October 2009
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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
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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 (
[email protected], [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
Natural Gas & Electricity (ISSN 1545-7893, Online ISSN 1545-7907 at Wiley InterScience, www.interscience.wiley.com) is published monthly, 12 issues per year, by Wiley Subscription Services, Inc., a Wiley Company, 111 River Street, Hoboken, NJ 07030-5774. Copyright © 2009 Wiley Periodicals, Inc., a Wiley Company. All rights reserved. No part of this publication may be reproduced in any form or by any means, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the publisher or authorization through the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600. Permission requests and inquiries should be addressed to the Permissions Department, c/o John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774; Tel.: (201) 748-6011, Fax: (201) 748-6008, or go to http://www. wiley.com/go/permissions. Periodicals postage paid at Hoboken, NJ, and at additional mailing offices. Subscription price (2010): One year print only: $1,483 in U.S., Canada, and Mexico; $1,555 outside North America. Electronic only: $1,483 worldwide. A combination price of $1,632 in U.S., Canada, and Mexico, $1,704 outside North America, includes the subscription in both electronic and print formats. All subscriptions containing a print element, shipped outside U.S., will be sent by air. Payment must be made in U.S. dollars drawn on a U.S. bank. Claims for undelivered copies will be accepted only after the following issue has been received. Please enclose a copy of the mailing label. Missing copies will be supplied when losses have been sustained in transit and where reserve stock permits. Please allow four weeks for processing a change of address. Address subscription inquires to Subscription Manager, Jossey-Bass, a Wiley Company, 989 Market Street, San Francisco, CA 94103-1741; Tel.: (888) 378-2537, (415) 433-1767 (International); E-mail:
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[email protected]. Other Correspondence: Address all other correspondence to: Natural Gas & Electricity, Isabelle Cohen-DeAngelis, Executive Editor, Professional/Trade Division, c/o John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774. Indexed by ABI/Inform Database (ProQuest) and Environment Abstracts (LexisNexis). Editorial Production, Wiley Periodicals, Inc.: Ross Horowitz This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If expert assistance is required, the services of a competent professional should be sought.
Editorial Advisory Board
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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
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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
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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
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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
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© 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
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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 october 2009
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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
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© 2009 Wiley Periodicals, Inc. / DOI 10.1002/gas
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Exhibit 10. Mapping Financial Options to Strategic Investments
Investment Opportunity
Variable Call 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
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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. Natural Gas & electricity
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