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: 0.40. 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 50 percent chance that she can sell the shopping center to a large department store chain for $5 million over her construction cost, which excludes the land; and there is a 50 percent chance that she can sell it to an insurance company for $8 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 60 percent chance that she can sell the apartments to a real estate investment corporation for $2,000 each over her construction cost; there is a 40 percent chance that she can get $2,500 each over her construction cost.

the best alternative is to sell the shopping center to the insurance company

Explanation:

Step 1:  

Facts given in the case

Current rezoning policy = 4 home / acre

Cost of land = $3, 000, 000

Rezoning alternative: (RZ)

Probability of rezoning = 0.40

Additional costs = $1, 000, 000

Alternatives: 1 shopping center (SC) or 1, 400 apartments (AP)

Probability of selling shopping center to large department store chain (DS) = 0.50

Profit from selling shopping center to large department chain store excluding land cost = $5,000, 000

Probability of selling shopping center to insurance company (IC) = 0.50

Profit from selling shopping center to insurance company excluding land cost = $8,000, 000

Probability of selling 1, 400 apartments to real estate investment (RE) = 0.60

Profit from selling the to a real estate investment = 1, 400 x $2, 000 = $2, 800, 000

Probability of selling 1, 400 apartments to others (OT) = 0.40

Profit from selling 1, 400 apartments to others excluding land cost = $2, 500 x 1, 400 = $3, 500, 000

Non- rezoning alternative: (NRZ)

Probability of non-rezoning = 0.60

Number of homes to be built (H)= 500 homes (mock figure as full question is not given)

Profit from selling 500 homes excluding the land cost = $3, 500 x 500 = $1, 750, 000

(mock figures as complete question is not given)

What is the best alternative?  

Land if rezone, build shopping center and sell it to the insurance company

It has the highest profits = $8, 000, 000

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