A builder has located a piece of property that she would like to buy and eventually build on. The land is currently zoned for 4 homes per acre, but she is planning to request new zoning. What she builds depends on approval of the zoning request and your analysis of this problem to advise her. With her input and your help the decision process has been reduced to the following costs, alternatives and probabilities:
Cost of land: 2 mill US
Probability of rezoning: 60%
If rezoned, an additional cost of 1 mill US
If the land is rezoned the contractor must decide whether to build a shopping center or 1.500 apartments. If she builds a shopping center she estimates 70% chance that she can sell it to a large department chain for 4 mill US over her construction cost (which excludes the cost of land), and she estimates 30% chance that she can sell it to an insurance company for 5 mill US over construction cost.
If instead of the shopping center she decides to build the 1.500 apartments she places probabilities on her profit as follows: 60% chance that she can sell the apartments for 3.000 US each over construction cost and 40% that she gets only 2.000 US for each apartment.
If the land is not rezoned she can only build 600 homes on which she expects to make 4.000 US each over construction cost (as before excluding cost of land).
Draw a decision tree of this problem and determine the best solution and the expected net profit.