## 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

Figure 6.9: The Option to Expand a Project

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 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 follows:

Call Value= 100 (0.6803) -150 (exp(-004)(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

Million

Value of Option to Expand = $ 36.30 Million

NPV of Project with option to expand = - $ 20 million + $ 36.3 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.

## Lessons From The Intelligent Investor

If you're like a lot of people watching the recession unfold, you have likely started to look at your finances under a microscope. Perhaps you have started saving the annual savings rate by people has started to recover a bit.

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