making use of real options simple an overview and applications in flexibl

The Engineering Economist, 50: 2553Copyright 2005 Institute of Industrial EngineersISSN: 0013-791X print / 1547-2701 onlineDOI: 10.1080/00137910590917026

MAKING USE OF REAL OPTIONS SIMPLE: AN OVERVIEWAND APPLICATIONS IN FLEXIBLE/MODULAR DECISIONMAKING

Lenos Trigeorgis

Bank of Cyprus Chair Professor of Finance, University of Cyprus,Nicosia, Cyprus and President, Real Options Group

This article focuses on how the use of real options can be made simple,providing an overview of the power of flexible and modular decision mak-ing and its use in various applications across industries. After commonreal options are discussed through a comprehensive example, the arti-cle reviews the key lessons and implications of real options thinking forflexible decision making. It then proceeds to propose a modular problemstructuring approach that allows simplifying of complex real option prob-lems by decomposing them into a few basic building-block option types (re-viewed) connected by some basic decision operators. The resulting problem-structuring option map is depicted in a range of illustrative applicationsin various industries. Past areas of application of real options as well asresearch challenges ahead are also discussed.

INTRODUCTION

In an increasingly uncertain and dynamic global market place, managerialflexibility has become essential for firms to successfully take advantageof favorable future investment opportunities, respond effectively to tech-nological changes or competitive moves, or otherwise limit losses fromadverse market developments. Thinking of future investment opportunitiesas real options has provided powerful new insights that in many waysrevolutionized modern corporate resource allocation. Real options empha-sizes the importance of waiting (e.g., McDonald and Siegel [34]) or stagingflexibility, suggesting that managers should either wait and see until sub-stantial uncertainty is resolved and the project is more clearly successful,

Address correspondence to Lenos Trigeorgis, Bank of Cyprus Chair Professor of Finance,University of Cyprus, 75 Kallipoleos, P.O. Box 20537, CY 1678, Nicosia, Cyprus. E-mail:[email protected]

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requiring a premium over the zero-NPV, or they should stage the decisionso that they can revise the situation at critical milestones to either proceedto the next stage or abandon. During the waiting or staging period, new in-formation can be revealed that might affect the desirability of the project;if future developments turn out worse than expected, the firm has implicitinsurance protecting it against downside losses by choosing not to proceedwith the project.

Real options also introduces a new insight with respect to the role andimpact of uncertainty on investment opportunity value that runs counterto conventional thinking. Since management is asymmetrically positionedto capitalize fully on upside opportunities while it can limit losses on thedownside, more uncertainty can be beneficial for option value. More can begained from opportunities in highly uncertain or volatile markets becauseof the exceptional upside potential and limited downside risk that resultfrom managements flexibility to proceed or not proceed with the project.

From a strategic perspective, of course, it may not always be benefi-cial to wait and see. For example, by making an early strategic R&Dinvestment, a firm may not only develop more cost-efficient or higher-quality products or processes that can result in a sustainable cost or othercompetitive advantage, but may be able to positively influence compet-itive behavior and earn a higher market share down the road. In somecases a firm anticipating competitive entry may make a strategic invest-ment commitment (e.g., in excess production capacity) early on such thatit can preempt competition altogether. Therefore, optimal investment tim-ing generally involves a trade-off between wait-and-see flexibility and thestrategic value of early commitment. Moreover, early investing may itselfopen up a set of new options embedded in the commercial project (e.g., tolater expand, abandon, or switch to alternative uses), whose value may alsobe enhanced by higher uncertainty, but is realized through early investing.Thus, the presumed depressive impact of uncertainty on investment is notthat clear-cut. The above new considerations of investment under uncer-tainty suggest the need to adopt an expanded or strategic NPV criterion,able to capture managements flexibility to alter planned investment deci-sions as future market conditions change as well as the strategic value ofcompetitive interactionsbesides the value of expected cash flows fromcommitted assets (e.g., see Trigeorgis [50, 52, 55, 56]).

The rest of the article is organized as follows: The next section providesan overview of some common real options through a comprehensive ex-ample. Key lessons we have learned about real options in terms of maininsights and implications are then discussed, followed by discussion onsimplifying real-life problems and reducing them to a basic problem struc-ture. A review of real options applications is given next, while the finalsection catalogues challenges that future research must focus on more.

Making Use of Real Options Simple 27

OVERVIEW OF COMMON REAL OPTIONS:A COMPREHENSIVE EXAMPLE

The following example involving a natural resource extraction and pro-cessing facility serves to review many of the most common options en-countered in long-term capital investment opportunities. A large naturalresources company has a one-year lease to start extracting minerals on un-developed land with potential reserves. Initiating the project may requirecertain exploration costs, to be followed by construction of roads and otherinfrastructure outlays. Planned investment outlays are indicated as It , whileVt indicates the value of the projects expected operating cash flows at timet . The initial investment in exploration is I0, and the investment in roads andother infrastructure in the first period is I1. This is expected to be followedby capital outlays, I2, for the construction of a new processing facility. Ex-traction can begin only after construction is completed; i.e., cash flows aregenerated only during the operating stage that follows the last outlay. Dur-ing construction, if market conditions deteriorate, management can chooseto forego future planned outlays past the current stage. Management mayalso choose to reduce the scale of operation by c%, saving a portion, IC ,of the last outlay (I2) if the market is weak.

The processing plant can also be designed up front such that, if mineralprices (or the quantity of reserves) turn out unexpectedly high, the rateof production can be enhanced by x% with a follow-up outlay of IE toinstall extra capacity. At any time, management may salvage a portionof its investment by selling the processing plant and equipment for theirsalvage value or switch them to an alternative use value, At . An associatedrefinery plant, which may be designed to operate with alternative sourcesof energy inputs, can convert the raw mineral into a variety of refined by-products. We enumerate hereafter the real options embedded in this typeof project.

1. The option to defer investment. The lease enables managementto defer investment for up to one year and benefit from the res-olution of uncertainty about mineral prices during this period.Management would invest I1 (i.e., exercise its option to extractthe mineral) only if mineral prices (or reserves) are sufficientlyhigh, but would not commit to the project, saving the plannedoutlays, if prices (or reserves) are low. Just before expiration ofthe lease, the value added will be the greater of the net valuecreated (that is, V1 I1) or $0, with value added represented asmax (V1 I1, $0). The option to defer or invest is thus analo-gous to an American call option on the gross present value ofthe completed projects expected operating cash flows, V1, with

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the exercise price being equal to the required outlay, I1. Sinceearly investment implies sacrificing the option to wait, this op-tion value loss is like an additional investment opportunity cost,justifying investment only if the value of cash benefits actuallyexceeds the initial outlay by a substantial premium. The optionto wait is particularly valuable in such resource extraction indus-tries, as well as in farming, paper products, and real estate devel-opment, due to high uncertainties and long investment horizons.

2. The option to stage investment. In most real-life projects, therequired investment is not incurred as a single up-front outlay.The actual staging of capital investment as a series of outlaysover time creates valuable options to continue with the projector abandon it at any given stage (e.g., after exploration if thereserves or mineral prices turn out very low). Thus, each stage(e.g., building necessary infrastructure) can be viewed as an op-tion on the value of subsequent stages by incurring the next costoutlay (e.g., I1) required to proceed to the next stage and cantherefore be valued similar to compound options. This option isvaluable in all R&D-intensive industries, especially biotechnol-ogy and pharmaceuticals; in highly uncertain, long-developmentcapital-intensive industries, such as energy-generating plants orlarge-scale construction; acquisition or market entry strategies;high-tech start ups; and venture capital.

3. The option to expand. If mineral prices, reserves, or other mar-ket conditions turn out more favorable than expected, manage-ment can accelerate the rate or expand the scale of production(by e%) by incurring a follow-up cost outlay (IE). This is sim-ilar to a call option to acquire an additional part (e%) of thebase-scale project, paying IE as exercise price. The investmentopportunity with the option to expand can be viewed as thebase-scale project plus a call option on future investment [i.e.,V + max(eV IE, 0)]. Given an initial design choice, manage-ment may deliberately select a more expensive technology withbuilt-in flexibility to expand production if and when it becomesdesirable. As discussed further below, the option to expand mayalso be of strategic importance, particularly if it enables thefirm to capitalize on new or future market growth opportuni-ties. When the firm buys vacant undeveloped land, or when itbuilds a flexible plant in a new geographic location (domesticor overseas) to position itself to take advantage of a develop-ing potentially large market, it essentially acquires or puts inplace an expansion or growth option. This option, which will beexercised only if future market developments turn out favorable


at a future date, but not otherwise, can oftentimes make a seem-ingly unprofitable (based on passive NPV) base-case investmentworth undertaking.

4. The option to contract. If market conditions turn out weaker thanoriginally expected, management can operate below capacity oreven reduce the scale of operations (by c%), thereby saving partof the planned investment outlays (IC). This flexibility to mitigateloss is analogous to a put option on part (c%) of the base-scaleproject, with exercise price equal to the potential cost savings(IC), giving max(IC cV, $0). The option to contract (just as theoption to expand) may be particularly valuable in the case ofnew product introductions in uncertain markets. The option tocontract may also be important in choosing among technologiesor plants with a different construction-tomaintenance cost mix,where it may be preferable to build a plant with lower initialconstruction costs and higher maintenance expenditures in orderto acquire the flexibility to contract operations by cutting downon maintenance if market conditions turn out unfavorable.

5. The option to temporarily shut down (and re-start) operations.Actually, the plant does not have to operate (i.e., extract the min-eral) in each and every period automatically. In fact, if mineralprices are such that cash revenues are not sufficient to cover vari-able operating (e.g., maintenance) costs, it might be better notto operate, temporarily. If prices rise sufficiently, operations canstart up again. Thus, operation in each year can be seen as acall option to acquire that years cash revenues (C) by paying thevariable costs of operating (IV) as exercise price, i.e., max(C IV,0). If switching costs (between the operating and idle modes) aresubstantial, delays in switching may arise (hysteresis). Optionsto alter the operating scale (i.e., expand, contract, or shut down)are typically found in natural resource industries, such as mineoperations, facilities planning and construction in cyclical in-dustries, fashion apparel, consumer goods, and commercial realestate.

6. The option to abandon for salvage value. If the quantity of re-serves turns out low, if mineral prices suffer a sustainable decline,or if the operation does poorly for some other reason, manage-ment does not have to continue incurring the fixed costs. In-stead, management may have a valuable option to abandon theproject permanently in exchange for its salvage value, that is theresale value of its capital equipment and other assets in second-hand markets. This option can be valued as an American putoption on current project value with exercise price the salvage or

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best alternative use value, entitling management to receive V +max(A V, 0) or max(V, A). Naturally, more general-purposecapital assets would have a higher salvage and option abandon-ment value than special-purpose assets. Valuable abandonmentoptions are generally found in capital-intensive industries, suchas in airlines and railroads, in financial services, and in new prod-uct introductions in uncertain markets.

7. The option to switch inputs or outputs. Suppose the associatedmineral processing operation can be designed to use alternativeforms of energy inputs (e.g., fuel oil, gas, or electricity) to convertthe raw mineral into a variety of output by-products. This wouldprovide valuable built-in flexibility to switch from the current in-put to the cheapest future input, or from the current output to themost profitable future product mix, as the relative prices of theinputs or outputs fluctuate over time. In fact, the firm should bewilling to pay a certain premium for such a flexible technologyover a rigid alternative that confers no or less flexibility. Indeed,if the firm can in this way develop more uses for its assets rel-ative to its competitors, it may be at a significant comparativeadvantage. Generally, process flexibility can be achieved not onlyvia technology (e.g., by building a flexible facility that can switchamong alternative energy inputs), but also by maintaining rela-tionships with a variety of suppliers, changing the mix as theirrelative rates change. Subcontracting policies may allow furtherflexibility to contract the scale of future operations at a low costin case of unfavorable market developments. A multinationalcompany may similarly locate production facilities in variouscountries in order to acquire the flexibility to shift productionto the lowest-cost producing facilities as the relative costs, otherlocal market conditions, or exchange rates change over time. Pro-cess flexibility is valuable in feedstock-dependent facilities suchas oil and minerals, electric power, chemicals, crop switching,and supplier relationships in many industries. Product flexibility,enabling the firm to switch among alternative outputs, is morevaluable in industries such as automobiles, consumer electron-ics, toys, or pharmaceuticals, where product differentiation anddiversity are important and/or product demand is volatile. Insuch cases, it may be worthwhile to install a more costly flexiblecapacity to acquire the ability to alter product mix or productionscale in response to changing market demands.

8. Corporate growth options. As noted, another version of the ear-lier option to expand, of considerable strategic importance, iscorporate growth options that set the path of future opportunities.


Suppose, in the above example, that the proposed processingfacility is based on a new, technologically superior process formineral refinement developed and tested internally on a pilotplant basis. Although the proposed facility in isolation may ap-pear unattractive, it could be only the first in a series of similarfacilities if the process is successfully developed and commer-cialized and may even lead to entirely new mineral by-products.More generally, many early investments (e.g., R&D, a lease onundeveloped land or a tract with potential oil reserves, a strate-gic acquisition, or an information technology network) can beseen as prerequisites or links in a chain of interrelated projects.The value of these projects may derive not so much from their ex-pected directly measurable cash flows, but rather from unlockingfuture growth opportunities (e.g., a new-generation product orprocess, related mineral reserves, access to a new or expandingmarket, strengthening of the firms core capabilities or strate-gic positioning). An opportunity to invest in a first-generationhigh-tech product, for example, is analogous to an option onoptions (an inter-project compound option). Despite a seem-ingly negative NPV, the infrastructure, experience, and poten-tial by-products generated during the development of the first-generation product may serve as spring boards for developinglower-cost or improved-quality future generations of that prod-uct, or even for generating new applications into other areas. Butunless the firm makes that initial investment, subsequent genera-tions or other applications would not even be feasible. The infras-tructure and experience gained can be proprietary and can placethe firm at a competitive advantage, which may even reinforceitself if learning cost curve effects are present. Growth optionsare found in all infrastructure-based or strategic industries, es-pecially in high tech, R&D, and industries with multiple productgenerations or applications (e.g., semiconductors, computers,pharmaceuticals), in multinational operations, and in strategicacquisitions.

In a more general context, such operating and strategic adaptability rep-resented by such a set of corporate real options can be achieved at variousstages during the value chain, from switching the factor input mix amongvarious suppliers and subcontracting practices, to rapid product design andmodularity in design, to shifting production among various products orcountries rapidly and cost-efficiently in a flexible system or multinationalnetwork.

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LESSONS AND IMPLICATIONS FOR FLEXIBLEDECISION MAKING

The insight gained from viewing investment opportunities through a realoptions lens can be quite powerful. Real options analysis provides a numberof insightful lessons and implications, summarized below.

1. Uncertainty and flexibility are two key determinants of the valueof an asset or firm. Their understanding calls for an expandedvaluation criterion. The traditional valuation paradigm based oncash flows from expected plans under the implicit assumption ofpassive management has proven inadequate in dynamic settings.The role of uncertainty in the presence of managerial flexibility isnot necessarily penalizing, as conventional wisdom would haveus believe. Greater variability of potential outcomes around theexpected (mean) result may be beneficial in the presence of op-tions and an asymmetric managerial position. Managerial flexi-bility to revise future decisions when there are deviations from theexpected plans introduces beneficial asymmetry in the distribu-tion of project value returns by enabling upside (value-creation)opportunities to be exploited fully while limiting downside lossesby choosing not to proceed or abandon. The resulting skewing ofthe probability distribution of expected project returns towarda more positive outcome calls for an expanded (strategic) NPVcriterion to also capture the additional value of managerial op-erating flexibility and other strategic interactions:

Expanded (or Strategic) NPV = passive NPV+ Option Premium (ROV) (Flexibility value+ Strategic value)

Based on this expanded criterion, it can be seen that it may nowbe justified to accept projects with negative (passive) NPV ofexpected cash flows (if this is offset by a larger option premium orreal option value as a result of additional flexibility and strategicvalue), or delay investment with positive NPV until a later timewhen expanded NPV would be maximized under uncertainty.

2. Managerial flexibility or real option value (ROV) may be higher(other things the same) for firms or industries facing higher un-certainty; for investment opportunities with longer horizons orthat can be delayed longer; when (real) interest rates are higher;or for multi-stage (compound) options.


3. Higher uncertainty tends to increase the value of the option todefer (a single, irreversible, proprietary) investmentprovidedthere are small or no early exercise benefits (analogous to div-idends), strategic interactions or other embedded options. Theflexibility to delay or wait and see enables acquiring more orbetter information and making a more informed future decision,potentially avoiding a mistake from premature investment in casethings would develop unfavorably. This higher value to wait andsee necessitates a higher critical investment threshold: the crit-ical project value, V , must be at a significant premium abovethe required investment cost, I , before it is justifiable to investand sacrifice the option to wait. The implication of this is thathigher uncertainty would presumably lead to investing less orlater (other things the same), with potentially significant macroe-conomic implications. I should caution, however, that this holdsunder the provisional conditions made above (and relaxed later)and may be different in different contexts, so it is questionablewhether empirical studies on investment based on macro datacan verify the presumed depressive role of uncertainty on invest-ment (in terms of lower or delayed investment) if the provisionalconditions are not confirmed to be carefully satisfied.

4. If one can reverse a decision (with ease or little cost), it is easierto make it (e.g., invest) in the first place. A multinational cor-poration would find the decision to enter a new foreign countryeasier if it can get out with limited damage in case of unfavorabledevelopments. This principle holds in general contexts beyondbusiness investment. For example, the decision to get marriedmight be easier in societies where it is easier to receive divorce(in Islamic parts of India men can obtain divorce simply by pro-claiming the word 3 times). In deciding whether to move fromthe United States to a smaller, more risky country, it helps tomake the decision if one has U.S. citizenship rights. These rightsgive the individual the option to reverse the decision and operatein the best of the two countries over time, just as locating plantsin several countries enables a multinational corporation to op-erate in the best subset of several countries and shift productionfrom one country to another to take advantage of fluctuationsor differences in exchange rates, labor costs or other productioninputs, tax regimes, etc.

5. Under uncertainty, it is prudent to stage an investment or proceedwith decision plans in stages. Staging the investment or decisionplans provides valuable flexibility to continue to the next stage(receiving the option value from continuing) or to abandon (exit)

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midway. Continuation (e.g., financing of subsequent stages inventure capital) should be contingent on the success of earlierstages.

6. Multistage opportunities may have significant growth (com-pound) option value that may justify making strategic invest-ments despite having negative NPV. Consider, for example, atwo-stage growth option. The first stage involves investing in amanufacturing facility in Spain to introduce a new product that isexpected to generate moderate cash flows from the Spanish mar-ket. The second stage would involve a 10-fold expansion into thebroader European market 3 years later. The first-stage NPV ofthe expected cash flows from investing in the Spanish marketis negative, and committing now to enter the European marketon an expanded scale seems ten times as bad. But the companydoes not have to commit to European expansion now. Instead,it has an option to wait and see how the Spanish and Euro-pean demand develops and expand to the European market ifand only if it appears favorable to do so 3 years from now. Theopportunity to expand in Europe, valued as an option, may welloffset the negative NPV of the first-stage investment (in effectthe option premium or exercise price that needs to be paid toacquire the European expansion option) and can justify makingthis strategic multistage investment on strategic grounds. Em-pirically, companies in industries with higher uncertainty thatinvolve multistage (compound) options tend to have a higherproportion of their stock price deriving from growth opportuni-ties (PVGO/P), providing an indirect confirmation of the validityof real option theory predictions.

7. If investing would open up or create other options within theproject (e.g., to later expand, abandon, or switch to alternativeuses), then more uncertainty would also increase the flexibilityvalue of these other embedded optionsincreasing the value ofearly investing in the first place. For this reason (and the otherreasons listed below), higher uncertainty would not necessarilysuppress or delay investment.

8. In the presence of competition in an oligopoly setting, early in-vestment may have strategic value by influencing the equilibriumactions (quantity or price setting) of competitors in a way ben-eficial to the investing firm or even by preempting competitiveentry altogether in some cases. Thus, the option value of wait-ing must be traded off against the strategic commitment value ofearly investing. Again, the impact of higher uncertainty on invest-ment is not clear-cut; in fact, it may not even vary monotonically


with demand as shifts in demand may lead to shifts in the typeof equilibrium games and different market structure outcomes(e.g., from a Nash duopoly to a Stackelberg leader/follower gameor a monopoly) in different demand zones leading to value dis-continuities as a function of demand. The value of the strategicinvestment and the optimal competitive strategy (e.g., to investnow or wait) depends on whether the resulting benefits of theinvestment are proprietary or shared and whether they are dam-aging or benefiting the competitor, as well as on whether compet-itive reaction is expected to be contrarian (opposite to the actionof the investing firm) or reciprocating (similar to the action ofthe investing firm). When the investment benefits are proprietaryand the pioneer can get stronger at the expense of its competitor,it should commit to an early investment (aggressive) strategy ifthe competitors reaction is contrarian; e.g., if it will retreat andcut its market share under quantity competition as the pioneerexpands its own market share. However, when the benefits areshared, thereby benefiting the competitor as well, and a contrar-ian competitor would respond aggressively, taking advantage ofthe pioneers accommodating position, the firm should follow aflexible wait-and-see strategy rather than subsidizing an aggres-sive competitor while itself paying the full cost. The above canbe reversed under reciprocating (price) competition. If the bene-fits are shared and will benefit a competitor who will reciprocatewhen treated nicely (e.g., by maintaining high prices) the optimalstrategy might be to invest early (but not aggressively). On thecontrary, if the benefits are proprietary and will hurt a competi-tor who will retaliate by entering into a price war, it may makebetter sense to wait or not invest.

9. Competitive pressure may induce firms (e.g., in a winner takesall innovation race) to invest prematurely, resulting in a subop-timal prisoners dilemma situation. Each of the two firms (likeprisoners), being afraid that it may be preempted by the otherand lose all (the most severe punishment), would rush to investprematurely (give in), rather than wait (hold out), which maybe the preferred outcome. A joint research venture may enablethe two firms to more fully appropriate the flexibility value fromwaiting (avoiding the prisoners dilemma) by coordinating andjointly optimizing against demand uncertaintybesides sharingand saving on the investment cost. A limitation is that, in col-laborating, a firm gives up the possibility to outwit its rivals andgain a competitive advantage or strategic value over the otherfirm.

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10. Multiple options embedded in a project may interact; i.e., optionvalue additivity may break down. The presence of a later optionenhances the value of the underlying asset for a prior option,while exercising an earlier option may alter the scale of (and inthe case of the option to abandon, may extinguish) a later option.The value of a portfolio or combination of embedded optionstypically is less than the sum of separate or independent optionvalues. Therefore, using an analytic formula like Black-Scholesto determine the values of separate options and then add themup may be misleading. The error from adding up separate optionvalues may be of the same order of magnitudebut in the op-posite directionas the error from ignoring options altogether.That is, a wrongly executed options analysis can be as dangerousas a nave NPV analysis.

11. Options to switch (among the cheapest of several inputs, best ofseveral outputs, or most profitable countries of operation) pro-vide valuable flexibility and risk management value. Traditionalmean-variance portfolio theory based on the notion that risk isundesirable and must therefore be minimized (for a given ex-pected return) is inadequate; it needs to be extended for portfo-lios of (potentially interdependent) options, incorporating highermoments. The flexibility to adjust plans when deviating fromexpectations by improving the upside potential while limitingthe downside risk adds asymmetry or skewness (third moment),while potential volatility dependence on project value, competi-tive jumps, and technological disruptions may introduce fat tailsand kurtosis (fourth moment). The very notion and role of riskmust also be revisited when flexibility is present. With optionsto choose the best of several alternatives (or on the maximum orminimum of several assets) or options to switch from one modeof operation or being to another, lower correlation tends to in-crease the relative volatility and option value of a flexible systemor network. When the value of one alternative drops, an option tochoose the best or switch to another alternative is worth more ifthe value of that second alternative tends to increase (that is, if ithas negative correlation with the first). For this reason, multina-tional corporations (MNCs) operating in several countries wouldprefer to select the next strategic location (to be added to theirmultinational network portfolio) to have lower correlation (withthe existing structure), not so much in order to diversify and re-duce risk, but rather in order to increase the relative volatilityand option value of the flexible network. Risk is not necessarilysomething to be avoided or be penalized for, but rather can be


seen as a window of opportunity for the more flexible and in-novative corporations to create more value by leveraging theiropportunity choices while limiting losses.

12. When switching among operating modes or strategies, thepresence of significant switching costs (e.g., to enter, exit, orshut down) may induce a hysteresis, inertia or delay/lag ef-fect. Even though immediate switching may be attractive basedon short-term cash-flow considerations, it may be long-term op-timal to wait, e.g., due to a high switching cost or probabilityof switching back later. Examples involving hysteresis effects in-clude continuing operations of a currently unprofitable mine oroil field despite temporarily suppressed prices; the Japanese autoproducers who, once they entered the U.S. market in profitabletimes, kept hanging on in the United States despite incurringlosses in subsequent years; lags in hiring and firing by compa-nies as business moves to an up and down cycle; and delays inseeking divorce despite an unhappy marriage. All these casesinvolve irreversible or costly-to-reverse decisions that justify de-laying a switching decision for a while since a re-switch back tothe current situation is either infeasible or would occur only aftera costly impairment of infrastructure, goodwill, etc.

MODULAR STRUCTURING AND SIMPLIFYING OF COMPLEXREAL OPTION PROBLEMS

Most real-life problems involve more complex combinations of the above(and occasionally other) options. However, one can simplify a complexinvestment decision problem structure by decomposing it into a few basicbuilding-block option types (such as the standard options in the previoussection) connected by some basic decision operations. Figures 1AD re-view some basic or common types of real options. In the figures, optionsare illustrated with a hexagonal symbol, shown in the second column, withthe relevant payout shown at the bottom depending on option type (e.g.,C + V for a call option; for shorthand, the max( , 0) is implied by theoption symbol itself and is omitted). A hat () over the investment costto be paid (C) or the (gross) PV of project cash flows (V ) indicates thatthey are uncertain (stochastic). The third column in Figure(s) 1 presents arelevant authors analytic model (e.g., Black-Scholes for the call option towait in Figure 1A). The last column lists actual case applications (mostlyfrom the authors experiences) most appropriate for that type of option.Figure 1A reviews the options to wait (call on project value V ) and to ex-pand (call on e% of V ) using the Black-Scholes [7] formula (on V or eV ,

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Figure 1A. Basic/common option types.

respectively), to abandon or contract (put on c% of V), and Margrabes [30]option to exchange or switch one asset for another (here cost C for projectvalue V). Figure 1B focuses on compound options, including the simplecompound (or pure growth) option by Geske [12], sequential two-stage

Figure 1B. Basic option types: Compound options.


Figure 1C. Basic option types: Max options.

compound exchange option, and an N -stage compound exchange op-tion representing a numerical generalization of the above. Figure 1Creviews options involving the max, including the Stulz [45] and John-son [18] models on European options to pay cost C by a given maturity to

Figure 1D. Basic option types: And options.

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acquire the max of two or more assets, and the generalized max (OR)operator on the best of 2 or more option alternatives (e.g., applicable inanalyzing the choice among the best of two product standards, the digitaland analog, in the case of Philips Electronics). Combinations of the abovetypes of options and their possible interactions leading to non-additivityof separate option values are discussed in Trigeorgis [53]. Figure 1D il-lustrates basic AND type options. They include the sum of N parallel (orstrategically independent) options shown vertically, such as expanding ge-ographically in continents A, B, and C or introducing new services D, E,and F, each involving the right to pay (stochastic) cost Ci by time ti toacquire underlying asset value Vi (i = 1, . . . , N ). They also include mod-eling manufacturing operations of a plant (e.g., Shell Chemicals flexibleplastic manufacturing plant) as the sum of T European operating optionsacross time (shown horizontally), provided switching costs are negligible.Each year of operation may be modeled as a European option to exchangea variable operating cost (C) for the value of generated cash flows (V ),using the Margrabe option to exchange one asset for another, or as an op-tion to incur the variable cost (C) to obtain the maximum revenue fromproducing the best of two (or more) products, using the Stulz or Johnsonoptions on the maximum of several assets. In general, this approach mayaccommodate a generic option payout of the form cC + aV 1 + bV 2 +function (V 1, V 2. . . ) where C , V 1, V 2, . . . can be uncertain (stochastic)variables and constants a, b, c can be of any sign. Such generic options(hexagons) can occur in any combinations over multiple stages, connectedwith one or more of four basic decision operators (with the OR, AND, AVGoperators shown in squares), to represent the basic option structure of mostreal life problems.

The four basic decision operations commonly encountered are illus-trated in Figure 2. They involve (a) the choice of the best among sev-eral mutually exclusive alternatives (OR or MAX); (b) the sum of several(parallel or strategically independent) options (AND); (c) the probabilisticaverage (AVG) of several follow-on options across various technical sce-narios weighted by their corresponding actual probabilities, or investingin a portfolio (weighted average) of several technological or other op-tions by allocating a portion of a given budget in each of these options;and (d) recursive multistage or compound/sequential options (COMP) thatmay provide not only their own cash flows but also provide follow-onoptions. In all the above basic decision operators, both the cost of ex-ercising an option (C) and the present value of resulting project cashflows (V ) may be uncertain. Although Figure 2 illustrates decision oper-ators involving 2 decision branches or two stages, these are readily ex-tended to N decision branches or to N stages (as illustrated in subsequentfigures).


Figure 2. Basic decision operations.

Valuation would proceed in a recursive (even modular) manner startingfrom the end and moving backward following the standard risk-neutraloption valuation procedure. Figure 3A illustrates a standard basic problemstructure (combination of standard options and decision operators) for tworeal-life applications taken from two entirely different industries. The en-ergy industry case involves a staged power plant construction with optionsto abandon midstream and later expand. The pharmaceutical industry caseinvolves valuing R&D during the clinical trials phase and determining thevalue of the patent rights for a new drug (also involving options to aban-don and to expand into a related niche). The basic problem structure andrelated option maps look remarkably similar, despite differences in prob-lem context and industry characteristics. In both situations each firm facesa compound (COMP) or multistage option to start (in an early stage) andthen complete (at a later stage) a development process (building a plant orcompleting clinical trials), followed by an option on the best alternative(OR), either to continue with commercial production operations (also in-volving a later option to expand) or to abandon for a salvage or sale value.Since the interim decision on the option to complete development/continueor abandon partly depends on the value of the subsequent option to laterexpand, that option must be determined first, starting from the end, andthen used in the backward valuation process along the way to make theearlier choice (to continue or abandon) in the previous step, and so on.

42 L. Trigeorgis

Figure 3A. Similar basic structure from different industry applications.

Figure 3B. Details on Glaxo case application.


Figure 4. Eli Lilly case application problem structure.

Figure 3B illustrates the problem structuring option map for the abovepharmaceutical case (Glaxo) with more details on the timing, staged costs,base project value (present value of cash flows from launching the oralversion of the drug), expansion costs and factors, salvage (sell) value, etc.

Figure 4 illustrates the problem structuring for another pharmaceuticalcompany (Eli Lilly), involving a committed decision to launch a basicversion of a drug (PTCA) and options to pursue two extensions (AMI andAngina). As shown in the top figure, the second drug extension (AMI) maybe introduced alone or following the first extension (Angina), in which caseit may benefit from both structural synergies (since the decision to launchAMI would benefit from prior knowledge of the success of the precedingAngina introduction) as well as from economic synergies (as the costs ofconvincing doctors of the benefits of the AMI extension would be lower,and the market expansion factor higher, following prior introduction ofAngina). The lower figure casts the above managerial decision problem asinvolving the choice between a sequential (compound option) vs. a parallel(sum of independent options) marketing expansion strategy.

Figure 5 illustrates the problem structuring for two HBS case appli-cations involving probabilistic options (AVG). In the Arundel case (toppanel), the success of a first movie will be revealed in the theatres by year1 with probability p, leading to an (call) option to make a sequel moviewithin the subsequent 2 years. In the Antamina case (lower panel), the

44 L. Trigeorgis

Figure 5. Probabilistic (AVG) case applications.

winner of a government bid will have 2 years to decide whether to incurthe development cost, C2, to receive the value of copper and zinc reserves,V , which depends on the stochastic copper and zinc prices (Pc, Pz). Theprobabilities of high (H), medium (M) and low (L) reserves, accountedfor through the AVG decision operator, would weigh the resulting optionvalues conditional on finding high, medium, or low reserves in year 2.

Figure 6A illustrates use of the AND operator to access the growthoption value of a high-tech IPO. Tiscalis existing business at the timeof the IPO was only fixed-line telephony, but its management envisionedplans to first offer e-commerce services in Italy and then expand them in

Figure 6A. Tiscali (AND) case application: Growth option value of high-tech IPO.


Figure 6B. Details on Tiscali case application.

the broader European market (a compound option). It also expressed plansto acquire a UMTS license that would enable it to offer integrated 3rdgeneration mobile services. More details on Tiscalis problem structuringand option map are given in Figure 6B. Figure 7 illustrates the optionmap for staging network (NW) infrastructure for a leading UK telecomoperator. Each staged network investment (e.g., NW1) provides the sumof 3 options: (a) expand by acquiring new business clients by the way thenetwork would be physically laid out, (b) switch customers initially using alow-bandwidth technology to a high-bandwidth one, and (c) proceed to thenext stage (NW2), involving similar such options, and so on. The readercan appreciate that there is no analytic, closed-form solution or an easymodeling approach for such problems, but they can readily be handledthrough the recursive and modular structure proposed herein.

PAST AREAS OF APPLICATION

Besides theoretical developments, real option applications have been re-ceiving increased attention. Real options valuation has been applied in avariety of contexts, such as in natural resource investments, land devel-opment, leasing, flexible manufacturing, government subsidies and regula-tion, R&D, new ventures and acquisitions, foreign investment and strategy,

46 L. Trigeorgis

Figure 7. Telecom case application problem structure: Staging network(NW) infrastructure.

and elsewhere. The review below is just indicative and is in no way meantto be exhaustive or capture all the important contributions.

Natural Resource Investments

Early applications naturally arose in the area of natural resource invest-ments due to the availability of traded resource or commodity prices, highvolatilities, and long durations, resulting in higher and better option valueestimates. Brennan and Schwartz [8, 9] utilize the convenience yield de-rived from futures and spot prices of a commodity to value the optionsto shut down or abandon a mine. Paddock, Siegel, and Smith [37] valueoptions embedded in undeveloped oil reserves and provide empirical ev-idence that option values are better than actual DCF-based bids in valu-ing offshore oil leases. Trigeorgis [50] values an actual minerals projectconsidered by a major multinational company involving options to cancelduring construction, expand production, and abandon for salvage. Bjerk-sund and Ekern [5] value a Norwegian oil field with options to defer andabandon. Morck, Schwartz, and Stangeland [36] value forestry resourcesunder stochastic inventories and prices. Laughton and Jacoby [27] exam-ine biases in the valuation of real options and long-term decision makingunder a mean-reversion price process. Kemna [20] shares her experienceswith Shell in analyzing actual cases involving the timing of developing anoffshore oil field, valuing a growth option in a manufacturing venture, andthe abandonment decision of a refining production unit.


Land Development

Titman [47], Williams [57], and Quigg [40] show that the value of vacantland should reflect not only its value based on its best immediate use (e.g.,from constructing a building now), but also its option value if develop-ment is delayed and the land is converted into its best alternative use inthe future. It may thus pay to hold land vacant for its option value even inthe presence of currently thriving real estate markets. Quigg [39] reportsempirical results indicating that option-based land valuation that incorpo-rates the option to wait to develop land provides better approximations ofactual market prices. In a different context, McLaughlin and Taggart [35]view the opportunity cost of using excess capacity as the change in thevalue of the firms options caused by diverting capacity to an alternativeuse. Grenadier [14] developed a model of real estate development, offeringan explanation for observed market behavior in land development, such asoverbuilding.

Flexible ManufacturingThe flexibility provided by flexible manufacturing systems, flexible produc-tion technology, or other machinery having multiple uses has been analyzedfrom an options perspective by Kulatilaka [24, 25], Triantis and Hodder[48], Kulatilaka and Trigeorgis [26], and Kamrad and Ernst [19], amongothers. Kulatilaka [25] values the flexibility provided by an actual dual-fuelindustrial steam boiler that can switch between alternative energy inputs(natural gas and oil) as their relative prices fluctuate, and finds that the valueof this flexibility far exceeds the incremental cost over a rigid, single-fuelalternative. Baldwin and Clark [2] study the flexibility created by modular-ity in design that connects components of a larger system through standardinterfaces.

Leasing Contracts

Copeland and Weston [10], Lee, Martin, and Senchack [28], McConnelland Schallheim [33], and Trigeorgis [54] value various operating optionsembedded in leasing contracts. Grenadier [13] uses real options to developa model that can be used to price different types of leasing contracts.

R&D/Innovation

Kolbe, Morris, and Teisberg [23] discuss option elements embedded inR&D projects. Option elements involved in the staging of start-up ventures

48 L. Trigeorgis

are also discussed in Sahlman [41] and Willner [58]. Grenadier andWeiss [15] examine the situation in which a firm has projects that involvesequential innovation. Their valuation incorporates the learning that assiststhe valuation and decision-making pertaining to future innovations.

Security Analysis

Real options have been advocated as an approach to valuing companies insecurity analysis. For example, Mauboussin [32] discusses how real optionsvaluation can be used to supplement traditional valuation approaches. Hesuggests that real options valuation is particularly useful in valuing com-panies that are R&D intensive as well as Internet companies. Kester [21]estimates that the value of a firms growth options is more than half themarket value of equity for many firms, even 7080% for more volatileindustries. Similarly, Pindyck [38] suggests that growth options representmore than half of firm value if demand volatility exceeds 20%. Berger et al.[4] empirically access investors valuation of the abandonment option.

Foreign Investment

Baldwin [1] discusses various location, timing, and staging optionspresent when firms scan the global marketplace. Bell [3], and Kogut andKulatilaka [22], among others, examine entry, capacity, and switching op-tions for firms with multinational operations under exchange rate volatility.Hiraki [17] suggests that the Japanese bank-oriented corporate governancesystem serves as the basic infrastructure that enables companies to jointlydevelop corporate real options.

Other Applications

Strategic acquisitions of other companies also often involve a number ofgrowth, divestiture, and other flexibility options, as discussed by Smith andTriantis [44]. Luchrman [29] discusses viewing strategy as a portfolio ofreal options. Smit and Ankum [42] and Smit and Trigeorgis [43] proposea game-theoretic approach to corporate investment strategy. Mason andBaldwin [31] value government subsidies to large-scale energy projects asput options, whereas Teisberg [46] provides an option valuation analysis ofinvestment choices by a regulated firm. Various other option applicationscan be found in areas ranging from shipping [6] to environmental pollutionand global warming (e.g. [16]). The potential for future applications itselfseems like a growth option.


RESEARCH CHALLENGES AHEAD

Despite significant progress in recent years, some long-standing gaps andchallenges remain. Here is a list of challenging issues that future researchmust still address:

1. Studying more actual case applications and tackling real-life im-plementation issues and problems.

2. Studying investments (such as in R&D, pilot or market tests, orexcavations) that can generate information and learning (e.g.,about the projects prospects) by extending/adjusting optionpricing and risk-neutral valuation.

3. Exploring in more depth endogenous competitive counterac-tions and a variety of competitive/market structure and strategicissues using a combination of game-theoretic industrial organi-zation with option valuation tools.

4. Better modeling of the various strategic and multistage growthoptions.

5. Extending real options in an agency context recognizing that thepotential (theoretical) value of real options may not be realizedin practice if managers, in pursuing their own agenda (e.g., ex-pansion or growth, rather than firm-value maximization), misusetheir discretion and do not follow the optimal exercise policiesimplicit in option valuation. This raises the need to design properincentive contracts by the firm (taking also into account asym-metric information) and develop a more dynamic, option-basedextension of economic value added.

6. Better recognizing that real options may interact not only amongthemselves but with financial flexibility options as well, and un-derstanding the resulting implications for the combined, inter-dependent corporate investment and financing decisions.

7. On the practical side, applying real options to the valuation offlexibility in related areas, such as in competitive bidding, infor-mation technology, or other platform investments, internationalfinance options, and so on.

8. Using real options to explain empirical phenomena that areamenable to observation or statistical testing, such as examiningempirically whether the management of firms that are targets foracquisition may sometimes turn down tender offers in part due tothe option to wait in anticipation of receiving better future offers.We also need more empirical studies to confirm other qualifiedpredictions of options theory, such as the impact of uncertaintyon investment.

50 L. Trigeorgis

9. Doing more field or survey studies to test the conformity of the-oretical real option valuation and its implications with manage-ments intuition and experience, as well as with actual data whenavailable.

10. Developing a more credible general portfolio theory for (pos-sibly interdependent) options under budget or other constraintsthat recognizes the potentially beneficial role of uncertainty inthe presence of flexibility to select the best subset among alterna-tive options. Finally, applying this to address important strategicportfolio problems in various contexts, such as management of aportfolio of start-up ventures by a venture capitalist, developmentof a pipeline portfolio of R&D opportunities by a pharmaceu-tical company, or selection of a subset of technologies to investin by a telecom company, and dynamic revision of the subset ofinvested technologies as uncertainties and their relative meritschange over time.

REFERENCES

[1] Baldwin, C., Competing for capital in a global environment, Midland CorporateFinance Journal, Vol. 5, 1987, pp. 4364.

[2] Baldwin, C. and K. Clark, Modularity and real options, Working Paper,Harvard Business School, 1993, Boston, MA.

[3] Bell, G., Volatile exchange rates and the multinational firm: Entry, exit, andcapacity options, In L. Trigeorgis (ed.), Real Options in Capital Investment: NewContributions, New York, Praeger, 1994.

[4] Berger, P.G., E. Ofek, and I. Swary, Investor valuation of the abandonmentoption, Journal of Financial Economics, Vol. 42, 1996, pp. 257287.

[5] Bjerksund, P. and S. Ekern, Managing investment opportunities under priceuncertainty: From last chance to wait and see strategies, Financial Man-agement, Vol. 19, 1990, pp. 6583.

[6] Bjerksund, P. and S. Ekern, Contingent claims evaluation of mean-revertingcash flows in shipping, in L. Trigeorgis (ed.), Real Options in Capital Investment:New contributions (NY: Praeger, New York,). 1994.

[7] Black, F. and M. Scholes, The pricing of options and corporate liabilities,Journal of Political Economy, Vol. 81, 1973, pp. 637659.

[8] Brennan, M. and E. Schwartz, A new approach to evaluating natural resourceinvestments, Midland Corporate Finance Journal , 1985, pp. 3747.

[9] Brennan, M. and E. Schwartz, Evaluating natural resource investments, Jour-nal of Business, Vol. 58, 1985, pp. 135157.

[10] Copeland T. and J. F. Weston, A note on the evaluation of cancellable operatingleases, Financial Management, Vol. 11, 1982, pp. 6067.

[11] Dixit, A., Investment and hysteresis, Journal of Economic Perspectives, Vol. 6,1992, pp. 6787.


[12] Geske, R., The valuation of compound options, Journal of Financial Economics,Vol. 7, 1979, pp. 6381.

[13] Grenadier, S.R., Valuing lease contracts: A real-options approach, Journal ofFinancial Economics, Vol. 38, 1995, pp. 297332.

[14] Grenadier, S.R. The strategic exercise of options: Development cascades andoverbuilding in real estate markets, Journal of Finance, Vol. 51, 1996, pp. 16531679.

[15] Grenadier, S.R. and A. M. Weiss, Investment in technological innovations: Anoption pricing approach, Journal of Financial Economics, Vol. 44 No. 3 1997,pp. 397416.

[16] Hendricks, D., Optimal policy responses to an uncertain threat: The case ofglobal warming, Working Paper, Harvard University Kennedy School of Gov-ernment, Boston, MA, 1991.

[17] Hiraki, T., Corporate governance, long-term investment orientation, and realoptions in Japan, in L. Trigeorgis (ed.), Real Options in Capital Investment: NewContributions (Praeger, New York), 1994.

[18] Johnson, H., Options on the maximum or the minimum of several assets,Journal of Financial and Quantitative Analysis, Vol. 22, 1987, pp. 277284.

[19] Kamrad, B. and R. Ernst, Multiproduct manufacturing with stochastic inputprices and output yield uncertainty, In L. Trigeorgis (ed.), Real Options in CapitalInvestment: New Contributions (Praeger, New York), 1994.

[20] Kemna, A., Case studies on real options, Financial Management, Vol. 22, 1993,pp. 259270.

[21] Kester, W. C., Todays options for tomorrows growth, Harvard Business Review,Vol. 62, 1984, pp. 153160.

[22] Kogut, B. and N. Kulatilaka, Operating flexibility, global manufacturing, andthe option value of a multinational network, Management Science, Vol. 40, 1993,pp. 123139.

[23] Kolbe, A. L., P. A. Morris, and E. O. Teisberg, When choosing R&D projects,go with long shots, Research-Technology Management, 1991, pp. 3540.

[24] Kulatilaka, N., Valuing the flexibility of flexible manufacturing systems, IEEETransactions in Engineering Management, Vol. 35, 1988, pp. 250257.

[25] Kulatilaka, N., The value of flexibility: The case of a dual-fuel industrial steamboiler, Financial Management, Vol. 22, 1993, pp. 271279.

[26] Kulatilaka, N. and L. Trigeorgis, The general flexibility to switch: Realoptions revisited, International Journal of Finance, Vol. 6, 1994, pp. 778798.

[27] Laughton, D. G. and H. D. Jacoby, Reversion, timing options, and long-termdecision-making, Financial Management, Vol. 22, 1993, pp. 225240.

[28] Lee, W., J. Martin, and A. Senchack, The case for using options to evaluatesalvage values in financial leases, Financial Management, Vol. 11, 1982, pp. 3341.

[29] Luehrman, T., Strategy as a portfolio of real options, Harvard Business Review,Vol. 76, 1998, pp. 8999.

[30] Margrabe, W., The value of an option to exchange one asset for another, Journalof Finance, Vol. 33, 1978, pp. 177186.

52 L. Trigeorgis

[31] Mason, S. P. and C. Baldwin, Evaluation of government subsidies to large-scaleenergy projects: A contingent claims approach, Advances in Futures and OptionsResearch, Vol. 3, 1988, pp. 169181.

[32] Mauboussin, M. J., Get real: Using options in security analysis, Frontiers ofFinance, Vol. 10, 1999, pp. 230.

[33] McConnell, J. and J. Schallheim, Valuation of asset leasing contracts, Journalof Financial Economics, 1983, pp. 237261.

[34] McDonald, R. and D. Siegel, The value of waiting to invest, Quarterly Journalof Economics, Vol. 101, 1986, pp. 707727.

[35] McLaughlin, R. and R. Taggart, The opportunity cost of using excess capacity,Financial Management, Vol. 21, 1992, pp. 1223.

[36] Morck, R., E. Schwartz, and D. Stangeland, The valuation of forestry resourcesunder stochastic prices and inventories, Journal of Financial and QuantitativeAnalysis, Vol. 24, 1989, pp. 473487.

[37] Paddock, J., D. Siegel, and J. Smith, Option valuation of claims on physicalassets: The case of offshore petroleum leases, Quarterly Journal of Economics,Vol. 103, 1988, pp. 479508.

[38] Pindyck, R., Irreversible investment, capacity choice, and the value of the firm,American Economic Review, Vol. 78, 1988, pp. 969985.

[39] Quigg, L., Empirical testing of real option-pricing models, Journal of Finance,Vol. 48, 1993, pp. 621640.

[40] Quigg, L., Optimal land development, In L. Trigeorgis (ed.), Real Options inCapital Investment: New Contributions (Praeger, New York), 1994.

[41] Sahlman, W., Aspects of financial contracting in venture capital, Journal ofApplied Corporate Finance, Vol. 1, 1988, pp. 2336.

[42] Smit, H.T.J. and L.A. Ankum, A real options and game-theoretic approachto corporate investment strategy under competition, Financial Management,Vol. 22, 1993, pp. 241250.

[43] Smit, H.T.J. and L. Trigeorgis, Strategic Investment: Real Options and Games,Princeton University Press, Princeton, NJ, 2004.

[44] Smith, K.W. and A. Triantis, The value of options in strategic acquisitions,In L. Trigeorgis (ed.), Real Options in Capital Investment: New Contributions(Praeger: New York), 1994.

[45] Stulz, R., Options on the minimum or the maximum of two risky assets: Anal-ysis and applications, Journal of Financial Economics, Vol. 10, 1982, pp. 161185.

[46] Teisberg, E., An option valuation analysis of investment choices by a regulatedfirm, Management Science, Vol. 40, 1994, pp. 535548.

[47] Titman, S., Urban land prices under uncertainty, American Economic Review,Vol. 75, 1985, pp. 505514.

[48] Triantis A. and J. Hodder, Valuing flexibility as a complex option, Journal ofFinance, Vol. 45, 1990, pp. 549565.

[49] Trigeorgis, L., A conceptual options framework for capital budgeting, Advancesin Futures and Options Research, Vol. 3, 1988, pp. 145167.

[50] Trigeorgis, L., A real options application in natural resource investments, Ad-vances in Futures and Options Research, Vol. 4, 1990, pp. 153164.


[51] Trigeorgis, L., A log-transformed binomial numerical analysis method for valu-ing complex multi-option investments, Journal of Financial and QuantitativeAnalysis, Vol. 26, 1991, pp. 309326.

[52] Trigeorgis, L., Real options and interactions with financial flexibility FinancialManagement, Vol. 22, 1993, pp. 202224.

[53] Trigeorgis, L., The nature of option interactions and the valuation of invest-ments with multiple real options, Journal of Financial and Quantitative Analysis,Vol. 28, 1993, pp. 120.

[54] Trigeorgis, L. Evaluating leases with complex operating options, EuropeanJournal of Operational Research, Vol. 91, 1996b, pp. 315329.

[55] Trigeorgis, L., Real Options: Managerial Flexibility and Strategy in Resource Allo-cation, The MIT Press, Cambridge, MA, 1996.

[56] Trigeorgis, L. and S. P. Mason, Valuing managerial flexibility, Midland Corpo-rate Finance Journal, Vol. 5, 1987, pp. 1421.

[57] Williams, J., Real estate development as an option, Journal of Real EstateFinance and Economics, Vol. 4, 1991, pp. 191208.

[58] Willner, R., Valuing start-up venture growth options, In L. Trigeorgis (ed.),Real Options in Capital Investment: New Contributions. Praeger, New York,1994.

BIOGRAPHICAL SKETCH

LENOS TRIGEORGIS is the Bank of Cyprus Chair Professor of Finance at the Universityof Cyprus ([email protected]). He is also President of the Real Options Group (www.rogroup.com). He previously taught at Boston University, Columbia University, and theUniversity of Chicago. He holds a Ph.D. (DBA) from Harvard University. He publishedwidely in numerous journals on corporate finance, competition and strategy, and has writ-ten a number of books on real options with MIT Press, Oxford University Press, PrincetonU. Press, and others. He is internationally known as the author of Real Options (recentlytranslated in Japanese), which is considered path-breaking for the field. He recently also pub-lished a co-authored book, Strategic Investment. His consulting experiences include BritishPetroleum, the Fiat Group, Cable & Wireless, Swisscom, Andersen Consulting/Accenture,Ernst & Young, Morgan Stanley, and the U.S. government.

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