-option valuation process is grounded
in financial option mathematics. An option’s
value is often represented using the payoff diagram shown in Exhibit 1. The value of the option is dependent on the uncertain underlying
price, the strike price, the market volatility, the
amount of time until the option expires, and the
risk-free interest rate.
Like the financial option, a real option also
has a corresponding payoff diagram shown in
Exhibit 2. A manager has an option to go forward with a capital investment project (a long
call) at a breakeven price (the strike price) on or
before an expiration date. The value of the project largely depends on the potential of uncertain
gains (volatility).
As shown in Exhibit 3, the real-option value
of a project is described in two parts: the intrinsic
and the extrinsic. The total project value is the sum
of these two. In Exhibits 1, 2, and 3, the intrinsic
value is represented by the bold line and the extrinsic value is represented by the dashed line. In Exhibit 3, two possible outcomes of the underlying
Exhibit 2. The Option Value of an Investment Project
Due to Uncertainty
DOI 10.1002/gas / © 2009 Wiley Periodicals, Inc.
3
variables are noted by points A and B. At point A,
the project only has extrinsic value. At point B, the
project has both intrinsic and extrinsic value.
The probability distribution of the underlying project uncertain variables can be superimposed onto the payoff diagram as shown in Ex-
Exhibit 3. An Option’s Intrinsic and Extrinsic Value
Exhibit 4. The Underlying Probability Distribution
Driving Value
hibit 4. The width of the distribution depends
on the market volatility and the time to expiration. As the volatility of the underlying variables
increases, the value of the option also increases.
In the case of a call option, the value of the option is equal to the area under the probability
distribution forward of the strike price.
The probability distribution of the underlying
uncertain variables can also be described as a function of time. The longer we can wait for a particular outcome, the more likely the outcome will
be achieved. We use what is called the “Cone of
Uncertainty,” shown in Exhibit 5, to describe the
possible outcomes over time and to represent the
path that uncertainties can follow through time.
The Cone of Uncertainty is a visual representation of a multitude of financial engineering techniques that are available to solve for the
price progression. These techniques have names
like Geometric Brownian Motion (GBM),
Mean Reversion Jump Diffusion, GARCH,
Binomial Trees, Partial Differential Equations
(PDEs), Finite Differences, Two Factors, Regime Switching, Black-Scholes, and others.
Exhibit 6 demonstrates the Cone of Uncertainty for a GBM price process and the mean
trend forecast. The GBM is the underlying distribution of the Black-Scholes equation. Using
the idea of the Cone of Uncertainty, the relationship between the time to expiration and the size
of the probability distribution can be measured.
The option value is related to the area under the
resulting probability distribution.
Comparing the Real-Option and
Discounted Cash Flow Results
Exhibit 5. The Cone of Uncertainty—Uncertain Value
Over Time
4
© 2009 Wiley Periodicals, Inc. / DOI 10.1002/gas
The Cone of Uncertainty is a convenient
starting point for describing how the conventional DCF result compares to the real-option
result. Because options are not explicitly evaluated, the DCF result converges to the average of
the probability distribution.
DCF considers the present value of an expected stream of cash flows. If the net present
value (NPV) is positive, the project should be
completed. Using option terminology, we call the
expected DCF value the intrinsic value. Consider
the example shown in Exhibit 7. The NPV is the
sum of the DCF—in this example, $14 million.
In practice, DCF valuation professionals will
consider various scenarios to examine the risks
and opportunities of uncertain variables. In ExNatural Gas & electricity
october 2009
hibit 8, two scenarios examine reduced cash flow
following years 1 and 2. The technique is used
by management to consider possible mitigation
strategies, including abandoning the project if
prices drop severely. However, the approach
does not provide any indication as to the probability of abandonment or how the possibility
impacts the overall project value.
If appropriately constructed, the scenarios in
Exhibit 8 begin to express the information contained in the Cone of Uncertainty and the realoption method. In the real-option method, both
the positive and negative possibilities are formulated and the options to change the projected
cash flow are explicitly include in the analysis. In
Exhibit 9, the analysis considers the opportunity
to expand the project if prices are favorable and
to abandon the project if prices are unfavorable.
Both the ability to abandon if project economics
turn negative and the ability to expand if project
economics turn positive have economic value. In
practice, an option-payoff expression or engineering model is used to explicitly capture the change
in cash flow from expansion or abandonment.
The results are folded back to a total project value
that includes both the intrinsic and extrinsic value
components. The extrinsic value is equal to the
option value—the savings and reward expected
by proactively managing change.
As we have formulated the problem, the total
project value has two parts—the DCF value and
the real-option value. The DCF value represents
the expected outcome given all that we know
about the project today. The real-option value
considers the possible changes to the project
economics given the distribution of uncertain
outcomes. The DCF and real-option results
correspond to the intrinsic and extrinsic components respectively of the total project value.
Exhibit 6. Black-Scholes Assumes Geometric
Brownian Motion
additional revenue by arbitraging prices. The
Black-Scholes equation for pricing options has
at least five important variables that can be reinterpreted from a real-option perspective. These
are shown in Exhibit 10.
The pro-forma cash flow for this project
represents the price spread between the existing fuel and the new secondary fuel source. In
the DCF model, the spread is valued at today’s
market. Using the real-option model, we want
to value the benefit of low-probability, highconsequence widening of price spreads. We add
an additional complexity in that the volatility
term changes each period. Year 1 cash flows are
more certain than year 2 and so forth. Because
each period is different, we will model this as
a strip of European call options—each year is
valued independently, and the overall project
value is the sum of the individual options. To
illustrate how the two results are used in the
overall valuation, the analysis splits the results
Exhibit 7. The Discounted Cash Flow Result Mapped
to Uncertainty
An Example Using the BlackScholes Equation
As mentioned earlier, the Black-Scholes equation is one method we can use to solve for the
project option value. In this example, we look
at the economics of adding dual-fuel capability
at an electric generation facility. With different
numbers, the pro forma could also represent the
economics of adding a thermal storage system
at an industrial complex, purchasing gas storage at a refinery, or other projects. Because of
the proposed upgrade, all of these can generate
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DOI 10.1002/gas / © 2009 Wiley Periodicals, Inc.
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Exhibit 8. Discounted Cash Flow Scenarios With an Option for Abandonment
into a DCF component and a real-option component. The DCF result represents the expected
or intrinsic outcome. The Black-Scholes equation is then used to value the upside premium
associated with favorable future outcomes. How
exactly does the Black-Scholes equation do that?
By referring back to Exhibit 6, the Black-Scholes
equation projects the distribution of revenue
(i.e., the Cone of Uncertainty idea) through a
given expiration date. The formula then averages the value from the strike price through the
tail of the distribution.4
Because the additional value is only possible if
market conditions move in our favor, the value
is considered extrinsic. Some have argued at this
point that because it is extrinsic, it should not be
included in the total value. However, the extrinsic value is analogous to an insurance policy. The
policy may never be called, but that does not make
it worthless. The DCF value and the real-option
premium together equal the total project value.
The pro-forma, option mapping, and Black-Scholes option values are shown in Exhibit 11.
Note that the extrinsic valuation problem
measures the spread “at-the-money” (i.e., S =
X). By doing so, the option value results contain
only information about potential gain above the
expected DCF results. Transferring the results
back to the Cone of Uncertainty shown in Exhibit 12, we can see how the DCF expected
results work together with the option value to
arrive at a total project value.
Exhibit 9. The Cone of Uncertainty Representing Risk and Opportunity
6
© 2009 Wiley Periodicals, Inc. / DOI 10.1002/gas
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october 2009
Exhibit 10. Mapping Financial Options to Strategic Investments
Investment Opportunity
VariableCall Option
Present value of a project’s operating assets to be acquired
Expenditure required to acquire the project assets Length of time the decision may be deferred Time value of money
Riskiness of the project assets Limitations of the Real-Option
Approach
The method can be used with any expected
project cash flow that depends on future market
conditions and can be characterized by an expiration date and volatility term. But there are limitations that can reduce the usefulness of the approach. First, the real-option approach requires
knowledge about the uncertain variables driving
value. Second, the process of deriving cash flow
from future optionality must be understood.
The method requires an understanding of volatility and project risk. Interestingly, the DCF
S
X
T
R
s2
Stock price
Exercise price
Time to expiration
Risk-free interest rate
Variance of returns on stock
technique will often use a risk-adjusted rate of
return to account for particular uncertainty. But
the result of this technique is to reject riskier
projects, the opposite of the real-option result
that finds additional value in uncertainty.
It is often helpful to split the pro forma into
discretionary and nondiscretionary cash flow.
The discretionary cash flow represents the project optionality. That is, the company can choose
to invest or not to invest, based on how things
look when the time comes. Discretionary cash
flow is best analyzed using a real-option approach. The nondiscretionary component can
Exhibit 11. Project Valuation Pro-Forma
s
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DOI 10.1002/gas / © 2009 Wiley Periodicals, Inc.
7
Exhibit 12. Intrinsic and Extrinsic Project Value
Mapped to Uncertainty
be analyzed using traditional DCF methods. If
the option has several stages with varying uncertainty, each component can be analyzed separately as a strip of options, the final answer being
the discounted sum of the strip of options. If the
project cannot be split into component parts,
the real-option volatility measure would need to
be a weighted sum of the certain nondiscretionary cash flow and the uncertain discretionary
cash flow.
Examples of Real-Option
Programs
The dual-fuel upgrade is a special class of valuation problem that focuses on the future uncertain spread between prices. The same process
is used to value other spread problems including
the following:
• Transportation Assets: The ability to change
oil tanker destination port to capture favorable price spreads. The pro-forma cash flow
represents the price spread between the destination prices today (intrinsic value). The option value represents the possible changes in
the spreads on the date the final destination
port needs to be called (extrinsic value).
• Storage Assets: The ability to charge and discharge a storage facility to maximize asset
time spread value. The pro-forma cash flow
represents today’s time spread (intrinsic
value). The option value represents all future
trading possibilities between now and some
future date (extrinsic value).
• Generation Assets: A generating unit can be
modeled as a strip of options on the spark
8
© 2009 Wiley Periodicals, Inc. / DOI 10.1002/gas
spread. When the generating unit’s spark
spread is positive, natural gas should be turned
into electricity. The DCF pro-forma cash flow
represents the price spread between the forward gas and electricity prices today (intrinsic
value). The option value represents the value
of possible changes in the spreads in the future
(extrinsic value).5
• Demand-Side Management Programs: Realoption theory is used to value demand-response programs. The call option in this example gives the energy supplier the right to
purchase energy from the demand-response
participant at the agreed-upon strike price.
Lowering the strike price increases the possibility of curtailment, but also increases the
participant’s incentive payments. If we split
the value into energy and capacity components, the DCF value can represent the capacity payment equal to the expected avoided fossil generator ancillary value (intrinsic value),
and the energy payment can equal the “insurance value” of possible low-probability, highconsequence events (extrinsic value).6
NOTES
1. Brennan, M. J., & Schwartz, E. S. (1985). Evaluating natural
resource investments. Journal of Business, 58(2), 135–157.
2. Black, F., & Scholes, M. (1973). The pricing of options and
corporate liabilities. Journal of Political Economy, 81, 637–654.
3. Amran and Kulatilaka identify a four-step solution process:
framing and orienting, data and validation, reviewing results
against financial market benchmarks, and identifying contractual opportunities that might improve the investment
design. Amran, M., & Kulatilaka, N. (1999). Real options,
managing strategic investment in an uncertain world. Cambridge, MA: Harvard Business School Press.
4. In this example, we calculate the intrinsic and extrinsic separately. The DCF result is used for the intrinsic and Black-Scholes is used for the extrinsic. However, the problem can also
be formulated so that both the intrinsic and extrinsic components are calculated using the Black-Scholes equation. In that
case, the intrinsic component calculated by Black-Scholes is
the difference between the “settled” or expected revenue and
the strike price. For a more detailed explanation of option
pricing, see Hull, J. (2002). Options, futures and other derivatives (5th ed.). Upper Saddle River, NJ: Prentice Hall.
5. For an example, see Deng, S., Johnson, B., & Sogomonian,
A. (2001). Exotic electricity options and the valuation of
electricity generation and transmission assets. Decision Support Systems, 30, 383–392.
6. Skinner, R. K., & Ward, J. (2009). Applied valuation of demand response under uncertainty: Combining supply-side
methods to value equivalent demand-side resources. Presented
at the 32nd IAEE International Conference, http://www.
usaee.org/usaee2009/submissions/OnlineProceedings/Applied%20Valuation%20of%20Demand%20Response%20
Under%20Uncertainty%20-%20Final%20.pdf.
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october 2009