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Initial Investment in Project

Present Value of Expected
Project has negative
Cash Flows
NPV in this range
Project's NPV turns
positive in this range

Note that this payoff diagram is that of a call option ““ the underlying asset is the project,
the strike price of the option is the investment needed to take the project; and the life of
the option is the period for which the firm has rights to the project. 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.

Obtaining The Inputs For Option Valuation
On the surface, the inputs needed to apply option pricing theory to valuing the
option to delay are the same as those needed for any application: the value of the
underlying asset; the variance in the value; the time to expiration on the option; the strike
price; the riskless rate and the equivalent of the dividend yield. Actually estimating these
inputs for product patent valuation can be difficult, however.

Value Of The Underlying Asset
In the case of product options, the underlying asset is the project itself. The
current value of this asset is the present value of expected cash flows fro initiating the
project now, which can be obtained by doing a standard capital budgeting analysis. There
is likely to be a substantial amount of noise 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 for why the project delay option has value. If the expected cash

flows on the project were known with 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.

Variance In The Value Of The Asset
As noted in the prior section, there is likely to be considerable uncertainty
associated with the cash flow estimates and the present value that measures the value of
the asset now, 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. First, if similar projects have been introduced in the past,
the variance in the cash flows from those projects can be used as an estimate. Second,
probabilities can be assigned to various market scenarios, cash flows estimated under
each scenario and the variance estimated across present values. Finally, the average
variance in firm value of publicly traded companies which are in the business that the
project will be in can be used. Thus, the average variance in firm value of bio-technology
companies can be used as the variance for the option to delay a bio-technology 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 a
option to do a project in a stable business will be less than the value of one in an
environment where technology, competition and markets are all changing rapidly.

There is a data set on the web that summarizes, by sector, the variances in firm
value and stock prices.

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 equivalent to 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.

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 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.

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.6 If the cash flows are evenly distributed over time, and the life of the patent is
n years, the cost of delay can be written as:

Annual cost of delay =
Thus, if the project rights are for 20 years, the annual cost of delay works out to 5% a

6.7. ˜: Cost of Delay and Early Exercise
For typical listed options on financial assets, it is argued that early exercise is almost
never optimal. Is this true for real options as well?
a. Yes
b. No

Illustration 6.10: Valuing a patent
Assume that a pharmaceutical company has been approached by an entrepreneur
who has patented a new drug to treat ulcers. The entrepreneur has obtained FDA approval
and has the patent rights for the next 17 years. While the drug shows promise, it is still

6 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.

very expensive to manufacture and has a relatively small market. Assume that the initial
investment to produce the drug is $ 500 million and the present value of the cash flows
from introducing the drug now is only $ 350 million. The technology and the market is
volatile, and the annualized standard deviation in the present value, estimated from a
simulation is 25%.7
While the net present value of introducing the drug is negative, the rights to this
drug may still be valuable because of the variance in the present value of the cash flow.
In other words, it is entirely possible that this drug may not only be viable but extremely
profitable a year or two from now. To value this right, we first define the inputs to the
option pricing model:
Value of the Underlying Asset (S) = PV of Cash Flows from Project if introduced now
= $ 350 million
Strike Price (K) = Initial Investment needed to introduce the product = $ 500 million
Variance in Underlying Asset™s Value = (0.25)2 = 0.0625
Time to expiration = Life of the patent = 17 years
Dividend Yield = 1/Life of the patent = 1/17 = 5.88%
Assume that the 17-year riskless rate is 4%. The value of the option can be estimated as
Call Value= 350 exp(-0.0588)(17) (0.5285) -500 (exp(-0.04)(17) (0.1219)= $ 37.12 million
Thus, this ulcer drug, which has a negative net present value if introduced now, is still
valuable to its owner.

6.8. ˜: How much would you pay for this option?
Assume that you are negotiating for a pharmaceutical company that is trying to buy this
patent. What would you pay?
a. $ 37.12 million
b. More than $ 37.12 million
c. Less than $ 37.12 million

7 This simulation would yield an expected value for the project of $350 million and the standard deviation
in that value of 25%.


Practical Considerations
While it is quite clear that the option to delay is embedded in many projects, 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. One way of doing this is to run a series
of simulations capturing as many scenarios for the future as possible and then calculating
the variance in the present values derived from these simulations. An alternative is to use
the variances in stock prices of firms involved in the same business; thus, the stock price
variance of publicly traded biotechnology firms may be used as a proxy for the variance
of a biotechnology project™s cash flows.
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 value follows a
diffusion process, and that the variance in value remains unchanged over time, may be
difficult to justify in the context of a project. 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.
Unlike the example above, in which the firm had exclusive rights to the project for 20
years, often the firm™s rights may be less clearly defined, both in terms of exclusivity and
time. 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.

6.9. ˜: Exclusive Rights and the Option Feature
A firm in an extremely competitive sector is faced with a project that has a negative net
present value currently and wants to know how much the option to delay the project is
worth. Which of the following would you think is the right response?

a. It should be the value from the option pricing model
b. It should be zero
c. Neither

Implications Of Viewing The Right To Delay A Project As An Option
Several interesting implications emerge from the analysis of the option to delay a
project as an option. First, a project may have a negative net present value based upon
expected cash flows currently, but it may still be a “valuable” project because of the
option characteristics. Thus, while a negative net present value should encourage a firm
to reject a project, it should not lead it to conclude that the rights to this project are
worthless. Second, a project may have a positive net present value but still not be
accepted right away because the firm may gain by waiting and accepting the project in a
future period, for the same reasons that investors do not always exercise an option just
because it is in the money. This is more likely to happen if the firm has the rights to the
project for a long time, and the variance in project inflows is high. To illustrate, assume
that a firm has the patent rights to produce a new type of disk drive for computer systems
and that building a new plant will yield a positive net present value right now. If the
technology for manufacturing the disk drive is in flux, however, the firm may delay
taking the project in the hopes that the improved technology will increase the expected
cash flows and consequently the value of the project.

The Option to Expand a Project
In some cases, firms take projects because doing so allows them either to take on
other projects or to enter other markets in the future. In such cases, it can be argued that
the initial projects are options allowing the firm to take other projects, and the firm
should therefore be willing to pay a price for such options. A firm may accept a negative
net present value on the initial project because of the possibility of high positive net
present values on future projects.

The Payoffs to the Option to Expand
To examine this option using the same framework developed earlier, 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 project. This scenario implies the option payoffs shown in Figure 6.9.

Figure 6.9: The Option to Expand a Project

PV of Cash Flows

Cost of Expansion

Present Value of
Expansion has negative NPV
Expansion NPV turns positive Expected Cash Flows
in this range
in this range

As you can see, at the expiration of the fixed time horizon, the firm will enter the new
market or take the new project if the present value of the expected cash flows at that point
in time exceeds the cost of entering the market.

Illustration 6.11: Valuing an Option to Expand: Disney Entertainment
Assume that Disney is considering investing $ 100 million to create a Spanish
version of the Disney channel to serve the growing Mexican market. Assume, also, that a
financial analysis of the cash flows from this investment suggests that the present value
of the cash flows from this investment to Disney will be only $ 80 million. Thus, by
itself, the new channel has a negative NPV of $ 20 million.
One factor that does have to be considered in this analysis is that if the market in
Mexico turns out to be more lucrative than currently anticipated, Disney could expand its
reach to all of Latin America with an additional investment of $ 150 million any time
over the next 10 years. While the current expectation is that the cash flows from having a

Disney channel in Latin America is only $ 100 million, there is considerable uncertainty
about both the potential for such an channel and the shape of the market itself, leading to
significant variance in this estimate.
The value of the option to expand can now be estimated, by defining the inputs to
the option pricing model as follows:
Value of the Underlying Asset (S) = PV of Cash Flows from Expansion to Latin
America, if done now =$ 100 Million
Strike Price (K) = Cost of Expansion into Latin American = $ 150 Million
We estimate the standard deviation in the estimate of the project value by using the


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