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Option to extend or shorten. It is possible to extend the life of an asset or a contract by paying a fixed amount of money—an exercise price. Conversely, it is possible to shorten the life of an asset or a contract. The option to extend is a call, and the option to shorten is a put. Real estate leases often have clauses that are examples of the option to extend or shorten the lease.
Option to scope up or scope down. Scope is the number of activities covered in a project. Its optionality is expressed in terms of the ability to switch among alternative courses of action at a decision point in the future. Scope is like diversification—it is sometimes preferable to be able, at a
3 An American option can be exercised at any time up to the maturity date of the option. A European option
can only be exercised on the maturity date.
higher exercise cost, to chose among a wide range of alternatives. Buying the option to have greater scope is a call.
Switching options. The option to switch project operations is a portfolio of options that consists of both calls and puts. Restarting operations when a project is shut down is equivalent to an American call option. Shutting down operations when unfavorable conditions arise is equivalent to an American put option. The cost of restarting (or shutting down) operations may be thought of as the exercise price of the call (or put). A project whose operation can be turned on and off (or switched between two distinct locations, and so on) is worth more than the same project without the flexibility to switch. A flexible manufacturing system with the ability to produce two products is a good example of this type of option, as is peak-load power generation and the ability to exit and reenter an industry.
Compound options. These are options on options. Phased investments are a good example. You may have a factory that can be built as a sequence of real options, each contingent on those that precede it. The project can be continued at each stage by investing a new amount of money (an exercise price). Alternatively, it might be abandoned for whatever it can fetch. Other examples are research and development programs, new product launches, exploration and development of oil and gas fields, and an acquisition program where the first investment is thought of as a platform for later acquisitions.
Rainbow options. Multiple sources of uncertainty produce a rainbow option. Most research and development programs have at least two sources of uncertainty—technological and product-market uncertainty. The latter is represented by the evolution of the uncertain price of the product from a value that is relatively well known today, to less certain values that are affected by the state of the economy as well as other uncertain influences in the future. Thus, product- market uncertainty increases through time. Technological uncertainty, on the other hand, is reduced over time by conducting research until we learn what the product is and what its capabilities are. A similar type of rainbow option is exploration and development of natural resources like oil reserves.
In this section, we compare three decision methodologies: net present value (NPV), decision tree analysis (DTA), and option pricing methods. We also introduce the fundamental concept behind option pricing. This is that a replicating portfolio of priced securities can be found that has the same payouts as the option and therefore has the same market value. This is also called a zero-arbitrage condition, or the law of one price, because assets
with the same payouts should have the same prices in the absence of arbitrage profits.
We use a simple deferral option to illustrate. Suppose that you have the opportunity to invest $115 at the end of the year in a project that has a 50-50 chance of returning either $170 or $65 in cash flows. The risk-free rate, r, is 8 percent. You have found a perfectly correlated or twin security that has payouts of $34 and $13 and is trading in the market for a price of $20 per share. Note that the payouts of the twin security are exactly one-fifth of the payouts on our project in each state of nature. There are two ways to use the twin security to help value our project. First, we can estimate the cost of capital for the twin security and apply it to the expected cash flows of our project—a traditional approach. The cost of capital is calculated as the rate that equates the present value of the expected cash flows with the present value of the twin security as follows:
Since the twin security has perfectly correlated payouts, it has the same risk as our project and we can use the same risk-adjusted discount rate, 17.5 percent, to discount the expected cash flows on the project. The value of the project is therefore,
PV = I -5(5170) +.5 [565)]
A second approach is to create a replicating portfolio—one that uses the expected cash flows of the priced securities to replicate the cash flows of our project. Suppose we choose N shares of the twin security and B dollars of a risk-free bond to compose our replicating portfolio. In the favorable state of nature this portfolio must yield $170,