Decision TreeCase Study

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 USD
Probability of rezoning: 0.50
If rezoned, an additional cost of 1 mill USD
The builder plan is to invest 12 million for construction

If the land is rezoned the contractor must decide whether to build a shopping center or 1100 apartments. If she builds a shopping center she estimates 50% chance that she can sell it to a large department chain for 6 mill USD over her construction cost (which excludes the cost of land), and she estimates 50% chance that she can sell it to an insurance company for 4 mill USD over construction cost.

If instead of the shopping center she decides to build the 1100 apartments she places probabilities on her profit as follows: 40% chance that she can sell the apartments for 2700 USD each over construction cost and 60% that she gets only 24000 USD for each apartment.

If the land is not rezoned she can only build 400 homes on which she expects to make 3705.41 USD each over construction cost (as before excluding cost of land).

The constructor is also aware of the interest rate offered by banks that is 3% annually compoinded monthly to two-year time deopsits.

Draw a decision tree of this problem and determine the best solution and the expected net profit.





Sample Solution