Problem
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 is planning to 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 costs, alternatives, and probabilities:
Cost of land: $3 million.
Probability of rezoning: 0.50.
If the land is rezoned, there will be additional costs for new roads, lighting, and so on, of $1 million.
If the land is rezoned, the contractor must decide whether to build a shopping center or 1,400 apartments that the tentative plan shows would be possible.
If she builds a shopping center, there is a 40 percent chance that she can sell the shopping center to a large department store chain for $6 million over her construction cost, which excludes the land; and there is a 60 percent chance that she can sell it to an insurance company for $3 million over her construction cost (also excluding the land). If, instead of the shopping center, she decides to build the 1,400 apartments, she places probabilities on the profits as follows:
There is a 50 percent chance that she can sell the apartments to a real estate investment corporation for $2,600 each over her construction cost; there is a 50 percent chance that she can get only $2,500 each over her construction cost. (Both exclude the land cost.)
If the land is not rezoned, she will comply with the existing zoning restrictions and simply build 550 homes, on which she expects to make $3,800 over the construction cost on each one (excluding the cost of land).
a. What is the expected value for the rezoned shopping center? (Enter your answer in millions rounded to 2 decimal places.)
Expected value $
million
b. What is the expected value for the rezoned apartments? (Enter your answer in millions rounded to 2 decimal places.)
Expected value $
million
c. If the land is rezoned, what must the contractor decide?
Build shopping center
Build apartments
d. What is the expected revenue (excluding the cost of land) associated with buying/developing the property? (Enter your answer in millions rounded to 2 decimal places.)
Expected value $
million
e. What is the expected net profit (including the cost of land) associated with buying/developing the property? (Negative amount should be indicated by a minus sign. Enter your answer in millions rounded to 2 decimal places.)
Expected value $
million