Decision making under uncertainty–real options to the rescue?

Miller, Luke T

ABSTRACT

Real options analysis (ROA) has been identified in the literature as a quantitative means to evaluate the flexibility inherent in the decision-making process. From an engineering economics perspective, this paper highlights applications, real-world users, modeling approaches, ROA assumptions, and future research directions. Through identifying and systematizing the current literature, a concise summary of modeling concerns and a road map for future modeling efforts and applications is discussed. More specifically, this paper supports research efforts to combine decision analysis tools with financial option pricing techniques to develop a real option framework that will be accepted in industry to make decisions in today’s fast-paced and highly competitive business environment.

INTRODUCTION

Major corporations annually allocate substantial funds for a variety of investment projects. Most strategic investment projects, such as R&D, investment in information technology, and e-commerce projects, are typically not made on the expectation of immediate payoffs, but rather on the expectation of creating future profitable investment opportunities. The payoff from strategic investments may occur in many forms and at unknown times in the future. The payoff, moreover, can be multi-stage, with one successful project leading to additional successful investments.

To properly evaluate such projects, some corporations are now using an options approach rather than the traditional discounted cash flow (DCF) technique. The options approach, called Real Options Analysis (ROA), considers all future investment opportunities along the value chain, allowing a more flexible assessment of strategic projects. When traditional DCF methods are naively applied to evaluate strategic projects, future opportunities that create value are often ignored in the valuation process. This results in too little strategic investment. In contrast to naive DCF valuations, ROA provides for better corporate strategic investment decisions in terms of value added.

The purpose of this paper is to survey the current real options’ landscape, discuss ROA relevance to engineering economic decisions, indicate modeling limitations, and suggest future research issues. The next section discusses the benefits of a real options approach and its importance to engineering economics decisions. After summarizing applications and real-world users of real options, the paper discusses the common modeling approaches utilized in the literature. Then, assumptions used to alleviate the shortcomings of the current valuation approaches are compared and contrasted. The paper concludes by identifying future research directions for modeling efforts and applications.

WHY REAL OPTIONS?

To compare various capital investment alternatives, corporate planners have long used such methods as the payback method, internal rate of return (IRR), and net present value (NPV). However, it is not widely appreciated that these methods require the assumption of perfect certainty of project cash flows, even though this is rarely the case in real world situations. The popular NPV criterion works best for cost-reduction type problems when future cash flows are relatively certain. But, the DCF techniques fail when used to evaluate strategic investments where the payoff is uncertain. More specifically, there are three main limitations of DCF-based techniques when applied in situations of uncertainty [42].

First, selecting an appropriate discount rate poses problems. Under the DCF methodology an analyst projects all the future cash flows (including investments) associated with an asset, discounts them using an appropriate discount rate reflecting uncertainty, and sums them to compute the NPV. While this approach is intuitively appealing and simple, deciding upon the proper discount rate is difficult. If a project involves high uncertainty, a high discount rate, which reflects a high-risk premium, is used.

Second, DCF techniques ignore the flexibility to modify decisions along the value chain as new information arrives. This multi-stage investment framework is useful for understanding and managing investment risk as well as capturing the flexibility associated with investments through early uncertainty resolution.

Finally, investment decisions are typically viewed as now or never type decisions rather than decisions that may be delayed. The NPV approach, for example, leads to accepting a project immediately if NPV is positive. This is a passive method that works well in deterministic situations, but under conditions of uncertainty has limited applicability.

USING REAL OPTION ANALYSIS TO VALUE RISKY ASSETS

ROA is a promising valuation tool for strategic corporate investment decisions whereby projects are viewed as real options that can be valued using financial option pricing techniques. Technically, ROA enables managers to bundle a number of possible outcomes into a single investment. These outcomes may have separate time periods, uncertainty levels, and may be in the form of subsequent options. They also need not be mutually exclusive. Companies may pursue multiple options simultaneously. To calculate an option value using ROA, managers do have to estimate the cash flows and uncertainties of each possible outcome, which involves some effort. But the estimation of possible outcomes increases managers’ awareness of the full array of benefits generated by strategic investments.

Under ROA, any corporate decision to invest or divest in real assets is simply an option. Option holders have the right but not the obligation to make an investment, similar to a financial call or put option on a common stock. Hence, based on the options framework a decision-maker has greater flexibility and an improved method to value these opportunities [42, 43]. Managerial flexibility is very important from a strategic decision-making perspective in an uncertain economic environment. It allows corporate decision-makers to keep investment options open, which provides a means to profit from uncertain market conditions. Options are unique because they have limited downside loss and represent a natural framework to capture and value flexibility.

RELEVANCE OF REAL OPTIONS ANALYSIS TO ENGINEERING ECONOMIC DECISIONS

ROA enables managers to make discretionary decisions to invest in highly uncertain capital expenditures. Valuation of real options, such as the option to defer, expand, contract, abandon, has helped managers to effectively allocate corporate resources by considering strategic flexibility. The option framework allows managers to regard two factors as advantageous in increasing the value of investment projects. First, greater volatility does not translate into greater losses, because losses are limited to the initial investment. In addition, it produces greater gains because the option enables you to capture upswings. Second, the real options’ value increases with a longer decision horizon. In the case of traditional discounted cash flow (DCF) approaches, a lengthy time horizon just increases the project uncertainty, which lowers the project’s value.

This observation could lead to thinking that some fundamental changes have to be made in the field of engineering economics. In other words, most engineering economic decisions involve real assets, so the concept of ROA would be a natural complement to address uncertainty. First, we will review the typical approaches to handling uncertainty in engineering economic decisions:

* Conduct a sensitivity analysis to determine the greatest source of uncertainty.

* Conduct a scenario analysis by creating the best and worst case scenarios to gauge the level of overall project uncertainty.

* Conduct a probabilistic analysis (normally using Monte Carlo simulation) to assess the likelihood of each potential outcome (or to obtain the probability distribution of the project outcome).

* Conduct a Bayesian analysis to reassess the random variables by obtaining additional information.

* Select the best course of action based on the expected utility maximization principle. (If we solely rely upon the expected monetary value, we are in fact, implicitly assuming a liner utility function.) Instead of computing the expected utility, we may compute the equivalent certainty amount ($) for each periodic probabilistic cash flow and discount them by using a risk-free interest rate. But this approach requires the decision-maker’s utility function. One popular approach commonly suggested for practitioners is to use a higher discount rate (or risk-adjusted discount rate) to account for both the risk and the time value of money. Certainly this risk-adjusted discount rate approach is not a precise technique.

Under a ROA, the decision-maker can hedge the uncertainty by creating a twin security (replicating) portfolio; thus it is not required to obtain the decisionmaker’s utility function in valuing the option strategies. Since the decisionmaker can perfectly hedge the risk, the proper interest rate to use in the valuation is the risk-free interest rate. This is one of the most promising features of the option valuation techniques. Although the creation of a twin security (replicating portfolio) is rather straightforward for most financial options, it is not so for real options as real assets are not traded like financial assets (stocks or bonds). Therefore, many researchers have attempted to bridge the gap between financial option pricing theory and real option valuation. For certain situations, we may directly borrow the pricing concept used for financial options to value real assets. For many other situations, directly applying financial option pricing techniques would be a stretch. Therefore, the purpose of this paper is to survey what types of research issues have been addressed in the literature and what kinds of progress have been made in resolving some of these conceptual issues.

HISTORY OF REAL OPTIONS

First coined by Myers [91] in 1977, the real options framework views decisionmakers with the option to invest, grow, or abandon a project contingent upon the arrival of new information. Benchmarking off of the much researched and practiced financial risk management derivative products, real options attempt to quantify uncertain environments in a world of competition and `real-time’ technology. Scholes [105] defines “any security as a derivative if its price (or value) dynamics depends on the dynamics of some other underlying asset or assets and time.” Using this concept, the value of a project can be viewed as a derivative of input costs, output yield, time, and uncertainty.

The seminal work of Black and Scholes [10] and Merton [85] in 1973 provided a method to properly value options. Their work led to an explosion of research in pricing all derivative products (also known as contingent claims) and to the wide acceptance and use of the Chicago Board Options Exchange (CBOE). Using Black, Scholes, and Merton concepts, companies are able to utilize financial derivative products to hedge risks unique to their business operations. Today, it is estimated that a nominal value of $70 trillion (Merton [86]) in financial derivative products, including futures, forwards, and options, is traded on the marketplace. Due to the apparent success of financial derivatives, it only seemed natural to utilize the contingent claims valuation process to assess project selection at the firm level.

Academia usually identifies evaluation techniques that are in-line with theory, and it takes many years for practitioners to adopt such ideas. Take for example, standard discounted cash flow (DCF) tools. First identified in the 1950s, the use of net present value (NPV) and cost of capital techniques did not replace payback period until the 1980s. In fact, in a survey by Gitman and Vandenberg [39], they compared cost of capital techniques used by major U.S. firms between 1980 versus 1997. After surveying the Fortune 1000 companies, only 35% of firms used cost of capital techniques in 1980. It wasn’t until 1997 that 70% of firms utilized it. Additionally, in 1997 many firms have begun to differentiate between project risks, with 77% adopting some form of varying hurdle rate in their NPV analysis. Slow adoption into practice is not unusual, and real options analysis (ROA) has begun its acceptance in a similar fashion (i.e. first identified more than 20 years ago, but just now entering into the firm’s decision-making process).

However, there is one major difference between ROA vs. DCF and payback period vs. DCF. ROA should not be viewed as an entirely new decision framework that will supplant all existing techniques. Our view is that DCF and ROA should be viewed as complementary decision-making tools. DCF techniques should be used for certain decision environments, whereas, ROA should be utilized for others. DCF tools should be used for decisions involving a moderately straightforward business structure, unsophisticated projects, and a steady environment that allows for dependable forecasts. Whereas, ROA should be utilized for uncertain business decisions that rely on the value of additional information. Therefore, ROA may be more useful for actively managing existing projects by delaying further investment and expanding or abandoning commitments. In order to perform a ROA, standard DCF tools are needed to calculate inputs for the option valuation. Therefore, a DCF approach should be performed first anyhow; only to be followed-up with the more labor intensive ROA, as necessary. FIGURE 1 provides a schematic of the complementary nature of ROA and DCF.

Lint and Pennings [70] agree with this sentiment of ROA complementing DCF analysis. In analyzing a new product development, they recognized that projects fall into one of four quadrants:

Quadrant 1 – Projects with high-expected payoff and low volatility. These projects represent the ideal decision-making environment. Traditional DCF analysis should be performed and projects should be activated as soon as possible.

Quadrant 2 – Projects with low expected payoff and low volatility. Traditional DCF tools should be used and the project should be abandoned as soon as possible.

Quadrant 3 – Projects with high-expected payoff and high volatility. These projects are more representative of today’s investment in technology and highly competitive markets. ROA should be utilized to quantify this risk and decisions should be made with the arrival of new information.

Quadrant 4 – Projects with low expected payoff and high volatility. Similar to Quadrant 3, ROA should be used and these projects should only be activated with the arrival of “good” information.

More specifically to engineering economic decisions, Park and Herath [961 divide the investment categories according to varying levels of uncertainty – the higher the uncertainty; the more a ROA will impact these decisions. Both high/low uncertainty replacement and expansion decisions are discussed in this context, as well as, mergers and acquisitions, research & development, and abandonment options.

Despite the complementary nature of ROA and DCF, ROA does provide additional benefits. As noted in Kogut and Kulatilaka [62], due to the evolution of institutions, methods of organization, and rules developed over the last century, firms have developed evaluation tools that address short-term profitability. If firms start viewing platform investments (i.e. invest a little now and wait for information) as long-term profit opportunities, then ROA can be used to quantify these long-term ventures. Rausser and Small [991 view these platform investments as “information rents” or option premiums. In other words, companies should view the costs of laying the foundation for long-term investments as the price to pay for the option to enter some business segment in the future.

Additionally, the value of an option comes from both the uncertainty of the investment environment and from the decision-maker’s ability to take action to make the most of the opportunities created by that uncertainty. In essence, ROA is a means to quantify risk and uncertainty of individual projects on a risk-return framework similar to financial markets; thus, ROA’s goal is to increase shareholder value. ROA allows some subjectivity to be removed from the decision process by providing a means of applying an objective, market-based measure of value to uncertain situations. From a modeling perspective, ROA minimizes the need to identify the decision-maker’s utility function and the firm’s risk-adjusted discount rate. It also provides a method to evaluate a nonlinear, or asymmetric, payoff function due to kinked economies of scale and production being a function of demand.

HOW WIDELY PRACTICED?

A large portion of real options applications have been published within the last five years, however, ROA applications date back to the mid-1980s. Earlier work focused on natural resource applications because of the existence of a publicly traded futures market to proxy option parameters. For example, Brennan and Schwartz [16] in 1985 utilized ROA to evaluate a natural resource investment using stochastic control theory to determine optimal policies for developing, managing, and abandoning projects. Since then, real options application papers have addressed numerous areas of industry to include biotechnology, manufacturing and inventory, natural resources, research & development, stock valuation, strategy, and technology. TABLE 1 provides a grouping of some of the application papers in the standard areas. Similar tabulations can be found in Trigeorgis [120] and Lander and Pinches [65]. For educational purposes, the papers are listed in each category from more straightforward applications to complex developments. For those new to real options, it is recommended to read the starred “*” applications first.

UNUSUAL APPLICATIONS – REAL OPTIONS EVERYWHERE

In addition to the strategic decision areas, it is also worth noting some “unique” applications of real options to a variety of economic decisions. Mahajan [73] develops a ROA for pricing expropriation risk of a foreign project and points to the fact that many multinational firms maybe acting sub-optimally in handling their foreign exchange risk and country risk. Brown and Davis [ 17] compare two mutually exclusive projects with unequal service lives. In a real option framework, they include the option to switch from one project to another, in addition to the standard annual equivalent analysis. Saphores [ 104] uses ROA to determine the optimal number of times to spray a pest population during a farming season. Viewing the pest density as the uncertainty, a decision framework for a risk-neutral farmer is developed. Cortazar, Schwartz, and Salinas [29] evaluate firms complying with national laws to keep pollutants to certain levels. The option to invest in environmental technologies is analyzed, which leads to some surprising results. Due to the expensive technology, many firms should either cut back production or pay the fines levied for producing too many pollutants instead of investing in environmental technologies. Finally, Panayi and Trigeorgis [97] develop a compound option model to evaluate the international bank expansion of the Bank of Cyprus growing into the U.S.

STRATEGIC ENGINEERING ECONOMIC DECISIONS

The use of ROA for engineering economic decisions is similar and overlaps with some of the applications listed in TABLE 1. Most of the applications listed in the manufacturing and inventory areas apply to decisions within the industrial engineering context. In addition, ROA could be used for uncertainty management in the following sectors: (1) equipment and process selection, (2) replacement decisions, (3) new products and capacity expansion, (4) cost reduction evaluations, and (5) capital budgeting.

Some work has already been done in these well-defined engineering economics decision areas. Using ROA, Mauer and Ott [78] consider the standard replacement decision confronted with uncertainty in operating costs, procurement costs, salvage value, tax credit, tax rate, depreciation rate, and technology. A product’s life cycle is evaluated using ROA by Bollen [12]. McLaughlin and Taggart [83] consider the problem of converting excess capacity from one product to another in a real options framework. They conclude that standard NPV analysis can lead to somewhat distorted conclusions because NPV does not consider both the production and investment options implicit/explicit in the decision. Meier, Christofides, and Salkin [84] incorporate contingent claims and integer programming into a capital budgeting framework to identify an optimal project portfolio.

ROA is a powerful technique to value the flexibility allotted decisionmakers within their business climate. It provides a technique to link market information with strategic engineering economic decisions. Advancing current research in real options will ensure that the engineering economics field keeps pace with today’s complicated business environment by aligning project selection with firm goals.

REAL-WORLD USERS

Not only do the above application papers point to the applicability of ROA in numerous areas, but also many firms and managers have adopted a real options perspective that is now being utilized to remain competitive and strategically poised. According to Lavoie and Sheldon [68], the U.S. invested $7.9 billion in biotechnology R&D and earned $14.6 billion in revenues on that investment, compared with all of Europe investing $1.2 billion in R&D and earning $1.4 billion. They emphasize that U.S. firms understand investing in R&D is an option premium, even though they might not be using actual option valuation procedures. For example, the pharmaceutical giant Merck & Co. has been using ROA for over the last eight years to guide management intuition for R&D expenditures. Also, in 1990, Hoffman-La Roche cut a market-based real options deal with Genentech, a California biotech firm, in which La Roche paid an option premium to buy Genentech publicly traded stock at certain dates in the future for a certain price. Therefore, La Roche was able to mitigate any technical risk it would have assumed by doing the research itself, and turned it into a market-based risk handled with the use of option pricing. As noted in Stuart [115], Amgen Company also used ROA to value and purchase the $100 million cancer drug Abarelix. Amgen utilized ROA in the negotiation phase to set a notto-exceed price that was higher than what the standard mergers & acquisitions analysis provided. Thus, Amgen was quantitatively aware of the value to purchase the drug and used ROA to acquire that knowledge.

ROA has found its way into other key business segments. Texaco and BP Amaco use real options as a gauge to value unexplored oil fields. As noted in Coy [31], Anadarko Petroleum used an option’s framework to outbid competitors for a tract of land in the Gulf of Mexico. Hewlett-Packard used ROA to help match supply with demand for its printers to save costs on over– customizing at its manufacturing facility. The Tennessee Valley Authority used ROA in a 1994 decision to contract out for 2,000 megawatts of power instead of building its own plants. New England Electric used options pricing to defer investing in a $52 million hydropower turbines project for one of its plants in Vermont. Airbus Industry uses options analysis to value contractual options with purchasers of its aircraft; in essence, an airline can pay a premium to lock in a price to pay for an aircraft, versus waiting and then paying the “going” rate for that aircraft. Intel Corp and Toshiba Corp use real options tools to help in the negotiating process of valuing licenses. Cadence Design Systems Inc. used ROA to set a minimum floor for a licensing agreement for its electronic design products. And finally, consulting companies are claiming ROA to be the next big thing to sell to clients.

To date, mostly natural resource, utility, and R&D firms are utilizing ROA due to the accessibility of publicly traded prices to proxy option parameters. However, two empirical studies of large firms indicated that managers already subjectively value options and would like to acquire “accessible” techniques for ROA. In Howell and Jagle [481, 82 mid to upper level managers from 9 major British companies responded to a ROA survey of case studies. Using the BlackScholes (B-S) equation to acquire a theoretical option value benchmark, 85% of the managers surveyed overvalued the growth option (as compared with the calculated B-S value) by 11% using only their ‘expert’ judgment and no formal option valuation tools. This indicates that managers are subjectively valuing growth options over and above standard DCF tools. From the survey it appeared that managers accounted for variations in the present value of the project correctly, but were inconsistent in dealing with varying levels of volatility. In addition, more experienced managers and managers from oil and pharmaceutical industries were more accurate in their subjective option valuations. In Busby and Pitts [18], questionnaires were sent to the Finance Directors of all firms in the FT-SE 100 Index. About 50% of the directors recognized options within their businesses, with most options identified as either growth or abandonment. Thirty-five percent of respondents thought that options were highly or extremely important in influencing investment decisions, however, more than 75% did not have procedures for real option valuation.

These anecdotal results point to a growing acceptance of ROA in today’s business climate. The next section summarizes the current real option modeling approaches utilized in the case studies.

MODELING APPROACHES

Currently, two separate modeling approaches are utilized to value real options: discrete- and continuous-time. Multinomial lattices constitute the discrete-time approach and closed-form equations, stochastic differential equations, and Monte Carlo simulation comprise the continuous-time approaches. Another area involves merging decision analysis techniques and financial option valuation tools and will be discussed later in the paper. All of these approaches benchmark off of financial option valuation procedures and are well documented in the literature. Good textbooks to learn financial option pricing techniques are Hull [49] and Wilmott [123]. Dixit and Pindyck [35] and Copeland and Antikarov [25] demonstrate these financial option-pricing techniques in a real options framework. In addition, a monograph by Sick [107] provides a summary of financial option pricing in the context of real options. FIGURE 2 compares the advantages and disadvantages of each modeling approach. This section will briefly introduce these approaches and point to representative case studies for examples.

LATTICE APPROACH

The lattice approach assumes the underlying asset follows a discrete, multinomial, multiplicative stochastic process throughout time to form some form of ‘tree’. The option value is then solved recursively from the end nodes of the tree. The advantage of using a lattice approach is the intuitive valuation procedure and the flexible valuation process. The decision-maker can observe option values throughout the tree, and the tree structure supports delay, growth, contraction, American-style, exotic, and compound option valuation. A number of useful lattice approaches for ROA can be found in the finance literature. Cox, Ross, and Rubinstein [30] in 1979 developed the standard binomial option approach. Also, in 1979 Rendleman and Banter [101] developed a binomial lattice valuation process. In 1986, Boyle [131 developed a trinomial tree, and in 1988 Boyle [14] developed a five-jump tree. In 1989, Madan, Milne, and Shefrin [72] generalized the binomial model to the multinomial case. A popular multinomial model used for real options valuation is the “He” model developed in 1990 [42]. In 1993, Tian [119] developed an alternative approach for the binomial and trinomial models, which could he useful for real options. In 1999, Detemple and Sundaresan [34] developed a binomial approach for nontraded asset valuation in the context of portfolio constraints. Using the He model, their approach addresses standard option assumptions violations such as no-short-sales and pricing when the nontraded payoff is imperfectly correlated with the price of a traded asset. In 2002, Herath and Park [45] demonstrate a lattice approach to value a compound real option.

Representative examples of these lattice approaches to valuing real options can be found in the following case studies. The binomial approach is used to value petroleum applications in Pickles and Smith [98] and Smit [108], research & development in Herath and Park [43], and excess plant capacity in McLaughlin and Taggart [83]. A trinomial example is shown in Childs and Triantis [20] to value R&D, and the He multinomial model is demonstrated in Imai and Nakajima [51] to value an oil refinery project.

CLOSED-FORM EQUATIONS

Several closed-form option valuation equations are developed in the ROA literature. For a given set of assumptions, all these equations reach an option value in a continuous-time context. The advantage of using the closed-form equations is the ease of which option values can be calculated. However, the limiting assumptions of the models need to be carefully studied, understood, and applied correctly. Therefore, for the ‘right’ applications, these equations can serve as valuable tools. Even for applications that do not exactly fit the assumptions, these equations can be used to reach approximate valuations.

Four closed-form equations are employed for ROA: Black-Scholes, Margrabe, Geske, and Carr. In 1973, Black and Scholes (B-S) [10] developed the first closed-form equation for valuing financial options and warrants. The majority of options pricing techniques used today are subsets of the B-S equation and approach. The B-S equation is used to value delay, abandon, and growth options. The option to exchange one asset for another was developed in 1978 by Margrabe [75]. The only difference between the B-S and Margrabe equations is the treatment of the option’s exercise price. B-S assumes the exercise price is deterministic, whereas, Margrabe treats it as a stochastic variable. The Margrabe equation is used to value delay, abandon, and growth options. (Note that Fischer [37] also developed a closed-form equation for option valuation with an uncertain exercise price.) In 1979, Geske [38] developed an equation to value compound options with deterministic exercise prices. The Geske model is used for sequential investment decisions, which are often found in R&D and technology decisions. Finally, in 1988, Carr [19] developed a compound option equation with stochastic exercise prices. Carr’s equation is used for the same applications as the Geske model.

Representative examples of these approaches to valuing real options can be found in the following case studies. Taudes [117] and Lee and Paxson [69] compare and contrast real option valuations using all four equations: B-S, Margrabe, Geske, and. Carr. Kumar [64] provides a good discussion and an example for the B-S and Margrabe model, and Jensen and Warren [53] demonstrate a straightforward application of the Geske model.

STOCHASTIC DIFFERENTIAL EQUATIONS

In order to derive the closed-form equations discussed above, a series of stochastic differential equations (SDE) with boundary conditions must be solved. However, many times solutions to the SDE do not exist and the partial differential equations must be solved numerically either using finite-difference methods or Monte Carlo simulation. From a ROA perspective, it is still applicable to derive a set of SDE to value the option, and then apply a numerical procedure to reach results. Using the SDE approach is the most complicated approach and requires some background in stochastic calculus. An introduction to SDE, finite-difference methods, and Monte Carlo simulation can be found in Wilmott [123], Hull [49], and Neftci [92].

Many real options applications utilize the SDE approach, and the following papers are a representative sample. Mauer and Ott [78] derive one closed-form solution and another model that must be solved numerically to value the replacement decision involving varying cost volatility, correlations, new equipment cost, salvage value, investment tax credit, tax rates, and deprecation rates. Kulatilaka [63] develops a more straightforward application evaluating the option to switch between different modes of operation on a dual-fuel boiler. Cortazar and Schwartz [27] evaluate a compound option model for a firm with fixed unit costs, the ability to modify production levels, and intermediate inventories. Cortazar and Casassus [26] develop a model for the optimal timing of a mine expansion that utilizes several SDE and numerous boundary conditions. Their paper describes and demonstrates a user-friendly computer implementation.

SIMULATION

Monte Carlo simulation is an extremely valuable tool to value both financial and real options. Due to the complex nature of developing SDE and the laborintensive lattice approach, the simulation technique provides an alternative means to reach option values. A brief overview of option valuation using simulation can be found in Hull [49] and Wilmott [123]. Despite the advantages of simulation, very few papers use it. One paper by Rose [1031 uses Monte Carlo simulation to value complex interacting real options for a large-scale infrastructure project.

ROA DRAWBACKS

Because current ROA modeling approaches are benchmarked from financial option pricing, numerous ‘holes’ exist in the real option valuation process. ROA deals with real assets and numerous option interactions, thus real options are generally more complex than financial options. In general, six parameters impact the option value including the underlying asset, risk, exercise price, expiration date, interest rates, and dividends. Each one of these areas’ drawbacks is summarized in FIGURE 3, and the following discussion highlights research and application concerns.

UNDERLYING STOCHASTIC PROCESS

Two modeling concerns exist for the underlying security: the movement of the underlying asset through time and whether or not the asset is traded on the market. From a decision-making perspective, assuming either a continuous- or discrete-time approach for the underlying asset does not drastically impact the option value. However, three stochastic processes and a combination of these processes are used in the literature (see Hull [49]): Geometric Brownian Motion (GBM), a Poisson jump process, and a mean-reverting process.

GBM is the standard diffusion process used for the underlying security. GBM is an assumption of the Black-Scholes equation and some form of it is used in virtually all ROA. Poisson jumps are used to replicate sudden and sharp movements (such as the arrival of new information) in the underlying assets value that GBM does not explain. For an example of a Poisson jump process, readers are referred to Brach and Paxson [15], which also contains a good literature survey on jump processes in ROA. A mean-reverting process describes an assets value that has a tendency to revert back to some long-run average level over time. Interested readers are referred to Hull [49] and Copeland and Antikarov [25] for a discussion of how interest rates, commodity prices, and unit/fixed costs are better modeled with a mean reverting process. From an options valuation perspective, the Poisson jump always increases the option value and a mean-reverting process can either increase or decrease the option value.

An alternative method to calculate the option value uses the terminal distribution of the underlying assets’ values. When these three stochastic processes are looked at over some defined time range, a terminal distribution can be observed. For example, the terminal distribution of GBM is a lognormal distribution. The terminal distribution of GBM with Poisson jumps and a mean– reverting process will vary with the size and frequency of the jumps and how quickly the process returns to its long-run average. For stock prices, a lognormal distribution is justified because a stock’s price can’t drop below zero (Note: The range of a lognormal distribution is zero to infinity). Because a real asset value can be negative, a pure GBM might not serve as an accurate depiction. Therefore, alternative stochastic processes need to be considered.

UNDERLYING TRADABILITY

A key assumption of financial option pricing involves buying and selling the underlying asset in an efficient market. However, because most real assets are not traded, several rectifying assumptions have developed to support the use of financial option pricing for real assets:

Trigeorgis [121] advocates finding a traded `twin security’ that is perfectly correlated with the real asset value. In practice, identifying a traded security that is perfectly correlated is difficult, if not, impractical. Therefore, it is recommended to select a twin security that is highly correlated and calculate the option value, but intelligently interpret the results. In practice, the twin security approach is used for three scenarios. (1) Natural resource decisions because of the existence of a publicly traded commodity futures market. (2) Firms evaluating a specific division within their company that find a traded stock of a `pure play’ company that mirrors their division’s value. (3) When the project being evaluated contributes significantly to the firm’s market value, the company’s own stock is selected as the twin security. If these scenarios are not present, then either of the following two assumptions is practiced.

Mason and Merton [77] make the assumption that the asset’s value should be treated as if it were traded in the market. Their rationale is that the real asset contributes to the market value of the publicly traded firm, and thus the real asset can be treated as if it were traded by itself. Therefore, the real asset value should be used as the underlying security.

Copeland and Antikarov [25] propose the marketed asset disclaimer (MAD). Combining the rationale of a `twin security’ and the Mason and Merton assumption, the MAD states that the real asset value is perfectly correlated with itself and is the best unbiased estimate of the market value of the real asset if it were traded. Therefore, the real asset value should be used as the underlying security.

RISK AND THE APPROPRIATE DISCOUNT RATE

A key assumption of financial option pricing is the existence of a replicating portfolio (consisting of a traded underlying asset and risk-free bond) that is used to hedge all risk in the option’s value. Because all the risks are ‘diversified’ away by this replicating portfolio, the appropriate discount rate to use in option valuation is the risk-free rate. This assumption generally holds-up for financial option pricing, but some concerns exist to compensate for the nontraded nature of real assets. The following summarizes discussions from the literature:

If the underlying tradability assumptions of Trigeorgis, Mason and Merton, and Copeland are used, then it is understood that the real option is valued like a financial option. Hence the risk-free rate is used for all discounting. (Note: Hevert, McLaughlin, and Taggart [46] study the impact of inflation on the riskfree discount rate for a growth option. Interestingly, they show that the option value actually decreases with an increase in inflation, even though the discount rate increases. This is contrary to standard option theory where the value of a growth option should increase with an increasing discount rate.)

Hull and White [501 and Hull [49] state for nontraded assets that the following relationship must be satisfied in selecting the discount rate: ni – (lambda)s = r – q. Where m = mean return of the underlying asset, s = standard deviation of underlying asset, lambda = market price of risk, r = risk-free rate, and q = continuous constant dividend yield. For traded assets, the option can always be valued by discounting the option’s expected pay-off at the risk-free rate. Therefore for traded securities, the option value is independent of the mean return of the underlying asset and market price of risk. Whereas, for a non-traded asset, it is dependent on the selection of the mean return and market price of risk. Put another way, instead of using r – q as the discount rate, the decision-maker’s estimates of m, lambda, and s are used to obtain the appropriate discount rate to be used in the option valuation.

Option risks can be divided into private and market risks. Private risks are unique to the firm, such as equipment failures and labor difficulties. Market risks are tied to the economy and include demand, competitive pricing schemes, and macroeconomic factors. According to standard financial portfolio theory all private (or unsystematic) risk can be mitigated by proper diversification (see any finance textbook). Thus, market (or systematic) risk is all that should concern the decision-maker. Because private risk is alleviated through portfolio diversification and market risk can be diminished through the option’s replicating portfolio, the proper discount rate to use for the ROA is the risk-free rate.

The following representative papers address the private/market risk issue in their ROA. Cortazar, Schwartz, and Casassus [28] evaluate a natural resource project by assuming private and public risks are independent. As such, the two risks are collapsed into one underlying continuous-time stochastic variable and the appropriate differential equations are derived to reach an option value. Kamrad and Ernst [54] evaluate mining and manufacturing ventures. Private risk is the quantity of resource that will be mined/drilled and market risk is the market price of that resource. By modeling the private risk as a random multiplier to the market price risk, an options value is determined. Chung [22] provides a standard application involving both risk types.

Smith and Nau [112] propose an alternative interpretation of private and market risk. In essence, it states that higher private risk will reduce the project value, whereas, higher market risk will increase its value. The total option value is then dependent upon the ratio of private to market risk.

Smith and Nau use the terminology `partially complete markets’ to define a project where the firm cannot mitigate the private risks, but can hedge the market risks. Their approach uses subjective beliefs and preferences (summarized by a utility function) to determine project values conditioned on the occurrence of a particular market state. There are three steps: (1) Calculate the effective certainty equivalent by taking expectations over a period’s private uncertainties conditioned on the outcome of the same period’s market uncertainties. Then, use a utility function and the risk-free rate. (2) Take expectations of the period’s market uncertainties using risk-neutral probabilities. [Note that using risk-neutral probabilities is equivalent to using standard financial option pricing techniques.] (3) Discount all appropriate cash flows at the risk-free rate.

In Smith and McCardle [111], this technique is employed for valuing oil properties. Additionally, a comparison is made between their approach and using a risk-adjusted discount rate, standard utility functions, and financial option valuation. Even though an ‘average’ risk-adjusted discount rate can be found to equate the two approaches, no single discount rate is correct because of the asymmetric payoff of the option. (See Hodder, Mello, and Sick [47] for a discussion on why the risk-adjusted discount rate varies with changes in value of the underlying asset.) For their example, the utility approach has a tendency to undervalue the option because it would overstate the risks that could be traded and hedged away. Finally, using only the financial option approach leads to an inflated project value because it assumes that all risk is market risk and can be alleviated through a replicating portfolio. This will understate the uncertainty because the entire project can be discounted at the risk-free rate. The private risk portion needs to be discounted at a higher rate.

VOLATILITY

A key parameter influencing the option value is estimating an ‘accurate’ volatility (or standard deviation) of returns for the underlying asset. For financial options either observing the historical return distribution or calculating implied volatilities from traded option prices is done. However, many real asset investments do not have historical return information nor are traded option prices available.

Estimating a reasonably accurate volatility is an important issue in ROA, and three approaches are identified in the literature: twin security information, Monte Carlo simulation, and closed-form expression. For projects where an appropriate twin security can be identified in the market (such as the futures market for natural resource projects), the historical return distribution of the twin security can be used as a proxy for the real asset volatility. Kelly [57] and Smit [108] provide an example of using the futures market to estimate volatility for natural resource projects. Copeland and Antikarov [25] estimate the volatility of a project by Monte Carlo simulation. After a cash flow statement is constructed using distributions and correlations for the inputs, a return distribution for the change in project value between two periods is developed through multiple simulation runs. The volatility of the project is then represented by the standard deviation of the project’s return distribution. Miller and Park [87] demonstrate this simulation approach in a manufacturing real options application. Finally, Davis [32] develops a closed-form expression to estimate project volatility as the product of the volatility of the firm’s output price and the price elasticity of the project’s value. In other words, the volatility is estimated from the sensitivity of the project value to changes in the spot price of the project’s output resource.

In addition, real options’ volatility can be composed of multiple sources of uncertainty and be stochastic or time dependent. Therefore, the correlations between the varying uncertainties need to be considered in the analysis. Positive correlations can lead to increased option values, whereas, independent or negative correlation could lower the option value. According to Hull and White [50], stochastic volatility has a relatively small impact on at-the-money options (estimated at a 2% difference for Black-Scholes’ values). However, for in- and out-of-the-money options, stochastic volatility could have a larger effect, especially considering multiple sources of uncertainty.

EXERCISE PRICE AND EXERCISE DATE

The exercise price and date for a ROA can be much different than financial option modeling dictates. It is recognized that stochastic exercise prices have been addressed by the closed-form equations developed by Margrabe [75], Fischer [37], and Carr [19], and that lattice models are flexible enough to handle the uncertainty. However, the exercise price for a ROA represents the cost of implementing a next phase or the revenue received from an abandonment option. With financial options, the exercise price is assumed to be one lump sum amount, whereas a real asset’s exercise price (consisting of a series of costs/revenues) could occur with several payments over time or be lumpy. Therefore, the option needs to be valued by factoring in some form of aggregated exercise price. Issues involving how this phenomenon should be addressed have not been clearly defined in the literature. Teisburg [118] does value a utility power plant construction project including lumpy and sequential cost outlays. However, there remains a need for further investigation into how exercise price segregation impacts various real option values.

Real options’ exercise dates may be unknown in advance, dependent upon the exercise of another real option, dependent upon private/market risk resolution, unusually long in duration, and may not be exercised immediately. In comparison, the financial option contract usually dictates expiration date constraints that are less than 18 months in time, with assumed instantaneous option exercise, Because ‘phases’ of a real option project may not be well defined or be dependent upon exogenous factors, the ‘correct’ exercise date to use in the valuation may be unknown. Many real option projects have indefinite or state of nature dependent exercise dates. Issues such as competition, changes in technology, macroeconomic factors, and unique risks to the firm can all effect option timing. Finally, real options may not be exercised immediately. Time may be needed to construct a facility, install equipment, and increase a trained labor force. Therefore, the standard financial option pricing techniques may not account for the additional uncertainty surrounding the exercise date. As with the segregated exercise price, the issue of how uncertainty surrounding the exercise date impacts the option value needs to be further explored.

DIVIDENDS

Any increase or decrease in the underlying asset value during the real options’ life could significantly impact the project value. With financial option pricing, dividends paid by the underlying asset reduce the call option and increase the put option value. In addition, the dividend payments are known in advance or can be modeled as a continuous payment over the option’s life. In contrast, real options ‘dividends’ (such as cash payouts, rental income, insurance fees, and licensing royalties) need to be accounted for and are considered a leakage in value by Amram and Kulatilaka [3]. For real options, the amount and timing of the dividend may be unknown or dependent upon private/market exogenous influences. Financial option techniques can be used as estimates to the impact of dividends in ROA, but separate models still need to be developed to more accurately account for the uncertainty. See Davis [32] for an approach to develop an expression for the dividend yield of a project as a result of fixed or declining production.

FUTURE RESEARCH DIRECTIONS

Benchmarking from financial option pricing techniques, ROA is becoming a practical tool for investment decisions. However, one key difference does exist between financial versus real option valuation. The end goal of financial option pricing is to sell a marketable security, whereas, the culmination of ROA should be to improve decision-making. Acquiring precise prices for financial options is a necessary condition for market makers to profitably market and sell derivative products to firms. In addition, firms need to understand more accurately how the option prices were derived, if the derivative product will mitigate targeted risks, and whether or not the market price of that derivative is justified given its potential benefits. On the other hand, ROA should be viewed as just another decision-support tool to be used in combination with payback period, return on investment, net present value, and internal rate of return. The real `bang for the buck’ for ROA is identifying an appropriate decision framework, recognizing the implicit/explicit real options, and calculating an enhanced project value. In other words, ROA results should gUide decision-makers to choose the best course of action, not necessarily to provide an ‘exact’ option price.

We strongly believe ROA will become vitally important for strategic decision-making in today’s world of uncertainty (other authors also agree with the strategic use of ROA, including Merton [861 and Trigeorgis [120]). However, several macro level issues need to be considered in this setting.

First, standard decision-making `rules of thumb’ may be challenged. For example, mean-variance analysis indicates that given two projects with equal expected returns, the project with the lower variance should be selected. However, in a ROA framework when either risk-neutral or risk-averse decisionmakers are confronted with two projects that have the same expected payoffs and varying levels of variance, the riskier project should be selected. Therefore, ROA should be viewed as a means to manage risk, not shy away from it.

Other factors will need to be considered as well. When firms adopt a ROA way of thinking, many unprofitable projects (in the short-term) will be accepted. Firms and investors must be cognizant of this shift in project selection and view many investments as long-term or platform strategies. This will force firms and investors to alter their evaluation criteria, and it could have a drastic influence on a firm’s internal structure and market valuations. For example, ROA will tend to increase the adoption of expensive platform investments that will not yield immediate financial benefits. At the same time, ROA will tend to decrease immediate investment in large irreversible decisions as the firm awaits new information.

As firms direct more investment to areas of greater market uncertainty, project selection will resemble a mutual fund manager selecting a certain stock for his/her portfolio. In the same manner that a stock portfolio’s risk is managed (or hedged) utilizing traded derivative products, firm decision-makers will need to learn to manage their project risk using a ROA framework.

Additionally, firms must decide the best course of action to implement ROA into their business. Some tough questions abound: When and if is it appropriate to use ROA? Which divisions or types of projects would ROA be most appropriate? How will the firm deal with certain divisions using standard DCF tools and others using ROA? How will investors value a firm with a mixed DCF/ROA selection criterion? Should firms reorganize to segregate steady– revenue versus platform projects? If segregation is appropriate and implemented, when should a project be moved from. the platform to the steady– revenue side of the business?

The remainder of this paper discusses future modeling and application areas for ROA. Modeling issues involve merging financial risk management, decision analysis, and real options valuation into a cohesive decision framework. In addition, modeling how new information, learning, and competition will be discussed. From an application perspective, this paper concludes with comments on using ROA in the service sector and stock valuation. FIGURE 4 summarizes the discussion for the remainder of this paper.

FUTURE MODELING AREAS

Modeling real assets within a ROA framework requires many estimates, interrelated inputs, and a careful interpretation of the results. For example, enough time and volatility can make any project seem acceptable. Hence, ROA should benchmark off of financial option pricing techniques, however, due to the more complex nature of real assets, modeling efforts should be placed in a proper context.

In fact, many ‘holes’ exist in financial option pricing methods themselves. A good summary of real world assumptions violations of the Black-Scholes equation can be found in Hull [49], and an empirical study of Black-Scholes values versus traded option values can be found in MacBeth and Merville [71]. Figlewski [36] used simulation to observe how inaccurate volatility estimates, indivisibilities, transaction costs, and bid-ask spread ranges impacted financial option values. Figlewski concluded that incorrectly estimating the volatility and finding the ‘correct’ rehedging policy pointed to the infeasibility of the BlackScholes equation, and that the Black-Scholes value should only be used as “good guidance” in deriving the true financial options price.

If financial option pricing methods do not exactly assess a financial option’s value, then using financial option valuation techniques to acquire ‘exact’ real options’ values makes little sense. For ROA most, if not all, of the modeling inputs are estimates. The underlying real asset value is the estimated present value of the project’s worth, the volatility is either proxied from the market or estimated using simulation, the unknown expiration date and exercise price are dependent upon one another, the exercise price could be stochastic or an aggregated series of cash outflows, and the dividends from real assets are approximations. Therefore, the decision-maker needs to be cognizant that the real option value calculated is a guesstimate of the ‘true’ option value. More complicated financial option pricing techniques, not discussed in this paper, can be used to address some of the ROA input shortcomings. However, implementing these techniques also introduces more estimates into the option value that require further modeling refinements. The bottom line is that there are diminishing returns to excessive modeling fine-tuning.

Instead of altering financial option pricing techniques to ‘fit’ real options, future ROA modeling efforts should concentrate on developing practical methods for improved decision-making. Mathematical `accuracy and complexity’ should be replaced with viable real option models that will be supported by practitioners. Several authors agree with these sentiments. In their industry real option survey, Busby and Pitts [18] found that managers believed the current ROA tools to be too complex in its present form. In addition, managers supposed that too much research effort was being placed on computational refinements instead of addressing the overall decision-making process. Neufville [93] states that getting exact input values for real options is unnecessary because ROA should support making a choice. Hence, “one only needs to know the relative value of alternatives, not their precise value.” Sick [107] states that it makes little sense to select a numerical technique to get an option price within 1% to 2% of the true theoretical value, when the real option inputs are in error of at least 10%. And finally, as Merton [86] cautions in his lecture for the Nobel Prize in Economics in 1997, “the mathematics of financial models can be applied precisely, but the models are not at all precise in their application to the complex real world… The models should be applied in practice only tentatively, with careful assessment of their limitations in each application.”

The remainder of this section discusses merging decision analysis with real options, alternative valuation approaches, and future modeling addendums.

ALTERNATIVE MODELING APPROACHES

We support numerous efforts of other researchers to expand ROA out of the realm of pure financial option pricing techniques. The following provides a discussion of their work and indicates future research areas.

Decision Analysis and Real Options

Smith [110] provides a lucid discussion of merging real options and standard decision analysis techniques. In essence, both approaches model decisions and uncertainties with ROA being very analogous to financial options and decision analysis tools evaluating risky cash flows. Smith believes that decision analyst would benefit from learning more about modeling stochastic processes and lattices, whereas, ROA analyst could learn more about probability assessment and inference. One key difference between the approaches involves the interpretation of hedged and unhedged risks. In Smith and Nau [ 112], three separate scenarios are discussed in the context of comparing real options to decision analysis:

Complete Markets: – Complete markets are those where every risk can be perfectly hedged using traded securities. It is concluded that a financial options approach and decision trees will provide equivalent results, however, decision trees must capture time and risk preferences properly using a utility function. Therefore, the financial option approach may be more practical.

Incomplete Markets – Incomplete markets are those where not every risk can be hedged with traded securities (i.e. private versus market risk). It is concluded that an options approach and decision trees will provide consistent results. When option pricing is confronted with incomplete markets, a unique option price does not exist. Instead, an upper and lower bound exist dependent upon how much of the risk can be hedged in the market. (Note: If all the risk is hedged, these bounds collapse to the unique solution of complete markets.) The less risk hedged, the wider the bounds. The value provided by decision trees will not exactly equal the option value; but will always fall within the bounds provided by the options approach.

Partially Complete Markets – Partially complete markets define the approach developed by Smith and Nau where risk is divided between private and market. This approach was discussed earlier in this paper, and the details will not be explained again. In summary, a utility function approach is used for the private risks and a financial options approach is used for the market risks.

Park and Herath [96] discuss how the expected value of perfect information (EVPI) {or equivalently the expected opportunity loss (EOL)} concept in standard decision analysis is equivalent to an options value. In Herath and Park [441, it is shown that the EVPI produces an equivalent result to the BlackScholes equation when certain assumptions are upheld. Lander and Shenoy [66] discuss the benefits of using an influence diagram (ID) to value a real option. This approach makes sense because IDs are mathematically equivalent to decision trees, and Smith and Nau [112] have shown that decision trees are equivalent to financial options. A benefit of using IDs versus decision trees is that decision trees grow combinatorically, whereas IDs grow linearly with added complexity.

Future research should focus on merging decision analysis with real options. The synergistic benefits of both approaches ought to yield practical decision tools. Take for example the following two areas that should be further incorporated into ROA: learning with new information and competition.

LEARNING WITH NEW INFORMATION

Much is written in the literature about the learning component of real options. However, besides using the standard compound option framework, little work has been done to incorporate the arrival of new information into an option’s value. Issues such as information costs, updating the option’s value to reflect the new information, the arrival of incomplete information, and an option’s ‘learning’ process all need to be addressed.

Several authors have begun implementing the learning component into a real options analysis. Sundaresan [116] provides a discussion on the need for including an incomplete information framework into real options valuation models. Childs and Triantis [20] place an R&D expenditure decision in the context of learning-by-doing and collateral learning between different projects. Bellalah [8] develops a continuous-time model of irreversible investment in the presence of information costs and points to the importance of considering information costs (or shadow costs) when considering an options value. Martzoukos and Trigeorgis [76] develop a model of learning with path– dependency to investigate the optimal timing of actions of information acquisition that result in reduction of uncertainty in order to enhance real option value. Their paper shows that information acquisition is costly and managers must trade-off between quality of learning and cost of learning — which leads to optimal timing of learning. Herath and Park [44] discuss a real options’ value in the context of EVPI and sampling information. In a Bayesian context, their paper highlights that the quality and cost of new information needs to be considered in an option’s value.

In addition to the existing research efforts to combine information and learning into the ROA, several other areas should be pursued. The following papers do not necessarily mention `real options’, however, many of the ideas could be incorporated into a ROA. Dating back to the early 1960’s, Arrow [61 provides a classic paper on learning by developing an economic model to show as firms accumulate experience their productivity increases. Arrow and Fisher [7] consider an irreversible investment decision. Their work indicates that working with only expected values (and not higher moments of the probability distribution) can lead to results that differ greatly from the optimum. If information about the costs and benefits in one period impacts a change in the expected value for future cash flows, then the overall net benefits will be reduced. Thus, in the face of uncertainty, the decision-maker should err on the side of under-investment and wait for additional information.

Merging Bayesian decision analysis with ROA was first introduced by Herath and Park [44], however, several other Bayesian approaches to new information should be considered. Although these papers do not explicitly mention real options, these concepts are relevant. Demers [33] explain why firms do not respond instantaneously to changes in input/output prices or productivity. Using irreversible decisions, uncertainty, and arrival of information as an explanation for the gradual investments, Demers constructs a model based on a risk-neutral firm which is uncertain about demand but has prior beliefs that are updated each period by Bayes’ law. The uncertainty leads to three actions (1) cautious investment behavior, (2) a time varying risk premium, and (3) a gradual adjustment in capital stock. The firm’s investment gradually reaches the long-run true state of demand through equilibrium. Hence, each firm will wait for further information in order to make a more accurate assessment of the state of nature. Grossman, Kihlstrom, and Mirman [40] develop a model analyzing the phenomena of learning and experimentation using a utility-function based dynamic economic model incorporating Bayesian learning. Put in the context of a consumer purchasing a drug with unknown reliability, the paper indicates uncertainty can be reduced at an ‘experimentation’ cost.

Using a learning curve to explicitly model the learning of an option would be a creative context for ROA. These two papers introduce learning curves to uncertainty and Bayesian revision. This concept could be extended to an explicit model of learning mapped directly to a real options’ value. Majd and Pindyck [74] study learning curves and optimal production under uncertainty. They develop a firm’s optimal decision policy assuming learning-by-doing and uncertainty about future prices. Mazzola and McCardle [79] merge Bayesian and learning curves by developing a theoretical model that finds a unique bounded value function satisfying a dynamic stochastic recursion, and thus the existence of an optimal policy.

Viewing the strategic impact of learning from a top-down perspective would provide a means to justify ROA increasing overall firm value. Most of the research on real options views individual projects within a firm. However, research from a firm level perspective indicating the benefits of the acceptance of ROA to the overall economy would be useful. The following paper by Stickel [113] addresses learning for two different firms: risk-neutral versus risk-averse. Their research shows that the risk-neutral firm should not necessarily try to reduce uncertainty. Instead, it should wait for the risk-averse firm to establish a risk management system, and then it should imitate the risk-averse firm’s approach. Overall, the paper calls for a closer look at risk management strategies and the economics of risk reduction.

Combining financial option pricing, Bayesian, learning curves, and strategic impacts of information, ROA would become a more practical and useful tool. As a final note on ROA and learning, for real assets should the option value calculated be viewed as the upper limit on the project value? It is known that the option value is equal to the expected value of perfect information. With real assets and projects, obtaining imperfect information is more probable. The real option value should be equal to the expected value of imperfect information (EVIl). As such, a possible link between EVII, incomplete markets, and partially incomplete markets may exist.

COMPETITION AND EXOGENOUS INFLUENCES

Numerous exogenous factors could impact the real option value. McGrath [81] and McGrath and Macmillan [82] discuss six key factors impacting the value of a real option:

Demand structuring – Uncertainty in demand is certain, however, the decision-maker can classify demand into structures with properties of monotonicity and convexity. Structuring demand correctly leads to an increase in option value.

Speed of adoption – Slow adoption of the project’s output could delay the onset of revenue streams, and it allows more time for competitors to enter the market. Hence, slow adoption will reduce the option value.

Blocking – Blocking refers to when a firm is denied access to inputs, applications, and the market. Blocking reduces both the mean and variance of benefits, and thus lowers the option value.

Expropriation – Occasionally firms must pay some form of entry fee to get in the market (i.e. licensing fee) which reduces the mean return and the option value. On the other hand, it can also increase the option value because it provides the firms the opportunity to get into markets it couldn’t have otherwise.

Matching – Matching occurs when competitors acquire some of a firm’s customer base using a different business approach. This loss of business leads to a reduction in the option value.

Imitation – Imitation occurs when a unique product becomes a commodity (i.e. market gets saturated with same product). Imitation will reduce the output price, may change the customer base, and will reduce the option value.

The decision-maker must be aware that waiting to invest may carry a premium such as a loss in market share and competitors actions. The firm must balance the value to defer and its deferral costs. Several authors have identified competitor entry into the ROA. Ottoo [95] discusses the impact of competitors on the R&D decision. They conclude that competitors can encourage efficient and speedier R&D investments. From a modeling perspective competition lessens the expected time to recovery, thus lowering the option value. Trigeorgis [121] uses a mixed-jump-diffusion-process to model the impact of competition. He defines the total project value equal to the standard net present value plus the option value minus competitive losses. Reiss [100] evaluates whether and when a firm should patent an innovation in the face of stochastic competition. Smit and Ankum [109] use the microeconomic concepts of economic rents (where firms can earn above the opportunity cost of capital in certain market environments – such as first to market) and basic game theory to develop a model and an example showing that competition erodes the value of a deferral option.

More research involving game theory and other decision analysis tools to represent competitor entry are necessary. In addition to competition, the numerous other factors listed by McGrath need to be considered and modeled appropriately. Developing ROA to include the impact of exogenous influences will lead real options to the strategic stage of planning in a world of uncertainty.

OTHER MODELING APPROACHES

Modeling approaches such as dynamic programming, economic models, financial risk management, and simplifying procedures have been identified in the literature to value real options. In the spirit of these approaches, it is presumed that other creative techniques could be identified to support the acceptance of ROA in practice. Anderson [5] advocates the use of a dynamic programming approach utilizing Bellman’s principle of optimality for ROA in incomplete markets. It is shown that dynamic programming produces the same results as option pricing when risk neutrality is assumed. Christiansen and Wallace [21] provide a very lucid and instructive explanation comparing the dynamic programming and standard option valuation approaches.

Abel, Dixit, Eberly, and Pindyck [1] show that the “q” theory approach, a tool in the macroeconomics literature, equals the options approach when evaluating expansion or contraction. The “q” theory valuation involves the returns to existing capital and the marginal value of the options to invest/disinvest. Using “q” theory effects of changes in the distribution of future shocks can be explored. In the context of stochastic dominance, their paper explains that changes in the tails of the distribution have little, if any, change in value of the option; whereas, changes in the intermediate range of the distribution do affect the incentive to invest. In conclusion, “q” theory and the option value approach reach the same conclusions, but each one offers a different insight into the investment decision. Ostbye [94] approaches the option valuation problem from the context of a restricted variable cost function and derives a new full static or long run equilibrium condition for capital in a factor demand model.

Using derivative products for risk management has permeated itself into the majority of medium- to large-sized firms. Firms identify risks and purchase derivatives to hedge these risks. In essence, for a premium companies can shift certain risks to other parties willing to accept them. Merging how firms use these traded risk products with ROA should provide some interesting results. Several authors have begun this process. Ritchken and Tapiero [102] use publicly traded option contracts to risk manage inventory decisions. The firm has three decisions: (1) build inventory, (2) enter into an options contract to buy for a future price, or (3) wait for demand and buy at the market price. In the context of hedging against price and quantity uncertainty, their paper discusses the conditions under which options contracts are superior or complement existing inventory strategies. Stowe and Su [114] utilize risk management products within a ROA. They develop a unique approach to value the inventory stocking problem by mapping the payoffs from an inventory policy onto the price of an underlying asset, constructing a portfolio of options that replicates these payoffs (basically creating a bull spread, bear spread, straddle, strangle, or any combination of put/call options), and then valuing the portfolio of options.

Any user-friendly approach or heuristic that approximates real options values would be supported. It is believed that any approach directly in-line with current techniques, such as NPV, would foster a wider and quicker acceptance of real options in practice. In an effort to provide an accessible ROA approach to practitioners, several researchers have developed methodologies or techniques using alternative means. Sharp [106] recommends a less mathematical approach to calculate real option values because the inputs for options’ calculations are at best guesses and only apply to the simplest of cases. In general, there are two general types of options: incremental (compound) and flexibility (expand, defer, etc.). First, the options should be identified, then the exercise environment should be evaluated, and finally a subjective aggregate option value should be estimated. Mitchell and Hamilton [89] divide projects into one of three categories: (1) Short-term projects – Use NPV, (2) Knowledge building projects — Just allocate costs of project and view these projects as part of doing business. No formal evaluation process is recommended, and (3) Strategic positioning — Use real options approach to evaluate platform investments. Aggarwal and Soenen [2] develop a simplified approach to value the exit value of a project. In the context of discounted payback period, the authors develop an Exit Net Present Value (ENPV). The ENPV is composed of the net after-tax operating cash flow plus the after-tax liquidation value of the project’s assets, discounted to the present. Lavin and Zorn [67] develops a methodology to value the option to abandon a project as a function of economic depreciation. Depreciation has similar parameters to options that drive its value — time, usage, maintenance, technology, and market conditions. Therefore, the annual economic depreciation (or market value from year to year) represents the cost of the option to continue the project for another year.

The development of alternative ROA approaches involves understanding current financial options, current modeling assumptions, and an appreciation of the decision process. Several other ideas to pursue are listed below:

* Standard financial option pricing involves the existence of a replicating portfolio to hedge market risks, and the cost to maintain this portfolio equals the option value. In a similar context, the decision-maker could estimate the cost that it would take to hedge the risk within a project. This cost could represent the option value. Whether alternative manufacturing processes are considered, a market survey is performed, derivative securities are purchased, or any other risk reducing activity in entered into, the costs involved could somehow be mapped to the real option value. A structured process to apply these costs to obtain an option value would provide easy-to-implement procedure utilizing information the firm needs to acquire anyway to make a decision.

* Alter existing cost of capital techniques, For example, Economic Value Added (EVA) is a project or division oriented decision tool that utilizes a hurdle rate. Even though EVA is project related, it does tie the project value to the market. In the same way, ROA is attempting to increase shareholder value by linking projects with their market value. Building upon EVA and related concepts, a ROA procedure could be developed.

* Explicitly altering financial options modeling ‘rules’. For example, standard options pricing assumes the option price would hold in a world of risk-neutrality (which assumes a risk-neutral probability distribution) and the appropriate discount rate is the risk-free rate. Benchmarking off of this concept, the decision-maker could assume the firm is risk-neutral and use the risk-free rate, estimate a utility function and use the risk-free rate, use the real probability distribution and discount with the risk-free rate (instead of the risk-adjusted rate), or use the financial option approach but discount with the risk-adjusted rate. A comparison of these ‘rules’ changes and how/when to use them would promote the acceptance of ROA in practice,

* Current discussion observes two risks in a ROA – private and market risk. An alternative interpretation of risk could point to three risks affecting a project – private, demand, and economic risk. Private risk represents the usual firm-specific risks that are usually uncorrelated with the market. Managers can proactively take actions to reduce uncertainty through experimentation or risk management practices. Demand risks are all the risks surrounding a firm’s output such as the size of the customer base, profitable output pricing, and competitor influences. Firms can influence demand risk, however, cannot alter it as well as private risks. Economic risks represent those exogenous factors completely out of the firm’s control such as interest rates and inflation. In some form, all three of these risks are somewhat dependent upon one another. For example, firms might not undertake new expenditures when the overall economy is down or demand risk has not been resolved. A modeling approach accounting for the three levels of risk would help firms identify which risks impact which business activities. Rules or techniques could be developed dependent upon which type of risk a certain project is exposed.

FUTURE APPLICATION AREAS

Real options applications exist in many areas, however, we will briefly comment on two subjects – stock valuation and service sector applications. Even though stock valuation has been addressed in the literature, we discuss additional inferences. Applications in the service sector are scarce, and there are opportunities for significant improvements in service sector decisions.

STOCK VALUATION

TABLE 1 highlights the papers using ROA to value traded securities. Unfortunately, most of these papers are used to justify high market valuations, and not to develop theoretical tools like the capital asset pricing model (CAPM) to gauge ‘correct’ stock prices. Kester [60] compares the capitalized value of the firm’s current earnings stream and its market value to estimate that at least 50% of the market value of the firm is represented by its growth opportunities (or options). Jagle [52] breaks the value of a stock into the value from the existing business plus the value of future growth opportunities. An empirical study is performed on over 21 publicly traded companies, from which an average of 70% of a firm’s market value are represented by those growth prospects. A binomial tree approach is constructed and implemented to value an initial public offering for a biotechnology company. Kellogg and Charnes [56] assess the value investors are assigning to biotechnology companies in a ROA context, and Kelly [57] models a real option to ascertain the value of a gold mine Initial Public Offering. Keeley and Punjabi [55] compare the standard DCF approach, a venture capitalists approach, and a real options approach to arrive at a value for a start-up company. Using real world data from 236 ventures to calculate option parameters for a compound option, it was found that the ROA value exceeded both of the other approaches.

Developing sound financial and economic theory that accounts for the growth opportunity market value of a firm using real options would be important for companies, as well as investors. Current CAPM theory uses the parameter beta to represent the risk of a company. However, beta focuses more on the current value of a firm, in the similar fashion that standard cost-volume-profit analysis only considers current capacity. Developing a similar ‘beta’ indicator that included the current value of the firm, its risk relative to the market, and future growth opportunities would advance the study of capital markets. It is believed that concepts and techniques from real options could be used in this pursuit.

To date, several authors have considered a firm’s life cycle in their ROA to value either a firm or projects within the firm. Some of these ideas could be expanded upon to develop general economic models. Bernardo and Chowdhry [91 use real options to value a firm’s growth alternatives. They claim that young firms specialize in a certain service/product, and then either expands into a large diversified firm or a large specialized firm. In general, young firms will be valued higher than older firms with the same resources because they have much more to learn than mature companies. Bollen [12] develops an options framework incorporating a stochastic product life cycle. Firms begin in a growth regime (with increasing demand), and then switch to a decay regime (with decreasing demand). The paper shows that the standard options approach undervalues the contraction option because it underestimates the probability that demand will most likely fall in the future and it overvalues the expansion option because it assumes demand is expected to grow indefinitely.

SERVICE SECTOR

Currently, the service sector comprises 80% of the U.S. employment and Gross Domestic Product (GDP). Any improvement in productivity or wealth creation in this sector will have a significant impact on national affluence. The service sector is becoming increasingly dynamic with upsurges in electronic-commerce and technological advances. Increased use of real time information (such as computerized order tracking) enables businesses to better match supply with demand. Firms can observe shifting demand and respond appropriately by instantly changing service schedules, work shifts, inventory levels, and capital spending plans. Already known for its increased productivity and greater manpower flexibility, the U.S. economy must now develop tools to respond to instant information, increased process data acquisition and analysis (data mining), shorter service runs, and more stringent quality requirements.

As traditional forecasting methods become increasingly ineffective, companies can adopt ROA to value projects with a wide-range of plausible future scenarios. To date, very few real options applications exist in the literature. Except for lease evaluation decisions (see Kenyon and Tompaidis [59]), the majority of service sector industries have not been examined. Several common attributes limiting the use of real options to the service sector include intangibility of the inputs/outputs, lack of inventories, non-quantifiable quality components of services, and lack of standards. It is believed that ROA could be applied to service sector decisions, with modifications for the additional uncertainties. Due to the large size of the service sector, any contribution would be well received.

Miller and Park [88] investigate a modeling framework for revenue optimization in the service sector using a real options approach to evaluate pricing decisions of services. The paper provides a decision framework for revenue enhancement in the service sector by identifying the strategic pricing options available to service firms. Then, a framework for market-based, real options decision tools is developed to ascertain optimal pricing strategies. The key elements of the approach include examining pricing decisions within the context of today’s market dynamics, developing real options modeling tools to determine optimal pricing strategies, and integrating these elements to allow for proactive monitoring and management of pricing decisions’ impact on service firm profitability. The approach allows decision-makers to directly incorporate market-driven perspectives by synchronizing service operations with organizational economic goals.

CONCLUSIONS

Many papers apply ROA without fully comprehending the modeling assumptions and/or violations. The authors believe this paper provides a relatively comprehensive overview of research to date on ROA found in the literature. Many contemporary issues were discussed, in addition to recommended future directions for research. The organization of this paper is unique in that it lists applications by area, real-world users of real options, categorized modeling approaches with applications, detailed ROA modeling concerns and assumptions, and provided future research directions for modeling and applications.

ROA is in its early developmental stage utilizing many components of financial option pricing. It is recommended for ROA to build upon this foundation, and merge with decision analysis and other approaches to become its own unique framework to address decision-making in a world of uncertainty. ROA has the advantages of linking market values to strategic decisions in today’s technology driven and highly competitive business environment. Future research initiatives in ROA will ensure that practitioners are supplied a viable, decision-making tool that will proactively manage risks and encourage wealth creation.

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LUKE T. MILLER

Auburn University

CHAN S. PARK

Auburn University

BIOGRAPHICAL SKETCHES

LUKE T. MILLER has experience as an operations research analyst and program manager as a captain in the United States Air Force (millelt@eng.auburn.edu). His work experience includes statistical modeling and analysis, scheduling, optimization, and decision analysis. He is a graduate of the University of Virginia (B.S.) and Auburn University (M.I.S.E), and is currently a Ph.D. student in Industrial Engineering at Auburn University. His main research interests are in real options, financial engineering, economic decision analysis, and corporate finance.

DR. CHAN S. PARK is a professor of industrial and systems engineering at Auburn University, Alabama (park@eng.auburn.edu). He received his B.S. from Hanyang University, his M.S.I.E. from Purdue University and his Ph.D. in industrial engineering from Georgia Institute of Technology. His main research interests include engineering/manufacturing economics, decision analysis, and real options analysis. Dr. Park has published numerous articles on these topics and received several research awards for his publications from the Society of Manufacturing Engineers, the American Society of Engineering Education, the

Institute of Industrial Engineers, and the Sigma Xi. He has also authored several texts, including Advanced Engineering Economics (John Wiley) and Contemporary Engineering Economics (Prentice Hall). Since 1997, he has been serving as Editor of the ENGINEERING EcONOMIST.

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