Question

1. You have an option to purchase all of the assets of the Overland Railroad for $1.5 billion. The option expires in nine months. You estimate Overland's current (month 0) present value (PV) as $1.65 billion. Overland does not generate a free cash flow (FCF) at the end of any quarter. In each quarter, Overland's PV either increases by 10% or decreases by 9.09%. The risk-free interest rate is 5% per quarter

risk free int. rate:          0.05

increase:                         0.1

decrease:                        0.0909

FCF                                    0

p =                                     0.738

PV=                                    1500  

0 months	3 months	6 months	9 months
			2196
		1997
			1815
	1815
			1815
		1650
			1500
1650	358
			1815
		1650
			1500
	1500
			1500
		1364
			1240

Answer 1

First of all we will calculate the payoff at every node taking strike price as 1500 as shown in figure below

then we will Start the solution from 9 month period to calculate the present value of payoffs using risk neutral probability

The answer comes to $ 358.05 Million