# Decision Tree and Expected Values

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: $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 or 1500 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 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 1500 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 that 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.

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#### Solution Preview

See attached file.

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

I went through the problem step by step. Each time there was an option, I added a branch on the decision tree. For each branch, I noted costs and probabilities.

I then found the probability of each outcome by multiplying the probabilities. For example, the probability that she could sell 1500 apartments for $200 each is:

0.4 (she can sell them for $2000) x 0.6 (the land ...