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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 the 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: \(2 million.

Probability of rezoning: 60.

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 or1, 500 apartments that the tentative plan shows would be possible. If she builds a shopping center, there is a 70 percent chance that she can sell the shopping center to a large department store chain for \(4 million over her construction cost, which excludes the land; and there is a 30 percent chance that she can sell it to an insurance company for \)5 million over her construction cost (also excluding the land). If instead of the shopping center, she decides to build the 1,500 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 \(3,000 each over her construction cost; there is a 40 percent chance that she can get only \)2,000 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 600 homes, on which she expects to make $4,000 over the construction cost on each one (excluding the cost of land).

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

Step by step solution

01

Decision tree

A Decision Tree is a sort of specialized system used to categorize and make probabilities primarily based totally on how a preceding set of problems have been solved and answered.

02

Calculation of the net expected net profit

Given: Cost of land= $62 million

Probability of rezoning =.60

Rezoning = - $2 million - $1 million + (0.7) ($4M) + (0.3) ($5)

= $1.3 Million

Rezoning = -$2M - $1M + (0.6) (3000) (1500) + (0.4) (2000) (1500)

= $900,000

Not Rezoning = ($4000) (600) - $2M

= $400,000.

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