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VALUING RISKY PROJECTS WITH REAL OPTIONS

The value of high-risk but potentially high-return technology projects can be calculated with Boeing's new real-option algorithm.

Scott Mathews


Scott Mathews is a Boeing Associate Technical Fellow and technical lead for business engineering within the Boeing research and development division, in Seattle, Washington. He provides technical consulting across Boeing for investment and risk models for new products and strategically significant projects. For the past 15 years he has been engaged in stochastic modeling, capital markets investment and financial analysis, and international strategic analysis. He has approximately 20 patents and patents pending in the field. Previously, he worked in the United States, Europe and Asia as an engineer in robotic control systems, artificial intelligence, and systems and software development. He has a B.S. from Cornell University in electrical engineering and control systems and an M.S. in finance from Seattle University. This article is adapted from Chapter 43 of the forthcoming book: The Handbook of Technology Management, 3 Volume Set, Hossein Bidgoli, Editor-in-Chief, John Wiley & Sons, Inc., 2009, Hoboken, N.J. scott.h.mathews@boeing.com


OVERVIEW: This article provides technologists with the business-case methods and tools to calculate the value of projects involving risky new technology or markets but that potentially offer higher returns in the long run. A typical business case using NPV analysis is presented for a new product, an air freighter. NPV is first extended to multi-scenario analysis and then to a “what-if” model using Monte Carlo simulation. Finally, a real-option value for the air freighter is calculated. Based on the same concept as traded financial options, a real option is a contingent investment in “real” physical assets such as a corporate technology project. Boeing's new real-option value algorithm, the Datar-Mathews Method, is both intuitive and transparent. It gives technology managers an investment and risk-modeling tool they can incorporate into strategic thinking and contingency planning.

KEY CONCEPTS: real options, investments, risk, Datar-Mathews Method, strategic decisions.

Project flexibility is inherently valuable. Profitability increases with the ability to change the direction of a project as knowledge is accumulated during the design phase. However, traditional project valuation-modeling methods, such as net present value (NPV), or, as it is occasionally termed, discounted cashflows (DCF), do not appropriately value flexibility or quantify risk. A major shortcoming of NPV analysis is that it fails to recognize that management has flexibility to alter the path of a project, and thus increase overall project value.

In the capital markets sophisticated financial options accurately capture the tradeoff between return and risk to reflect fair market value for securities worth billions of dollars. An options trader would lose his shirt using NPV in the capital markets, so why aren’t options more common in the corporate world? Until recently, option techniques were considered too complex to apply to corporate strategic investments. This article introduces a new real options approach developed at Boeing in which these challenges have been resolved through the availability of new spreadsheet add-in software.

Boeing's real option method provides technologists with investment and risk modeling tools and methods that can be incorporated alongside standard systems engineering design modeling techniques. The real option method and its extensions provide a mathematical foundation for a scientific and “engineering-like” approach to identifying risk and quantifying impact. In turn, they enhance the technology managers’ level of confidence in reducing risk through targeted allocation of mitigation funds, and help to shape project value outcomes that increase the likelihood of achieving strategic objectives.

Business Case for an Air Freighter Project

To illustrate a real options valuation, let us first examine a project using a simple business case analyzed from an NPV approach. Imagine Boeing has the opportunity to design and build a small aircraft specialized for air cargo transport. This case closely parallels one Boeing asked to be evaluated by a class of students in the Global Integrated System Engineering (GISE) graduate certificate program at the University of Washington.

There is a rapidly expanding market for high-value goods that are shipped efficiently from airports near a manufacturer and directly to airports near consumer market outlet locations. Historically, freighter planes were converted from older passenger planes. Inefficiency in design and weight of converted freighters makes the cost of transported cargo, as measured by ton-mile, uncompetitive with cargo transported by truck or by ship. A new specialized freighter might be competitive for transporting luxury goods. However, the specialty freighter remains a risky investment proposition because the air cargo market is difficult to forecast and therefore unit sales and price forecasts can vary greatly depending upon assumptions about the market.

An actual Boeing business case for an air freighter is complex, involving many factors, such as fuel price volatility, competition and the global economic environment. However, the valuation concepts presented in this paper can be sufficiently illustrated with the following simplified business case.

Table 1 sets forward example projections of revenues and costs using a most-likely NPV scenario based on assumptions about product strategy and market reception. The engineers and marketing analysts are requesting authorization to spend $75M (million) in R&D expenses over the next three years. The objective is to reduce uncertainty in order to be better informed about whether to launch the product. The funding will enable the engineers to develop a preliminary design and better determine recurring and non-recurring costs. Meanwhile, the marketing analysts will obtain a better estimate on the unit quantity and price of the air freighter. After three years, contingent on the success of the engineering efforts and a promising market forecast, Boeing would commit a one-time expenditure of $2.0B (billion) to launch the air freighter. This significant launch cost provides funds for final design, production facilities, FAA certification and marketing outlays.

The strategic investment question facing senior management in this example is whether to authorize the $75M R&D expenditure. Over the last half-century or so, corporations have answered that question by applying NPV analysis to determine whether project net profits exceed the initial investment. NPV of the net profits is commonly based on the value estimates for the business case variables reflecting the most likely outcome of assumptions about the product strategy and market reception (1). NPV analysis typically discounts all cashflows at a common rate: the Project Risk rate, a rate established by management to meet a required rate of return for project investments. This rate is sometimes referred to as a hurdle rate. Applying the Excel NPV function with the Project Risk discount rate of rp = 15 percent, the project net present value at Year 0, today, is estimated to be a negative $187M (see Table 2).

Under standard NPV decision-making, senior management would deny the request for initial funding of $75M because the freighter project is forecasted to lose money. Following that guidance, Boeing most likely would terminate the project, and engineering and marketing resources would be directed to other projects with positive NPV values. The termination of the R&D efforts would essentially preclude any near-term participation in the freighter market. Without consideration for strategic investments, the company is left unprepared should a plausible but lower probability upside scenario actually materialize, potentially leaving an opening for a competitor. Some managers might be tempted to declare the freighter project “strategic” and invest anyway in order to preserve the opportunity to explore the market potential. Of course, doing so would circumvent the discipline of financial decision-making.

Given the uncertainty of the market forecast for unit sales and price, there are good reasons for the project manager to be skeptical about a decision restricted to an analysis of a single most likely scenario, such as this NPV business case. This limiting approach is further reinforced by spreadsheet formatting that constrains each cell to a single value. Consequently, a business case spreadsheet typically reflects a single scenario, while eliminating other less probable though still plausible scenarios. The result is that a standard NPV analysis does not provide insight into the business case opportunities and risks at the margin, nor does it take into consideration management's ability to respond and take advantage of contingencies.

NPV mathematics, having originated in the banking industry for use in calculating interest on savings accounts, unfortunately are misapplied, especially when used to analyze projects that have high uncertainty. The result is that NPV analysis tends to justify only projects that are more conservative (bank-like), where uncertainty is inconsequential, the investment amount and timing is established, and the near-term outcome is more certain.

Table 1.—Most Likely Business Case

table 1 border=0

Table 2.—NPV Most Likely Results

table 2 border=0

Multi-Scenario Approach

To extend the NPV analysis beyond a single most-likely scenario, a common practice is to assess several scenarios. Typically, two additional scenarios are considered: an optimistic and a pessimistic one, which reflect different outcomes, more or less favorable, of the assumptions applied in the most likely case. These two scenarios are plausible, although lower probability than the most likely case.

To reduce the complexity in creating viable scenarios, the emphasis should be on identifying those half-dozen or so assumptions that are potentially consequential or impact 10 percent or more of the total value of the project. Factors impacting less than 10 percent of the project value are assumed to be manageable by a good project team, analogous to an insurance deductible, where minor scenario excursions do not pose a perilous risk. This is in line with standard engineering practices for a first- or second-draft design effort where the focus is on those components that contribute a substantial portion of the targeted function.

Begin the multi-scenario modeling process by envisioning three scenarios: optimistic, most likely, and pessimistic, such as Table 3. The most likely scenario estimates are premised on high-likelihood outcomes of assumptions, or contingencies, that a majority of experts (technology, engineering, marketing, finance, management) anticipate materializing, including engineering technical challenges and marketing response, all of which have quantifiable impact on cash flow estimates. The optimistic and pessimistic scenarios respectively are derived by positively and negatively challenging the assumptions.

Each scenario—optimistic, most likely and pessimistic—results in an operating profit forecast that corresponds to a plausible outcome within the market. Figure 1 shows a graph of the three operating profit scenarios as a cone of uncertainty, representing the range of variation of future events. There are also different scenarios for the launch cost. Table 4 provides the complete optimistic and pessimistic business case scenarios.

Calculations for optimistic and pessimistic project NPV values are $2,099M and ($1,568M) respectively. Given the wide disparity between the outcomes of the two scenarios with their respective contingencies, we understand there is substantial uncertainty in this business case. Clearly, the optimistic scenario has a significant profit opportunity. On the other hand, the pessimistic scenario forecasts market and engineering situations that result in substantial losses.

Although there is only a 10 percent chance of either scenario occuring, this additional information doesn’t provide any more clarity on whether senior management ought to commit the $75M R&D investment. What does become apparent, however, is that in the optimistic scenario, it is worthwhile in Year 3 for management to commit the one-time launch cost of approximately $2B. On the other hand, in the pessimistic (and the most likely) scenario, management should consider abandoning the project at Year 3, or at least delay committing the launch cost, to avoid substantial losses.

Which scenario will manifest itself will only become apparent by committing the upfront R&D investment and initiating the preliminary engineering and marketing activities. By Year 3 management will have obtained the information necessary to make a better decision. We will see how option analysis by Monte Carlo simulation does blend these three scenarios to provide the investment information management seeks.

Table 3.—Variables for Various Scenarios

table 3 border=0

“What-If ” Multi-Scenario Modeling

Just as Monte Carlo simulation technology at Boeing extends the ability to investigate “what if ” scenarios on matters of engineering concern where there is large uncertainty (such as performance, quality and operating stability), this same technology can be applied to scenarios for price, unit sales and cost for the air freighter business case. In fact, the term “business engineering” can be applied to the more advanced models, which combine both the business and engineering aspects of a project. Monte Carlo simulation offers the ability to incorporate into the analysis hundreds of scenarios, including those that are plausible albeit lower probability, but potentially consequential to the outcome of the project such as the optimistic and pessimistic scenarios (see Table 5).

We can develop a valuation approach that effectively uses this technology and provides a more useful estimate for the project than the NPV multi-scenario approach. The estimates of the annual operating profits of the three scenarios can be interpreted as representing the corners of a triangular distribution (2). Using Monte Carlo software, it is relatively straightforward to construct a range forecast triangular distribution for each year of the operating profit forecast. The annual values for the minimum (pessimistic), most likely, and maximum (optimistic) parameters form a triangular distribution range forecast for each year as shown in Figure 2. Similarly, the Year 3 launch cost also can be presented as a triangular distribution.

When the model is simulated, the Monte Carlo makes successive random draws of values, or “what-ifs,” from the annual operating profit and launch cost distributions. The simulation of successive random values is an emulation of the range of values of scenario forecasts, each with variations of the project assumptions. The Monte Carlo simulation generates a succession of “what-if ” net profit scenarios (a minimum of 500 draws or “trials” is recommended), each of which is valued using NPV mathematics, and is treated as a plausible cash flow forecast.

Figure 1

Figure 1.—Three operating profit scenarios are envisioned.

Table 4.—Optimistic and Pessimistic Business Case

table 4 border=0

Datar–Mathews Real Option Valuation Model

The relatively recent (2001) Datar–Mathews option pricing model attempts to provide a more transparent and intuitive approach to valuing project options. The D–M Method (U.S. Patent 6862579, © Boeing), as it is called, can be understood as an extension of the NPV multi-scenario Monte Carlo model with an adjustment for risk-aversion and economic decision-making.

The D–M Method uses two discount rates:

1. rp = 15%, the hurdle rate, for the project operating profits, those cashflows that are at market risk.

2. rf = 5%, for investments that are relatively secure and over which the corporation has fairly extensive control, such as the launch cost.

In advanced financial analyses, it is fairly common to discount various cash flows in accordance with the risk to those cash flows. The differential discount rate implicitly allows the D–M Method to correctly ‘risk-adjust’ the project value, accounting for the differing risks (3) within the project. The operating profits and the launch cost distribution ranges are both simulated with Monte Carlo, and discounted to Year 0. The net profit is the difference between the two discounted cashflows (OperatingProfits − LaunchCost). The result is the Year 0 net profit present value distribution (histogram) for the hundreds of cash flow scenario trials shown in Figure 3.

The project manager must be financially rational for the investments in the air freighter project (see Figure 4). The Terminated Outcomes section on the left tail of the present value distribution represents those scenarios in which the discounted launch cost is anticipated to exceed the operating profits. In these instances of negative net profit, the rational choice is to avoid potential substantial losses by terminating the project. The effect is as if operating profit and launch cost cash flows were zeroed out for these scenarios. On the other hand, the solid section on the right tail of the present value distribution indicates a successful project forecast. The right tail corresponds to the 32 percent of scenarios with a positive NPV outcome where the discounted operating profits exceed the launch cost.

The real option value can be understood as the average of the appropriately discounted Year 0 net profit, contingent on terminating the project if a loss is forecast. The payoff distribution illustrates that 68 percent of the scenarios are terminated with zero cash flow, while the remaining scenarios yield a range of positive net profits (Figure 5). The real option value, which is easily generated by the Monte Carlo software, is the average value of this payoff distribution, approximately $113M in this example. This value is the best estimate today of the discounted future expected net profit, conditional on rational decision making at the time of launch.

The $113M option value is the maximum amount the company would be willing to pay today for the opportunity to participate in the air freighter project. The company could choose to invest the total amount or a portion into its R&D effort. The engineers and marketing analysts are requesting authorization to spend $75M in R&D expenses over the next three years. Based on the real option value of the business prospects, management has the justification to invest in the freighter project. The real options approach delays the “go forward” or “terminate” decision until Year 3, when there is more information and a better decision can be made. Furthermore, it appears that management can purchase the freighter option ($75M) for less than its calculated value ($113M), an immediate boon to the shareholders.

Table 5.—Three-Scenario Monte Carlo Setup

table 5
Figure 2

Figure 2.—Monte Carlo range forecasts are fitted to the optimistic, most likely and pessimistic scenarios: top, middle and lower curves, respectively.

Figure 3

Figure 3.—Year 0 net profit present value distribution.

Figure 4

Figure 4.—Year 0 risk-averse rational decision distribution

The formal calculation of the real option value is done using the Boeing Datar–Mathews Method (4). The spreadsheet D–M Method formula is as follows:

The formula, which is a combination of Excel and Monte Carlo functionality, captures the intuition described above. The overscore bar in the equation represents a distribution—formally a random variable—of the discounted cash flows at time 0. The “operating profits” and “launch cost” are the present value distributions. The payoff distribution is created by simulating several hundred scenario trials, and calculating the MAX value, with a zero threshold for terminated projects representing no cash flow. The option value is the mean value of this payoff distribution.

An intuitive understanding of real options is useful during strategy discussions. An estimator for the real option value can be expressed as a function of positive NPV project outcomes in the following formula:

For example, in Figure 4 the risk-adjusted probability of positive NPV forecast is 32%, and the appropriately discounted mean net profits value (operating profits − launch costs) of the successful outcomes is $0.35B. Using these values in the above formula produces a real option value of the project given its contingencies:

A real options approach gives management the justification to commit a contingent strategic investment in technology, engineering and marketing R&D prior to the launch. These funds will enable the engineers and marketing analysts to advance the air freighter project to a state of readiness in preparation for the launch decision, while effectively reducing the uncertainty of that decision. Contrast this result with that of the NPV (a negative $187M) approach that would terminate the project even before initiating the R&D effort (5).

Real options methods work for strategic decisions because of their ability to simplify and manage complex investment problems, such as those at Boeing. The D–M Method has been used to get a better sense of value on some of Boeing's largest projects to date. A simplified version (see “Range Options,” next page) is the basis of value assessment for a portfolio of early-stage innovative business opportunities in one division of the company. Generally, it is not possible to know all of the potential factors that might affect the outcome of such investment. But it is sufficient in an uncertain environment to bound the problem, yet remain confident in the decision-making process. By acquiring the initial resources and information necessary for informed decisions, real options allows us to make better decisions at a future date while concentrating scarce investment resources on those truly promising opportunities. Real options thinking is an approach to project planning that extends the investment and risk modeling tools and methods to provide engineers with a solid financial economic construct to incorporate into strategic thinking and contingency planning.
Figure 5

Figure 5.—Year 0 payoff distribution.

Range Options: Option Values without Simulation

In very new business ideas we still would like to calculate an approximate real option value even though there has not been sufficient time or resources to gather the necessary quantitative information required for a complete cash flow simulation. An approximate option value can be estimated simply using range estimates of the present values of operating profits and launch costs.

Assume we are able to estimate the present value (PV0) of the operating profits and launch cost ranges (pessimistic, most-likely, and optimistic: Min, ML, Max, respectively), correctly observing the differential discount rates. In Figure 6A, below, two triangular distributions have been constructed from the present value ranges, one for the operating profits and the other for the launch cost. I shall illustrate this example using the approximate values from the preceding air freighter case.

The real option value is the expected value of the mean of the tail of a net profit distribution. The net profit distribution is the difference between the operating profit and the launch cost distributions. Assuming that the operating profits and the launch costs are independent (as are most business cases), we can approximate the magnitude of the launch cost by “collapsing” the triangular distribution to its mean value, a determined or “scalar” value. The imputed value for the net profit distribution is then calculated as the operating profit distribution minus the launch cost mean value shown in Figure 6B.

The real option value is calculated as the mean of the right tail (i.e., those values greater than zero) of the net profit triangle, times the probability of the right tail. The Table below provides the formulas for the mean and probability of a simple right triangle tail. (Other types of triangular sections, such as left tail quadrilateral, require somewhat more calculation effort.)

The range option value is a good approximation of true value of the business opportunity. The range option value will never quite equal that of a correctly calculated real option owing to the asymmetric nature of option calculations that are only fully captured with a simulation. However, the result is a real option value derived from simple range estimates of early-stage project operating profits and launch cost.—S.M.

Figure 6a Figure 6b

Figure 6A.—Present Value Distributions.

Figure 6B.—Range Option Concept.

Figure 6

Strategic Thinking and Contingency Planning

Much of the worth of real options resides not in the actual calculation of the option value, but rather in what is termed “real options thinking.” That is the application of real options logic without necessarily carrying out the detailed calculations. Savvy Boeing managers conduct their project management using processes and planning remarkably similar to real options thinking. In addition, when they articulate the challenges of the project using the language of real options, they provide structure for scenario and strategy discussions. The real options planning approach of a phased series of incremental risk-averse investments linked to the probability of a successful outcome contrasts with that of NPV-driven planning, which tends to commit large dollar amounts up front to a single course of action.

In the technology world, here are a few rules of thumb when we ought to apply real options thinking:

  • Uncertainty is large enough that it is sensible to wait for more information.
  • Uncertainty is large enough to make flexibility a consideration.
  • The investment decision is contingent on material assumptions or events.
  • The technology or product profitability is not in the current offering, but a future extension or derivative product where there are possibilities for future growth.
  • Project updates and mid-course strategy corrections are anticipated.

The real option-driven approach to project planning is tied to two key factors: an initial investment directed to reducing uncertainty followed by a contingency-based course of action. The first factor involves targeting of small investments toward engineering and marketing risk abatement initiatives prior to the launch commitment. As a result, at the downstream decision point of the irreversible launch investment, the project manager will be able to better determine which project scenario (optimistic, most likely, or pessimistic) is being borne out in reality.

Once the path or scenario is identified, the second factor is a contingent course of action associated with the scenario that preserves the original intent of the option valuation (see Table 6). If the pessimistic scenario is actualized, the manager can conserve the substantial launch cost investment, terminate the project immediately, and perhaps sell off any derived patented assets. If it is the optimistic scenario, the manager can invest the launch cost and garner the expected operating profits. If the actuality is the most-likely scenario, the manager may determine that it is worthwhile to delay the launch, and perhaps invest additional R&D funds to preserve the opportunity while also attempting to reduce the uncertainty further in order to make a clear decision later.

Table 6.—Course of Action, Contingent on Scenario Actualized at Launch Date

table 6 border=0

References

1. In most corporations, business cases applying NPV analysis typically will use, given a list of assumptions, the most-likely (technically the mode of the distribution) values estimates for cost, market price and volume, etc. However, NPV analysis correctly should use the mean value estimates. The difficulty is that most corporations do not have easy access to a sufficient quantity of historical actuals from which to derive a mean value. Additionally, by definition a new technology has no historical actuals.

2. Most risk distributions are skewed, including the triangular distributions used in the case. A skewed distribution captures the risky project concept of a low-probability but high-consequence phenomenon. Distributions other than triangular can be used. A lognormal distribution, used in formal options theory, is a type of skewed distribution, but its defining parameters, such as mean and standard deviation, are more difficult to determine in the context of standard engineering and business practices. The easily comprehensible parameters Max—Most Likely—Min that define a skewed triangular distribution can more or less approximate the more formal lognormal distribution without material impact on decision outcomes.

3. Note that the risk adjustment is the result of differential discounting, effectively shifting the relative values of the operating profit and the launch cost distributions discounted to Year 0. The launch cost cash flow is more highly valued, and therefore discounted at a lower rate, because it represents “cash on hand,” versus the operating profits that are anticipated but not guaranteed. This natural risk-averse perception of our world is captured in the adage, “A bird in the hand is worth two in the bush.”

4. The Datar-Mathews and the well-known Black-Scholes option methods are mechanically different representations of the same underlying economics, and, given the same constraints, calculate the same option value. The D-M method provides a better estimate of option value when the strict theoretical assumptions of Black-Scholes are compromised in real life. For example, the D-M method can easily deal with non-lognormal (such as triangular) cash flow distributions and a launch cost that is a range rather than a scalar value. More detail is provided in Chapter 43 of the forthcoming Handbook of Technology Management.

5. Distinguishing between strategic and tactical investment decisions provides a further rationale for using real options. Strategic decisions are risky because the investment resources are committed up front while the outcome benefits are far from certain. Having the option to cancel the project, if warranted, significantly reduces the corporate exposure to the tactical launch investment decision risk. This risk-lowering option practice enables companies to take on smaller, higher-risk but potentially higher-return projects while maintaining fiscal responsibility. In comparison, tactical decisions are made by fully committing whatever resources and information are on hand at the decision moment. For example, the launch commitment at Year 3 is a tactical decision, where the substantial launch investment is irreversible.

It is worthwhile to point out a subtlety about the financial risk of the project—there is no guarantee of positive net profits. The purchase of an option is a strategic decision, such as investing in R&D, which permits preliminary participation in a business venture that can be reevaluated later. A real option valuation does not preclude conditions at launch time from changing, necessitating a re-valuation of the prospective project profitability, or that the launch decision will be financially risk-free. Exercising a real option on a project nearly always exposes management to the subsequent tactical decision of whether or not to invest the significant launch costs in the risky underlying project/product asset. In contrast to a real option, when exercising a financial call option, the owner can eliminate the tactical risk of possessing an asset that might decline in value by using a so-called “cash settlement” on the exercise date (by simultaneously selling the equivalent shares of stock).

It is a tactical decision whether or not to “exercise” the project option and commit the substantial launch investment. An NPV analysis of the business case at the launch decision date can evaluate the proper conditions to exercise the option, i.e., the prospect for positive net profits with an appropriate discount rate to account for the risk. However, the evaluation does not preclude the possibility for conditions to change at a future date (perhaps an unanticipated souring of the air freighter market), and eventually result in an overall profit loss.

To Learn More

Mathews, Scott H., Datar, Vinay T. and Johnson, Blake. 2007. A Practical Method for Valuing Real Options. Journal of Applied Corporate Finance, Spring (19), No. 2, pp. 95-104.

Mathews, Scott H. and Salmon, Jim. 2007. Business Engineering: A Practical Approach to Valuing High-Risk, High-Return Projects Using Real Options. Tutorials in Operations Research. INFORMS.

Websites

Annual International Conference on Real Options: Theory Meets Practice. www.realoptions.org  The most important annual event on real options, organized by Real Options Group. A great collection of important papers to download from current and past conferences makes this website one of the main references for real options researchers and practitioners.

Investment Science. The purpose of this site is to promote and discuss modern investment analysis, ideas and techniques as applied to the pricing and management of real assets, or what has come to be known as Real Options. By Prof. David G. Luenberger of Stanford University's Department of Management Science and Engineering. www.investmentscience.com. See especially this site which discusses The Two-Rate Method of Discounting: http://investmentscience.com/Content/newsArticles/news3.html

Luehrman, Timothy A. His series of articles in Harvard Business Review presents a framework that can bridge the gap between the practicalities of real-world capital projects and real options for the general business audience. What's It Worth?: A General Manager's Guide to Valuation, May 1997; Investment Opportunities as Real Options: Getting Started on the Numbers, July 1998; Strategy as a Portfolio of Real Options, September 1998.

Real Options: Managing Strategic Investment in an Uncertain World. A website that supports the book of the same name. Extensive references. www.real-options.com