CHAPTER 8
REAL OPTIONS
The approaches that we have described in the last three chapters for assessing the
effects of risk, for the most part, are focused on the negative effects of risk. Put another
way, they are all focused on the downside of risk and they miss the opportunity
component that provides the upside. The real options approach is the only one that gives
prominence to the upside potential for risk, based on the argument that uncertainty can
sometimes be a source of additional value, especially to those who are poised to take
advantage of it.
We begin this chapter by describing in very general terms the argument behind
the real options approach, noting its foundations in two elements – the capacity of
individuals or entities to learn from what is happening around them and their willingness
and the ability to modify behavior based upon that learning. We then describe the various
forms that real options can take in practice and how they can affect the way we assess the
value of investments and our behavior. In the last section, we consider some of the
potential pitfalls in using the real options argument and how it can be best incorporated
into a portfolio of risk assessment tools.
The Essence of Real Options
To understand the basis of the real options argument and the reasons for its allure,
it is easiest to go back to risk assessment tool that we unveiled in chapter 6 – decision
trees. Consider a very simple example of a decision tree in figure 8.1:
Figure 8.1: Simple Decision Tree
$ 100
-$120
p =1/2
1-p =1/2
Given the equal probabilities of up and down movements, and the larger potential loss,
the expected value for this investment is negative.
Extract from “Strategic Risk Taking” by Aswath Damodaran
2
Expected Value = 0.50 (100) + 0.5 (-120) = -$10
Now contrast this will the slightly more complicated two-phase decision tree in figure
8.2:
Figure 8.2: Two-phase Decision Tree
p=1/3
1-p=2/3
-10
+10
+90
-110
p=2/3
1-p=1/3

Note that the total potential profits and losses over the two phases in the tree are identical
to the profit and loss of the simple tree in figure 8.1; your total gain is $ 100 and your
total loss is $120. Note also that the cumulative probabilities of success and failure
remain at the 50% that we used in the simple tree. When we compute the expected value
of this tree, though, the outcome changes:
Expected Value = (2/3) (-10) + 1/3 [10+(2/3)(90) + (1/3)(-110)] = $4.44
What is it about the second decision tree that makes a potentially bad investment (in the
first tree) into a good investment (in the second)? We would attribute the change to two
factors. First, by allowing for an initial phase where you get to observe the cashflows on a
first and relatively small try at the investment, we allow for learning. Thus, getting a bad
outcome in the first phase (-10 instead of +10) is an indicator that the overall investment
is more likely to be money losing than money making. Second, you act on the learning by
abandoning the investment, if the outcome from the first phase is negative; we will call
this adaptive behavior.
In essence, the value of real options stems from the fact that when investing in
risky assets, we can learn from observing what happens in the real world and adapting
our behavior to increase our potential upside from the investment and to decrease the
possible downside. Consider again the Chinese symbol for risk, as a combination of
danger and opportunity that we used in chapter 1. In the real options framework, we use
updated knowledge or information to expand opportunities while reducing danger. In the
context of a risky investment, there are three potential actions that can be taken based
3
upon this updated knowledge. The first is that you build on good fortune to increase your
possible profits; this is the option to expand. For instance, a market test that suggests that
consumers are far more receptive to a new product than you expected them to be could be
used as a basis for expanding the scale of the project and speeding its delivery to the
market. The second is to scale down or even abandon an investment when the
information you receive contains bad news; this is the option to abandon and can allow
you to cut your losses. The third is to hold off on making further investments, if the
information you receive suggests ambivalence about future prospects; this is the option to
delay or wait. You are, in a sense, buying time for the investment, hoping that product
and market developments will make it attractive in the future.
We would add one final piece to the mix that is often forgotten but is just as
important as the learning and adaptive behavior components in terms of contributing to
the real options arguments. The value of learning is greatest, when you and only you have
access to that learning and can act on it. After all, the expected value of knowledge that is
public, where anyone can act on that knowledge, will be close to zero. We will term this
third condition “exclusivity” and use it to scrutinize when real options have the most
value.
Real Options, Risk Adjusted Value and Probabilistic Assessments
Before we embark on a discussion of the options to delay, expand and abandon, it
is important that we consider how the real options view of risk differs from how the
approaches laid out in the last three chapters look at risk, and the implications for the
valuation of risky assets.
When computing the risk-adjusted value for risky assets, we generally discount
back the expected cash flows using a discount rate adjusted to reflect risk. We use higher
discount rates for riskier assets and thus assign a lower value for any given set of cash
flows. In the process, we are faced with the task of converting all possible outcomes in
the future into one expected number. The real options critique of discounted cash flow
valuation can be boiled down simply. The expected cash flows for a risky asset, where
the holder of the asset can learn from observing what happens in early periods and
adapting behavior, will be understated because it will not capture the diminution of the
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downside risk from the option to abandon and the expansion of upside potential from the
options to expand and delay. To provide a concrete example, assume that you are valuing
an oil company and that you estimate the cash flows by multiplying the number of barrels
of oil that you expect the company to produce each year by the expected oil price per
barrel. While you may have reasonable and unbiased estimates of both these numbers
(the expected number of barrels produced and the expected oil price), what you are
missing in your expected cash flows is the interplay between these numbers. Oil
companies can observe the price of oil and adjust production accordingly; they produce
more oil when oil prices are high and less when oil prices are low. In addition, their
exploration activity will ebb and flow as the oil price moves. As a consequence, their
cash flows computed across all oil price scenarios will be greater than the expected cash
flows used in the risk adjusted value calculation, and the difference will widen as the
uncertainty about oil prices increases. So, what would real options proponents suggest?
They would argue that the risk adjusted value, obtained from conventional valuation
approaches, is too low and that a premium should be added to it to reflect the option to
adjust production inherent in these firms.
The approach that is closest to real options in terms of incorporating adaptive
behavior is the decision tree approach, where the optimal decisions at each stage are
conditioned on outcomes at prior stages. The two approaches, though, will usually yield
different values for the same risky asset for two reasons. The first is that the decision tree
approach is built on probabilities and allows for multiple outcomes at each branch,
whereas the real option approach is more constrained in its treatment of uncertainty. In its
binomial version, there can be only two outcomes at each stage and the probabilities are
not specified. The second is that the discount rates used to estimate present values in
decision trees, at least in conventional usage, tend to be risk adjusted and not conditioned
on which branch of the decision tree you are looking at. When computing the value of a
diabetes drug in a decision tree, in chapter 6, we used a 10% cost of capital as the
discount rate for all cash flows from the drug in both good and bad outcomes. In the real
options approach, the discount rate will vary depending upon the branch of the tree being
analyzed. In other words, the cost of capital for an oil companies if oil prices increase
may very well be different from the cost of capital when oil prices decrease. Copeland
5
and Antikarov provide a persuasive proof that the value of a risky asset will be the same
under real options and decision trees, if we allow for path-dependent discount rates.1
Simulations and real options are not so much competing approaches for risk
assessment, as they are complementary. Two key inputs into the real options valuation –
the value of the underlying asset and the variance in that value – are often obtained from
simulations. To value a patent, for instance, we need to assess the present value of cash
flows from developing the patent today and the variance in that value, given the
uncertainty about the inputs. Since the underlying product is not traded, it is difficult to
get either of these inputs from the market. A Monte Carlo simulation can provide both
values.
Real Option Examples
As we noted in the introductory section, there are three types of options embedded
in investments – the option to expand, delay and abandon an investment. In this section,
we will consider each of these options and how they made add value to an investment, as
well as potential implications for valuation and risk management.
The Option to Delay an Investment
Investments are typically analyzed based upon their expected cash flows and
discount rates at the time of the analysis; the net present value computed on that basis is a
measure of its value and acceptability at that time. The rule that emerges is a simple one:
negative net present value investments destroy value and should not be accepted.
Expected cash flows and discount rates change over time, however, and so does the net
present value. Thus, a project that has a negative net present value now may have a
positive net present value in the future. In a competitive environment, in which individual
firms have no special advantages over their competitors in taking projects, this may not
seem significant. In an environment in which a project can be taken by only one firm

1 Copeland, T.E. and V. Antikarov, 2003, Real Options: A Practitioner’s Guide, Texere. For an alternate
path to the same conclusion, see Brandao, L.E., J.S. Dyer and W.J. Huhn, 2005, Using Binomial Decision
Trees to Solve Real-Option Valuation Problems, Decision Analysis, v2, 69-88. They use the risk-neutral
probabilities from the option pricing model in the decision tree to solve for the option’s value.
6
(because of legal restrictions or other barriers to entry to competitors), however, the
changes in the project’s value over time give it the characteristics of a call option.
Basic Setup
In the abstract, assume that a project requires an initial up-front investment of X,
and that the present value of expected cash inflows computed right now is V. The net
present value of this project is the difference between the two:
NPV = V - X
Now assume that the firm has exclusive rights to this project for the next n years, and that
the present value of the cash inflows may change over that time, because of changes in
either the cash flows or the discount rate. Thus, the project may have a negative net
present value right now, but it may still be a good project if the firm waits. Defining V
again as the present value of the cash flows, the firm’s decision rule on this project can be
summarized as follows:
If V > X Take the project: Project has positive net present value
V < X Do not take the project: Project has negative net present value
If the firm does not invest in the project, it incurs no additional cash flows, though it will
lose what it originally invested in the project. This relationship can be presented in a
payoff diagram of cash flows on this project, as shown in Figure 8.3, assuming that the
firm holds out until the end of the period for which it has exclusive rights to the project:2

2 McDonald, R. and D. Siegel, 2002, The Value of Waiting to Invest, Quarterly Journal of Economics,
v101, 707-728.
7

Note that this payoff diagram is that of a call option –– the underlying asset is the
investment, the strike price of the option is the initial outlay needed to initiate the
investment; and the life of the option is the period for which the firm has rights to the
investment. The present value of the cash flows on this project and the expected variance
in this present value represent the value and variance of the underlying asset.
Valuing an Option to Delay
On the surface, the inputs needed to value the option to delay are the same as
those needed for any option. We need the value of the underlying asset, the variance in
that value, the time to expiration on the option, the strike price, the riskless rate and the
equivalent of the dividend yield (cost of delay). Actually estimating these inputs for a real
option to delay can be difficult, however.
a. Value Of The Underlying Asset: In this case, the underlying asset is the investment
itself. The current value of this asset is the present value of expected cash flows from
initiating the project now, not including the up-front investment, which can be obtained
by doing a standard capital budgeting analysis. There is likely to be a substantial amount
of error in the cash flow estimates and the present value, however. Rather than being
viewed as a problem, this uncertainty should be viewed as the reason why the project
delay option has value. If the expected cash flows on the project were known with
8
certainty and were not expected to change, there would be no need to adopt an option
pricing framework, since there would be no value to the option.
b. Variance in the value of the asset: The present value of the expected cashflows that
measures the value of the asset will change over time, partly because the potential market
size for the product may be unknown, and partly because technological shifts can change
the cost structure and profitability of the product. The variance in the present value of
cash flows from the project can be estimated in one of three ways.
• If similar projects have been introduced in the past, the variance in the cash flows
from those projects can be used as an estimate. This may be the way that a consumer
product company like Gillette might estimate the variance associated with introducing
a new blade for its razors.
• Probabilities can be assigned to various market scenarios, cash flows estimated under
each scenario and the variance estimated across present values. Alternatively, the
probability distributions can be estimated for each of the inputs into the project
analysis - the size of the market, the market share and the profit margin, for instance -
and simulations used to estimate the variance in the present values that emerge.
• The variance in the market value of publicly traded firms involved in the same
business (as the project being considered) can be used as an estimate of the variance.
Thus, the average variance in firm value of firms involved in the software business
can be used as the variance in present value of a software project.
The value of the option is largely derived from the variance in cash flows - the higher the
variance, the higher the value of the project delay option. Thus, the value of an option to
delay a project in a stable business will be less than the value of a similar option in an
environment where technology, competition and markets are all changing rapidly.
c. Exercise Price On Option: A project delay option is exercised when the firm owning
the rights to the project decides to invest in it. The cost of making this investment is the
exercise price of the option. The underlying assumption is that this cost remains constant
(in present value dollars) and that any uncertainty associated with the product is reflected
in the present value of cash flows on the product.
d. Expiration Of The Option And The Riskless Rate The project delay option expires
when the rights to the project lapse; investments made after the project rights expire are
9
assumed to deliver a net present value of zero as competition drives returns down to the
required rate. The riskless rate to use in pricing the option should be the rate that
corresponds to the expiration of the option. While this input can be estimated easily when
firms have the explicit right to a project (through a license or a patent, for instance), it
becomes far more difficult to obtain when firms only have a competitive advantage to
take a project.
d. Cost of Delay (Dividend Yield): There is a cost to delaying taking a project, once the
net present value turns positive. Since the project rights expire after a fixed period, and
excess profits (which are the source of positive present value) are assumed to disappear
after that time as new competitors emerge, each year of delay translates into one less year
of value-creating cash flows.3 If the cash flows are evenly distributed over time, and the
exclusive rights last n years, the cost of delay can be written as:

!
Annual cost of delay =
1
n

Thus, if the project rights are for 20 years, the annual cost of delay works out to 5% a
year. Note, though, that this cost of delay rises each year , to 1/19 in year 2, 1/18 in year 3
and so on, making the cost of delaying exercise larger over time.
Practical Considerations
While it is quite clear that the option to delay is embedded in many investments,
there are several problems associated with the use of option pricing models to value these
options. First, the underlying asset in this option, which is the project, is not traded,
making it difficult to estimate its value and variance. We would argue that the value can
be estimated from the expected cash flows and the discount rate for the project, albeit
with error. The variance is more difficult to estimate, however, since we are attempting
the estimate a variance in project value over time.
Second, the behavior of prices over time may not conform to the price path
assumed by the option pricing models. In particular, the assumption that prices move in
small increments continuously (an assumption of the Black-Scholes model), and that the

3 A value-creating cashflow is one that adds to the net present value because it is in excess of the required
return for investments of equivalent risk.
10
variance in value remains unchanged over time, may be difficult to justify in the context
of a real investment. For instance, a sudden technological change may dramatically
change the value of a project, either positively or negatively.
Third, there may be no specific period for which the firm has rights to the project.
For instance, a firm may have significant advantages over its competitors, which may, in
turn, provide it with the virtually exclusive rights to a project for a period of time. The
rights are not legal restrictions, however, and could erode faster than expected. In such
cases, the expected life of the project itself is uncertain and only an estimate. Ironically,
uncertainty about the expected life of the option can increase the variance in present
value, and through it, the expected value of the rights to the project.
Applications of Option to Delay
The option to delay provides interesting perspectives on two common investment
problems. The first is in the valuation of patents, especially those that are not viable today
but could be viable in the future; by extension, this will also allow us to look at whether
R&D expenses are delivering value. The second is in the analysis of natural resource
assets – vacant land, undeveloped oil reserves etc.
Patents
A product patent provides a firm with the right to develop and market a product.
The firm will do so only if the present value of the expected cash flows from the product
sales exceed the cost of development, however, as shown in Figure 8.4. If this does not
occur, the firm can shelve the patent and not incur any further costs. If I is the present
value of the costs of developing the product, and V is the present value of the expected
cash flows from development, the payoffs from owning a product patent can be written
as:
Payoff from owning a product patent = V - I if V> I
= 0 if V ≤ I
Thus, a product patent can be viewed as a call option, where the product itself is the
underlying asset.4

4 Schwartz, E., 2002, Patents and R&D as Real Options, Working Paper, Anderson School at UCLA.
11
Figure 8.4: Payoff to Introducing Product
Present value of expected
cashflows on product
Net Payoff to
introducing product
Cost of product
introduction

We will illustrate the use of option pricing to value Avonex, a drug to treat
multiple sclerosis, right after it had received FDA approval in 1997, but before its parent
company, Biogen, had decided whether to commercialize the drug or nto. We arrived at
the following estimates for use in the option pricing model:
• An internal analysis of the drug at the time, based upon the potential market and the
price that the firm can expect to charge, yielded a present value of expected cash
flows of $ 3.422 billion, prior to considering the initial development cost.
• The initial cost of developing the drug for commercial use was estimated to be $2.875
billion, if the drug was introduced immediately.
• The firm had the patent on the drug for the next 17 years, and the 17-year Treasury
bond rate was 6.7%.
• The average historical variance in market value for publicly traded bio-technology
firms was 0.224.
• It was assumed that the potential for excess returns exists only during the patent life,
and that competition will wipe out excess returns beyond that period. Thus, any delay
in introducing the drug, once it is viable, will cost the firm one year of patent-
protected excess returns. (For the initial analysis, the cost of delay will be 1/17, the
following year, it will be 1/16, the year after, 1/15 and so on.)
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Based on these assumptions, we obtained the following inputs to the option pricing
model.
Present Value of Cash Flows from Introducing Drug Now = S = $ 3.422 billion
Initial Cost of Developing Drug for commercial use = K = $ 2.875 billion
Patent life = t = 17 years Riskless Rate = r = 6.7% (17-year T.Bond rate)
Variance in Expected Present Values =σ2 = 0.224
Expected Cost of Delay = y = 1/17 = 5.89%
Using these inputs in an option pricing model, we derived a value of $907 million for the
option,5 and this can be considered to be the real options value attached to the patent on
Avonex. To provide a contrast, the net present value of this patent is only $ 547 million:
NPV = $3,422 million - $ 2,875 million = $ 547 million
The time premium of $ 360 million ($907 million -$547 million) on this option suggests
that the firm will be better off waiting rather than developing the drug immediately, the
cost of delay notwithstanding. However, the cost of delay will increase over time, and
make exercise (development) more likely. Note also that we are assuming that the firm is
protected from all competition for the life of the patent. In reality, there are other
pharmaceutical firms working on their own drugs to treat multiple sclerosis and that can
affect both the option value and the firm’s behavior. In particular, if we assume that
Upjohn or Pfizer has a competing drug working through the FDA pipeline and that the
drug is expected to reach the market in 6 years, the cost of delay will increase to 16.67%
(1/6) and the option value will dissipate.
The implications of viewing patents as options can be significant. First, it implies
that non-viable patents will continue to have value, especially in businesses where there
is substantial volatility. Second, it indicates that firms may hold off on developing viable
patents, if they feel that they gain more from waiting than they lose in terms of cash
flows; this behavior will be more common if there is no significant competition on the
horizon. Third, the value of patents will be higher in risky businesses than in safe
businesses, since option value increases with volatility. If we consider R&D to be the
expense associated with acquiring these patents, this would imply that research should
13
have its biggest payoff when directed to areas where less is known and there is more
uncertainty. Consequently, we should expect pharmaceutical firms to spend more of their
R&D budgets on gene therapy than on flu vaccines.6
Natural Resource Options
In a natural resource investment, the underlying asset is the natural resource and
the value of the asset is based upon two variables - (1) the estimated quantity, and (2) the
price of the resource. Thus, in a gold mine, for example, the value of the underlying asset
is the value of the estimated gold reserves in the mine, based upon the current price of
gold. In most such investments, there is an initial cost associated with developing the
resource; the difference between the value of the asset extracted and the cost of the
development is the profit to the owner of the resource (see Figure 8.5). Defining the cost
of development as X, and the estimated value of the developed resource as V, the
potential payoffs on a natural resource option can be written as follows:
Payoff on natural resource investment = V - X if V > X
= 0 if V≤ X
Thus, the investment in a natural resource option has a payoff function similar to a call
option.7

5 This value was derived from using a Black Scholes model with these inputs. With a binomial model, the
estimated value increases slightly to $915 million.
6 Pakes, A., 1986, Patents as Options: Some Estimates of the Value of Holding European Patent Stocks,
Econometrica, v54, 755-784. While this paper does not explicitly value patents as options, it examines the
returns investors would have earned investing in companies that derive their value from patents. The return
distribution resembles that of a portfolio of options, with most investments losing money but the winners
providing disproportionate gains.
7 Brennan, M. and E. Schwartz, 1985, Evaluating Natural Resource Investments, The Journal of Business,
v58, 135-157.
14
Figure 8.5: Payoff from Developing Natural Resource Reserves
Value of estimated reserve
of natural resource
Net Payoff on
extracting reserve
Cost of Developing
reserve

To value a natural resource investment as an option, we need to make assumptions about
a number of variables:
1. Available reserves of the resource: Since this is not known with certainty at the outset,
it has to be estimated. In an oil tract, for instance, geologists can provide reasonably
accurate estimates of the quantity of oil available in the tract.
2. Estimated cost of developing the resource: The estimated development cost is the
exercise price of the option. Again, a combination of knowledge about past costs and the
specifics of the investment have to be used to come up with a reasonable measure of
development cost.
3. Time to expiration of the option: The life of a natural resource option can be defined in
one of two ways. First, if the ownership of the investment has to be relinquished at the
end of a fixed period of time, that period will be the life of the option. In many offshore
oil leases, for instance, the oil tracts are leased to the oil company for several years. The
second approach is based upon the inventory of the resource and the capacity output rate,
as well as estimates of the number of years it would take to exhaust the inventory. Thus, a
gold mine with a mine inventory of 3 million ounces and a capacity output rate of
150,000 ounces a year will be exhausted in 20 years, which is defined as the life of the
natural resource option.
15
4. Variance in value of the underlying asset: The variance in the value of the underlying
asset is determined by two factors – (1) variability in the price of the resource, and (2)
variability in the estimate of available reserves. In the special case where the quantity of
the reserve is known with certainty, the variance in the underlying asset's value will
depend entirely upon the variance in the price of the natural resource. In the more
realistic case where the quantity of the reserve and the oil price can change over time, the
option becomes more difficult to value; here, the firm may have to invest in stages to
exploit the reserves.
5. Cost of Delay: The net production revenue as a percentage of the market value of the
reserve is the equivalent of the dividend yield and is treated the same way in calculating
option values. An alternative way of thinking about this cost is in terms of a cost of delay.
Once a natural resource option is in-the-money (Value of the reserves > Cost of
developing these reserves), the firm, by not exercising the option, is costing itself the
production revenue it could have generated by developing the reserve.
An important issue in using option pricing models to value natural resource
options is the effect of development lags on the value of these options. Since the
resources cannot be extracted instantaneously, a time lag has to be allowed between the
decision to extract the resources and the actual extraction. A simple adjustment for this
lag is to reduce the value of the developed reserve to reflect the loss of cash flows during
the development period. Thus, if there is a one-year lag in development, the current value
of the developed reserve will be discounted back one year at the net production
revenue/asset value ratio8 (which we also called the dividend yield above).9
To illustrate the use of option pricing to value natural reserves, consider an
offshore oil property with an estimated reserve of 50 million barrels of oil; the cost of
developing the reserve is expected to be $ 600 million, and the development lag is two
years. The firm has the rights to exploit this reserve for the next 20 years, and the

8 Intuitively, it may seem like the discounting should occur at the riskfree rate. The simplest way of
explaining why we discount at the dividend yield is to consider the analogy with a listed option on a stock.
Assume that on exercising a listed option on a stock, you had to wait six months for the stock to be
delivered to you. What you lose is the dividends you would have received over the six-month period by
holding the stock. Hence, the discounting is at the dividend yield.
9 Brennan, M.J., and E.S. Schwartz, 1985, Evaluating Natural Resource Investments, Journal of Business
58, pp. 135-157.
16
marginal value per barrel of oil is $12 currently10 (price per barrel - marginal cost per
barrel). Once developed, the net production revenue each year will be 5% of the value of
the reserves. The riskless rate is 8%, and the variance in ln(oil prices) is 0.03. Given this
information, the inputs to the option pricing model can be estimated as follows:
Current Value of the asset = S = Value of the developed reserve discounted back
the length of the development lag at the dividend yield = $12 * 50 /(1.05)2 = $
544.22
If development is started today, the oil will not be available for sale until two years from
now. The estimated opportunity cost of this delay is the lost production revenue over the
delay period; hence, the discounting of the reserve back at the dividend yield.
Exercise Price = Cost of developing reserve = $ 600 million (assumed to be both
known and fixed over time)
Time to expiration on the option = 20 years
In this example, we assume that the only uncertainty is in the price of oil, and the
variance therefore becomes the variance in oil prices.
Variance in the value of the underlying asset (oil) = 0.03
Riskless rate =8%
Dividend Yield = Net production revenue / Value of reserve = 5%
Based upon these inputs, the option pricing model yields an estimate of value of $97.08
million.11 This oil reserve, though not viable at current prices, is still a valuable property
because of its potential to create value if oil prices go up.12
The same type of analysis can be extended to any other commodity company
(gold and copper reserves, for instance) and even to vacant land or real estate properties.

10 For simplicity, we will assume that while this marginal value per barrel of oil will grow over time, the
present value of the marginal value will remain unchanged at $ 12 per barrel. If we do not make this
assumption, we will have to estimate the present value of the oil that will be extracted over the extraction
period.
11 This is the estimate from a Black-Scholes model, with a dividend yield adjustment. Using a binomial
model yields an estimate of value of $ 101 million.
12 Paddock, J.L. & D. R. Siegel & J.L. Smith (1988): “Option Valuation of Claims on Real Assets: The
Case of Offshore Petroleum Leases”, Quarterly Journal of Economics, August 1988, pp.479-508. This
paper provides a detailed examination of the application of real options to value oil reserves. They applied
the model to examine the prices paid for offshore oil leases in the US in 1980 and concluded that
companies over paid (relative to the option value).
17
The owner of vacant land in Manhattan can choose whether and when to develop the land
and will make that decision based upon real estate values. 13
What are the implications of viewing natural resource reserves as options? The
first is that the value of a natural resource company can be written as a sum of two
values: the conventional risk adjusted value of expected cash flows from developed
reserves and the option value of undeveloped reserves. While both will increase in value
as the price of the natural resource increases, the latter will respond positively to
increases in price volatility. Thus, the values of oil companies should increase if oil prices
become more volatile, even if oil prices themselves do not go up. The second is that
conventional discounted cash flow valuation will understate the value of natural resource
companies, even if the expected cash flows are unbiased and reasonable because it will
miss the option premium inherent in their undeveloped reserves. The third is that
development of natural resource reserves will slow down as the volatility in prices
increases; the time premium on the options will increase, making exercise of the options
(development of the reserves) less likely.
Mining and commodity companies have been at the forefront in using real options
in decision making and their usage of the technology predates the current boom in real
options. One reason is that natural resource options come closest to meeting the pre-
requisites for the use of option pricing models. Firms can learn a great deal by observing
commodity prices and can adjust their behavior (in terms of development and
exploration) quickly. In addition, if we consider exclusivity to be a pre-requisite for real
options to have value, that exclusivity for natural resource options derives from their
natural scarcity; there is, after all, only a finite amount of oil and gold under the ground
and vacant land in Manhattan. Finally, natural resource reserves come closest to meeting
the arbitrage/replication requirements that option pricing models are built upon; both the
underlying asset (the natural resource) and the option can often be bought and sold.

13 Quigg, L, 1993] Empirical Testing of Real Option-Pricing Models », Journal of Finance, vol.48, 621-
640. The author examined transaction data on 2700 undeveloped and 3200 developed real estate properties
between 1976-79 and found evidence of a premium arising from the option to wait in the former.
18
The Option to Expand
In some cases, a firm will take an investment because doing so allows it either to
make other investments or to enter other markets in the future. In such cases, it can be
argued that the initial investment provides the firm with an option to expand, and the firm
should therefore be willing to pay a price for such an option. Consequently, a firm may
be willing to lose money on the first investment because it perceives the option to expand
as having a large enough value to compensate for the initial loss.
To examine this option, assume that the present value of the expected cash flows
from entering the new market or taking the new project is V, and the total investment
needed to enter this market or take this project is X. Further, assume that the firm has a
fixed time horizon, at the end of which it has to make the final decision on whether or not
to take advantage of this opportunity. Finally, assume that the firm cannot move forward
on this opportunity if it does not take the initial investment. This scenario implies the
option payoffs shown in Figure 8.6.

As you can see, at the expiration of the fixed time horizon, the firm will enter the new
market or take the new investment if the present value of the expected cash flows at that
point in time exceeds the cost of entering the market.
19
Consider a simple example of an option to expand. Disney is considering starting
a Spanish version of the Disney Channel in Mexico and estimates the net present value of
this investment to be -$150 million. While the negative net present value would normally
suggest that rejecting the investment is the best course, assume that if the Mexican
venture does better than expected, Disney plans to expand the network to the rest of
South America at a cost of $ 500 million. Based on its current assessment of this market,
Disney believes that the present value of the expected cash flows on this investment is
only $ 400 million (making it a negative net present value investment as well). The
saving grace is that the latter present value is an estimate and Disney does not have a firm
grasp of the market; a Monte Carlo simulation of the investments yields a standard
deviation of 50% in value. Finally, assume that Disney will have to make this expansion
decision within 5 years of the Mexican investment, and that the five-year riskfree rate is
4%. The value of the expansion option can now be computed using the inputs:
S = Present value of expansion cash flows = $ 400 million
K = Cost of expansion = $ 500 million
σ = Standard deviation in value (from simulation) = 50%
t = 5 years
r = 4%
The resulting option value is $167 million.14
The practical considerations associated with estimating the value of the option to
expand are similar to those associated with valuing the option to delay. In most cases,
firms with options to expand have no specific time horizon by which they have to make
an expansion decision, making these open-ended options, or, at best, options with
arbitrary lives. Even in those cases where a life can be estimated for the option, neither
the size nor the potential market for the product may be known, and estimating either can
be problematic. To illustrate, consider the Disney example discussed above. While we
adopted a period of five years, at the end of which the Disney has to decide one way or
another on its future expansion into South America, it is entirely possible that this time
frame is not specified at the time the store is opened. Furthermore, we have assumed that

14 This value was computed using the Black-Scholes model. A binomial model yields a similar value.
20
both the cost and the present value of expansion are known initially. In reality, the firm
may not have good estimates for either before making the first investment, since it does
not have much information on the underlying market.
Implications
The option to expand is implicitly used by firms to rationalize taking investments
that have negative net present value, but provide significant opportunities to tap into new
markets or sell new products. While the option pricing approach adds rigor to this
argument by estimating the value of this option, it also provides insight into those
occasions when it is most valuable. In general, the option to expand is clearly more
valuable for more volatile businesses with higher returns on projects (such as
biotechnology or computer software), than in stable businesses with lower returns (such
as housing, utilities or automobile production). Specifically, the option to expand is at the
basis of arguments that an investment should be made because of strategic considerations
or that large investments should be broken up into smaller phases. It can also be
considered a rationale for why firms may accumulate cash or hold back on borrowing,
thus preserving financial flexibility.
Strategic Considerations
In many acquisitions or investments, the acquiring firm believes that the
transaction will give it competitive advantages in the future. These competitive
advantages range the gamut, and include:
• Entrée into a Growing or Large Market: An investment or acquisition may allow the
firm to enter a large or potentially large market much sooner than it otherwise would
have been able to do so. A good example of this would be the acquisition of a
Mexican retail firm by a US firm, with the intent of expanding into the Mexican
market.
• Technological Expertise: In some cases, the acquisition is motivated by the desire to
acquire a proprietary technology, that will allow the acquirer to expand either its
existing market or into a new market.
21
• Brand Name: Firms sometime pay large premiums over market price to acquire firms
with valuable brand names, because they believe that these brand names can be used
for expansion into new markets in the future.
While all of these potential advantages may be used to justify initial investments that do
not meet financial benchmarks, not all of them create valuable options. The value of the
option is derived from the degree to which these competitive advantages, assuming that
they do exist, translate into sustainable excess returns. As a consequence, these
advantages can be used to justify premiums only in cases where the acquiring firm
believes that it has some degree of exclusivity in the targeted market or technology. Two
examples can help illustrate this point. A telecommunications firm should be willing to
pay a premium for Chinese telecomm firm, if the latter has exclusive rights to service a
large segment of the Chinese market; the option to expand in the Chinese market could
be worth a significant amount.15 On the other hand, a developed market retailer should be
wary about paying a real option premium for an Indian retail firm, even though it may
believe that the Indian market could grow to be a lucrative one. The option to expand into
this lucrative market is open to all entrants and not just to existing retailers and thus may
not translate into sustainable excess returns.
Multi-Stage Projects/ Investments
When entering new businesses or making new investments, firms sometimes have
the option to enter the business in stages. While doing so may reduce potential upside, it
also protects the firm against downside risk, by allowing it, at each stage, to gauge
demand and decide whether to go on to the next stage. In other words, a standard project
can be recast as a series of options to expand, with each option being dependent on the
previous one. There are two propositions that follow:
• Some projects that do not look good on a full investment basis may be value creating
if the firm can invest in stages.
• Some projects that look attractive on a full investment basis may become even more
attractive if taken in stages.
22
The gain in value from the options created by multi-stage investments has to be weighed
off against the cost. Taking investments in stages may allow competitors who decide to
enter the market on a full scale to capture the market. It may also lead to higher costs at
each stage, since the firm is not taking full advantage of economies of scale.
There are several implications that emerge from viewing this choice between
multi-stage and one-time investments in an option framework. The projects where the
gains will be largest from making the investment in multiple stages include:
(1) Projects where there are significant barriers to entry from competitors entering the
market, and taking advantage of delays in full-scale production. Thus, a firm with a
patent on a product or other legal protection against competition pays a much smaller
price for starting small and expanding as it learns more about the product
(2) Projects where there is significant uncertainty about the size of the market and the
eventual success of the project. Here, starting small and expanding allows the firm to
reduce its losses if the product does not sell as well as anticipated, and to learn more
about the market at each stage. This information can then be useful in subsequent
stages in both product design and marketing. Hsu argues that venture capitalists
invest in young companies in stages, partly to capture the value of option of
waiting/learning at each stage and partly to reduce the likelihood that the entrepreneur
will be too conservative in pursuing risky (but good) opportunities.16
(3) Projects where there is a substantial investment needed in infrastructure (large fixed
costs) and high operating leverage. Since the savings from doing a project in multiple
stages can be traced to investments needed at each stage, they are likely to be greater
in firms where those costs are large. Capital intensive projects as well as projects that
require large initial marketing expenses (a new brand name product for a consumer
product company) will gain more from the options created by taking the project in
multiple stages.

15 A note of caution needs to be added here. If the exclusive rights to a market come with no pricing power
– in other words, the Government will set the price you charge your customers – it may very well translate
into zero excess returns (and no option value).
16 Hsu, Y., 2002, Staging of Venture Capital Investment: A Real Options Analysis, Working paper,
University of Cambridge.
23
Growth Companies
In the stock market boom in the 1990s, we witnessed the phenomenon of young,
start-up, internet companies with large market capitalizations but little to show in terms
of earnings, cash flows or even revenues. Conventional valuation models suggested that it
would be difficult, if not impossible, to justify these market valuations with expected
cash flows. In an interesting twist on the option to expand argument, there were some
who argued that investors in these companies were buying options to expand and be part
of a potentially huge e-commerce market, rather than conventional stock.17
While the argument is alluring and serves to pacify investors in growth companies
who may feel that they are paying too much, there are clearly dangers in making this
stretch. The biggest one is that the “exclusivity” component that is necessary for real
options to have value is being given short shrift. Consider investing in an internet stock in
1999 and assume that you are paying a premium to be part of a potentially large online
market in 2008. Assume further that this market comes to fruition. Could you partake in
this market without paying that upfront premium a dot-com company? We don’t see why
not. After all, GE and Nokia are just as capable of being part of this online market, as are
any number of new entrants into the market.18
Financial Flexibility
When making decisions about how much to borrow and how much cash to return
to stockholders (in dividends and stock buybacks), managers should consider the effects
such decisions will have on their capacity to make new investments or meet unanticipated
contingencies in future periods. Practically, this translates into firms maintaining excess
debt capacity or larger cash balances than are warranted by current needs, to meet
unexpected future requirements. While maintaining this financing flexibility has value to
firms, it also has costs; the large cash balances might earn below market returns, and
excess debt capacity implies that the firm is giving up some value by maintaining a
higher cost of capital.

17 Schwartz, E.S. and M. Moon, 2001, Rational Pricing of Internet Companies Revisited, The Financial
Review 36, pp. 7-26. A simpler version of the same argument was made in Mauboussin, M., 1998, Get
Real: Using Real Options in Security Analysis, CSFB Publication, June 23, 1999.
18 This argument is fleshed out in my book, “The Dark Side of Valuation”, published by Prentice-Hall.
24
Using an option framework, it can be argued that a firm that maintains a large
cash balance and preserves excess debt capacity is doing so to have the option to take
unexpected projects with high returns that may arise in the future. To value financial
flexibility as an option, consider the following framework: A firm has expectations about
how much it will need to reinvest in future periods, based upon its own past history and
current conditions in the industry. On the other side of the ledger, a firm also has
expectations about how much it can raise from internal funds and its normal access to
capital markets in future periods. Assume that there is actual reinvestment needs can be
very different from the expected reinvestment needs; for simplicity, we will assume that
the capacity to generate funds is known to the firm. The advantage (and value) of having
excess debt capacity or large cash balances is that the firm can meet any reinvestment
needs in excess of funds available using its excess debt capacity and surplus cash. The
payoff from these projects, however, comes from the excess returns that the firm expects
to make on them.
Looking at financial flexibility as an option yields valuable insights on when
financial flexibility is most valuable. Using the framework developed above, for instance,
we would argue that:
• Other things remaining equal, firms operating in businesses where projects earn
substantially higher returns than their hurdle rates should value flexibility more than
those that operate in stable businesses where excess returns are small. This would
imply that firms that earn large excess returns on their projects can use the need for
financial flexibility as the justification for holding large cash balances and excess debt
capacity.
• Since a firm’s ability to fund these reinvestment needs is determined by its capacity to
generate internal funds, other things remaining equal, financial flexibility should be
worth less to firms with large and stable earnings, as a percent of firm value. Young
and growing firms that have small or negative earnings, and therefore much lower
capacity to generate internal funds, will value flexibility more. As supporting
evidence, note that technology firms usually borrow very little and accumulate large
cash balances.
25
• Firms with limited internal funds can still get away with little or no financial
flexibility if they can tap external markets for capital – bank debt, bonds and new
equity issues. Other things remaining equal, the greater the capacity (and willingness)
of a firm to raise funds from external capital markets, the less should be the value of
flexibility. This may explain why private or small firms, which have far less access to
capital, will value financial flexibility more than larger firms. The existence of
corporate bond markets can also make a difference in how much flexibility is valued.
In markets where firms cannot issue bonds and have to depend entirely upon banks
for financing, there is less access to capital and a greater need to maintain financial
flexibility.
• The need for and the value of flexibility is a function of how uncertain a firm is about
future reinvestment needs. Firms with predictable reinvestment needs should value
flexibility less than firms in sectors where reinvestment needs are volatile on a
period-to-period basis.
In conventional corporate finance, the optimal debt ratio is the one that minimizes the
cost of capital and there is little incentive for firms to accumulate cash balances. This
view of the world, though, flows directly from the implicit assumption we make that
capital markets are open and can be accessed with little or no cost. Introducing external
capital constraints, internal or external, into the model leads to a more nuanced analysis
where rational firms may borrow less than optimal and hold back on returning cash to
stockholders.
The Option to Abandon an Investment
The final option to consider here is the option to abandon a project when its cash
flows do not measure up to expectations. One way to reflect this value is through decision
trees, as evidenced in chapter 6. The decision tree has limited applicability in most real
world investment analyses; it typically works only for multi-stage projects, and it requires
inputs on probabilities at each stage of the project. The option pricing approach provides
a more general way of estimating and building in the value of abandonment into
investment analysis. To illustrate, assume that V is the remaining value on a project if it
continues to the end of its life, and L is the liquidation or abandonment value for the same
26
project at the same point in time. If the project has a life of n years, the value of
continuing the project can be compared to the liquidation (abandonment) value. If the
value from continuing is higher, the project should be continued; if the value of
abandonment is higher, the holder of the abandonment option could consider abandoning
the project .
Payoff from owning an abandonment option = 0 if V > L
= L-V if V ≤ L
These payoffs are graphed in Figure 8.8, as a function of the expected value from
continuing the investment.

Unlike the prior two cases, the option to abandon takes on the characteristics of a put
option.
Consider a simple example. Assume that a firm is considering taking a 10-year
project that requires an initial investment of $ 100 million in a real estate partnership,
where the present value of expected cash flows is $ 110 million. While the net present
value of $ 10 million is small, assume that the firm has the option to abandon this project
anytime in the next 10 years, by selling its share of the ownership to the other partners in
the venture for $ 50 million. Assume that the variance in the present value of the
expected cash flows from being in the partnership is 0.09.
The value of the abandonment option can be estimated by determining the
characteristics of the put option:
27
Value of the Underlying Asset (S) = PV of Cash Flows from Project
= $ 110 million
Strike Price (K) = Salvage Value from Abandonment = $ 50 million
Variance in Underlying Asset’s Value = 0.06
Time to expiration = Period for which the firm has abandonment option = 10 years
The project has a 25-year life and is expected to lose value each year; for simplicity, we
will assume that the loss is linear (4% a year).
Loss in value each year = 1/n = 1/25 = 4%
Assume that the ten-year riskless rate is 6%. The value of the put option can be estimated
as follows:
Call Value = 110 exp(-.04)(10) (0.9737) -50 (exp(-0.06)(10) (0.8387) = $ 84.09 million
Put Value= $ 84.09 - 110 + 50 exp(-0.06)(10) = $ 1.53 million
The value of this abandonment option has to be added on to the net present value of the
project of $ 10 million, yielding a total net present value with the abandonment option of
$ 11.53 million. Note though that abandonment becomes a more and more attractive
option as the remaining project life decreases, since the present value of the remaining
cash flows will decrease.
In the above analysis, we assumed, rather unrealistically, that the abandonment
value was clearly specified up front and that it did not change during the life of the
project. This may be true in some very specific cases, in which an abandonment option is
built into the contract. More often, however, the firm has the option to abandon, and the
salvage value from doing so has to be estimated (with error) up front. Further, the
abandonment value may change over the life of the project, making it difficult to apply
traditional option pricing techniques. Finally, it is entirely possible that abandoning a
project may not bring in a liquidation value, but may create costs instead; a
manufacturing firm may have to pay severance to its workers, for instance. In such cases,
it would not make sense to abandon, unless the present value of the expected cash flows
from continuing with the investment are even more negative.
28
Implications
The fact that the option to abandon has value provides a rationale for firms to
build in operating flexibility to scale back or terminate projects if they do not measure up
to expectations. It also indicates that firms that focus on generating more revenues by
offering their customers the option to walk away from commitments may be giving up
more than they gain, in the process.
1. Escape Clauses
When a firm enters into a long term risky investment that requires a large up front
investment, it should do so with the clear understanding that it may regret making this
investment fairly early in its life. Being able to get out of such long-term commitments
that threaten to drain more resources in the future is at the heart of the option to abandon.
It is true that some of this flexibility is determined by the business that you are in; getting
out of bad investments is easier to do in service businesses than in heavy infrastructure
businesses. However, it is also true that there are actions that firms can take at the time of
making these investments that give them more choices, if things do not go according to
plan.
The first and most direct way is to build operating flexibility contractually with
those parties that are involved in the investment. Thus, contracts with suppliers may be
written on an annual basis, rather than long term, and employees may be hired on a
temporary basis, rather than permanently. The physical plant used for a project may be
leased on a short-term basis, rather than bought, and the financial investment may be
made in stages rather than as an initial lump sum. While there is a cost to building in this
flexibility, the gains may be much larger, especially in volatile businesses. The initial
capital investment can be shared with another investor, presumably with deeper pockets
and a greater willingness to stay with the investment, even if it turns sour. This provides a
rationale for join venture investing, especially for small firms that have limited resources;
finding a cash-rich, larger company to share the risk may well be worth the cost.
None of these actions are costless. Entering into short term agreements with
suppliers and leasing the physical plant may be more expensive than committing for the
29
life of the investment, but that additional cost has to be weighed off against the benefit of
maintaining the abandonment option.
2. Customer Incentives
Firms that are intent on increasing revenues sometimes offer abandonment
options to customers to induce them to buy their products and services. As an example,
consider a firm that sells its products on multi-year contracts and offers customers the
option to cancel their contracts at any time, with no cost. While this may sweeten the deal
and increase sales, there is likely to be a substantial cost. In the event of a recession,
customers that are unable to meet their obligations are likely to cancel their contracts. In
effect, the firm has made its good times better and its bad times worse; the cost of this
increased volatility in earnings and revenues has to be measured against the potential gain
in revenue growth to see if the net effect is positive.
This discussion should also act as a cautionary note for those firms that are run
with marketing objectives such as maximizing market share or posting high revenue
growth. Those objectives can often be accomplished by giving valuable options to
customers – sales people will want to meet their sales targets and are not particularly
concerned about the long term costs they may create with their commitments to
customers – and the firm may be worse off as a consequence.
3. Switching Options
While the abandonment option considers the value of shutting an investment
down entirely, there is an intermediate alternative that is worth examining. Firms can
sometimes alter production levels in response to demand and being able to do so can
make an investment more valuable. Consider, for instance, a power company that is
considering a new plant to generate electricity and assume that the company can run the
plant at full capacity and produce 1 million kilowatt hours of power or at half capacity
(and substantially less cost) and produce 500,000 kilowatt hours of power. In this case,
the company can observe both the demand for power and the revenues per kilowatt-hour
and decide whether it makes sense to run at full or half capacity. The value of this
switching option can then be compared to the cost of building in this flexibility in the first
place.
30
The airline business provides an interesting case study in how different companies
manage their cost structure and the payoffs to their strategies. One reason that Southwest
Airlines has been able to maintain its profitability in a deeply troubled sector is that the
company has made cost flexibility a central component in its decision process. From its
choice of using only one type of aircraft for its entire fleet19 to its refusal, for the most
part, to fly into large urban airports (with high gate costs), the company’s operations have
created the most flexible cost structure in the business. Thus, when revenues dip (as they
inevitably do at some point in time when the economy weakens), Southwest is able to
trim its costs and stay profitable while other airlines teeter on the brink of bankruptcy.
Caveats on Real Options
The discussion on the potential applications of real options should provide a
window into why they are so alluring to practitioners and businesses. In essence, we are
ignoring that the time honored rules of capital budgeting, which include rejecting
investments that have negative net present value, when real options are present. Not only
does the real options approach encourage you to make investments that do not meet
conventional financial criteria, it also makes it more likely that you will do so, the less
you know about the investment. Ignorance, rather than being a weakness, becomes a
virtue because it pushes up the uncertainty in the estimated value and the resulting option
value. To prevent the real options process from being hijacked by managers who want to
rationalize bad (and risky) decisions, we have to impose some reasonable constraints on
when it can be used and when it is used, how to estimate its value.
First, not all investments have options embedded in them, and not all options, even if
they do exist, have value. To assess whether an investment creates valuable options that
need to be analyzed and valued, three key questions need to be answered affirmatively.
• Is the first investment a pre-requisite for the later investment/expansion? If not, how
necessary is the first investment for the later investment/expansion? Consider our
earlier analysis of the value of a patent or the value of an undeveloped oil reserve as
options. A firm cannot generate patents without investing in research or paying

19 From its inception until recently, Southwest used the Boeing 737 as its workhorse, thus reducing its need
31
another firm for the patents, and it cannot get rights to an undeveloped oil reserve
without bidding on it at a government auction or buying it from another oil company.
Clearly, the initial investment here (spending on R&D, bidding at the auction) is
required for the firm to have the second option. Now consider the Disney expansion
into Mexico. The initial investment in a Spanish channel provides Disney with
information about market potential, without which presumably it is unwilling to
expand into the larger South American market. Unlike the patent and undeveloped
reserves illustrations, the initial investment is not a pre-requisite for the second,
though management might view it as such. The connection gets even weaker when
we look at one firm acquiring another to have the option to be able to enter a large
market. Acquiring an internet service provider to have a foothold in the internet
retailing market or buying a Brazilian brewery to preserve the option to enter the
Brazilian beer market would be examples of such transactions.
• Does the firm have an exclusive right to the later investment/expansion? If not, does
the initial investment provide the firm with significant competitive advantages on
subsequent investments? The value of the option ultimately derives not from the cash
flows generated by then second and subsequent investments, but from the excess
returns generated by these cash flows. The greater the potential for excess returns on
the second investment, the greater the value of the option in the first investment. The
potential for excess returns is closely tied to how much of a competitive advantage
the first investment provides the firm when it takes subsequent investments. At one
extreme, again, consider investing in research and development to acquire a patent.
The patent gives the firm that owns it the exclusive rights to produce that product, and
if the market potential is large, the right to the excess returns from the project. At the
other extreme, the firm might get no competitive advantages on subsequent
investments, in which case, it is questionable as to whether there can be any excess
returns on these investments. In reality, most investments will fall in the continuum
between these two extremes, with greater competitive advantages being associated
with higher excess returns and larger option values.
to maintain different maintenance crews at each airport it flies into.