1.) Two construction companies are bidding against one another for the right to construct a new community center building. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according to the distribution shown in this table:

Buffalo Valley's Bid Bid Probability

$160,000 0.3

$165,000 0.4

$170,000 0.2

$175,000 0.1

Furthermore, Fine Line Homes estimates that it will cost $160,000 for its own company to construct this building. Given its fine reputation and long-standing service within the local community, Fine Line Homes believes that it will likely be awarded the project in the event that it and Buffalo Valley Construction submit exactly the same bids. Find the bid that maximizes Fine Line's expected profit.

2.) A company is determining whether to build a large production plant or whether to build a small plant with the option of expanding the plant after two years. The relevant uncertainty is the average demand for the product. The company believes that demand could be high initially (first two years), followed either by continued high demand or followed by diminished, low demand, or the demand could be low initially, in which case it will continue to be low. The monetary values for each outcome are as follows:

A large plant with high volume would yield $1,000,000 annually in cash flow. A large plant with low volume would yield only $100,000 because of high fixed costs and inefficiencies. A small plant with low demand would be economical and would yield an annual cash income of $350,000. A small plant, during an initial period of high demand (first two years), would yield $450,000 per year, but this would drop to $400,000 yearly in the long run due to increased maintenance to maintain the high output. If the small plant were expanded to meet sustained high demand, it would yield $700,000 cash flow annually, and so would be less efficient than a large plant built initially. If the small plant were expanded but high demand were not sustained, estimated annual cash flow would be $50,000. It is estimated that a large plant would cost $3 million to put into operation, a small plant would cost $1.3 million, and the expansion of the small plant would cost an additional $2.2 million.

The company executives would like to consider the expected monetary values over a 10-year time horizon. The decision tree is shown below.

Round answers to 1 decimal place in units of $M.

a. What is the expected monetary value of building the large plant? $M b. What is the expected monetary value of building the small plant? $M c. If the company is risk neutral, which plant should it build? Enter either "Large" or "Small"