Company A (the acquirer) is currently considering acquiring Company T (the target). Company A will be making a take-it-or-leave it offer to Company T. The main complication is this: the value of the company T depends directly on the outcome of a major oil exploration project it is currently undertaking. The very viability of Company T depends on the exploration outcome. In the worst case (if the exploration fails completely), the company under current management will be worth nothing – $0/share. In the best case (a complete success), the value under current management could be as high as $100/share. Given the range of exploration outcomes, all share values between $0 and $100 per share are considered equally likely. By all estimates the company will be worth considerably more in the hands of Company A than under current management. In fact, whatever the value under current management, the company will be worth 50 percent more under the management of Company A than under Company T. The offer must be made now, before the outcome of the drilling project is known to Company A. In contrast, Company T will know the results when deciding whether or not to accept the offer. In addition, Company T is expected to accept any offer by Company A that is greater than or equal to the (per share) value of the company under its own management. 

(a) Suppose that Company A makes an offer X ? [0, 100] per share. Calculate probability that the offer is accepted by Company T. 

(b) If the offer X is accepted, what is the expected value of the acquisition to Company A? (Hint: think about why offer of X is accepted and its implications for the value of the company)

 (c) Calculate the optimal offer X company A should make