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Bussiness Examination Paper

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|15. |Binomial valuation 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): |
| |[pic] |
| |The risk-free interest rate is 2% per quarter. |
| |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). |
| |Suppose you can only exercise your option now, or after nine months (not at month 3 or 6). Would you exercise now? |
| |Suppose you can exercise now, or at month 3, 6, or 9. What is your option worth

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