4 Oilfield Review

Unlocking the Value of Real Options

William BaileyBenoît CouëtRidgefield, Connecticut, USA

Ashish BhandariEl Paso CorporationHouston, Texas, USA

Soussan FaizStrategic Management ConsultantWalton on Thames, Surrey, England

Sundaram SrinivasanSugar Land, Texas

Helen WeedsUniversity of EssexColchester, England

Management often has flexibility in carrying out projects, capitalizing on new

information and new market conditions to improve project economics. Real-options

analysis provides a means to determine the value of flexibility in future activities.

In the early 1990s, Houston-based AnadarkoPetroleum Corporation outbid competitors forthe Tanzanite block in the Gulf of Mexico. Itfound oil and gas there in 1998 and was produc-ing within three years. The Tanzanite discoveryis significant not so much for an abundance ofoil and gas, but that in bidding for it Anadarkobroke with industry tradition. Rather than usingonly conventional discounted cash flow (DCF) tohelp it decide what the block was worth and howmuch to bid for the lease, the company opted fora new technique called real-options valuation(ROV). ROV gave Anadarko the confidence tooutbid others because it suggested that therewas more to Tanzanite than met the eye.1

Anadarko now routinely uses ROV when makinginvestment decisions.

Options embedded in, or attached to, physi-cal or real assets are real options. These aredistinct from options relating to financialassets—securities and other financial claims.ROV is a process by which a real or tangibleasset with real uncertainties can be valued in acoherent manner when flexibility—or potentialfor options—is present.

Most oil companies still use DCF to appraisepotential investments. This method has servedthem well. Increasingly, however, companies areasking whether ROV might be used to comple-ment DCF. ROV supporters argue that it gives atruer value than DCF only because the ROVmodel more closely reflects the variability anduncertainty in the world. ROV often can high-light extra value in projects, value that is

possibly hidden or even invisible when DCF isused alone. Some companies that use ROV arereluctant to divulge parameter details of theirmodels because of fears that revealing thosedetails gives away a competitive advantage.

ROV is not on the verge of displacing DCF. In fact, real-options valuation employs DCF asone of its tools. In practice, ROV combines andintegrates the best of scenario planning, portfolio management, decision analysis andoption pricing.

This article reviews DCF and describes howROV overcomes some, but not all, of its short-comings. After explaining the parallels anddifferences between financial options and realoptions, it examines two of the many methods ofvaluing options, the Black-Scholes formula and binomial lattices. ROV is illustrated by acase study of a liquefied natural gas (LNG)transport option. A series of linked, syntheticexamples describes several simple forms of binomial lattices.

Discounting Cash FlowsDiscounted cash flow analysis is relatively simple. It predicts a stream of cash flows, in andout, over the expected life of a project, then dis-counts them at a rate—typically the weightedaverage cost of capital (WACC)—that reflectsboth the time value of money and the riskinessof those cash flows. The time value of moneyindicates that money held in the future is worthless than money held now, because money we

For help in preparation of this article, thanks to SteveBrochu, BP, Houston, Texas.ECLIPSE is a mark of Schlumberger.

Winter 2003/2004 5

have in hand can be invested and earn interest,whereas future money cannot.2

The crucial item in any DCF calculation isnet present value (NPV), the present value ofcash inflows minus the present value of cashoutflows, or investments (right). A positive NPVindicates that the investment creates value. Anegative NPV indicates that the project asplanned destroys value.

A DCF analysis provides clear, consistentdecision criteria for all projects (see “WorkingOut Net Present Value,” page 6). However, it alsohas limitations:3

• DCF is static. It assumes that a project plan isfrozen and unalterable and that managementis passive and follows the original plan irre-spective of changing circumstances. However,management tends to modify plans as circum-stances change and uncertainties areresolved. Management interventions tend toadd value to that calculated by DCF analysis.

1. Coy P: “Exploiting Uncertainty,” Business Week(US edition) no. 3632 (June 7, 1999): 118–124.

2. Hussey R (ed): Oxford Dictionary of Accounting.Oxford, England: Oxford University Press (1999): 131. In a deflationary economy, money in the future may notbe worth less than money held now.

3. Mun J: Real Options Analysis: Tools and Techniques forValuing Strategic Investments and Decisions. New York,New York, USA: John Wiley & Sons (2002): 59.

Oil p

rice

Time

> Net present value (NPV) calculation. A discount factor—based on a 10%discount rate—applied to future cash flows indicates the greater value of cashin hand compared with future cash. In this case, the difference between theNPV and undiscounted cash flow is almost a thousand, regardless of thecurrency used.

Time n Cash flow Discountfactor

Present valueof cash flow

Present

One year

Two years

Undiscounted cash flow

Net present value

Discount factor = 1/(1+Discount rate)n.

0

1

2

–5000

+4500

+3000

+2500

1.0000

0.9091

0.8264

–5000

+4091

+2479

+1570

6 Oilfield Review

A series of examples using a fictitious fieldand simple synthetic models is presented inthis article to illustrate some key valuationconcepts. This section sets up the case anddetermines the net present value (NPV).

The fictitious Charon field in the SargassoSea is an anticline, divided into two blocks bya fault. The reservoir interval consists of shal-low marine sediments up to 200-ft [61-m]thick, capped by a sealing shale. The operator,Oberon Oil, has devised a development plan toobtain first oil in three years. The plan callsfor drilling six wells tied back to a dedicatedproduction platform that can handle 50 mil-lion scf/D [1.4 million m3/d] of produced gasfrom the live oil. Expected development costswill be $177.5 million spread over three years(above right).

Company experts assign values to key reservoir properties, such as porosity and per-meability, based on probability distributions(below right). The oil/water contact is notknown precisely, which impacts the estimateof oil in place. Several geological realizationsare constructed and used for simulation mod-els. Hydrocarbon resources are computed forlow, median and high estimates—consideredrepresentative of the oil in place occurring atthe 5%, 50% and 95% values of the probabilitydistribution (next page, top).

Decision-making is based on these threerepresentative scenarios. ECLIPSE oil produc-tion predictions are made for each realization(next page, bottom). Oil production declinewith time for this fictitious case can reason-ably be modeled as a hyperbolic function,making the results easier to use for predic-tion. A standard discounted cash flow (DCF)model computes project NPV. The oil price isassumed to be $25/bbl at the start of the pro-ject and to increase 1% per year, with a taxrate of 33% for net positive revenue and no tax paid for negative net revenue. In this sce-nario, the median-case NPV for Charon field is $236.3 million.

A Synthetic-Reservoir Example

Working Out Net Present Value

> Investment schedule for the synthetic Charonfield. The three-year construction schedule isbroken into five equal-length time periods. Thesefive time steps are used in later examples.

Period Time, years Total development cost,million $

1

2

3

4

5

0.6

1.2

1.8

2.4

3.0

50.0

75.0

107.5

150.0

177.5

> Reservoir model of the synthetic Charon field. This ECLIPSE reservoir model provided input forobtaining production predictions, using a large number of simulations with geostatisticallyderived porosity and permeability values.

0.0 0.2 0.4

Oil saturation

0.6 0.8

Well 2Well 5

Well 4

Well 6Well 3

Well 1

Winter 2003/2004 7

• DCF assumes future cash flows are predictableand deterministic. In practice, it is often difficult to estimate cash flows, and DCF canoften overvalue or undervalue certain types of projects.

• Most DCF analyses use a WACC discount fac-tor. But instead of a WACC, companies oftenuse a company-wide hurdle rate that may beunrepresentative of the actual risks inherentin a specific project.

The first two limitations relate to circum-stances changing after a project begins. A newDCF analysis can be performed to reflect the newcircumstances, but it may be too late to influencebasic project decisions, since the project isalready under way. The third limitation aboveresults from companies adopting a company-widehurdle rate for consistency rather than carefullyrecalculating a WACC for each project.

A sensitivity analysis can enhance informationprovided by DCF analysis. The consequences ofpossible changes to key variables—for example,interest rates, cash flows and timing—are evalu-ated to determine the results of a number of“what if” scenarios. However, the choice of whichvariables to alter and how much to alter them issubjective.4 Sensitivity analysis makes assump-tions about future contingencies, rather thanincorporating those contingencies as they occur.

Embracing Uncertainty and Adding ValueUnlike DCF, ROV assumes that the world is characterized by change, uncertainty and competitive interactions among companies. Italso assumes that management has the flexi-bility to adapt and revise future decisions inresponse to changing circumstances.5 Uncer-tainty becomes another problem component tobe managed. The future is regarded as one thatis full of alternatives and options, both of whichmay add value.

The word option implies added value. Whenwe speak of keeping our options open, havingmore than one option, or not foreclosing on ouroptions, the underlying implication is that justholding the option usually has value, whether ornot we exercise it. The same is true of real options.

4. Bailey W, Couët B, Lamb F, Simpson G and Rose P: “Taking a Calculated Risk,” Oilfield Review 12, no. 3(Autumn 2000): 20–35.

5. Trigeorgis L: “Real Options: A Primer,” in Alleman J and Noam E (eds): The New Investment Theory of RealOptions and Its Implications for Telecommunications Economics. Boston, Massachusetts, USA: Kluwer (1999): 3.

> Results of model realizations. Three models represent the low (5%), median(50%) and high (95%) production predictions in Charon field.

Oil/watercontactdepth, ft

Field-wide average,ratio of net-to-gross thickness

Averageporosity

Original oilin place,million BOE

Initial oilproduction,B/D

0.65

0.75

0.85

9625

9650

9675

Low

Median

High

12.5%

14.4%

16.3%

138.6

228.2

350.4

25,384

27,930

28,225

> Calculation of Charon net present value (NPV). Production begins in the third year of the projectand declines (top). The low (5%), median (50%) and high (95%) probability model predictions areshown. The project’s cumulative cash flow for the median case shows the expenditures in thefirst three years followed by income over the remainder of the project (bottom). The median-caseNPV of the project is $236.3 million.

0 500 1000

Prod

uctio

n ra

te,

B/D

1500 2000 2500 3000

Time, days

3500 4000 4500 5000 5500 6000

30,000

25,000

20,000

15,000

10,000

5,000

Median

Median case

Low

High

0

0 500 1000

Pres

ent v

alue

, mill

ion

$

1500 2000 2500 3000

Time, days

3500 4000 4500

236.3

5000 5500 6000

250

–150

–100

–50

0

50

100

150

200

–200

Real-options analysis draws heavily on thetheory of financial options.6 Financial optionsare derivatives; they derive their value fromother underlying assets, such as shares of a com-pany stock. A financial option is the right, butnot the obligation, to buy or sell a share on (orsometimes before) a particular date at a particu-lar price. The price at which a share can bebought or sold, if the option holder chooses toexercise the right, is known as the exercise, orstrike, price. The two main kinds of options are acall option—to buy the share at the exerciseprice—and a put option—to sell the share atthe exercise price (below right).

If the share price exceeds the exercise price,a call option is said to be in the money. If itexceeds it by a large amount, it is termed deepin the money. If the share price fails to reachthe exercise price, the option is said to be out ofthe money. An investor would not exercise anout-of-the-money option since doing so wouldcost more than the market price for the share.This is where the caveat that the option holderhas the right but not the obligation to buy theshare at the exercise price is important. Theinvestor allows the option to lapse if exercisingit would not be beneficial.

Financial options can be further subdividedinto many types.7 Two of the most common areEuropean and American options. A Europeanoption can be exercised only on the expirationdate specified in the option contract. An American option may be exercised at any timeup to and including the expiration date.

Options have two important features. First,they give an option holder the possibility of alarge upside gain while protecting from down-side risk. Second, they are more valuable whenuncertainty and risks are higher.

Financial and Real OptionsReal-options valuation applies the thinkingbehind financial options to evaluate physical, orreal, assets. By analogy with a financial option, areal option is the right, but not the obligation, totake an action affecting a real physical asset at apredetermined cost for a predetermined periodof time—the life of the option.8 While real andfinancial options have many similarities, theanalogy is not exact.

ROV allows managers to evaluate realoptions to add value to their firms, by givingmanagers a tool to recognize and act uponopportunities to amplify gain or to mitigate loss.9

While many managers are not accustomed toevaluating real options, they are familiar withthe concept of project intangibles. ROV givesmanagers a tool to move some of those intangi-bles into a realm where they can be dealt with ina tangible and coherent fashion.

Petroleum developments and mining opera-tions were among the first examples used byROV pioneers to demonstrate the parallelsbetween real and financial options (see “How OilCompanies Use Real-Options Valuation,” nextpage).10 The exploration, development and pro-duction stages of an oilfield project can be seenas a series of linked options.11

At the exploration stage, the company hasthe option to spend money on exploration and,in return, receive prospective oil and gasresources. This is like a stock option, whichgives the holder the right, but not the obligation,to pay the exercise price and receive the stock.

Money spent on seismic surveys and explorationdrilling is analogous to the exercise price; theresources are analogous to the stock. An explo-ration option expires the day the lease terminates.

Once the company has exercised its option toexplore, it is in a position to decide whether toexercise a second option, the option to developthe field. This gives the company the right, butnot the obligation, to develop the resources atany time up to the relinquishment date of thelease for an amount of money given by the costof development. If the company exercises thedevelopment option, it obtains hydrocarbonresources that are ready to be produced.

The final option is the option to produce. Thecompany now has the right, but not the obliga-tion, to spend money on extracting the oil and gasfrom the ground and sending it to market. It willdo so only if a number of uncertainties areresolved, most notably that the oil price is likelyto reach a level that makes production profitable.

This series of options is called a sequentialor compound option because each optiondepends on the earlier exercise of another one.12

8 Oilfield Review

6. Bishop M: Pocket Economist. London, England: ProfileBooks in association with The Economist Newspaper(2000): 197.

7. Wilmott P: Paul Wilmott on Quantitative Finance,vol 1. New York, New York, USA: John Wiley & Sons(2000): 217.

8. An option may be attached to a real asset or to cashflows associated with that asset. Stewart Myers firstcoined the term “real options” in 1985. For more informa-tion: Copeland T and Antikarov V: Real Options: APractitioner’s Guide. New York, New York, USA: Texere(2001): 5.

9. Brealey R and Myers S: Principles of Corporate Finance,6th Edition. Boston, Massachusetts, USA: Irwin/McGraw-Hill (2000): 619.

10. Paddock J, Siegel R and Smith J: “Option Valuation ofClaims on Real Assets: The Case of Offshore PetroleumLeases,” The Quarterly Journal of Economics 103, no. 3(August 1988): 479–485.

11. This simple series of linked options ignores any contractual obligations to drill or develop that mayaccompany a lease.

12. Copeland and Antikarov, reference 8: 12–13.

> Call and put options.

Call option—the right, but not the obligation, to buy shares at the exercise price withina given time period.

Put option—the right, but not the obligation, to sell shares at the exercise price within agiven time period.

Widgets, Inc., has a moderately volatile share price with a current price of $100. For a small fee, an investor may buy a call option with an exercise price of $110. If the shareprice subsequently rises to $120, the option holder would exercise the option to buy theshares for the agreed exercise price of $110 and sell them on the open market for $120,making a profit of $10 per share less the option-purchase fee.

Alternatively, if the investor has a put option with an exercise price of $90 and shares ofWidgets, Inc. fall below $90, it will benefit the option holder to buy shares from the openmarket at the lower price and exercise the option to sell them at $90. Both examplesignore the usual transaction fees paid to a broker.

Winter 2003/2004 9

Companies as diverse as BP, ChevronTexaco,Statoil, Anadarko and El Paso have shown aninterest in real-options valuation (ROV). Theyusually regard it as complementary to tech-niques like discounted cash flow (DCF) anddecision-tree analysis rather than as a stand-alone method of valuation.

In the mid-1990s, the executive manage-ment of Texaco (now ChevronTexaco) wassplit over what to do with a significant lease-holding in a developing country. The leaseincluded several existing oil discoveries andmany other substantial undeveloped discover-ies. It was at an early stage of exploitation.1

Part of the management team wanted to sellthe asset, using the proceeds for more capital-efficient projects, while others on the teamfelt it could lead to other lucrative follow-upopportunities and the development of valu-able relationships in the region.

The company management used ROV todecide which action would be better for thecompany. Results from the ROV substantiatedparts of both viewpoints. Even after keyoptions values had been included, the ROVindicated the asset was far less valuable thansuggested by DCF. However, there was suffi-cient value to convince Texaco to retain theasset until some of the uncertainties wereresolved, but to be prepared to sell if the pricewas right. Moreover, ROV enabled a majorrestructuring of the base plan. Texaco believedthat ROV helped its executives reach a betterstrategic understanding of its holding.2

A recent analysis of a transaction that tookplace in the early 1990s involving Amoco (now BP) and independent oil and gas com-pany Apache Corporation showed howreal-options analysis can disclose value that isnot apparent when using DCF analysis alone.3

In 1991, after a strategic review, Amocodecided to dispose of some marginal oil andgas properties in the United States. It formeda new, separate company, MW Petroleum

Corporation, to hold its interests in 9500 wellsspread across more than 300 fields. Apacheindicated interest in obtaining the properties,but Iraq’s invasion of Kuwait in the spring ofthat year had pushed oil prices to historicheights while increasing price uncertainty.

Amoco and Apache agreed on most of theprovisions for the MW Petroleum transaction,but disagreed on oil-price projections. The gapwas about 10 percent. The two companiesfound common ground by agreeing to sharethe risk of future oil-price movements. Amocogave Apache a guarantee that if oil prices fellbelow an agreed price-support level in thefirst two years after the sale, Amoco wouldmake compensating payments to Apache. Forits part, Apache would pay Amoco if oil or gasprices exceeded a designated price-sharinglevel. The MW Petroleum portfolio included121 million barrels of oil equivalent (BOE)[19.2 million m3] of proven oil and gasreserves, plus 143 million BOE [22.7 millionm3] of probable and possible reserves.

This transaction was reexamined by inde-pendent analysts in 2002. They compared adeterministic DCF valuation of MW Petroleumassets with a real-options valuation. The DCFvalue of $359.7 million was $80 million lessthan the ROV result of $440.4 million, indicat-ing additional value in the assets not includedin the DCF analysis.4 In comparison, the pur-chase price agreed on by Amoco and Apachewas $515 million plus 2 million shares ofstock. Both methods gave values short of theactual price, but the ROV valuation was muchcloser than the DCF one.

In a third example, Anadarko, a Houston-based independent, is an enthusiast for ROV.5

A recent ROV analysis by the company exam-ined the impact of deferring a project untilnew technologies became available.6

Anadarko had a deepwater developmentopportunity that the company approached intwo stages. At the end of the first, exploration

stage, uncertainties about the amount of oiland gas in place had been resolved. In thedevelopment phase, the operator could decideto develop the field using conventional meansor wait and develop the field using new subseacompletion technology that at that time wasstill at the research and development stage.

Conventional analysis neglecting the valueof flexibility showed that development of thefield using current technology would yield avalue of $4 million. Including the flexibilityassociated with being able to wait until newtechnology was available—using a deferraloption and waiting until the new technologywas ready—increased the value to $50 million.

How Oil Companies Use Real-Options Valuation

1. Faiz S: “Real-Options Application: From Successes inAsset Valuation to Challenges for an Enterprise WideApproach,” paper SPE 68243, Journal of Petroleum Technology 53, no. 1 (January 2001): 42–47, 74. Thispaper was revised for publication from paper SPE62964, originally presented at the SPE Annual Techni-cal Conference and Exhibition, Dallas, Texas, USA,October 1–4, 2000.

2. Faiz, reference 1.3. Chorn L and Sharma A: “Project Valuation: Progressing

from Certainty through Passive Uncertainty to Active Project Management,” paper SPE 77585, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, September 29–October 2,2002.

4. Tufano P: “How Financial Engineering Can Advance Corporate Strategy,” Harvard Business Review 74,no. 1 (January–February 1996): 143–144.

5. In its 2001 annual report, Anadarko says that it “seeks to maximize enterprise value by maintaining a strong balance sheet and applying option theory to assist investment decision-making.”

6. Rutherford SR: “Deep Water Real Options Valuation:Waiting for Technology,” paper SPE 77584, presented at the SPE Annual Technical Conference and Exhibi-tion, San Antonio, Texas, USA, September 29–October2, 2002.

The extraction option is contingent on exercis-ing the development option, which is contingenton exercising the exploration option. At eachstage, a company obtains information to deter-mine whether the project should be taken to thenext stage.

Comparing Financial- and Real-Option Parameters The variables used to value a financial option canbe compared with their analogs in real options.An option to develop oil reserves, for example, issimilar to a financial call option (below).

The NPV of the developed hydrocarbonreserves—what they would be worth at today’sprices—is similar to the price of the underlyingstock, S, in a financial option. The NPV of theexpenditure needed to develop the reserves islike a financial option’s exercise price, X. Thetime left on an exploration and production(E&P) lease is equivalent to the time to expira-tion of a financial option, T. The risk-free rate ofreturn, rf —the rate of return on a guaranteedasset, such as a government bond—is identicalfor both financial and real options. The volatilityof cash flows from an E&P project, includinghydrocarbon price uncertainty, is analogous tothe volatility of stock prices, σ. Finally, profitsforegone because production has been delayedare like the lost dividends in the financialoption, δ. As long as management holds an unex-ercised option to invest in a project, it foregoesthe money that would have flowed from it hadthe project been producing revenue.

The analogies between real and financialoptions are not exact. Trying to force realoptions into a conventional financial-optionsframework may result in misleading outcomes.One key difference in the two options types isthat the exercise price of a financial option is

normally fixed. For a real option, this price isassociated with development costs, and may bevolatile, fluctuating with market conditions, service company prices and rig availability. In theE&P industry, volatility is usually a consolidatedvalue comprising the uncertainty involved inmany things, including oil prices and productionrates. Determining volatility in real options canbe difficult.

Another key difference between financialand real options lies in uncertainties surround-ing an option’s underlying asset. With a financialoption the uncertainty is external. The option isan arrangement between two outsiders—the option writer and the option purchaser—neither of whom can influence the rate of returnon the company’s shares.13 In contrast, a com-pany that owns a real option can affect theunderlying asset—for example, by developingnew technologies for the asset—and the actionsof competitors—for example, by developing anadjacent property first, as described later in thisarticle—which in turn can affect the nature ofthe uncertainty that the company faces.14

Black-Scholes Option ValuationReal options often are valued using financial-option pricing techniques. However, real-optionvaluation can be extremely complex, so anyfinancial-option technique can provide only arough valuation. Two approaches are discussedin this article: the Black-Scholes formula (aclosed-form solution) and binomial lattices.

Early attempts to use DCF to value optionsfoundered on the appropriate discount rate touse and in calculating the probability distribu-tion of returns from an option. An option isgenerally riskier than the underlying stock butnobody knows by how much.15

The insight of Fischer Black, Myron Scholesand Robert Merton, who derived the Black-Scholes-Merton formula—more commonlyreferred to as Black-Scholes—was that optionscould be priced using the arbitrage principlewith a portfolio that is constructed to be risk-free, overcoming the need to estimatedistributions of returns at all.16 They showed thatit was possible to establish the value of anoption by constructing a replicating portfolio,which consists of a number of shares in theunderlying asset and a number of risk-freebonds. The portfolio is constructed in such a waythat its cash flows exactly replicate those of theoption. Prices of bonds and of underlying sharesare directly observable in the financial market,so the value of the replicating portfolio is known.If the option were sold for a price that is differ-ent from that of the replicating portfolio, therewould be two identical assets—the option andthe replicating portfolio—selling for differentprices at the same time. Any investor would thenuse the strategy of arbitrage, buying the cheaperof the two and selling the more expensive toprofit from the unequal prices.

The existence of the replicating portfolioimplies that there is a combination of the optionand the underlying asset that is risk-free. Ineffect, the risk-free rate is used as the discountrate during the option-pricing calculation and isusually taken to be the interest rate on a govern-ment-guaranteed financial instrument like a USTreasury Bond.17

The Black-Scholes formula has fairly limitedapplicability. The formula is a closed-form solu-tion to a more general expression—theBlack-Scholes partial differential equation—for the case of European puts and calls, whichcan be exercised only on their maturity date.Most real options are not analogs of Europeanoptions. However, the Black-Scholes partial differential equation itself has far wider applicability. With appropriate boundary conditions, this partial differential equation canbe solved—usually numerically—to evaluatemany types of options, such as American andcompound options.

A numerical method using binomial latticesis applicable across a wide range of options.Since this process of valuation can be visualizedin a diagram, lattices are comparatively easy tounderstand, although actual problems typicallyare more complex than the simple latticesshown in this article.

10 Oilfield Review

> Comparison of financial and real options. The variables of a financial call option can berelated to similar variables for a real option to develop oil reserves.

Financial and Real Options Compared

Financial call option Variable Real option to develop hydrocarbon reserves

Stock price

Exercise price

Time to expiration

Risk-free interest rate

Volatility of stock price

Dividends foregone

S

X

T

rf

σδ

Net present value of developed hydrocarbon reserves

Present value of expenditure to develop reserves

For example, time remaining on lease, time to first oil or gas

Risk-free interest rate

Volatility of cash flows from hydrocarbon reserves

Revenue or profits foregone

Winter 2003/2004 11

Binomial-Lattice Option ValuationBinomial lattices allow analysts to value bothEuropean and American-type options.18 Thissection describes how to construct a lattice for asimple European call option.

A lattice is a way to show how an asset’svalue changes over time, given that the asset hasa particular volatility. A binomial lattice has onlytwo possible movements in each time step—upor down. It looks like a fan laid on its side. ROVuses two lattices, the lattice of the underlyingasset and the valuation lattice.

Lattice of the underlying asset—The under-lying asset pricing lattice, also known simply asthe lattice of the underlying, is read from left toright and indicates how possible future asset values could evolve. The value of the left-mostnode is the NPV of the underlying asset, as cal-culated from the DCF model. In each timeinterval, the value of the asset increases by amultiplicative factor u (greater than 1), or

decreases by a multiplicative factor d (between0 and 1), represented as a step up or a stepdown the lattice (above). The factors u and d,which determine the upward and downwardmovements at each node, are functions of thevolatility of the underlying asset and the lengthof time between the periods under considera-tion. The right-hand nodes of the latticerepresent the distribution of possible futureasset values.

The most difficult issue in constructing thelattice of the underlying asset is estimatingvolatility. This value must reflect the uncertain-ties, both economic and technical, in the valueof the underlying asset, and the way in whichthese uncertainties evolve over time.19 Methodsfor estimating volatility are nontrivial, and a discussion of these methods is beyond the scopeof this article.

13. The case of company executives who are given shareoptions as an incentive to improve company value is an exception.

14. Copeland and Antikarov, reference 8: 111–112.15. Ross S and Jaffe J: Corporate Finance. Boston,

Massachusetts, USA: Irwin (1990): 576.16. The Black-Scholes formula estimates the value of a call

option, C:C = S * e – δ T * {N(d 1)} – Xe – r

fT * {N(d 2)},

where d 1 = {ln(S/X) + (rf - δ + σ2/2) T}/ (σ * √–T),d 2 = d 1 - σ * √–T,

and where N(d) = cumulative normal distribution func-tion, ln is the natural logarithm and other terms aredefined in the text.

17. Rogers J: Strategy, Value and Risk—The Real OptionsApproach. Basingstoke, England: Palgrave (2002): 61.

18. In a European option, uncertainty is assumed to be fullyresolved at expiration. However, valuation of American-type options can be more complex and caution isrequired. An American option can be exercised at anytime prior to expiration, but that does not mean that alluncertainty has been resolved at the time the decision ismade. New information about project uncertainties islikely to be streaming in all the time, so the decision isbased on incomplete information. Unless all pertinentuncertainty has been resolved, it might be prudent towait until the last moment to decide on the option.

19. Some ROV specialists argue that it is better to keep technical and market uncertainties separate, especiallywhen managerial decision-making is tied to the resolutionof technical uncertainty.

> Construction of a lattice of the underlying asset. The deterministic value for the asset today, such as a stock price, goes into theleft-most lattice node (left). In the first time step, this value can increase by a multiplicative factor, u, which is based on the volatility,σ, and length of the time step, ∆T, or it can decrease by the inverse of that factor, d. Each node in subsequent time steps can similarlyincrease or decrease, resulting in an expanding lattice. Results from a five-step lattice are coarse. As the number of steps increases,∆T becomes smaller and the resolution increases as the lattice becomes larger. A probability distribution of future assets (greencurve) can be obtained from the values in the right-hand column of a lattice with thousands of steps (right). The assumptionsgoverning the definition of u and d factors always give rise to a log-normal distribution of asset value at expiration—this is a basicassumption of the Black-Scholes model.

S0

S0u1

S0d1

S0u2

S0u1d1

S0d2

S0u2d1

S0u3

S0d4

S0u1d3

S0u2d2

S0u4

S0u5

S0u4d1

S0u3d2

S0u2d3

S0u1d4

S0d5

S0u3d1

S0u1d2

S0d3

Large Lattice

u = exp(σ √∆T )

d = 1u

Pric

e

Probability

Probability distribution of future assets

0 1 2 3 4 5

In summary, the lattice of the underlyingillustrates the possible paths that an underlyingasset value—like a stock’s price, and similarlydesignated as S—will take in time, given that ithas a certain volatility.

Valuation lattice—The valuation lattice hasexactly the same number of nodes and branchesas the lattice of the underlying asset (above).Analysts work backward from the values in theterminal nodes at the right side to the left side ofthe lattice. The value placed in each terminalnode is the maximum of zero and the differencebetween value S and exercise price X, MAX(S – X,0). Disallowing negative values reflects theholder’s right to refuse to exercise an option withnegative value.

From these starting values in the terminalnodes, it is possible to work backwards throughthe lattice—using a process called backward

induction—to obtain an option value at the far-thest left node of the lattice. Backwardinduction relies on a factor p, the risk-neutralprobability of a movement in the price of theunderlying asset. This is the probability thatwould prevail in a world in which investors wereindifferent to risk. Applying this to each pair ofvertically adjacent nodes in the lattice providesthe real-option value at the farthest left node ofthe lattice.

Binomial lattices are often referred to asbinomial trees. However, the two methods operate differently. Trees require an analyst tospecify probabilities and appropriate discountrates at each node, which can be highly subjec-tive. ROV, embodying ideas such as risk-neutralprobability for financial uncertainty and risk-free rate of interest, is less subjective.20

12 Oilfield Review

20. Mun, reference 3: 242–245.

> Construction of a valuation lattice. Nodes in a valuation lattice are constructed from right to left.The asset value, such as a stock price, S, at expiration is taken from the lattice of the underlyingasset. The exercise cost, X, is known in advance. The nodes in Column 5 contain the differencebetween stock and exercise price, unless that difference is negative, in which case the node containszero. The value in the node labelled C comes from the two adjacent Column 5 nodes, A and B, anduses the risk-neutral probability, p, as shown in the formula (bottom left). Remaining nodes and columnsare constructed similarly, from right to left. The single node on the left contains the value of the option.

$67.66 A

B

C

$80

$50

$20

$0

$0

$0

0 1 2 3 4 5

Excercise costX = $100

Maximum (S–X, 0)Stock price, S,at expiration

$180

$150

$120

$90

$60

$30

OptionValue

C = [p*A+(1-p)*B]*exp (-rf*∆T )

p = exp (rf*∆T )-d

u-d

Oberon, operator of the fictitious Charonfield, has reservations about the eventualeconomic viability of the field. To protectitself from a negative result, the companyhas entered into negotiations with ThalassaEnergy, which is eager to add Sargasso Seaassets to its portfolio. Thalassa offersOberon, for an up-front premium of $45 mil-lion, a guarantee to take over the Charonfield and reimburse Oberon all developmentcosts incurred up to the exercise date, ifOberon chooses to exercise the option. Thesalvage value at any time is assumed to bethe amount invested at that point. Oberonperforms a real-options valuation (ROV) todetermine whether the flexibility to recoupdevelopment expenses is worth the priceasked by Thalassa.

The ROV involves four steps: identifyingthe underlying asset, determining its volatil-ity, constructing the lattices and interpreting option value.

Oberon identifies the underlying asset asCharon’s project NPV. This NPV exhibits alog-normal probability distribution, so thevolatility of the underlying asset is based on the logarithm of the future cash flows.Monte Carlo simulation on the DCF modelindicates that the implied annual volatility is 66.41%, including both private and publicuncertainties.

The engineers construct a lattice of theunderlying asset with 0.6-year time stepsusing a five-step binomial lattice (next page).The asset value, S, or Oberon’s NPV for theproject without any flexibility from salvagepotential, is $236.3 million (see “Working OutNet Present Value,” page 6). The risk-freerate for the three-year period under consider-ation is 5% per year. The valuation anddecision lattices are identical in form to thatof the lattice of the underlying asset.

Synthetic-Reservoir Development Guarantee

Salvage an Investment

Winter 2003/2004 13

These lattices allow Oberon to interpretoption value. The added flexibility providedby the Thalassa contract increases Charon’sNPV to $285.5 million. This is the value arational, frictionless, free market would,given the same information, assign to theproject. It is $49.3 million more than the NPVwithout flexibility—simply because of thepresence of the salvage option.

An offer to provide this flexibility for $45million should be accepted by Oberon man-agement since it appears that Thalassaunderpriced the option by $4.3 million, thedifference between the option value and thepremium price. This apparent underpricingindicates that Thalassa has a different per-ception of risk and uncertainty than Oberon.

> Real option for salvage. The lattice of theunderlying asset begins with the project netpresent value in the left node and projectspotential future values to the right (top right).The up and down multiplying parameters, uand d, are calculated from the inputs ofvolatility, σ, and the time step size, ∆T (topleft). The salvage value is based on invest-ment to date (middle left). The valuation anddecision lattice has the same form as the lat-tice of the underlying, but it is constructedfrom right to left (middle right). The last col-umn of the valuation lattice is constructed bycomparing the equivalent node in the latticeof the underlying with the salvage value atthe final time step (bottom right). If the sal-vage value is greater, that amount is enteredand the salvage decision is noted. Otherwise,the value from the node in the lattice of theunderlying is used for the valuation-latticenode, and the decision is to retain owner-ship. The value in the node in the next columnto the left comes from back-regression fromtwo adjacent nodes, as indicated by thearrows. That value involves the risk-neutralprobability, p, the risk-free interest rate, rf,and the time step size, ∆T (bottom left).

Retain ownership

Retain ownership

Salvage

Salvage

Salvage

1849.4

661.0

257.3

172.3

172.3

3093.3

1105.7

395.2

141.3

50.5

18.0

Valuation and decision lattice Lattice of underlying

Work from right to left

Valuation and decision lattice

Lattice of the underlying asset

420.6

285.5

668.1

275.3

209.1

175.2

1105.7

1849.4

3093.3

407.4 395.2

661.0

257.3

200.4 177.5

1105.7

172.3

167.2 177.5

172.3

177.5

start

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

retain

retain

retain

salvage

salvage

salvage

Salvage Value

Value,million $Period Years

Input Parameters

1

2

3

4

5

0.6

1.2

1.8

2.4

3.0

50.0

75.0

107.5

150.0

177.5

σ = 66.41%∆T = 0.6u = exp(σ√∆T ) = exp(0.6641*√0.6) = 1.67265

d = =

= 0.59785

p =

=

= 0.40250

1 1

exp(0.05*0.6)-0.59785 1.67265-0.59785

u-dexp(rf *∆T)-d

u 1.67265

Salvage if < 177.5

Retain ownership

1

2

5

3

4

1

2

5

3

4

395.2

236.3

661.0

236.3

141.3

84.4

1105.7

1849.4

3093.3

395.2 395.2

661.0

236.3

141.3 141.3

1105.7

84.4

50.5 50.5

30.2

18.0

Example: backward-inductioncalculation

3093.3 1105.7 * (1-p)]*exp(-rf*∆T)[ *p+

1849.4=

3093.3

1105.7

395.2

177.5

177.5

177.5

Types of Real Options Analysts generally classify real options by thetype of flexibility they give the holder.21 Theoptions may occur naturally, or may be built intoa project. Management can defer investment,expand or contract a project, abandon for sal-vage or switch to another plan. Compoundoptions also can be created.22

Option to defer investment—An opportunityto invest at some point in the future may bemore valuable than an opportunity to investimmediately. A deferral option gives an investorthe chance to wait until conditions becomemore favorable, or to abandon a project if condi-tions deteriorate. An E&P lease, for example,may enable an oil company to wait until presentuncertainties about oil and gas prices and aboutdevelopment technology have been resolved.The company would invest in exploration anddevelopment only if oil price increased enoughto ensure that developed acreage on the leasewould be profitable. If prices declined, the com-pany would allow the lease to lapse or would sellthe remainder of the lease to another company.The exercise price of the option is the moneyrequired to develop the acreage.

Option to expand or contract a project—Once a project has been developed, managementmay have the option to accelerate the produc-tion rate or change the scale of production. Inan oil or gas field, there might be the option toincrease production by investing in an enhancedoil recovery plan or by drilling satellite wells.The original investment opportunity is definedas the initial project plus a call option on afuture opportunity.

Option to abandon for salvage—If oil andgas prices go into what seems likely to be a prolonged decline, management may decide toabandon the project and sell any accumulatedcapital equipment in the open market. Alterna-tively, it may sell the project, or its share in theproject, to another company whose strategicplans make the project more attractive (see “Sal-vage an Investment,” page 12). Selling forsalvage value would be similar to exercising anAmerican put option. If the value of the projectfalls below its liquidation value, the company canexercise its put option.

Option to switch to another plan—A switch-ing option can provide a hedge against thelikelihood that another technology or projectwill be more economic sometime in the future(see “Switch Option,” page 16).

Sequential or compound options—Realoptions may lead to additional investmentopportunities when exercised. The process ofexploration, development and productiondescribed earlier in this article was a sequen-tial option.

This list of options is not exhaustive. Manyother types of options are available. El Paso Cor-poration, the largest pipeline company in NorthAmerica and a leading provider of natural gasservices, used a location spread option—relyingon a difference in a price between different loca-tions—to evaluate a new line of business. Variousother spread options are possible, for examplebased on different prices at different times or atdifferent stages of commodity processing.

Real Options for LNG TransportEl Paso owns a liquefied natural gas (LNG) terminal at Elba Island, Georgia, USA, one ofonly four land-based terminals in the USA. Thecompany investigated purchasing transport vessels and expanding into the LNG transportbusiness. Each tanker, outfitted specifically foruse in LNG transport with a regasification capa-bility for downloading at offshore buoys calledenergy-bridge buoys, costs several hundred mil-lion US dollars.

The essence of the problem facing the evalua-tion team was how to value shipping anddiversion flexibility. The company had a variety ofpotential LNG sources and destinations, and theevaluation was intended to determine how manytanker ships El Paso should purchase.

El Paso felt DCF was deficient for this analy-sis. The LNG market and its related shippingwere relatively new ventures for El Paso, and thecompany had no history for forecasting the rev-enues and costs required by DCF. Even if thoseforecasts had been available, the DCF techniquedoes not have the flexibility necessary to reflectthe additional value of a price difference betweendelivery locations that occurs only for a brief timeperiod. The team tried to model the simple caseof a fixed source and destination using DCF, butthe model could not correctly value inbuiltoptions allowing El Paso not to sell if the LNGdelivery price did not cover variable expenses.

The base case for this ROV involves trans-porting LNG from a terminal in Trinidad, WestIndies, to the company’s Elba Island facility. TheLNG producer in Trinidad would pay for infras-tructure costs to enable this base-case trade andwould in turn receive the netback gas price,which is the gas price at Elba Island less thecost of shipping and regasification and less themargin paid to El Paso. For example, for theanalysis presented here this margin wasassumed to be $0.20/MMBtu [$0.19/million J].The NPV of this business over 20 years was$176.7 million.

The first option evaluated included diversionflexibility—adding a second destination termi-nal offshore New York, New York, USA. El Pasoevaluated both intrinsic and extrinsic values forthis option. The intrinsic value of this spreadoption represents the difference in price—thebasis spread—between the Georgia and NewYork markets (next page). The extrinsic valueincludes the effects of time and reflects theprobability that the basis spread will changeover the 20-year period of the analysis.

In this spread option, El Paso would buy the LNG on the basis of the Elba Island priceand sell it at the New York price, when thatchoice adds value. Otherwise, El Paso would sellat Elba and receive no incremental value. Withan average basis spread of $0.62/MMBtu[$0.59/million J], the total intrinsic value of thisspread option is $558.7 million. In this model, El Paso would assume the costs for convertingthe terminals and purchasing an additional shipto effect this option. The net value of the optionafter those expenses is $68.5 million. Includingthe variability over time gives an additionalextrinsic value of $101.7 million.

The company then added in the value of hav-ing multiple choices of source and destination,termed a rainbow option. The value of a rainbowoption increases with increased price volatilityat the individual locations, and it also increaseswhen the cross-correlations between prices arelow. With two additional destination options, off-shore New York and Cove Point, Maryland, USA,there is an additional value of $14.8 million,even though the price correlations betweenthese pairs of locations are high. The rainbowoption value increases when there is more flexi-bility in source and destination locations. Incertain scenarios with additional sources in the

14 Oilfield Review

21. Rogers, reference 17: 49; and Trigeorgis, reference 5:5–10.

22. A project with many embedded options can be difficult to evaluate using the simple forms of the Black-Scholesand lattice models presented in this article.

Winter 2003/2004 15

Middle East and Africa and additional destina-tions in Europe and North America, El Pasofound the rainbow option added more than $100million to the value of each ship.

The evaluation team provided a caveat to thecompany. Spread options tend to overestimateavailable flexibility, because contractual obliga-tions would have to be maintained. In addition,the effects of price shifts caused by any reduc-tion in supply were not included in the analysis.

Although real-options analysis indicated apositive value to a business model based on LNGimports to the USA and to diversion flexibility asa value-maximizing technique for shipping, ElPaso made a strategic business decision not toenter this market.

Alternatives and OptionsIn the English language the word option may beused in two technically different senses. In ROVthe term option (or real option) is used todenote a decision that may be deferred to sometime in the future, and that is accompanied bysome uncertainty that can be resolved. On theother hand, in common parlance, an option cansimply be an operational alternative, which is adecision that is to be made today and for whichthere is no future recourse.

For example, a company may decide to drill awell in a certain location. If the well is dry, thenthe company has lost the cost of drilling. Thewell location was an operational alternative, adecision that had to be made there and then.However, if there were another party guarantee-ing some minimum return on the well, thecompany drilling the well would have a realoption, because it could decide in the futurewhether to call on that guarantee, thereby mini-mizing any downside risk and maximizing anyupside potential.

A project containing an option is alwaysworth more than one with just a correspondingalternative. This is because deferral allows anowner to eliminate unfavorable outcomes whileretaining favorable ones. This is often referredto as optionality. A project having only a set ofalternatives has no such cushion. The decision,which must be made today, is effectively irre-versible. The estimated NPV must average overall outcomes, both favorable and unfavorable.

Both options and alternatives can be computed using standard lattice-type method-ologies (see “True Option and an AlternativeValued under Uncertainty,” page 18). Alterna-

tives may often be evaluated using simpler meth-ods that automatically average out the possibilities. For example, a forward contract,which obligates the holder of the contract to buyor sell an asset for a predetermined price at apredetermined time in the future, may be valuedsimply, without the volatility assumption that isrequired in the Black-Scholes or lattice valua-tion of a European option.

Within the class of options there are many dis-tinctions. One is the distinction between financialand real options that has been discussed. Anotheris that between options that are purely inter-nal—residing solely within the companyitself—and ones in which an outside party pro-vides flexibility for some agreed up-frontpayment. Many real options possess just an inter-nal character, while financial derivatives normallyexist in the presence of a contracted externalparty. Fortunately, all these option types can becomputed using the same techniques, mostnotably standard lattice-type methodologies.

Real-World Complications A real-options methodology attempts to modelbehaviors of real properties. However, the manypossibilities created by human ingenuity limitany such modeling. Actual situations typicallyhave many embedded options, making any anal-ysis complicated. The few examples discussed inthis section illustrate a few types of complica-tions that may have to be dealt with in usingreal options.

The holder of a financial option is guaran-teed that the option may be held until theexpiration date and, apart from general marketmovement, its value cannot be undermined bythe actions of other individuals. In most realoptions, there is no such guarantee.

Two oil companies might hold identicalleases on adjoining blocks. In effect, they wouldboth have identical options to spend money onexploration and receive undeveloped resourcesin return.

> Liquified natural gas (LNG) transport routes in a spread option. El PasoCorporation evaluated the LNG transport business using a base case betweenTrinidad, West Indies, and its terminal at Elba Island, Georgia, USA. Thecompany considered purchasing transport ships with regasificationcapabilities to give it the capability to transport gas to other locations, suchas Cove Point, Maryland, USA, or New York, New York, USA. This rainbowoption increased the value of the business opportunity.

USA New York City

Cove Point

Elba Island

TRINIDAD

0

0 1000 2000 3000 km

500 1000 1500 2000 miles

Land-based terminal

Offshore transfer buoy

Base-case trade route

Spread-option trade routes

(continued on page 18)

16 Oilfield Review

At this time, the design criteria for the fictitiousCharon field project have been established and a three-year development phase is about to begin. A critical technical issue is the gas-throughput capacity of a surface separator.Economic analysis suggests a maximum separator capacity of 50 million scf/D [1.4 million m3/d]. A facilities contractor,Proteus Fabrication Inc., has been commis-sioned to design, fabricate and install it.

Although a 50 million scf/D throughputdesign—termed Case 50—is deemed ade-quate, an upside production potential of anextra 10 million scf/D [286,000 m3/d] is possi-ble. A 60 million scf/D [1.7 million m3/d]separator—Case 60—would be more expen-sive, and Charon might not have enoughproduction potential to utilize it fully. The com-pany would like to delay the design-capacitydecision for as long as possible.

Proteus can implement this design changewithin the first year of construction, but can-not make changes after the first year. Theimplementation cost to switch from a smallerto a larger design, set at $17.72 million, isequivalent to an option exercise price, X.

In addition to this exercise price, Proteusinsists on an additional up-front nonrefund-able payment. This up-front paymentaccommodates changing the initial design toallow for later expansion and covers a possibleoverrun on the agreed exercise price. Oberoninitiates a simple switching-option study todetermine what the initial payment to Proteusshould be.

Case 50 and Case 60 are independent caseswith different cash-flow NPVs and volatilities.ECLIPSE modeling establishes the static NPV,excluding switching costs, and associatedvolatility of the two cases (top right).Values for Case 60 are obtained in manner similar to Case 50, the base case used in the previous examples.

A switching option can be analyzed by con-structing two lattices, one for each of the twounderlying assets (next page). The simplestcase assumes these two lattices are completely

correlated—each step up or down in oneunderlying lattice corresponds with the samestep in the other. In this way, nodes in the twocases can be directly compared to construct avaluation lattice for the upgrade.

The valuation lattice is obtained by sub-tracting the upgrade cost, $17.72 million, from

the last column of the Case 60 lattice, compar-ing this to the last column of the Case 50lattice, and selecting the larger value at eachnode. This reflects Oberon’s right to choosethe better of the two cases in any eventuality.The option value is then computed by back-ward induction using the Case 50 risk-neutralprobabilities, p.

Synthetic-Reservoir Surface-Separator Decision

Switch Option

> Comparison of volatility and net present value (NPV) for two surfaceseparator cases in the synthetic Charon example.

Case 50 Case 60

Throughput, million scf/D

Volatility

NPV, million $

50

66.41%

236.27

60

71.28%

228.99

> Effect of lattice size on option valuation. The coarse, five-step lattice hasbeen used for illustrative purposes only, yielding a less accurate option valuethan the more refined 200-step lattice. At the $17.72 million switching cost,that finer lattice indicates the option value is $1.653 million.

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.050 15

17.72

200-steplattice

Five-steplattice

10Switching cost, million $

Switc

hing

opt

ion

valu

e, m

illio

n $

2520

Switching option value forfive-step lattice is 1.305

Switching option value for200-step lattice is 1.653

Winter 2003/2004 17

Changing the cost to upgrade affects thevalue of the upgrade option (previous page,bottom). In this case, the five-step lattice istoo coarse, resulting in an unrealistic kink inthe result. A finer 200-step lattice resolves thekink and indicates that it would be appropri-ate for Oberon to pay Proteus a $1.653 million

premium for the option to switch in the firstyear at the stated upgrade price. In an actualcase, final decisions would be based on finerlattices than the five-step lattices used in these illustrations.

With this arrangement Oberon gains the ability to demand a design change resulting in

accelerated cash and throughput from reser-voir production, if conditions warrant. Proteusgets an up-front premium of $1.653 millionand a locked-in payment of $17.72 million ifOberon chooses to upgrade the facility. Pro-teus has a cash incentive to explore morecost-effective and efficient design solutionsfor the upgrade.

< Lattices for synthetic Charon sur-face separator cases. Case 50 andCase 60 have different lattices ofthe underlying asset, but the latticestructure is the same, allowing anode-by-node comparison betweenthem (top). Nodes in Case 60 aregreyed out, except for the final col-umn, to indicate that no decision ismade until the end of one year. Thelast column of the valuation latticeis constructed by comparing thevalue of Case 50 to equivalent nodevalue of Case 60 minus the imple-mentation cost of $17.72 million(bottom). This also provides thedecision to keep Case 50 or switchto Case 60. The other nodes of thevaluation lattice are constructed byback-regression, using the risk-neu-tral probabilities from Case 50, thebase case. The value of the projectwith the switch option is$237.57 million.

236.27317.97

175.56

427.93

236.27

130.45

317.97

575.91

72.02

130.45

236.27

775.071,043.10

575.91

317.97

175.56

96.93

53.52

427.93

175.56

96.93

228.99314.96

166.48

433.21

228.99

121.04

314.96

595.86

63.98

121.04

228.99

819.571,127.26

595.86

314.96

166.48

88.00

46.52

433.21

166.48

88.00

0(Now)

1(0.2 year)

2(0.4 year)

3(0.6 year)

4(0.8 year)

5(1.0 year)

0(Now)

1(0.2 year)

2(0.4 year)

3(0.6 year)

4(0.8 year)

5(1.0 year)

Case 50 Underlying Lattice

Case 60 Underlying Lattice

Decision and Valuation Lattice

237.57320.85

175.64

434.24

236.46

130.45

589.77

72.02

130.45

236.27

805.441,109.64

578.14

317.97

175.56

96.93

53.52

428.91

175.56

96.93

Start

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

continue

Switch to Case 60

Switch to Case 60

Keep Case 50

Keep Case 50

Keep Case 50

Keep Case 50Lattice node values, million $

MAX(Case 50, Case 60-17.72)

318.40

Actions of one company can affect the busi-ness results of the other. Most governments nowinsist on unitization, an arrangement thatrequires parties on both sides to jointly developreserves located on more than one lease or auc-tioned tract. Each party pays a share of the costsand receives a proportionate amount of the revenues. In a sense, when governments do this, they are ensuring the purity of the realoptions involved.

It is possible to conceive of circumstances—such as constructing a pipeline to an area whereonly one is needed—in which if Company A tookup the option to invest, it would preempt Com-pany B from doing so, rendering B’s optionworthless, or certainly worth less. The real-options approach attaches a positive value todelay, but in instances such as this one, delaycan undermine value.23

Finally, the parameters used in real-optionscalculations can be difficult to determine. Thereis no simple road map to computing volatilityand there is still debate over the correctapproach to finding this value. Obtaining an esti-mate often entails performing a Monte Carlosimulation on the existing DCF model and exam-ining the standard deviation of the naturallogarithm of the cash-flow returns. The cost ofdeferment requires knowledge of the profitsforegone during the period prior to exercising anoption, but the value of the missed cash flowsmay be poorly known.

Financial-option pricing relies on an assump-tion that the underlying asset can be traded,meaning there is a large liquid market for theasset. This is often not true for real options. Fac-tors affecting the prices of financial options arealso easier to determine—that is, more trans-parent—than those for real options.

The simplified discussion in this article isintended only to introduce the concept of realoptions. It uses simple examples that correlatewith financial options. Use for an actual case istypically more complicated, with an expandingarray of possible options available, as demon-strated in the El Paso LNG case. Ultimately, realoptions are not financial options. The tech-niques of financial options provide a basis for

18 Oilfield Review

23. For a discussion of such investment behavior: Weeds H:“Strategic Delay in a Real Options Model of R&D Compe-tition,” Review of Economic Studies 69 (2002): 729–747.

24. Trigeorgis, reference 5: 3.

The fictitious Charon field, operated by Oberon Oil, has been producing for a fewyears. Production is declining and water cut is increasing in some of the wells. Engineerspropose a production-enhancement operationinvolving water shutoff on one of the wells.Their analysis has determined what incremental production is likely to be from this intervention.

With DCF, the expected NPV of the incre-mental cash flow, which is the option assetvalue S, is $1,280,000, excluding the actualintervention cost. The cost of the intervention,or exercise price X, is $750,000. The resultingNPV is $530,000.

Analysts estimate a 40% volatility of the incremental cash flow subject to oil price andtechnical uncertainties, and use a 5% risk-freerate of interest.

The service provider offers Oberon twochoices:1. Pay the $750,000 job cost up-front and

accept whatever may happen.2. Pay an additional up-front premium to the

service provider for the right to claim backsome or all the job cost if the incrementalnet revenue generated from this interven-tion is negative after one year. The second choice provides Oberon with

protection from downside risk, up to the costof the job, but the intervention would stillhave an unlimited upside potential. For exam-ple, if after one year the net incremental cashflow (after job cost) were negative $100,000,then the service provider would reimburseOberon that sum. Oberon’s net incrementalcash flow from this operation would be zero.In effect, this option offered by the serviceprovider provides a cost-reimbursement guar-antee for an agreed up-front premium. Oberonwants to calculate what a reasonable value forthis up-front premium should be.

The first choice is a pure operational alter-native—to intervene or not to intervene. IfOberon takes this choice, then any job cost issunk; the decision to spend money on the job is

irreversible. This arrangement is an alternative,not an option in the sense discussed in thisarticle. A valuation lattice for this alternativediffers from an ROV lattice in that the right-hand terminal nodes of the valuation latticecontain the simple term, S-X, rather than theconventional terms used in those nodes, thatis, the maximum of zero and S-X—MAX(S-X,0)(next page).

The difference between the alternative andreal-option lattices—$8,198—represents thepremium the service provider should theoreti-cally demand in order to agree to a contractedcost-reimbursement provision. It is small inthis case because there is a small likelihoodthat the provision would be required and theoption would be exercised.

The NPV of $530,000 undervalues this pro-ject. Even with no reimbursement provision,the value added to the asset from the inter-vention is $36,578 more than the NPV. Thisadditional value emerges solely because of thepresence of volatility in the underlying asset.Adding the revenue reimbursement provisionincreases this net value by $44,776 beyond theNPV calculation.

Synthetic-Reservoir Intervention

True Option and an Alternative Valued under Uncertainty

Winter 2003/2004 19

evaluating real options, but an expert in ROVshould be consulted to assure the techniquesare properly applied.

These complications should not dissuade acompany from using real options. Valuationexperts can determine when ROV should beused, and when other methods, such as decisiontrees incorporating Monte Carlo simulation, aremore appropriate. Working with managers andexperts in other disciplines, valuation expertscan help place a value on the options inherent inmany projects.

The Real-Options MindsetActually recognizing options that are embeddedin a project takes practice. Managers often learnto discern options simply by brainstorming withone another about the project.

In many ways, having a real-options mindsetis as important as using the mathematics. Real-options thinking emphasizes and valuesmanagement flexibility. It recognizes that in aworld characterized by change, uncertainty andcompetitive interactions, management can beactive. It can alter and modify plans as newinformation becomes available or as new possi-bilities arise.24 It can be reactive to changingcircumstances or proactive—intervening to takeadvantage of possibilities that may improve thevalue of the project. If management understandsthat flexibility is valuable, it will look for thatflexibility in its projects and capitalize on it toincrease shareholder value. —MB, MAA

> Comparison of an option and an alternative. The lattice method can be used tovalue an alternative. Both use the same lattice of the underlying (top). For anoption, the right-hand column is the maximum value of zero and the differencebetween the underlying value and the $750,000 implementation cost (middle).The values for an alternative can be negative, because the function is simply thedifference between the value and the implementation cost (bottom). This leads toan $8,198 difference in value between the option, valued at $574,776, and thealternative, valued at $566,578.

0(Now)

1(0.2 year)

2(0.4 year)

3(0.6 year)

4(0.8 year)

5(1.0 year)

Lattice of the underlying asset

Valuation lattice with true option

Valuation lattice with alternative

Max(S-X, 0)

S-X

Lattice node values, $

1,280,0001,530,731

1,070,338

1,830,577

1,280,000

895,019

1,530,731

2,189,157

625,827

895,019

1,280,000

2,617,9773,130,796

2,189,157

1,530,731

1,070,338

748,416

523,317

1,830,577

1,070,338

748,416

566,578810,139

349,746

1,102,742

552,166

167,184

795,582

1,454,008

–116,711

152,481

537,463

1,875,4392,380,796

1,439,157

780,731

320,338

–1,584

–226,683

1,088,039

335,189

13,267

574,776810,248

365,671

1,102,742

552,378

198,119

795,582

1,454,008

0

153,291

537,463

1,875,4392,380,796

1,439,157

780,731

320,338

0

0

1,088,039

334,604

73,335