# Westcliff University Finance for Business Binomial Model Questions

## Question Description

I’m working on a economics question and need an explanation to help me learn.

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):

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

1. 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).
2. Suppose you can only exercise your option now, or after nine months (not at month 3 or 6). Would you exercise now?
3. Suppose you can exercise now, or at month 3, 6, or 9. What is your option worth today? Should you exercise today, or wait?