1. Suppose you currently own 100 shares of stock in ABC Company. You have decided to sell the stock, but haven't decided whether you will sell today or sell in exactly two weeks. Today, the stock sells for $35.00 per share. Based on historical data, you have assessed that the stock has a 60% chance of going up to $40.00 and a 40% chance of going down to $30.00 at the end of the two week period. You are further deciding whether to seek the advice a consultant, who works for a nearby brokerage rm. You feel the consultants expertise could provide better estimates on the probabilities of the stock going up to $40.00 or down to $30.00 at the end of the two week period [assume that only these two stock prices are possible]. There would be a $100.00 charge for the advice, but you would receive the advice in a matter of hours. You have obtained this consultant's advise before and have found it to be quite good. When stock prices actually went up, he had correctly predicted they would go up 85% of the time. When stock prices actually went down, he had correctly predicted they would go down 95% of the time. Order the decisions and uncertainties you face in this decision problem and aggregate them into a decision tree. After labeling both the endpoint values in terms of protability and the probabilities within the tree, perform backwards induction to determine the optimal strategy. Assume you are an expected value decision maker. 2. A small real estate investment rm is considering a new project A piece of land has become available for purchase which has the potential to be the site of a new ofce building the rm is considering building and leasing. A decision regarding the purchase of the land must be made immediately because there is another interested buyer. The land can be purchased for $100,000. The cost of constructing the new ofce building will depend upon what interest rates are at the time of construction since this part of the project must be nanced. If interest rates are low, the construction costs [including nancing costs) will be $600,000. If interest rates are high, the construction costs [including nancing costs) will be $1,000,000. The rm expects interest rates to be low with probability .4 and high with probability .6. If the rm decides to buy the land, then their decision to build or not will be determined after the interest rate uncertainty has been resolved. If the building is built, the income gained from leasing it will depend upon whether the rm can lease all of the ofce space, or only a fraction of it. The rm expects that it will achieve full occupancy with 30