9. Timing options (S23.2) 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 free cash flow (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

$2,970 – 50 = $2,920

(+10%)

PV – $2,700

$2,455 – 50 = $2,405

(–9.09%)

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).