Two companies are developing a 50-50joint venture with an NPV of $25 million. The annual volatility of the venture is 20% and its WACC is 12%. The risk-free rate is 5%. One of the companies wants to buy the right from the other to acquire its 50% share in a year for $15 million.
(a) Using a two-period model (six months per period), what is the maximum price the company should be ready to pay for the option?
(b) Using a three-period model (four months per period), how does the option price change?
(c) How can we use the Black-Scholes formula to solve this problem? What is the option price if we use the Black-Scholes formula?
(d) Which of the three prices would you use to make a decision and why?
(e) What price would you use if the buyer wants the right to buy the share at any time during the year?