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Problem

You have an option to purchase all of the assets of the Overland Railroad for $2.5 billion. The option expires in nine months. You estimate Overland’s current (month 0) present value (PV) as $2.7 billion. Overland generates after-tax free cash flow (FCF) of $50 million at the end of each quarter (i.e., at the end of each three-month period). If you exercise your option at the start of the quarter, that quarter’s cash flow is paid out to you. If you do not exercise, the cash flow goes to Overland’s current owners.

In each quarter, Overland’s PV either increases by 10% or decreases by 9.09%. This PV includes the quarterly FCF of $50 million. After the $50 million is paid out, PV drops by $50 million. Thus the binomial tree for the first quarter is (figures in millions):

Month 0 (now)    Month 3 (end of quarter)

PV before payout – FCF = end-of-quarter PV

The risk-free interest rate is 2% per quarter.

a. Build a binomial tree for Overland, with one up or down change for each three-month period (three steps to cover your nine-month option).

b. Suppose you can only exercise your option now, or after nine months (not at month 3 or 6). Would you exercise now?

c. Suppose you can exercise now, or at month 3, 6, or 9. What is your option worth today? Should you exercise today, or wait?

Step-by-step solution

Option gives the right to the option buyer to buy or sell a predetermined quantity of the underlying asset at a specific price and at a predetermined date. Binomial valuation model determines the option value at which the option should be bought.

Given:

Step 1 of 4

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Comment

a.

Given the other information in the problems the binomial tree for the company for each month is prepared.

The option values are given in parentheses. The value of the options is computed using the risk neutral method.

For example if we find out the value for sixth moth (required for b.). Let the probability for the rise in the asset value is “p”. If the investor is risk neutral then:

In the sixth month the value of the asset is $3,162 as given in the figure, the value of the option is thus calculated as:

Similarly all the option values as given above are calculated.

In the sixth month the value of the asset is $2,815 or 2,318 as given in the figure, the value of the option is thus calculated as:

Comment

b.

If the option is not exercised now, the value of the option is $327, which is more than the value of the option if it will be exercised at $200. Hence, from the calculation given above in (a), the option should not be exercised now. It should be exercised when the value is less than the exercise price.

Comment

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Step 3 of 4

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c.

The value of the option today is $327 as shown in the option tree. If the option is exercised in month 3, the value including dividend is $2,970 and if exercised the value will become

If not exercising the value of the option is $491. The value of the option will be more after then he will receive the dividend and the value of the option increases. Hence, should not be exercised now.

Comment

Step 4 of 4

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Chapter 22, Problem 13P

You have an option to purchase all of the assets of the Overland Railroad for $2.5 billion. The option expires in nine months....

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