Please show the work for each answer (answer's are correct)

Question 3 A developer is examining the economic feasibility of a potential purchase of a parcel of land. Zoning restrictions limit development of the land to either a shopping mall or an office building. Building the mall is a larger endeavor. The developer believes there is a 25% chance that the mall will be built instead of the office. If the mall is built, there is a 5% chance that it will become very popular, resulting in economic success and a payoff of $500 million. However, malls are going out of popularity, so there is a 95% chance that it will result in economic failure, with a payoff of $40 million (that is a loss of 40 million dollars). Building the office is more reliable. The developer assigns a 75% probability that an office will be built. If it is, there is a 60% chance that it will be an economic success, resulting in a $20 million payoff. There is a 40% chance that it will be an economic failure resulting in a payoff of $30 million (that is a loss of 30 million dollars). Note that the purchase price of the land is already incorporated in the payoffs listed above. a. What is the expected value of this purchase? Should the developer make this purchase? (4 pts) Overall EV is -3.25 million. The developer should not make the purchase. b. Now suppose that if the developer purchases the land, she can choose whether to build a mall or an office on the land. Draw a decision tree for this problem. What is the new expected value of the purchase? Should the developer make this purchase? (6 points) New EV of purchase is 0 . She is indifferent about making the purchase. c. Continue from part b. What is the minimum payoff for economic success of the mall for which the developer would choose to build a mall over an office? (4 pts) 760 million d. How many root nodes are in the decision tree? How many end nodes (also called terminal or leaf nodes) are in the decision tree? (2 points) 1 root and 4 leaf nodes