Assignment task: A builder has located a piece of property that she would like to buy and eventually build on. The land is currently zoned for four homes per acre, but she will request new zoning. What she builds depends on approval of zoning requests and your analysis of this problem to advise her. With her input and your help, the decision process has been reduced to the following cost, alternatives, and probabilities:
Cost of land: $2 million.
Probability that the rezoning request is approved: 0.60.
If the land is rezoned, there will be additional costs for new roads, lighting, and so on, of $1 million.
If the land rezoning is approved, the contractor must decide whether to build a shopping center or 1,500 apartments that the tentative plan shows would be possible. If she builds a shopping center, there is a 70 percent chance that she can sell the shopping center to a large department chain for $4 million; and there is a 30 percent chance that she can sell it to an insurance company for $5 million. If, instead of the shopping center, she decides to build the 1,500 apartments, she places probabilities on the profits as follows: There is a 60 percent chance that she can sell the apartments to a real estate investment corporation for $3,000 each; there is a 40 percent chance that she can get only $2,000 each.
If the land rezoning is not approved, she will comply with the existing zoning restrictions and simply build 600 homes, on which she expects to make $4,000 over the construction cost on each one.
Draw a decision tree of the problem and determine the best solution and the expected net profit.