Question

Joe Builder has located a piece of property that he plans to buy and build on and then sell to a third party. The land is currently zoned for four homes per acre, however Joe is planning to request that to be rezoned. What Joe builds depends on the approval of the rezoning request and your analysis of his situation. With his input and your help the decision process has been reduced to the following costs, alternatives and probabilities:

Cost of land : $2 million

Probability of rezoning: 0.60

If the land is rezoned, there will be additional costs for new roads, lighting, etc. of $1 million. This will be referred to as property improvements.

If the land is rezoned, Joe must decide whether to build a shopping center or 1,500 apartments. In either case, Joe is planning to sell the property after he has built either the shopping center or apartments. He is certain that he can sell the property, although there are probabilities associated with who would be the buyer. If a shopping center is built, it can be sold to either an insurance company for a profit of $5 million before the cost of the land and the property improvements or to a large department store chain for a profit of $4 million before the cost of the land and property improvements are considered. The probability of selling it to the department store chain is 70 percent so that the probability of selling it to the insurance company is 30 percent. If instead of the shopping center, he decides to build the 1,500 apartments, the probabilities on the profits for selling them are as follows:

40 percent chance he can get a profit of $2,000 for each apartment before the cost of the land and property improvements are considered or 60 percent chance he can get a profit of $3,000 for each apartment before the cost of the land and property improvements are considered.

If the land is not rezoned, Joe will comply with the existing zoning restrictions and simply build 600 homes on which he expects to make a profit of $4,000 on each one before the cost of the land is considered.

Using the decision tree and expected value approach, determine the best solution for Joe and his expected net profit. In providing your answer include your decision tree.

Answer 1

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Answer

IF THE LAND IS NOT REZONED WE GET REVENUES=600*4000=240000

COSTS =   2000000

EXPECTED PROFITS= .4*(240000-2000000) < 0—LOSSES ARE MADE

IF LAND IS REZONED TOTAL COSTS =3 MILLION

EXPECTED REVENUES FROM BUILDING APPARTMENTS=.4*(2000*1500) +.6*(3000*1500)= 3900000

EXPECTED REVENUES FROM SHOPPING CENTRE=.3*(5 MILLION) +.7*(4 MILLION)= 4300000

TOTAL EXPECTED PROFITS FROM APPARTMENTS= .6*(3900000-3000000)=540000

TOTAL EXPECTED PROFITS FROM SHOPPINF CENTRE= .4*(4300000-3000000)=520000

SINCE EXPECTED PROFITS ARE HIGHER FROM APPARTMENTS, THEY MUST BE BUILT.