The Case for Real Options Made Simple

VOLUME 19 | NUMBER 2 | SPRING 2007

APPLIED CORPORATE FINANCEJournal of

A M O R G A N S T A N L E Y P U B L I C A T I O N

In This Issue: Valuation, Capital Budgeting, and Disclosure

Enterprise Valuation Roundtable Presented by Ernst & Young

8 Panelists: Richard Ruback, Harvard Business School;

Trevor Harris, Morgan Stanley; Aileen Stockburger,

Johnson & Johnson; Dino Mauricio, General Electric;

Christian Roch, BNP Paribas; Ken Meyers,

Siemens Corporation; and Charles Kantor, Lehman Brothers.

Moderated by Jeff Greene, Ernst & Young.

The Case for Real Options Made Simple 39 Raul Guerrero, Asymmetric Strategy

Valuing the Debt Tax Shield 50 Ian Cooper, London Business School, and Kjell G. Nyborg,

Norwegian School of Economics and Business Administration

Measuring Free Cash Flows for Equity Valuation: Pitfalls and Possible Solutions 60 Juliet Estridge, Morgan Stanley, and Barbara Lougee,

University of San Diego

Discount Rates in Emerging Markets: Four Models and an Application 72 Javier Estrada, IESE Business School

Rail Companies: Prospects for Privatization and Consolidation 78 James Runde, Morgan Stanley

A Real Option in a Jet Engine Maintenance Contract 88 Richard L. Shockley, Jr., University of Indiana

A Practical Method for Valuing Real Options: The Boeing Approach 95 Scott Mathews, The Boeing Company, Vinay Datar,

Seattle University, and Blake Johnson, Stanford University

Accounting for Employee Stock Options and Other Contingent Equity Claims: Taking a Shareholder’s View

105 James A. Ohlson, Arizona State University and

Stephen H. Penman, Columbia University

38 Journal of Applied Corporate Finance • Volume 19 Number 2 A Morgan Stanley Publication • Spring 2007

The Case for Real Options Made Simple

by Raul Guerrero, Asymmetric Strategy

he stock in trade of fi nancial analysts is ultimately their intellectual capital: industry knowledge and company specifi cs, to be sure, but also strategy and marketing frameworks and fi nancial tech-

niques. Keeping up with new approaches is an important part of the analyst’s job, and presumably each analyst makes a personal calculation of costs and benefi ts when choosing which new ideas to invest in. My work with clients suggests that the costs and benefi ts of learning to apply real options analysis (RO) are not well understood, and that this is keep-ing some analysts away from a technique that could help them argue and analyze their cases more effectively.

Some analysts seem to believe that the main benefi t of RO is “more accurate valuations,” and that the cost is “lots of math.” The goal of this article is to give you a different perspective. The benefi ts of RO are different and more far-reaching; the costs are less than you might expect. On the benefi t side, I will briefl y argue that RO is critical to align-ing the words and the spreadsheets of fi nancial analysts, and is an important extension of discounted cash fl ow analysis (DCF) that is unlikely to fade away. I will spend more effort on the cost side, which unfortunately has come to dominate the discussion of RO. It is not widely appreciated that 90% of any RO problem can be implemented and communicated effectively without diffi cult math by explicitly separating the expected value and discount rate calculations.

Figure 1 shows the approach that my colleagues and I have found works best for presenting the benefi ts and costs of RO. In this article, I focus on the fi rst loop in Figure 1, which is the minimum level of detail that will allow you to use RO to reach easy-to-communicate quantitative results. This fi rst loop deals mostly with foundation concepts that are common to DCF, but that are often skipped over, perhaps in a rush to get to the material that is unique to RO. Of the four building blocks shown in Figure 1, you will likely have been exposed to the fi rst three in MBA fi nance courses that covered DCF. My observation, however, is that this material does not sink in, and taking it for granted as a foundation for RO is generally a mistake. The good news is that if clients buy into this fi rst loop, they tend to accept the textbook answers

for the proper discount rate and for how to handle potential problems. For the newcomer to RO, loop one is the most important area to focus on; for the experienced user, loop one is still the best place to look for ways to improve your communication with clients.

A First Look at the Benefi tsFlexibility is an important aspect of corporate action that is not well modeled by traditional fi nancial tools. Crafting an effective strategy typically has two critical, but in some ways confl icting, objectives: making the most of what a company is, and preparing for what it can be.1 As explored in business bestsellers such as Built to Last and Built to Last and Built to Last The Innovator’s Dilemma, satisfying both the focus and the fl exibility mandates of strat-egy creates tension within companies, since they may require different capabilities, organizational structures, and cultures. The job of corporate managers is to strike the optimal balance between these two goals; the analyst’s job is to assess manage-ment’s effectiveness in achieving that balance. Both need a common measuring stick to weigh one mandate against the other, and both face the challenge arising from the differ-ences between them.

In particular, preparing for the unknown future involves adapting to that future as it unfolds. The analyst’s toolkit adapting to that future as it unfolds. The analyst’s toolkit adaptingcontains many qualitative descriptions of this adaptation, all of which implicitly follow an “if/then/else” structure. For example, an analyst might want to discuss the fast-follow-ing capability of a consumer electronics fi rm. Using words, she will argue that if the leader in a new product category meets with success, then the follower will enter (perhaps based on a proven ability in designing around patents); otherwise (else) the follower will do nothing and so avoid investing in a market that did not take off. Traditional DCF cannot refl ect this if/then/else structure of decision-making, but RO can.

RO belongs in the analyst’s toolkit for three reasons. First, it allows the spreadsheet to refl ect the story the analyst intends to tell. Second, it allows the analyst to make quantitative judgments about growth opportunities while still remaining in the apples-to-apples world of fi nancial analysis. Despite the differences and tension between the two types of strategic

T

1. Marcus’s Big Winners and Big Losers (Wharton School Publishing, 2006) presents an excellent discussion of this split and includes an interesting appendix that summa-rizes which side of this divide many popular management books emphasize.

39Journal of Applied Corporate Finance • Volume 19 Number 2 A Morgan Stanley Publication • Spring 2007

action (focus and fl exibility), we can assess and comment on them both using a common measure as long as we use fi nancial tools (DCF and RO) that refl ect their key features. 2

Third, RO is a gateway technique for new directions in fi nan-cial valuation. As Robert McDonald argued in this journal a year ago, 3 RO simply adds a responsive, dynamic invest-ment approach to DCF. In the pages that follow, I promise to review exactly what that means. For the moment, the point to absorb is that RO is just DCF plus learning and responding. In the knowledge economy, what could be more important for an analyst to grapple with than strategic learning? RO is not another fad that you can choose to take or leave; rather it is an important extension of DCF that incorporates a simple model of learning. Anything that might eventually supplant RO—say, a better model of strategic learning—would almost certainly draw heavily on its foundations.

How Much Effort Will It Cost You? How much does the analyst need to know in order to start using RO right away? Our work with clients suggests there are four conceptual hurdles to clear:

1. Recognize what a traditional DCF implies for capex spending.

2. Accept the necessity of probabilistic modeling.3. Understand the concept of running value.4. Match smart capex decisions to related benefi ts.

Table 1 presents an overview of the issues that my

colleagues and I typically face when working with equity analysts and corporate decision-makers.

These are for the most part simpler concepts than those that are typically explored in depth in most RO articles. This more practical focus is made possible by a strict separation of the calculations of the expected value of strategic action and the discount rate appropriate for that action. Everything you would like to say about a company is part of the expected value discussion, and the four steps above are almost exclu-sively focused on that effort. The discount rate can be set aside as a separate, fi nal step. Using this approach, analysts can convincingly argue their investment thesis to a client, working sequentially through the steps above. I can also offer you an important bonus for working through the steps proposed: steps one through three apply equally to traditional DCF and to RO. Your investment in thinking through these issues will pay a dividend in the form of a sharpened under-standing of DCF, regardless of whether you take the step toward RO or not.

Building Block 1: Recognize What a Traditional DCF Implies for Capex SpendingThe fi rst building block demonstrates why a tool like RO might be needed. Implicit in every traditional DCF analysis is the assumption that the capital expenditure schedule is fi xed at time zero and never deviated from again.4 Consider this assumption in the case of building out telecommunications infrastructure. Let’s assume you are analyzing a company

2. Alternately, analysts can use scorecard-based tools to discuss strategic options. This approach is rich in detail but suffers from its inability to deliver a dollar value that can be compared to the output of a DCF valuation.

3. Robert McDonald, “The Role of Real Options in Capital Budgeting,” Journal of Applied Corporate Finance, Vol. 18 No. 2 (Spring 2006).

4. In this context, capital expenditure refers to any outlay which generates future benefi ts, regardless of how it would be classifi ed for accounting reasons.

Figure 1 The Order of Presentation of the Benefi ts and Costs of RO Matters. Completing Loop One First is the Best Way to Learn and to Present RO.

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that plans to build a metro ring around a large city this year, a second ring around another city in two years, and fi nally a national ring four years from now.

If you use a typical DCF analysis, you are modeling a situa-tion where the company will invest in the second and third phases regardless of what happens between now and the physi-cal groundbreaking for those stages. The company’s investment strategy and schedule do not change with the passing of time and collection of new information. This is why professors increasingly refer to “traditional” DCF as static DCF.static DCF.static 5

Most analysts are not aware of this implicit, no-fl exibil-ity assumption in DCF analysis. It is essential for you to recognize, and communicate clearly to your own clients, that traditional DCF assumes a static investment schedule. There is no disagreement among fi nance theorists on this point. The disagreements begin only when we consider how we might change the static investment assumption, a possibility we will change the static investment assumption, a possibility we will changeexplore later.

Before you gather the fi rst input in a strategic or fi nancial analysis, it is clear that a static investment schedule will often be a poor qualitative description of how the company will manage any form of build-out. After all, what does manag-ing a build-out mean if not responding to changing cost and revenue outlooks with changes in the original plan—speed-ing up, slowing down, or canceling later phases? Of course, in some cases the analyst may believe that the probability of

things going horribly wrong or wonderfully right is small enough to ignore and that the possibility of changes to the schedule can be comfortably assumed away. It is also possible that the company can credibly commit to building all three phases in the hope of scaring away competitors. In that case, it may be smart for the company to build out, regardless of the future, in order to build a reputation as a tough competi-tor. If one of these two cases is what you intend to model, then DCF is the right tool.6 If not, you must be aware that your analysis is built on the premise of an unchanging invest-ment schedule—an assumption that could have a signifi cant impact on value.

As a test, you can ask yourself how a large investor would react to a defi nitive statement from management that the original capex plan will be adhered to regardless of future developments. Which type of investor would never accept this pre-commitment from management? A Venture Capitalist. An investor in bio-tech. An investor in an innovative technology that may or may not take off. In each of these areas, the think-ing and language of if/then/else pervades all discussions.

But let me give you a more mundane example. Block-buster Video, with retail stores plus mail delivery of DVDs, and Netfl ix, the leader in mail delivery of DVDs, are now locked in a strategic battle in the DVD rental space that has yet to play out. Would an investor in Blockbuster accept a grand statement by management of an intent to “stay the

5. People writing about RO face a diffi cult terminology question. Static-DCF and dy-namic-DCF (RO) are both forms of discounted cash fl ow analysis and are probably the most descriptive terms. However, using the term “static-DCF” can make the reader think I am referring to something other than what they do every day. Therefore, in this article whenever I use the terms DCF or traditional DCF, I mean static DCF. When I need to point out the commonality between static and dynamic DCF, I write out discounted cash fl ow analysis.

6. A third possibility is that the company may lack the political will to cancel a high-profi le project. These are non-trivial concerns and major areas of research. My point is only that the analyst should decide what he believes, then attempt to refl ect those beliefs properly in the fi nancial analysis.

Building Block

Issue Raised by Clients Quick Answer

1 How come no one ever pointed out to me before that DCF assumes a static investment schedule?

No reason to raise this issue too loudly unless you are prepared to discuss the “fi x,” which is RO

2 Why should I bother to use probabilistic modeling when DCF doesn’t require it?

DCF uses the same machinery, but hides it in the discount rate calculation

2 Now that I’ve written down my distribution, I am the fi rst one in a long line to doubt it.

You are working with the same information as with DCF, but you have made it explicit and therefore open to discussion

3 I’m not comfortable with your assumption that there will be a single best estimate available at the future decision date

There is always a single best estimate available at a given point in time, analogous to the single number output of a DCF analysis

3 I have little confi dence that my distribution today is related to what will really happen tomorrow

Some stability between forecast and realization underpins all of economics. Your discomfort may stem from not tracking what you know when. Alternately, you may be right, but then all forms of quantitative reasoning are suspect.

Table 1


course” and follow any particular investment/disinvestment schedule (Blockbuster is currently selling and downsizing some retail locations)? The answer is no. Most analysts writing about this contest are presenting it in terms such as, “… if Netfl ix achieves this, then Blockbuster will try to do that ….” The possible reactions of Blockbuster to a changing environment are central to the qualitative story the analysts are writing. No single, static course of action we can model would be consistent with the way we would write about this contest.

Building Block 2: Accept the Necessity of Probabilistic ModelingTo model the impact of a responsive as opposed to a static investment schedule, we must work with probabilistic esti-mates of future project value. The good news is that analysts already write about strategic opportunities in terms of entire projects. As can be seen in Figure 2, DCF works with the individual cash fl ows of a project, whereas RO aggregates the cash fl ows and works at the project-value level. The bad news is that explicitly modeling a distribution of project values tends to raise two issues. First, it gives the appearance that, while RO relies on probabilistic modeling, DCF does not. Second, there is a general aversion to the explicit modeling of probability distributions that the analyst must be prepared to overcome.

When you work up a DCF analysis, you probably do not sketch out little probability distributions. Although this may be partly because you are already used to working with DCF, it is primarily because the distribution is only implicitly refl ected in the discount rate. When we use Blockbuster’s beta and the Capital Asset Pricing Model to discount a particular cash fl ow of a project, we are modeling a specifi c relationship between the cash fl ow and Blockbuster’s stock (namely, that the two have the same systematic risk, as illustrated in Figure 3). The stock has a probability distribution associated with it,

and we are assuming that the cash fl ow has a related distribu-tion. Hence, if you are a user of DCF, you should feel at least some comfort in drawing probability distributions around cash fl ows. By extension, you should feel equally comfortable drawing probability distributions for project values of the kind shown in Figure 4. For the moment, hold onto the idea that DCF uses the same machinery that RO will use by the end of building block four.

The probability distributions in DCF are implicit. By contrast, the distributions of project values for RO are explicit and form a black and white target ready for critique. This invariably leads to someone questioning the reliability of the forecast. The useful question in such cases, however, is almost never “is it perfect?,” but rather “is it the best alternative?” Much of the criticism I read of explicit modeling in general and RO in particular boils down to the charge that “it’s not perfect.” The analyst must avoid framing the problem in this manner and insist on a comparison among alternatives.

What are the alternatives to the explicit modeling of distributions? In light of the fi nance 101 refresher above, we know that DCF and RO rely on similar assumptions. Hence, the analyst’s choice is between:

• staying within the cash f low framework (DCF or RO), accepting that probabilistic modeling is necessary, and working to improve the inputs, or

• leaving the cash fl ow framework altogether, perhaps

Figure 2 DCF Acts at the Cash Flow Level, While RO Acts at the Project-value Level.

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Figure 3 If We Had a Particular Use for it, We Could Draw a Distribution Around Each Cash Flow for a DCF Analysis.

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Figure 4 Graphical Representation of a Probability Distribution for Project Values

for a comparable multiples approach.You have probably experienced the following: You

carefully weigh the risks involved in a project and enumer-ate them in the research note. You consolidate them as best you can, using imperfect information and proxies, and come up with high, medium, and low estimates. Then someone says, “I just don’t believe it.” At this point, one approach is to work with the skeptic and revisit inputs and estimates. This approach has the virtue of at least holding out the potential for improving your research process. If you fi nd yourself arguing explicitly about the range of possible cell-phone penetration rates in India fi ve years from now, you are at worst asking the right questions, and at best helping your own clients frame a diffi cult data problem. Alternatively, you can leave the cash fl ow framework and use another tool—P/E ratios, for example. But this choice comes with its own set of costs and benefi ts. In general, ratios offer simplicity in return for far less depth of analysis.

So what if you or your client lives in the P/E ratio world, where probability distributions only rarely visit? There are two kinds of P/E (or similar ratio) users. The fi rst essentially believes that next quarter’s or next year’s earnings drive a company’s stock price. The second uses ratios as a kind of shorthand DCF. RO has something to offer the latter. The shorthand-DCF user attempts to refl ect earnings beyond the next year in his choice of the target P/E ratio. For example, an analyst who claims that Blockbuster’s medium-term competi-tive position is improving and therefore raises his P/E target is working in the shorthand mode. This type of analyst already

attempts to refl ect strategic value in his choice of P/E, and “real options thinking” may sharpen his ability to set the right target ratio. The best analysts I know in the shorthand-DCF tradition, however, follow Pablo Picasso’s example; that is, they learn to draw like everyone else fi rst, and only then move on to their own individual styles. 7 I believe that some analysts have internalized DCF well enough that they can confi dently translate a qualitative statement such as “Block-buster is getting out of poorly performing retail stores more quickly than anticipated” into an increase in P/E from 18 to 20. There is no reason why such analysts could not eventually learn to do the same with RO-based arguments. My advice to these analysts: spend some time within the classical tradition of cash fl ow forecasting fi rst.

The bottom line on building block two is this: The shift from DCF to RO does not add much of a burden as far as probabilistic modeling goes. It is the shift from a hidden, implicit distribution to a visible, explicit distribution that tends to make some people uneasy. Be prepared to argue that this is appearance, not substance, and do not accept compari-sons to perfection. The only comparisons worth making are those between workable alternatives.

Building Block 3: Understand the Concept of Running ValueIn their popular book Thinking Strategically, Avinash Dixit and Barry Nalebuff urge readers to “look forward and reason back.” That logic is the heart of the fi nal two building blocks. The probability distribution developed in step two provides the range of values to look forward to, but in order to break into that distribution we must rely on the concept of running value.

Let’s say that in 2007 we have estimated a probability distribution for the developed value in 2010 of a parcel of raw land. To be more precise, the distribution is an estimate of the 2010 value that is based on the information available in 2007. When we actually get to 2010, one of two things will happen. First, we may sell the land or otherwise be able to get several quotes for the value of the land. In that case, it is clear that we will observe a value in 2010. Second, we may not be able to get observe a value in 2010. Second, we may not be able to get observea market quote, but we can still value the land in 2010 using static DCF. In that case, we “observe” an estimate of the value of the land. Note that this would be an estimate of the 2010 value of the land based on the information available in 2010. As discussed below, this estimate is a number, not a distribu-tion. As we travel in time from 2007 to 2010, we learn more and more about the 2010 value of the land, and our probability distribution eventually shrinks to a single value.

That is all well and good, but we cannot wait three years to observe our valuation. Instead, we carry out a thought

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7. Picasso famously claimed, “When I was twelve I could draw like Rafael, but it has taken me my whole life to learn to paint like a child.”


experiment in 2007. We look forward to 2010, and imagine observing a value for the land then. How much do we expect the developed land to be worth at that time? Having created the probability distribution in 2007, we already have our answer. We expect the value to be one random draw from that distribution. Each individual draw is a running best estimate of value.8

Of course, there is nothing special about any particular draw. We must repeat this process a large number of times, using a Monte Carlo simulation enginer, to pick many draws of the running value. The results of a simulation only have meaning in the aggregate, and the fi rst step to using this tool is to become comfortable with the aggregate of the project value. As Figure 5 shows, if we start with a distribution, draw individual values from the distribution, repeat many times, and aggregate the results, we simply regenerate the original distribution. In building block four, we will do something much more interesting. We will learn how to “break into” the distribution to change it to account for responsive (i.e. dynamic) investment decisions.

There are two issues that come up at this stage. First, analysts are sometimes distracted or confused by the argument that a single best estimate of project value will exist in the future. Second, clients ask about the relation-ship between the forecasts of running value (the draws

from the distribution) and the subsequent realized running values.

Even with traditional DCF valuations, some analysts want to continue to show that they are uncertain about their valuation after all of the modeling is complete. They would like to show an entire distribution of time-zero values, for example, as an explicit way of reminding their clients of the uncertainty that surrounds their fi nal answer.9 Since they do not fully accept the existence of a best estimate of value at time zero, they naturally resist working with forecasts of future best estimates. Recall, however, that although we speak loosely of discounting cash fl ows, we are really discounting the expected value of a cash fl ow distribution. Discounting with a risk-adjusted rate effectively transforms a future cash fl ow distribution into a future cash fl ow distribution into a future present (time zero) present (time zero) presentvalue—that is, a single number, not another distribution.10

The single number output of a model is never meant to represent certainty, and it should always be interpreted as a best estimate of value based on imperfect inputs. This issue matters in the current context because we will soon try to compare a capex cost to a project benefi t and, when so doing, we will want to compare one number with another, not a number with a distribution.

When clients express discomfort with putting their probability distributions to work by sampling running values from them, they typically have a vague notion that forecasts may not prove very accurate after the fact. The poster child for the difference between forecasts of running value and subsequent realized values is sildenafi l citrate, the angina drug that became Viagra in 1998. Analysts who valued sildenafi l in 1996 presumably had probability distri-butions in mind for the value of the drug as, say, an angina treatment ten years later. After the fact, these forecasts proved to be much too low. Doesn’t that suggest that those 1996 analysts did something wrong? No. Valuation is about calculating the fair value of an investment, conditional on the information that is available at the time of the analysis. Analysts are always striving to have more information than the market; but if the information does not yet exist, neither the market nor the analyst can have it. Therefore, we cannot fault the sildenafi l analysts; they were calculating reasonable estimates of value given what they knew in 1996. Remember that, even when we are thinking about values ten years out, our ultimate goal is to get a valuation today, and we can only

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Figure 5 Clients Often Find it Useful to Think Their Way Around the Circular Logic from Distribution to Individual Draws to the Collection of a Large Number of Draws.

8. As I am using it, this concept is close to, but not exactly the same as Luenberger’s running present value (Investment Science, Oxford Press, New York, 1998 pp 88). We are both concerned with the distribution of possible present values at time T, conditional on the information available at time 0. Running present value is the expectation of that distribution. My running value is a random draw from the same distribution.

9. I have actually never worked with anyone who believes the result of a valuation is precise, but Aswath Damodaran believed it was enough of an issue to list his Myth 3: “A good valuation provides a precise estimate of value” (Investment Valuation, Wiley, New York 1996 p.3), and added that analysts, “have to give themselves a reasonable margin for error in making recommendations on the basis of valuations.” Point taken, but the margin of error is much better understood as a shift down from the best estimate, not a

distribution around it. More subtle, the analyst should always be aware of what is inside his modeling technique and what is outside. Discounted cash fl ow approaches yield single numbers for time 0, not distributions, and a safety margin would be outside of the model.

10. Brealey and Myers, Principles of Corporate Finance, 5th edition, (McGraw-Hill page 255). You can discount a set of simulated future cash fl ows with a riskless rate to get a time zero distribution. You can then use the market price of risk to reduce that distribution to the same single best estimate you would get with the usual discounting approach. In this case all you have done is separate the time value of money calculation and the risk calculation.


work with the information available today.11

The challenge of forecasting is certainly not unique to RO. But more than in DCF, and much more than in the use of P/E ratios, RO does rely on explicit statements about possi-explicit statements about possi-explicitble future outcomes. This is why the analyst who wants to use it must be prepared to address the various issues raised in the fi rst three building blocks. As I have already argued, however, the worst thing that happens when someone disagrees with an explicit forecast is that you gain a new data point. Also, you might take heart in knowing that you are not the fi rst professionals forced to rely on diffi cult-to-forecast, explicit probability distributions. Some equity and derivative traders have relied on these tools for decades, and quantitative hedge funds are the latest high-profi le group to take up the challenge of probabilistic modeling.

Building Block 4: Match Smart Capex Decisions to Related Benefi tsWe are now ready to return to building out telecoms infrastruc-ture in a responsive manner. Figure 6 shows the state of play, through the fi rst three building blocks, applied to the analysis of the telecoms build-out. To apply the fourth and fi nal step, we ask ourselves, for each draw, will the company continue with the project? If the draw of the probability distribution exceeds the

capex cost, we model going ahead with the project by count-ing the operating profi t and the capex. If profi t does not exceed capex, we model not going ahead with the project by record-ing zero for the capex (we chose not to invest) and zero for the related profi t (see Figure 7 for an illustration).

After just a few times doing this exercise, it is clear that this particular form of strategic fl exibility allows you to cut off the lower tail of the distribution. That is the net effect of modeling the capex schedule in a manner that is respon-sive to the future conditions. At fi rst this can have a feel of assuming that you win every time, but this is not the case. All this process does is to refl ect a new and entirely plausible assumption that at the future decision date, the corporate manager will choose not to proceed with those projects that look bad to her at that time.

We can draw on the earlier discussion of information to get a better handle on what Figure 7 does and does not say. We will need a set of dates in order to keep the information content straight, so let’s assume that time zero is June 2007 and that the go/no-go decision for the build-out of the second metro ring will be made in June 2009. We split the discus-sion up into three pieces, based on what we know at three different points in time.

Figure 6 Preparing to Apply the Final Step for Calculating the Expected Future Value of a Responsive Decision.

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11. I am fi nessing a subtle point here. Some “known-unknown” information must account for the spread of the future project values. Otherwise, the ten-year-out forecast would be a number, not a distribution. What we are really talking about assuming away here are “unknown–unknowns.” To draw the analogy to stock prices, we don’t know what the value of IBM stock will be in three years, but we do have some confi dence that it will

be within a certain distribution which captures known-unknowns. We assume nothing completely unexpected will occur to IBM stock—i.e., we ignore unknown- unknowns. There is scant economic machinery for dealing with unknown-unknowns. Lest you con-fuse the source of the terminology (!), the reference is Wideman, R.M. 1992 Project and Program Risk Management, Project Management Institute, Newton Square, PA.


Figure 7 When We Apply Responsive, Probabilistic Thinking, the Net Result is to Shift the Operating Profi t Distribution Down by the Cost of Capex and to Cut Off the Outcomes Below Zero.

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Part 1: Based on Information Available in 2007As we have already discussed, if we want to value the second stage today, we must assume that no major unanticipated information arrives between 2007 and 2009. In this case, we can estimate the probability distribution for 2009 values and apply RO. Note that this is exactly the same assumption we would have to make to use DCF (made explicitly) or PE ratios (made implicitly).

Part 2: Based on Information Available in 2009Unexpected new information may arise between 2007 and 2009. We may fi nd gold while we are digging the tunnels for the fi ber optical cable, or we may discover an archeologi-cal site that prevents further development. Regardless of the actual outcome, we can make a good assumption about how managers will act: they will build out the metro ring if the 2009 present value of operating profi ts is greater than the 2009 capex level. That is all that cutting off the tail of the distribution signifi es: the company will not press ahead with a money-losing project. If we wanted to, we could make differ-ent behavioral assumptions. We could assume the company builds out regardless of the value and cost estimates in order to gain a reputation for being a tough competitor, or owing simply to managerial inertia or empire-building. Both of those are valid modeling choices that DCF handles well, but they are not what analysts typically intend to refl ect in their analyses.

Part 3: Based on Information Available in 2011It is entirely possible that bad news arrives after 2009 and makes the second metro ring lose money, after the fact. This would mean only that the company made a good decision in 2009 that did not work out. Investment decision-making is probabilistic in nature, and there is always the chance of an undesirable outcome from a reasonable bet. This is a further reason why truncating the distribution in RO in no way implies that the company always wins with its investments.

The infrastructure example holds one more lesson. Once

we assume a management team that scans the current environ-ment responsively, we lay bare interesting operational questions that analysts should address. For example, would the company consider building the national ring without the second metro ring, or visa-versa? The possible combinations quickly add up, especially if the company is actually planning to build a larger number of metro rings. If the company announced fi ve metro rings plus a national ring, the number of possible combinations of yes /no (e.g. build three metro rings and not the national, build just the national, etc.) quickly gets unwieldy (2^6 = 64 combinations). Complexity is part of the reality of business, but the analyst should feel no obligation to mechanically discuss all 64 combinations. In fact, part of his value added is to help his client reduce that complexity (say, through an observation such as, “it is hard for us to believe that the company can succeed in any metro market if it does not succeed in the fi rst one”). In an age when all calculations are computerized, however, there is less and less of an excuse for the analyst not to value all 64 combinations (less if there are dependencies) and then draw out interesting insights from the complete analysis.

I hope you can now see that the key step is really building block two, where we encoded all of our industry and company knowledge into the probability distribution, and that every-thing else builds from there. Estimating the center of that distribution is what analysts already do every day, so expand-ing the central value to a distribution is the part that may be a little new. Once we have the distribution, we perform the thought experiment of stepping into the future with a random draw of operating profi ts and compare that draw to the capex cost of buying those profi ts. In this way, we capture the wait-and-see nature of responsive decision-making. You may have to practice before you internalize this approach, but I hope you agree that something like what I have described is really what happens inside companies. Managers do reconsider the best information available before proceeding with build-outs, before launching product extensions, and before expanding foreign operations.


The Expected Value of the Truncated DistributionCalculating the expected value of a truncated distribution is the only mathematical challenge in the fi rst loop of Figure 1. There are at least three ways to do this.12 First, you can actu-ally use the Black-Scholes equation to get the expected value,13

but that would not achieve the simplicity we are aiming for. You can use simulation, which is the best all-around solution, or you can work with a histogram-like, discrete distribution and use pencil and paper to estimate the expected value (as illustrated in Figure 8).

It is clear that if you have a discrete distribution in front of you, you can easily calculate the “center of mass” of the truncated distribution. This works very well for simple set-ups where there is one capex cost and one source of risky operat-ing cash fl ows, a structure that will probably account for most of your early applications of RO. I prefer the paper and pencil approach for teaching clients where the numbers are coming from. For two sources of risk, and for more complicated struc-tures, however, you will have to use simulation (or a related technique) to calculate the expected value.

Let’s say you are analyzing an IT company that faces signifi cant uncertainty about both the capex cost and the value of a future phase of a project. The matching principle still works the same as described above. We draw from the capex distribution, draw from the project value distribution, and use the same go/no go logic applied above. Regardless of the complexity of the set-up, the numbers remain relatively simple since we are still using the familiar steps above, and you can show your client all or some of the draws in a spread-sheet.

As an aside, there is no better mathematical tool to intro-duce to a client than simulation. Writing in the context of portfolio construction and asset pricing, Nobel Prize winner William Sharpe uses simulation as a substitute for diffi cult math extensively and effectively in his new book Investors and Markets. For the expected value problem we face in this article, we are using it as a substitute for calculating integrals. More generally, simulation is the tool of choice for valuing the most complex fi nancial option, real option, and risk manage-ment problems.

12. A fourth would be to use binomial trees using the expected growth rate of the project instead of the risk free rate.

13. The mathematical form of the Black Scholes equation has nothing to do with fi -nance. It calculates an integral over a truncated distribution, period. I highly recommend you read the discussion in Hull about this (Options, Futures, & Other Derivatives Prentice Hall 2000 Appendix 11A in the 4th edition). I go through this with clients step by step,

because it is a great way to get comfortable with the idea that all of valuation is about calculating an expected value and a discount rate.

Figure 8 Real Option Value Comes from Cutting Off the Tail of the Distribution of Future Project Values in Order to Model Responsive Management.

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What About the Discount Rate?Up to this point, we have had no need to rely on the anal-ogy between truncated probability distributions and fi nancial options, and the word “option” has not played any signifi cant role. This is a major benefi t of splitting an RO valuation into separate calculations of expected values and discount rates. To calculate an expected value, the analyst has to address the series of conceptual issues discussed so far, but all of these are close to the core skill of analysts in aggregating indus-try and company knowledge into a forecast. Once we have the expected value, however, we cannot avoid choosing an appropriate discount rate, and to do that we do have to rely on an economic argument that ties truncated distributions to fi nancial options.

You may vaguely recall that f inancial options are discounted using the risk-free rate and that the market’s expectation of the growth of a stock does not enter into the calculation of the value for an option on that stock. This is true, but it is only half the story. In formulas and software programs, both fi nancial and real options are valued by calculating the expected value in a “risk-neutral” world, then discounting with the risk free rate. The risk-neutral world is one where all securities, be they small-cap tech stocks, utility stocks, or government bonds, earn the same risk-free return. We do not live in the risk-neutral world, but translating the problem to that set-up makes the computa-tions much easier. Many authors14 have done a very good job of explaining why this is an appropriate approach for pricing options, to which I can only add one observation: If you walk clients through the calculation of the expected value and then tell them that the appropriate discount rate is 30%, they may challenge the expected value but will usually accept your pronouncement on the discount rate.

For whatever reason, the general fi nancial community has decided that it is content to rely on specialist knowl-edge for some techniques but not others. The distinction is one between being a user and a producer. End-clients of research services are content to be users and not produc-ers of fairly complicated measures such as Value at Risk. These same clients insist on a producer-level understand-ing of valuations. Presumably, they make this choice for valuation because they have opinions about prospects for the economy, specifi c sectors, and individual companies. All of those opinions can and should be accommodated in the calculation of the probability distributions. In contrast, the industry-knowledge content of the discount rate calcula-tion is low. This may be why clients are willing to accept the opinion of an expert, the output of a software program, or even a number that is clearly ad-hoc. How many times have you seen a 30% or 40% discount rate applied in a

traditional valuation with no more justifi cation than a single line stating that bio-tech or emerging market or small cap investing is risky?

If you fi nd this discussion of discount rates not entirely satisfying, I applaud your view. Richard Shockley’s new book, An Applied Course in Real Options Valuation, and the 2006 article by Bob McDonald in this journal I cited earlier both present great next steps for you to take. Rather than attempt to reproduce their discussions in a few lines, I will instead simply jump to the answer. The appropri-ate discount rate for real options is higher than you could typically justify in a DCF. If the archetypal discount rate for DCF is 10%, the number to keep in mind for RO is closer to 30%.

To get an intuitive sense why the discount rate must be high for an option that pays off with upside potential, consider three investments—a home insurance policy, a broad index fund, and a fi nancial call option that delivers the type of truncated distribution (with the mass of the distribution above zero) that we have been discussing. Insurance pays off a lot when things look bad to us. An index fund pays off a little when things look bad and a lot when things look good, but on average it pays off about 10% when things are, well, average. Finally, we have the call option. Recall that most fi nancial investments move together, so if your call option is in the money, the other investments in your portfolio are probably also doing well. The call option pays off only when things look pretty good.

How do these payoff profi les map onto discount rates? Insurance is so valuable as an investment that we are willing to accept a negative expected return on it. That is, we really negative expected return on it. That is, we really negativedon’t expect (or hope) to recoup the value of our insurance premiums. The index pays a higher return than the insur-ance policy. Although it is natural to think of higher returns as “better,” it is just as valid to see the required return as the rate that must be paid in order to entice people to invest. In this sense, higher required return is the mark of a payoff profi le that represents a worse match with our needs. The call option pays off only when you need it least, so in order to entice you to buy this payoff, the expected return must be even higher than the index fund. Expected returns and discount rates are two sides of the same coin, so the discount rate for call options must be relatively high. The call option pays off only when things look pretty good

But where exactly will you get the discount rate from? In practical terms, we always separate the calculation of the real option value from the explanation of that value. The RO valuation is done using software, which works out the problem in the risk-neutral world in order to get the best answer possible. Separately, we calculate the expected value

14. Richard Shockley’s An Applied Course in Real Options Valuation (Thomson 2007) is my top recommendation.


in the transparent manner described above. The third and fi nal step is to back-justify the discount rate consistent with the answer.15 (See Figure 9)

Conducting the analysis in this manner adds a few extra steps, as it requires calculating the expected value twice, once in the real world and once in the risk-neutral world. This may be why you were not taught to think about fi nancial options using the real-world expectation, but instead were probably taught to use the risk-neutral world approach. The real-world approach, however, has an overwhelming advantage for the equity analyst or CFO who is either starting out with RO or is comfortable enough to rely on software but must justify the answer to a third party.

Does All of This Really Tell the Strategic Flexibility Story?Writing in 1954, the military strategist Basil Liddel-Hart classifi ed strategic action into two categories—direct and indirect—and anticipated the best current corporate strat-egy thinking by 50 years.16 A major part of strategy focuses on profi ting from the core and involves the tactical decisions companies must make this quarter and next year to continue to succeed. This is DCF territory, characterized by direct attacks on and defenses of existing markets. The second part of strategy, however, is characterized by what Liddel-Hart

refers to as indirect action. This is the part that recommends capturing the small hill, not because that ground has so much value per se, but because it may give you greater leverage to attack another area, depending on what you actually fi nd on the hilltop. This simple metaphor contains the three elements that analysts usually want to talk about when writing about strategic fl exibility: (1) a modest initial cost invested to gain a better perspective on the future; (2) learning that takes place between the initial outlay and any further investment; and (3) an if/then/else structure.17 These are also the key features of real options.

Where does this leave the pragmatic analyst next Monday? Analysts face a dynamic investment problem of their own, and they very wisely do not set their feet on paths that are likely to include unscalable mountains of math or uncross-able canyons of theory. I hope I have convinced you that the math is entirely manageable by focusing on the portion of the problem you care most about—discussing industry dynamics and competitive issues—and relying on software or subject matter experts for the part you care least about: the discount rate. And, as the fi nancial world itself continues to become ever more mathematical, I’ve tried to persuade you that tools like simulation will only continue to fi nd wider audiences. You can be a leader or you can be a follower, but it is unlikely you will escape using these types of tools in your career. RO

Figure 9 In Order to Work in the Real World and Not the Risk Neutral One, We Have to do the RO Problem Essentially Twice, But This is a Small Price to Pay for Transparency.

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15. My own opinion is that RO will advance with analysts owning the expected value calculation and discussion, and a math-savvy support person owning the discount rate. This person will be the right one to think through specifi c issues such as the difference between the normal distribution, which is what the analyst will naturally think in, and the lognormal distribution. The practical approach is to have the analyst defi ne an initial normal distribution, adjust it to fi t a lognormal distribution, then feed it back to the ana-lyst to see if they can live with it.

16. Liddel Hart – Strategy – Meridian 1991 edition of 1954 original.17. If the uncertainty resolves via a diffusion, if/then/else maps onto a Black-Scholes

type of set-up—if opex exceeds capex, invest, otherwise don’t. If the uncertainty also contains technical risk, if/then/else will further include a decision-tree-like component—if the drug passes stage II, continue, else, abandon (or sell). Much has been made in the last few years about decision tree analysis (DTA) as a rival to RO, but this is a non-issue in our opinion. A combination of DTA for technical risk and RO for market risk is clearly the way to go. As our Chief Scientist Andrea Gamba has often reminded me, RO is just DTA with the correct discount rate. Everything discussed in this paper is still applicable to this integrated approach, but an additional discussion on the difference between tech-nical and market risk would also be required.


is simply an extension of DCF, and it is better to learn to use simulation with problems where you already have a solid grounding.

The real challenges are the essentially philosophical questions we have explored in this article. These don’t lend themselves to a ten-minute call to a rushed client. Your fallback and mine is that DCF relies on the same set of assumptions about the usefulness of forecasting the future, though I am the fi rst to admit this can sound hollow. Your best approach is to be prepared for the questions that invari-

ably arise. This article attempts to help you do that. Most importantly, try to show your own clients the new issues you can explore once you take a dynamic view of the capex schedule. You already do it in words. Now you can begin to do it in numbers.

raul guerrero is Managing Partner at Asymmetric Strategy, a quan-

titative fi nance, valuation, and software fi rm. He can be reached at raul.

[email protected]

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Documents

The Case for Real Options Made Simple