Question 5: Binomial trees.

NanoTech (NT), a dominant PC software company, intends to make a tender offer for Ratiocyn, a rapidlygrowing developer of personal tax software. However, because of concerns about the predatory behavior of NT, it is possible that the antitrust division of the U.S. Department of Justice will decide that NT may not acquire Ratiocyn. The Justice Department will announce its decision in exactly two months. NT has announced that, if it is allowed to pursue the tender offer, it will make a cash offer of $60 per share for all outstanding shares. This is a very good offer, as the market value of Ratiocyn, should the tender offer not be allowed to go through, will fall immediately to $30 per share. The market value of Ratiocyn is currently $43 per share.The tender offer is structured in such a way that, upon approval of the Justice Department, a Ratiocynholder could tender and immediately receive $60 per share. The monthly, continuously-compounded risk-free rate for borrowing and lending is 1.00%.

1.Find the value of a call option on Ratiocyn, with strike price of 50, that will mature just after theJustice Departments ruling is tobeannounced. (Hint: Set Su = 60 Sd = 30)

2.Solve for the risk adjusted probability that the Justice Department will allow the tender offer to go through.

3.If the true probability of the tender offer going through is 50%, find the (monthly, simple) rate at which the market is discounting the cash flows from Ratiocyn common stock.

4.Now suppose a leak emerges from the Justice Department which shifts the true probability of a ruling in favor of NT to 40%, but the rate at which the market discounts the expected future cash flows from Ratiocyn remains the same as in question c. Does the price of the call change? If so, what is the new value?

5.We determined in class that the true probability of an up or down move is not important for pricing options. How do you reconcile this with your answer in part d)?