Question

1. Assume that Five Cities is a wholly owned subsidiary of CMI, that is, they are both run by the same management. In conjunction with building the plant, CMI can make a number of investments prior to the start of construction to increase the potential value of the completed plant. The possibilities for such investment are given below:

If CMI invests an additional:	The value of the plant will be:
0	3.2 million
.04 million	3.24 million
.11 million	3.315 million
.12 million	3.316 million

Also, the CMI management knows that construction costs for its Five Cities subsidiary may rise. There is a 75% chance that the cost of building the plant will be 2.8 million, and a 25% chance that it will be 3.29 million.

Assume that the goal of CMI/Five Cities management is to maximize expected profit (value of plant minus expected cost of building and additional investment). Note that they have four levels of additional investment they can choose (none, .04, .11, or .12 million), but must make this choice before they know the cost of construction. Note also that they may decide not to build the plant at all if construction costs turn out to be high, but will still lose the value of any additional investments, which have to be made before construction starts.

a. What will CMI’s optimal strategy be? That is, what level of additional investment will they choose, and will they actually build the plant if cost of building is high? Remember that expected profit for a strategy is .75 X (profit if construction costs are low) + .25 X (profit (or loss) if construction costs are high).

b. Assuming that CMI operates in a competitive market, the strategy chosen by CMI is the socially optimal one. Explain how we know this.

2. Assume all the facts are the same as in question 1, except assume once again that Five Cities construction is a separate company from CMI, and has signed a contract to do the construction project for a payment (in advance) of 3 million.

a. Suppose both parties know that the remedy for CMI in case of a breach will be a payment equal to the value of the unbuilt plant, where that value is determined based on whatever reliance investments CMI might have made (For example, if CMI invested an additional .04 beyond the 3 million it paid Five Cities, then in the event of breach Five Cities would have to pay 3.24 million to CMI – that is, return the 3 million it got from CMI plus the .04 that CMI invested in reliance plus .20 million that CMI expected in profit). Under these circumstances, what level of reliance investment would CMI undertake? If the costs turned out to be high, would Five Cities breach or perform? Explain.

b. The socially optimal outcome in this question is the same as in question 3, but in this question’s scenario the decisions made about how much to invest and whether the plant is built under various circumstances are different from the decisions made in question 3. What causes the socially sub-optimal decisions to be made in this scenario?

Answer 1