A large defense contractor is considering making a specialized investment in a facility to make helicopters. The firm currently has a contract with the government, which, over the lifetime of the contract, is worth $100 million to the firm. It is considering building a new production plant for these helicopters; doing so will reduce the production costs to the company, increasing the value of the contract from $100 million to $200 million. The cost of the plant will be $60 million. However, there is the possibility that the government will cancel the contract. If that happens, the value of the contract will fall to zero. The problem (from the company's point of view) is that it will only find out about the cancellation after it completes the new plant. At this point, it appears that the probability that the government will cancel the contract is 0.45.
a) Draw a decision tree reflecting the decisions the firm can make and the payoffs from those decisions. Carefully distinguish between chance nodes and decision nodes in the tree.
b) Assuming that the firm is a risk-neutral decision maker, should the firm build a new plant? What is the expected value associated with the optimal decision?
c) Suppose instead of finding out about contract cancellation after it builds the plant, the firm finds out about cancellation before it builds the plant. Draw a new decision tree corresponding to this new sequence of decisions and events. Again assuming that the firm is a risk-neutral decision maker, should the firm build the new plant?