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annualized standard deviation in firm value of publicly traded entertainment firms in the
Latin American markets, which is approximately 30%.
Variance in Underlying Asset™s Value = 0.302 = 0.09
Time to expiration = Period for which expansion option applies = 10 years
There is no cost of delay.
Assume that the ten-year riskless rate is 4%. The value of the option can be estimated as
Call Value= 100 (0.6803) -150 (exp(-0.04)(10) (0.3156)= $ 36.30 Million
This value can be added on to the net present value of the original investment in Mexico,
which has a negative NPV of $ 20 Million.
NPV of Disney Channel in Mexico = $ 80 Million - $ 100 Million = - $ 20
Value of Option to Expand = $ 36.30 Million
NPV of Project with option to expand = - $ 20 million + $ 36.3 million
= $ 16.3 million
Disney should invest in the Mexican project because the option to expand into the Latin
American market more than compensates for the negative net present value of the
Mexican project.

Tests for Expansion Option to have Value
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, we need to understand three key questions.

1. 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
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 investment. Now consider the Disney
investment in a Spanish channel, without which presumably it is unwilling to expand
into the larger Latin American market. Unlike the patent and undeveloped reserves
examples, the initial investment is not a pre-requisite for the second, though
management might view it as such. The connection gets even weaker, and the option
value lower, 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 Chinese brewery to preserve the option to
enter the Chinese beer market would be examples of less valuable options.
2. 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 the 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 expansion 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.
3. How sustainable are the competitive advantages? In a competitive market place,
excess returns attract competitors, and competition drives out excess returns. The
more sustainable the competitive advantages possessed by a firm, the greater will be
the value of the options embedded in the initial investment. The sustainability of
competitive advantages is a function of two forces. The first is the nature of the
competition; other things remaining equal, competitive advantages fade much more
quickly in sectors where there are aggressive competitors. The second is the nature of
the competitive advantage. If the resource controlled by the firm is finite and scarce
(as is the case with natural resource reserves and vacant land), the competitive
advantage is likely to be sustainable for longer periods. Alternatively, if the
competitive advantage comes from being the first mover in a market or from having
technological expertise, it will come under assault far sooner. The most direct way of
reflecting this competitive advantage in the value of the option is its life; the life of
the option can be set to the period of competitive advantage and only the excess
returns earned over this period counts towards the value of the option.
If the answer is yes to all three questions, then the option to expand can be valuable.

Practical Considerations
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 Home Depot example discussed above. While
we adopted a period of five years, at the end of which the Home Depot has to decide one
way or another on its future expansion in France, it is entirely possible that this time
frame is not specified at the time the store is opened. Furthermore, we have assumed that
both the cost and the present value of expansion are known initially. In reality, the firm

may not have good estimates for either before opening the first store, since it does not
have much information on the underlying market.

Implications of the Expansion Option
The option to expand is implicitly used by firms to rationalize taking projects that
may 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).
It can also be argued that research and development (R&D) provides one
immediate application for this methodology. Firms that expend large resources on
research and development argue that they do so because it provides them with new
products for the future. In recent years, however, more firms have stopped accepting this
explanation at face value as a rationale for spending more money on R&D, and have
started demanding better returns from their investments.

Research, Development and Test Market Expenses
Firms that spend considerable amounts of money on research and development or
test marketing are often stymied when they try to evaluate these expenses, since the
payoffs are often in terms of future projects. At the same time, there is the very real
possibility that after the money has been spent, the products or projects may turn out not
to be viable; consequently, the expenditure is treated as a sunk cost. In fact, it can be
argued that R & D has the characteristics of a call option ““the amount spent on the R&D
is the cost of the call option, and the projects or products that might emerge from the
research provide the options. If these products are viable (i.e., the present value of the
cash inflows exceeds the needed investment), the payoff is the difference between the
two; if not, the project will not be accepted, and the payoff is zero.
Several logical implications emerge from this view of R & D. First, research
expenditures should provide much higher value for firms that are in volatile technologies

or businesses, since the variance in product or project cash flows is positively correlated
with the value of the call option. Thus, Minnesota Mining and Manufacturing (3M),
which expends a substantial amount on R&D on basic office products, such as the Post-it
pad, generally receives less value for its research than does Intel, whose research
primarily concerns semi-conductor chips. Second, the value of research and the optimal
amount to be spent on research will change over time as businesses mature. The best
example is the pharmaceutical industry - pharmaceutical companies spent most of the
1980s investing substantial amounts in research and earning high returns on new
products, as the health care business expanded. In the 1990s, however, as health care
costs started leveling off and the business matured, many of these companies found that
they were not getting the same payoffs on research and started cutting back.

6.10. ˜: R & D Expenditures and Option Pricing
If we perceive research and development expenses as the price of acquiring options
(product patents), research and development expenditure will have most value if directed
a. areas where the technology is stable and the likelihood of success is high
b. areas where the technology is volatile, though the likelihood of success is low
c. Neither

In Practice: Are strategic considerations really options?
Many firms, faced with projects that do not meet their financial benchmarks, use
the argument that these projects should be taken anyway because of “strategic
considerations”. In other words, it is argued that these projects will accomplish other
goals for the firm or allow the firm to enter into other markets. While we are leery of how
this argument is used to justify poor projects, there are cases where these strategic
considerations are really referring to options embedded in projects - options to produce
new products or expand into new markets.
Take the example of the Disney Channel project described above. The project,
based upon conventional capital budgeting, has a negative net present value, but it should

be taken nevertheless, because it gives Disney the option to enter a potentially lucrative
market. Disney might well use the “strategic considerations” argument to take the project
The differences between using option pricing and the “strategic considerations”
argument are the following:
1. Option pricing assigns value to only some of the “strategic considerations” that firms
may have. For instance, the option to enter the Latin American market has value
because of the variance in the estimates of the value of entering the market, and the
fact that Disney has to take the smaller project (the Mexican venture) first in order to
get the option. However, strategic considerations that are not clearly defined or
include generic terms such as “corporate image” or “growth potential” may not have
any value from an option pricing standpoint.
2. Option pricing attempts to put a dollar value on the “strategic consideration” being
valued. As a consequence, the existence of strategic considerations does not
guarantee that the project will be taken. In the Disney example, the Mexican venture
should not be taken if the value of the option to enter the Latin American market is
less than $ 20 million.

The Option to Abandon a Project
The final option to consider here is the option to abandon a project when its cash
flows do not measure up to expectations. Generally, the option to abandon will generally
increase the value of a project and make it more acceptable. 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 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 it is higher, the project should be continued; if it is
lower, the holder of the abandonment option could consider abandoning the project “
Payoff from owning an abandonment option =0 if V > L
=L if V ¤ L
These payoffs are graphed in Figure 6.10, as a function of the expected stock price.

Figure 6.10: The Option to Abandon a Projectt
PV of Cash Flows from

Salvage Value from Abandonment

Unlike the prior two cases, the option to abandon takes on the characteristics of a put

Illustration 6.12: Valuing Disney™s option to abandon: A Real Estate Investment
Assume that Disney is considering taking a 25-year project which requires an
initial investment of $ 250 million in a real estate partnership to develop time-share
properties with a South Florida real estate developer, and where the present value of
expected cash flows is $ 254 million. While the net present value of $ 4 million is small,
assume that Disney has the option to abandon this project anytime by selling its share
back to the developer in the next 5 years for $ 150 million. A simulation of the cash flows
on this time-share investment yields a standard deviation in the present value of the cash
flows from being in the partnership of 20%.
The value of the abandonment option can be estimated by determining the
characteristics of the put option:
Value of the Underlying Asset (S) = PV of Cash Flows from Project
= $ 254 million
Strike Price (K) = Salvage Value from Abandonment = $ 150 million
Variance in Underlying Asset™s Value = 0.202 = 0.04
Time to expiration = Life of the Project =5 years
Dividend Yield = 1/Life of the Project = 1/25 = 0.04 (We are assuming that the project™s
present value will drop by roughly 1/n each year into the project)

Assume that the five-year riskless rate is 4%. The value of the put option can be
estimated as follows:
Call Value = 254 exp(0.04)(5) (0.9194) -150 (exp(-0.04)(5) (0.8300) = $ 89.27 million
Put Value= $ 89.27 - 254 exp(0.04)(5) +150 (exp(-0.04)(5) = $ 4.13 million
The value of this abandonment option has to be added on to the net present value of the
project of $ 4 million, yielding a total net present value with the abandonment option of $
8.13 million.

6.11. ˜: Abandonment Value and Project Life
Consider the project described above. Assume that three years into the project, the cash
flows are coming in 20% below expectations. What will happen to the value of the option
to abandon?
a. It will increase
b. It will decrease
c. It may increase or decrease, depending upon ..

Practical Considerations
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 can be estimated with noise 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 cash flows on the project are even more



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