Jenny Simpson, a local construction company's president, has located a piece of property that she would like to buy and eventually build on. The parcel of 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: $4 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 parcel of land is rezoned, Jenny Simpson must decide whether to build a shopping center or 1,100 apartments that the tentative plan shows would be possible. If she builds a upscale shopping center, there is a 30 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 70 percent chance that she can sell it to an insurance company for $6 million over her construction cost (also excluding the land). If, instead of the shopping center, she decides to build the 1,100 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 $1,500 each over her construction cost; there is a 50 percent chance that she can get $2,100 each over her construction cost. (Both exclude the land cost.)
If the parcel of land is not rezoned, she will comply with the existing zoning restrictions and simply build 450 homes, on which she expects to make $3,800 over the construction cost on each one (excluding the cost of land).
1) What is the expected value for the rezoned shopping center, if the rezoning cost is included?
2) What is the expected value for the rezoned apartment plan, if the rezoning cost is included?
3) What is the expected revenue, if the parcel land is not rezoned?
4) What is the expected net profit of this entire project?