Real Options Analysis in Strategic Decision Making: an applied approach in a dual options framework. TORBEN JUUL ANDERSON.

Full Text: COPYRIGHT 2000 Carfax Publishing Company

ABSTRACT There is growing interest in real options theoretical perspectives to guide both capital budgeting and strategic decisions in dynamic environments. In contrast to the conventional use of discounted cash flows in capital budgeting and competitive analysis in strategy, a strategic options perspective provides a more proactive assessment of future business opportunities under uncertainty. Real options theory has shown potential for analytical applications in strategic management, particularly to evaluate flexibility and timing issues. Yet the options approach has not been widely incorporated to analyse business opportunities and adaptability in strategic investment decisions. There is a discrepancy between the mathematical sophistication of option pricing models developed in financial economics and the theoretical applications in strategic management. The paper aims to bridge this conceptual gap and promote wider use of an options analytical approach. A basic dual options framework that distinguishes be tween abandonment and deferral option scenarios is presented to analyse different strategic investment situations. The framework explicates how firms invest in business development and explains the frequent deferral of strategic investments. Parameter sensitivities in the option evaluation models allow appraisal of value effects from environmental uncertainties, but also point to limits of excessive model refinements. Both advantages and limitations of the options analytical framework in strategy are discussed, and unresolved issues are outlined for future research efforts.

Introduction

Strategy is formed by important resource-committing actions that influence the business development of the firm (Mintzberg, 1978). In financial economics these commitment processes are embodied in corporate capital allocation decisions. However, conventional cash flow analysis has failed to capture the essence of strategic decision making, which invites the application of option theoretical perspectives in investment analyses (Myers, 1984). Decision makers routinely ignore recommendations derived from capital budgeting exercises and instead base their decisions on intuitive judgement, because traditional planning approaches fail to capture the full value of opportunities and adaptability under uncertainty. Real options analysis can fill this gap. Options theory has typically dealt with single investment situations, but recent contributions introduce integrative frameworks that are reconcilable with the prevailing strategy paradigm (Dixit & Pindyck, 1994; Trigeorgis, 1996). This research stream, without except ion, applies a high level of mathematical sophistication and makes a stark contrast to the largely conceptual applications of the options perspective in strategic management (Kogut, 1991; Bowman & Hurry, 1993; Sanchez, 1993; Hurry, 1994; McGrath, 1997). There is a need for more direct applications of the options theoretical perspectives in strategy analysis. It is noted that 'although the concept of strategic options seems pregnant with potential applications, it has largely remained an academic ex-post potential explanation of investment behavior rather than a framework for making investment decisions ex ante' (Bettis, 1994). Hence, a move towards actual measures is considered a natural next step in the application of the strategic options perspective (McGrath, 1997). But can the mathematical sophistication of option pricing theory be better applied to support strategic decision analysis? This is a fundamental issue addressed by this paper.

First, the paper presents prevailing thinking in financial economics and strategic management and discusses more recent developments in real options analysis. Then the importance of options analytical approaches are presented through a few examples, and the options analyses are related to conceptual developments in strategy. The paper identifies two fundamental options perspectives in strategic decision making, and presents decision situations where these perspectives can readily be applied as useful options analytical approaches. However, it is argued that there are diminishing returns to excessive model refinements, and that insightful discussions about model assumptions are more productive in the analysis of strategic opportunities. The paper promotes a basic dual options approach based on abandonment and deferral options perspectives to analyse the dynamics of strategic investment decisions.

Capital Budgeting and Strategic Management

In financial economics, capital budgeting decisions are seen to embody the essence of strategic management (Brealey & Myers, 1996). Capital budgeting typically uses cash flow analysis to evaluate individual projects, although investment decisions ideally should be considered from a corporate perspective. Shortcomings of conventional capital budgeting have been recognised, as cash flow analysis fails to express important organisational effects, e.g. organisational knowledge enhancement from particular resource-committing activities (Baldwin & Clark, 1992). Therefore, capital budgeting should also consider important intangible spillover effects that affect the whole corporation. That is, capital budgeting should support investment initiatives emerging in different parts of the firm, while resource commitments with overall corporate effects should be considered at the executive level. Ideally, capital budgeting integrates strategic planning, individual incentives, and corporate control (Trigeorgis, 1996). Strate gic management makes a similar distinction between resource-committing actions arising out of initiatives in different parts of the organisation and centrally planned actions.

A prevailing view on strategic management incorporates dual effects of intended top-down and emergent bottom-up processes. Strategic direction arises from pre-planned executive decisions as well as from resource-committing initiatives taken among the organisation's 'grass roots' (Hill & Jones, 1995). Conventional strategic analysis determines an optimal strategic fit between external business opportunities and internal organisational capabilities from an overall corporate perspective (Christensen et al., 1982). Some strategic planning models even incorporate capital budgeting to evaluate strategic alternatives (Ansoff, 1988). The predominant strategy paradigm adheres to a comprehensive process that entails environmental analysis, strategy formulation, implementation, evaluation, and control (Schendel & Hofer, 1979). However, the strategy-making process is not all deliberate and intended, but also arises from dispersed actions initiated within the organisation (Mintzberg, 1978). These strategic decisions infl uenced by diverse preferences among organisational decision makers have been depicted as 'garbage-can' and political processes (Cyert & March, 1992; Narayanan & Fahey, 1982). Important elements of strategy emerge from incremental organisational decisions as well as pre-planned implementation, and both aspects have been captured in the conceptualisation of strategy (Glueck & Jauch, 1984; Mintzberg & Waters, 1985). Indeed, some empirical evidence suggests that effective strategic decision making incorporates both comprehensive analytical considerations and responses to emerging opportunities (Bourgeois & Eisenhardt, 1988).

This brief overview draws contours of capital budgeting and strategic management approaches that are quite comparable in the way they incorporate the roles of central planning and new business projects arising from different parts of the firm. However, conventional strategy analysis has an emphasis on centralised planning activities, whereas capital budgeting approaches typically support single investment situations. Therefore, applying an options theoretical perspective to the firm's important strategic investment decisions complements and extends conventional analysis of strategic decision making.

In capital budgeting and strategic management alike, risk is traditionally perceived as a negative factor. High risk is reflected in high discount rates, which reduce the net present value of expected future cash flows from new business projects (Fisher, 1912; Brealey & Myers, 1996). Within the industrial economics tradition that has inspired the predominant strategy paradigm, risk is mirrored in the intensity of the industry's competitive forces. Return is determined by competitive forces arising from industry structure, entry barriers, power of suppliers and buyers, product substitutability, and adherence to generic strategies of cost leadership or differentiation (Porter, 1980). In this analysis, risk is associated with the level of competitive rivalry among firms in the industry that influences the level of economic returns and profit variability over time. The strategy prescription from this perspective is that firms should seek to reduce risk by neutralising the competitive forces in the industry. Howe ver, risk-induced procedures might play a much more proactive and dynamic role in the firm's strategy process than is generally recognised. This is accentuated by evidence that competition is becoming increasingly dynamic across industries (D'Aveni, 1994; Thomas, 1996).

It is commonly acknowledged that organisations must assume risk to create new business opportunities while risk is perceived manageable (Shapira, 1995). On the other hand, assuming excessive risk can jeopardise the future viability of the firm. The assessment of risk is critical in strategic analysis (Baird & Thomas, 1985). Hence, there is a need to develop approaches that better relate the dynamics of business risk to strategic decision making. We know that effective managerial responses to environmental change can lead to higher profitability. Contrary to the eventual elimination of endowment differences in perfectly competitive equilibrium models, the existence of 'uncertain imitability' among firms, e.g. where there are essential organisational processes that are difficult to replicate, can lead to excess returns (Lippman & Rumelt, 1982). Similarly, causal ambiguity arising from tacitness, complexity, and specificity of core skills applied by organisations can create sustainable competitive advantage (Reed & DeFilippi, 1990). In other words, uncertainty and environmental change, or risk, are fundamental prerequisites for the emergence of new competitive strategic responses. We need better analytical techniques to guide firms' strategic decisions under circumstances of increasingly dynamic competition. The application of option pricing theory provides an opportunity to make strategic decision analyses more effective. The following section describe s how this can be approached.

Real Option Structures

Recent work on real options analysis challenges the traditional premises of capital budgeting, and suggests that evaluation of option structures should be incorporated in the analysis of investment decisions (Dixit & Pindyck, 1995). An option structure constitutes a right, but not an obligation, to carry out particular actions some time in the future. All resource-committing actions in an organisation can be considered within such an option structure. When the resource commitments exert significant influence on the firm's business activities they are considered strategic option structures. Strategic options typically reflect new important business opportunities that influence the firm's development path. Option structures represent additional value, because they can be exercised under favourable conditions and lapsed under unfavourable conditions. The more environmental change that is envisaged during the life of the option structure the higher the additional value, because the firm has an opportunity to exer cise the option sometime at an extraordinary profit. Therefore, in an options perspective, expected variability and uncertainty represent potential future profit rather than a threat to current profitability. Evaluating an option structure entails an assessment of the value potential of the environmental dynamics that surround a new business opportunity, i.e. if the firm is sufficiently alert and responsive future uncertainty can be exploited. This perspective is in striking contrast to the conventional argumentation embedded in capital budgeting, where risk is exogenously imposed on the firm and is negatively related to business potential. As will become clear, the two opposing risk perspectives lead to different strategic investment decisions.

Real options relate to the firm's opportunity to use tangible and intangible assets in completely new or alternative ways in the future without having the obligation to do so. When making resource-committing decisions, assets can be arranged to enhance alternative uses. In this sense, real options provide flexibility to managerial decisions (Copeland et al., 1994). Options analysis can be applied to various types of asset flexibilities. It could comprise deferral of new activities, expansion of existing activities, abandonment of activities, contracting activities, switching use of assets, and various combinations of these options.

The value of the simple option structures can be estimate analytically based on Black and Scholes's equations (Black & Scholes, 1973; Hull, 1993; Trigeorgis, 1996). The value of continuous switching options can be derived as the sum of consecutive option structures (McDonald & Siegel, 1985). However, completely flexible switching options are rare in practice. When they exist, their values are influenced by alternative costs associated with deployments of core competencies that often are ignored (Bettis et al., 1992). Furthermore, options attached to the same underlying assets might interact in ways that reduce their aggregate value (Trigeorgis, 1996). These issues are important to keep in mind when construing real option structures around major resource commitments. This is particularly true if flexibility options are acquired at anything resembling their theoretical price, in which case excessive flexibility arrangements can actually deteriorate firm value.

The option to expand corresponds to a deferral option, because the decision not to defer is an expansion. Both the deferral and expansion options constitute call options providing opportunities to commence or extend business activity. Abandonment and contracting options are put options that provide opportunities to withdraw from or scale down business activity. Abandonment options can also be construed as options on options to expand future activity levels, where abandonment corresponds to lapsing the option to expand. When applying these options to practice, the realism of the underlying flexibilities should be carefully evaluated. Realised salvage values rarely match up to the expected values, and subcontractors are usually less than willing to live up to prior indications when environmental conditions are in their disfavour. Similarly, exploiting expansion options can easily lead to cost overruns, because they are typically exercised under circumstances of excess demand. Therefore, using option models to evaluate this type of capacity adjustment should be treated with caution, because theoretically derived option values might not reflect their true worth at the time of exercise.

Despite potential shortcomings associated with valuation of unrealistic real options arrangements, options theoretical perspectives can be very useful in decision analyses. In this regard, options to abandon and defer activities represent two very fundamental aspects of strategic decision making, namely the initial development of strategic options, and subsequent exercise of existing strategic options. This is discussed further in the following section.

Abandonment and Deferral Options

The conventional capital budgeting approach considers two alternatives: invest now or decline investment. Usually this approach does not consider possibilities of abandoning a project before completion nor opportunities to defer or postpone an investment. The possibility to abandon a project, if it later turns out to be less attractive, constitutes a valuable option. Similarly, the opportunity to defer an investment decision to times when some of the uncertainties might be eliminated creates a valuable option (Brealey & Myers, 1996).

The investment abandonment and deferral perspectives arguably have two major applications in strategic decision analyses. The abandonment option perspective applies particularly well to retractable investments. The deferral option perspective is particularly suited to the analysis of irreversible investment commitments. Research and development investments can usually be abandoned. The investments constitute sequential premiums paid to establish strategic options that eventually can establish alternative routes to future business expansion. Irreversible investment decisions refer to the subsequent resource commitments on real and intangible assets, e.g. production plants, sales outlets, training, market promotion, etc., associated with exercise of existing strategic options.

The option to abandon investments during an initial development period is discussed by means of a simple example (Example 1). The example considers a two-period scenario (t = 0 and 1). A firm makes investment commitments during an initial development period (t = 0), but can abandon the project simply by skipping subsequent investment outlays (t = 1).

Example 1: a firm can invest US$2 million now and another US$6 million the following year to complete the development of a new project. The project is expected to have a 50% chance of reaching a US$12 million value (good scenario, [V.sup.+]), and a 50% chance of a US$2 million value (bad scenario, [V.sup.-]) (see Figure 1).

Conventional capital budgeting calculates the present or future value of the projected cash flows to determine the project's value, but does so without considering the option to abandon the project. In this example the net value (NV) of the project at time 1 is US$--1.2 million, and would lead to a rejection of the project. If the option to abandon the project a year after commencement (t = 1) is taken into account the net value of the project is US$8 million, which would result in the pursuit of the project. Hence, the consideration of an abandonment option arrangement makes the firm engage in an opportunistic project that otherwise would be rejected. The option to abandon the investment has value, because it provides an opportunity for future gains while limiting the investment commitment if the project develops unfavourably. [1]

The option to postpone or defer investment decisions when the investment expenditures are irreversible creates an opportunity cost to investing under uncertain conditions (Dixit & Pindyck, 1995). As most investments in specific business activities represent non-recoverable costs, the opportunity cost consideration applies to investments associated with the exercise of strategic options. The effect of a deferral option on an irreversible investment decision is illustrated by another example (Example 2). The example refers to a two-period scenario (t = 0 and 1), considering three alternatives: invest now (t = 0), defer investment one period (t = 1), or decline the investment.

Example 2: a firm can invest US$10 million in a project now. The project is assumed to have a 50% chance of reaching a US$18 million value (good scenario, Va), and a 50% chance of a US$6 million value (bad scenario, V) (see Figure 2).

A conventional capital budgeting approach calculates a value of the proposed investment based on only two alternatives: invest or decline. The net present value of the investment at t = 1 is positive by US$2.2 million, i.e. a conventional cash flow analysis supports pursuit of the investment. However, the proposal is risky, because the investment has a 50% chance of gaining US$8 million, and a 50% chance of losing US$4 million. It is not obvious that this is an acceptable proposition.

When the conventional approach is extended to include the third alternative of deferring the investment, the investment has a positive net value at time t = 1 of US$4 million. Therefore, it is advantageous to postpone the investment until more is known about the future payoffs from the investment. The option to defer the investment has value, because it provides the potential for a higher return, while limiting the downside risk of the investment proposition. [2]

As shown by the examples, the consideration of abandonment opportunities adds flexibility to the firm's initial development of strategic options. It allows the firm to opt out of the project if circumstances develop unfavourably. By making relatively small resource commitments at the initial stages of strategic option developments, the firm reduces the sunk cost incurred in case of project abandonment. Similarly, the inclusion of deferral opportunities when arranging irreversible investments in a strategic options exercise adds flexibility to the firm's resource commitments. It allows postponement of commitments until times when circumstances are considered most opportune.

The abandonment and deferral option values can also be determined by applying option pricing theory. This normally requires a complete capital market so a portfolio of market securities can replicate the expected cash flows of the investment alternative (Hull, 1993; Dixit & Pindyck, 1994). The abandonment and deferral option values are found as the difference between the net present values of the option and invest now alternatives, and reach results similar to those of the examples (Smith & Nau, 1995). Applications of option pricing theory are discussed further in the following section.

A Dual Options Framework

Application of abandonment options during strategic option development, and deferral options during final investments in strategic options exercise, provides a systematic approach to analyse the dynamic evolution of strategic options (see Figure 3).

Abandonment options are typically construed as sequential or staged investment paths, so the firm has the opportunity to abandon the project at different points in time during the development period. Initial strategic option development investments cannot be considered perpetual, because they are supposed to lead to investment projects within foreseeable time. An initial development investment might lead to several business opportunities, each representing different potential irreversible resource commitments. Owing to the finite nature of initial staged abandonment options, the option value can be estimated on the basis of single option or simple compound option analysis. A simple compound option provides the opportunity to acquire another option at a later time (see Appendix, 'Continuous deferral option on irreversible investment'). The compound option can be seen, for example, as an initial research and development investment which, if it turns out to be successful, provides the opportunity to subsequentl y test the research results. If the test option has a positive outcome it in turn can lead to one or more irreversible investment commitments as the option to introduce new products or services is being exercised (Copeland et al., 1994).

The cash outlays in the initial research and development period are often relatively small compared with resource commitments at later development stages. In the subsequent testing period resource commitments increase progressively while the chance of success increases. The value effect of the abandonment option on smaller initial development investments is significant, so in most instances the consideration of one or two initial investment periods is sufficient to provide a qualitative assessment of the project potential. The imposition of such a relatively simple situation lends itself to computational methods based on analytical solutions. Alternatively, the inclusion of multiple investment stages requires the application of more complex numerical methods that are difficult to interpret for decision makers. The usefulness of a staged abandonment options approach is illustrated in an example (Example 3).

Example 3: a pharmaceutical company intends to spend US$10 million on a three year development programme with the purpose of devising a new drug. They think there is a 50% chance of success. If the project is successful, it will be followed by a three year testing programme at an estimated cost of US$100 million with an expected success rate of 90%. It is believed that the production and sale of the new drug will have a future value of US$250 million. Should the firm invest or not?

A conventional capital budgeting approach determines a net present value of the project of US$--0.5 million, which would lead to a rejection of the project (see Figure 4). Things change if the analysis considers the variability and uncertainty of the future cash flows rather than analysing a set cash flow stream. Assuming that the uncertainty of the projected cash flows is reflected in the expected variance in the investment value, then the value of the abandonment option can be estimated as a simple compound option (see Appendix, 'Compound call option using Black and Scholes's' solution). Under the given assumptions the value of the abandonment option is calculated as US$167.2 million, well above the capital budgeting valuation. These differences in project valuation illustrate the effects of the options theoretical approach, as the flexibility of the abandonment option adds considerable value to the initial development investment.

In contrast to the abandonment option, the deferral option in principle can be pursued indefinitely. Innovations are often introduced long after they have been developed (Rogers, 1995). In the continuous investment deferral option situation the analysis determines the time at which it is optimal to make the irreversible investment commitment, i.e. when investment deferral should be stopped. Hence, a continuous deferral option can be applied to determine an appropriate option value.

Option pricing theory is based on an assessment of the development of a central parameter (state variable) that influences the value of the investment. If more than one state variable is considered, the analysis is more complex, and an analytical solution might not exist. This paper argues that simpler analytical solutions are sufficient to effectively analyse most investment considerations, in which case the value of the investment itself appears the obvious state variable to consider. The investment value in turn depends on a number of economic variables, e.g. prices, demand, competition, etc., that are not explicitly considered in the analysis. Instead, these factors can be assessed indirectly through a priori assumptions about their influence on the investment value. Option pricing theory assumes that the value of the state variable, i.e. the investment value, follows the particular stochastic process described by a geometric Brownian motion with drift3 (Hull, 1993; Dixit & Pindyck, 1994). This simplifyi ng assumption allows derivation of numerical formulae based on replication of the project cash flows by a portfolio of traded securities often referred to as contingent claims analysis (see Appendix).

Therefore, option pricing theory can be applied to determine the value of the perpetual deferral option in a complete capital market, because the development in the investment value can be replicated by a portfolio of securities traded in the market (see Appendix, 'Option pricing approach'). If the capital market is incomplete, the option pricing cannot be based on a replicating securities portfolio. However, under the same assumptions of a stochastic development in the state variable, the value of the investment deferral option can be determined through a dynamic programming approach (Dixit & Pindyck, 1994) (see Appendix, 'Dynamic programming approach'). The dynamic programming approach leads to an analytical option pricing solution equivalent to the solution derived through contingent claims analysis provided that risk neutrality prevails, i.e. the discount rate equals the risk-free rate.

Hence, option theory and dynamic programming approaches yield similar solutions, provided that the stochastic process of the state variable in both instances is described by the same Brownian motion, and the firm is risk-neutral. This provides some freedom to choose the analytical approach. If the capital market is perfect, one can use contingent claims analysis, but if the capital market is imperfect a dynamic programming approach will reach comparable solutions. However, despite the appeal of the derived numerical solutions, their outcomes depend on assumptions made about essential parameters. The following discusses how assumptions about model parameters influence the valuation of staged abandonment and continuous deferral options.

Sensitivity of Option Values

The option pricing models devise reasonable descriptions of the stochastic nature of future value-creating opportunities. The basic assumption is that a central state variable influencing the investment value of a new activity follows a stochastic process of some type of Brownian motion. Under this simplifying assumption analytical solutions can be derived to determine the value of simple compound options and continuous deferral options. However, in devising these solutions the analyst makes fundamental assumptions about a number of central parameters in the derived formulas. These parameters include the risk-free rate (r), the future variance of the investment value ([[sigma].sup.2]), and the length of the initial investment period ([t.sub.1]) in staged abandonment options. In the case of continuous deferral options, other parameters are the investment value appreciation ([alpha]), the discount rate ([rho]), and the implied dividend pay-out rate ([delta] = [rho] - [alpha]). It is not possible to provide gene ral guidelines on how to determine the parameters correctly. Such analysis can appropriately involve people engaged in the specific business environment.

The model parameters reflect the characteristics of the environmental uncertainty surrounding the projected investment commitments. For example, the variance of the stochastic development in the investment value reflects the uncertainties associated with future demand, input prices, technological capabilities, etc. In continuous deferral options, assumptions about the investment value appreciation and the inversely related dividend pay-out rate reflect the intensity of competition and technological imitation in the industry. Therefore, sensitivity analysis based on different parameter assumptions can enhance the understanding of environmental effects on strategic decisions. In the following a number of examples illustrate how sensitivity analysis provides added insight to the dynamic circumstances of strategic investment decisions.

Even though model parameters influence the value of options, fairly large changes in these parameters rarely change the fundamental effects of abandonment options on initial development investment decisions. In the staged abandonment option example (Example 3) the option value continues to exceed the net present value of the investment under vastly different assumptions about variance, time, and interest rate levels. This type of value assessment within an abandonment options approach provides a useful analysis to judge and compare the firm's initial strategic investment decisions. In the analysis of irreversible investments associated with the exercise of strategic options, parameter sensitivities play a similarly important role. An example shows how sensitivity analysis can add insight to the dynamic circumstances of irreversible strategic investment decisions (Example 4).

Example 4: a telecommunication company has a 25% share of a smaller electronics firm. It has an opportunity to acquire the remaining 75% of the firm's equity in one year's time. The venture is expected to develop a new communication technology. After acquiring full ownership the telecommunication company is free to decide when to use the new technology. To introduce the new technology it is necessary to invest US$10 million in new manufacturing facilities. Use of the new communication technology is expected to lead to annual incremental net revenues of US$1.5 million for a very long time. Hence, the gross value of the investment (V), for practical purposes considered a perpetuity, is expected to be around US$15 million at an annual discount rate of 10%. How much should the firm he willing to pay for the remaining 75% share?

The conventional net present value of the investment opportunity amounts to US$4.5 million (= (15 - 10)/1.1). Hence, the investment is expected to be profitable, but the actual outcome varies with environmental conditions over time. To assess the effect of variance in the investment value, it is assumed to follow a stochastic process described by a Brownian motion with drift. The drift factor ([alpha]) is assumed to be 7%, reflecting the expected increase in the value of the investment, because it is believed that the technology can be further refined over time. It is hard to find a market portfolio that reflects the expected returns of the investment, but a discount rate (p) is settled at the level of 'best guesses' used in similar analyses, i.e. 10%. The difference between the discount rate and the drift factor is 3%, and equals an implied dividend pay-out rate ([delta]). The investment opportunity does not pay any dividend, so [delta] is interpreted as the opportunity cost associated with deferring the inv estment ascribed to the risk that competitors develop comparable technologies that would reduce the value of the investment. Finally, the variance of the future investment value ([[delta].sup.2]) is expected to be around 20%, reflecting the average variance of stocks in comparable firms. With these assumptions the value of the investment opportunity can be calculated using the dynamic programming solution (see Appendix, 'Dynamic programming approach').

The value of the investment opportunity consists of the net present value of the investment reflected in the intrinsic value, plus a time value depicted by the horizontal distance between the 'curved' lines and the intrinsic value line (see Figure 5). The option value arises from the flexibility of choosing the time to make the investment, which provides the firm with added gains by initiating the investment at the most opportune moment. The gross value of the investment of US$15 million corresponds to an option value of US$10 million. Therefore, the firm should be willing to pay up to US$7.5 million (=0.75 x 10) for the remaining 75% of the shares.

Making different assumptions allows an analysis of effects of different future environmental conditions. For example, lower uncertainty about future demand conditions can be reflected in lower variance in the expected investment value ([[sigma].sup.2]) from 20% to 5%. Such a reduction in variance decreases the value of the option substantially. In a very competitive situation the imitation of the new technology might be high, e.g. reflected in a doubling of the dividend pay-out rate from 3% to 6%, corresponding to a reduction of the drift rate from 7% to 4%. A lower drift rate reduces the option value substantially.

The example uses the deferral options approach to evaluate the acquisition of a new business opportunity. This analysis corresponds to the deferral option perspective applied to analyse irreversible investments associated with exercise of the firm's strategic options. When the firm commits to pursue a business opportunity, i.e. exercises a strategic option, it forgoes the option to defer the investment further. The appropriate decision rule in this situation is to invest only if the net present value of the project exceeds the value of the deferral option (Dixit & Pindyck, 1995). Under high uncertainty the deferral option has high value, and the net present value of the projected cash flow must be so much higher to trigger the investment. Therefore, under high uncertainty, investment in options exercises is less likely than under low uncertainty.

The options' value sensitivity shows that option pricing models do not provide fixed and ready answers, but establish an analytical framework that allows evaluation of the investment's value in different environmental scenarios. Expecting minute precision from the calculation is missing the point of the analytical mission. Instead, the analysis enables the decision maker to evaluate the stakes and opportunities associated with the investment decision. In this context the dynamic programming and contingent claims analyses are equally pertinent analytical methods. [4] In reality it makes little difference whether one is chosen above the other.

The abandonment option approach encourages investment in opportunistic projects that otherwise would be rejected. New research-and-development-related projects are recommended provided they represent sufficiently high opportunistic profit potentials. Conversely, the deferral option approach ensures that new strategic opportunities only are pursued when the present value of the investment exceeds the value of the deferral option, so the likelihood of premature pursuit of new business ventures is vastly reduced.

The simple compound option model can be made considerably more complex by including more sequential option stages. Similarly, the continuous deferral option model can be extended in various ways, e.g. by including mean-reverting and value jump processes to reflect moves towards assumed equilibrium prices and abrupt changes (Dixit & Pindyck, 1994). However, little is known about 'normal' returns from new strategic initiatives, and parameters in the basic models already incorporate effects of major environmental characteristics. Hence, it is not obvious that these refinements add very much. Extensive model refinements increase the complexity of finding solutions and can easily obscure the clarity of the analysis to an extent where it simply does not pay off to pursue them. [5] Therefore, the models of simple compound options and continuous deferral options appear sufficient for most practical investment considerations.

Options and Strategic Decision Making

Options perspectives in the strategy-related literature have typically focused on initial investments through joint ventures (Kogut, 1991; Hurry et al., 1992), entry through collaborative venturing (Chi & McGuire, 1996), and sequential market entries (Chang, 1995, 1996). The options perspective is deemed particularly helpful to consider investments in research ventures or new markets as ways to obtain cheap options on new business activities. Collaborative joint ventures and incremental market investments represent ways to limit the resource commitments to activities that might develop future business opportunities. Another application has estimated the value of different flexibility options, e.g. international manufacturing flexibilities (Kogut & Kulatilaka, 1994).

A few contributions impose a general option theoretical framework on the strategy formation process. Bowman and Hurry (1993) see options arising from continuous development of a firm's competencies, where new insight leads to the recognition of opportunities. Yet unrecognised opportunities are referred to as 'shadow options'. Strategy is formed by the sequential nature of the options and management's decisions regarding exercise of the strategic options. Bowman and Hurry distinguish between incremental options, denoting simple call and put options, and flexibility options that allow a switch to an alternative use of assets. The flexibility options can lead to strategic shifts in business activities whereas incremental options make the organisation more lenient within its existing business activities. Bowman and Hurry hypothesise that high-performing firms hold their options under uncertainty and exercise their options under certain environmental conditions. This logic is supported by a deferral option approa ch, which suggests that more irreversible investment commitments are made when environmental uncertainty is low.

Sanchez (1993) suggests that strategic flexibility is a useful conceptual framework in strategy. He primarily considers options in the firm's input and output markets. Sanchez distinguishes between different types of flexibility options. Product options give the firm the opportunity to introduce new products. Timing options allow the firm to choose the time to exercise the product options. Implementation options constitute opportunities to choose between alternative input sources when the product value chain is configured. The fundamental job of strategic managers is to ensure the identification, creation, and optimal exercise of the flexibility options. The increased flexibility imposed by the firm's strategic options set is seen to improve adaptability and responsiveness. Optimal strategic flexibility is achieved by value maximising the firm's strategic options set. Hence, the input flexibilities of each product value chain as they relate to product and timing options should be arranged to optimise the agg regate value of all the flexibility options in the firm.

In a recent article, McGrath (1997) develops a real options logic to analyse technology investment decisions. The analysis focuses on the commercialisation of the firm's existing technology options, and provides an interesting discussion of how complementary investments can change the firm's uncertainty profile. For example, investment in 'political lobbying' might reduce some uncertainties of the technology options and hence their theoretical values. This would reduce the opportunity costs associated with the exercise of the options, and thus enhance the pursuit of the technology investments. McGrath provides a thorough discussion of how various sources of uncertainty, e.g. technological risk, input cost variability, and demand conditions, can be influenced by different firm-specific capabilities.

It is a common characteristic of these options approaches that they primarily discuss handling of existing strategic options. Bowman and Hurry (1993) consider options creation as the identification of underlying shadow options rather than conscious resource commitments to develop future flexibility and opportunities. The costs associated with the development of strategic options are not explicitly considered in their conceptual framework. Options evolve over time without drawing on substantial resources. Once the strategic options have been identified, Bowman and Hurry suggest that optimal timing of options exercise is guided by the state of environmental uncertainty. Sanchez (1993) proposes that the establishment of as many flexibility options as possible along the firm's value chain is a strategic advantage. However, Sanchez does not consider options acquisition costs. The ultimate strategic management criterion is to optimise the value of the firm's aggregate options portfolio at any point in time, so the re is no prescription about option exercise. McGrath (1997) analyses the exercise of already developed strategic options. She argues that the firm's ability to influence environmental conditions in favour of their strategic options is the essence of the options perspective in strategic management, and her analysis lists ways in which a firm might pursue such influence.

Both Bowman and Hurry's (1993) and Sanchez's (1993) options perspectives make the implicit assumption that underlying options are established at negligible cost, whereas McGrath (1997) deals primarily with existing strategic options. It is important to identify this assumption up front, because the acquisition of voluminous options portfolios can be very costly and detrimental to firm value. Furthermore, to the extent that options are interacting, the aggregate value of the options portfolio can be considerably lower than is suggested by the theoretical values of the individual options. Establishing extensive options portfolios can lead to value deterioration rather than wealth creation. The consideration of abandonment options represents a way to evaluate more systematically the initial organisational resource commitments to develop new business opportunities. Hence, the abandonment option approach provides guidance to conscious investment decisions in support of strategic options development.

Bowman and Hurry (1993) propose general guidelines for the optimal exercise of a firm's options once they are identified and established. In contrast, Sanchez (1993) emphasises the value optimisation of the options portfolio, and says little about optimal exercise. However, effective options exercise is the ultimate determinant of firm performance within a given set of options. The application of deferral options to evaluate subsequent real asset investments is a useful way to consider whether and when to pursue new irreversible business opportunities. That is, the deferral option perspective can guide investment decisions that relate to the exercise of the firm's existing strategic options. McGrath (1997) implies that option pricing theory is not applicable to evaluating irreversible investment in new business opportunities, because technology assets have no continuous market trading and their prices are largely unknown. However, applying comparable valuation methods, e.g. dynamic programming, circumvents t his problem.

Discussion and Summary

The analysis suggests that two fundamental options perspectives can guide strategic decision making. The abandonment option perspective relates to initial investment in strategic options development, and the deferral option perspective relates to subsequent exercise of already developed strategic options. Existing strategy-related options theoretical frameworks do not distinguish between these two fundamental option perspectives (Bowman & Hurry, 1993; Sanchez, 1993; McGrath, 1997). It is indisputable that the establishment of appropriate real options can exert a positive influence on a firm's business development, competitive adaptability, and organisational performance. However, financial performance is eventually determined by the premiums paid for the firm's strategic options set, and how well the strategic options portfolio is executed. The application of initial abandonment and subsequent deferral option perspectives provides useful analytical frameworks to guide strategic investment decisions on strateg ic options acquisition and exercise. The options theoretical frameworks developed in strategic management offer little advice on investment in strategic options development. Similarly, there is limited advice on optimal options exercise. However, the analytical tools of the abandonment and deferral options approaches provide useful support to evaluate specific strategic option investments.

Applying an abandonment options approach to evaluate strategic options development attaches higher opportunistic value to future uncertainty compared with conventional capital budgeting, which punishes risky projects. The use of a deferral options approach to evaluate strategic options exercise considers additional opportunity costs that must be covered by cash flows from the business project. Hence, the application of option pricing theory in the dual options framework supports assessments of strategic options development and exercise.

Conclusions

Real options relate to the flexibility created around an organisation's use of both tangible and intangible assets. Hence, a portfolio of real options determines the extent to which a firm is 'physically' capable of adapting within reasonable time spans. Use of quantitative evaluation methods does not exclude intangible assets from the analysis, but limits their inclusion to assets that can be explicated. However, a real options approach does not explicitly consider all important tacit aspects of the firm's strategic options development, and therefore does not pretend to be universal. Nonetheless, it can support analysis of real option structures that improve the firm's ability to adapt and respond to changing environmental circumstances.

The real options approach can help assess the opportunistic potential of strategic options development, and the opportunity costs associated with exercise of strategic options. Option pricing theory provides useful analytical techniques that support both quantitative and qualitative strategic analyses based on assessments of the environmental risks associated with future business opportunities. A real options approach supports analysis of initial investments in real option development, and subsequent irreversible investments in real options exercises, which are crucial to the creation of firm value.

Firm value is determined by the premiums the firm pays to acquire its strategic options, and how well management executes its strategic options portfolio. Performance depends on the extent to which the right strategic options are developed at appropriate costs, and those strategic options are exercised in the most opportune business situations. This implies that management must develop relevant strategic options in view of the firm's perceived business potential. There is limited theoretical support to the process of creating strategic options, but the abandonment option approach supports analysis of specific investments in strategic options development. Similarly, no theories ensure that existing strategic options are exercised at the most opportune moments, but the deferral option approach supports analysis of specific investments in strategic options exercise. The implications of the dual options analytical framework based on staged abandonment and continuous deferral option perspectives are twofold: it m akes firms more willing to consider initial development investments in support of new strategic options creation, and it makes premature commitments to strategic ventures less likely.

Perhaps one of the most important aspects of the real options approach is that it can foster fruitful discussions about the strategic consequences of future business opportunities in uncertain environments, where uncertainty itself is opportunistic and not just a negative risk parameter. Real options analysis can provide quantitative evidence of the effects of different environmental conditions. This makes a compelling argument for the use of relatively simple analytical methods as proposed by this paper. It is more important that the strategic decision makers understand the methodological principles and assumptions, than that they get a marginally more 'correct' option valuation from a complex analytical method. With hindsight, no option valuations hold true ex post. It is the underlying ex ante discussions among managers that matter.

Notes

(1.) The option value at time 1 is equal to the value of the abandonment alternative minus the value of the fully committed investment decision, i.e. 2.0 (= 0.8 -(-1.2)). At time 0 the value of the option is 1.9 (= 2.0/1.05), assuming a risk-free rate of 5% p.a.

(2.) The option value at time 1 corresponds to the value of the deferral alternative minus the value of the two-alternative investment, i.e. 1.8 (= 4.0 - 2.2). At time t=0 the value of the option is 1.7 (= 1.8/1.05), assuming a risk-free rate of 5% p.a.

(3.) A stochastic process describes a variable changing over time in an uncertain manner. The process can be described by sequential values measured at regular time intervals, a discrete process, or by values measured in continuous time, a continuous process. A Markov process is a stochastic process where only the present value of the variable is used to predict the future value of the variable. A Brownian motion, or Wiener process, is a particular Markov process, where each incremental change in the value of the variable Vz is represented by a random drawing from a standardised normal distribution ([epsilon]), so that Vz = [epsilon][square root of]VT. Hence, a generalised Wiener process is described by the variable x as: Vx = aVt + b[epsilon][square root of]Vt, where the 'drift rate' is a per unit of time change, and 'noise' is b times a Wiener process. This is referred to as a 'Brownian motion with drift'.

(4.) The dynamic programming solution will usually determine slightly higher option values, because the discount is higher than the risk-free rate, and the option premium is positively related to the interest rate level. However, the differences in value are minimal.

(5.) Trigeorgis (1996) compares the estimated option values arising from different numerical approaches with the 'simple' Black and Scholes European option price formula, and does not find major discrepancies.

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Appendix: calculating option values

Compound Call Option Using Black and Scholes's Solution (Geske, 1979; Trigeorgis, 1996)

A simple compound option is an option providing the right to obtain a subsequent option on the same underlying asset. It assumes that the compound option value (C), the subsequent option value (S), and the underlying project value (V) all follow the same Brownian motion. A riskless portfolio can be created to replicate the value development of the compound option, where the value of the compound option at maturity ([t.sub.1]) equals max(S - E,0) E [equivalent] exercise price. This differential equation is solved using Ito's lemma to reach solutions similar to the Black and Scholes equation, which is a special case of this more extensive solution. The model assumes that the underlying project, or stock, pays no dividend:

C = VB(h + [sigma][square root][t.sub.1],k+[sigma][square root][t.sub.2],[gamma]) - [E.sub.2][e.sup.-rt2]B(h,k,[gamma]) - [E.sub.1][e.sup.-rt1]N(h),

where

h = [ln(V/[V.sup.*]) + (r - 0.5[[sigma].sup.2]) [t.sub.1]] / ([sigma][square root][t.sub.1])

k= [ln(V/[E.sub.2]) + (r - 0.5[[sigma].sup.2])[t.sub.2]]/([sigma][square root] [t.sub.2]),

where C is the compound call option premium; B(a, b, [gamma]) is the bivariate cumulative normal distribution function with upper integral limits a and b and correlation coefficient [gamma]; N() is the univariate cumulative normal distribution function; [[sigma].sup.2] is the variance of V; r is the risk-free rate; [t.sub.1] is the time to the first option's expiration date; [t.sub.2] is the time to the second option's expiration date; [E.sub.1] is the 'exercise price' of the first option; [E.sub.2] is the 'exercise price' of the second option; [V.sup.*] is the value of V above which the compound option should be exercised; and [gamma] = [square root][t.sub.1] / [t.sub.2].

Continuous Deferral Option on Irreversible Investment (Dixit & Pindyck, 1994)

Option pricing approach (contingent claims analysis). The expected future pattern of the investment value (V) is replicated by a securities portfolio (s). Hence, s is perfectly correlated with V, as their future values are assumed to follow the same Brownian motion with drift.

ds = [alpha]sdt + [sigma]sdz, where [alpha] is the drift rate (expected percentage rate of change in V, i.e. appreciation of investment value); and dz is the Brownian motion described as a random drawing from a standardised normal distribution, where each drawing is independent.

In a portfolio consisting of the investment opportunity (F(V)) and a short position of n ( = F'(V)) units of the replicating securities portfolio, the uncertainty elements of the investment opportunity are counterweighted by a perfectly correlated short market position. Hence, the total portfolio is risk-free, and its return equals the risk-free return. This differential equation can be expanded by applying Ito's lemma, and solved analytically:

[beta] = 0.5 - (r - [delta])/[[sigma].sup.2] + [square root][[(r - [delta])/[[sigma].sup.2] - 0.5].sup.2] + 2r / [[sigma].sup.2],

where [delta] = ([rho] - [alpha]), the 'dividend pay-out rate', i.e. the opportunity cost associated with deferral of investment; and [rho] is the discount rate.

Dynamic programming approach. This approach utilises Bellman's principle of optimality based on a time independent recursive decision rule (Bellman equation). The development in the investment value (dV) is described as follows:

dV = [alpha]Vdt + [sigma]Vdz.

The value of the investment opportunity (F(V, t)) is given by:

F(V, t) = [max.sub.u] [[pi](V, u, t) + E{dF}/dt] / [rho]

Throughout the path where the investment is being deferred the profit flow ([pi]) is zero. The expression of dF (the Bellman equation) can be expanded by applying Ito's lemma, and leads to an analytical solution:

F(V) = A[V.sup.[beta]]

A = [([beta] - 1).sup.[beta]-1]/[[([beta]).sup.[beta]][I.sup.[beta]-1]]

[beta] = 0.5 - ([rho] - [delta])/[[sigma].sup.2] + [square root][[([rho] - [delta])/[[sigma].sup.2] - 0.5].sup.2] + 2[rho] / [[sigma].sup.2]

[V.sup.*] = [beta] / ([beta] - 1)I,

where [V.sup.*] is the value of the investment, above which the investment deferral should be stopped and investment take place; and I is the required investment amount.

The solution is similar to the solution derived through contingent claim analysis. The only difference is found in the formula for the root [beta], where the discount rate ([rho]) has replaced the risk-free rate (r).