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 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: 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 1,200 apartments that the tentative plan shows would be possible. If she builds a shopping center, there is a 80 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 20 percent chance that she can sell it to an insurance company for $3 million over her construction cost (also excluding the land). If, instead of the shopping center, she decides to build the 1,200 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 $2,300 each over her construction cost, there is a 40 percent chance that she can get only $2,250 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 500 homes, on which she expects to make $4,200 over the construction cost on each one (excluding the cost of land). a. What is the expected value for the rezoned shopping center, if the rezoning cost is included (but land cost is excluded)? (Do not round your intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Negative amounts should be indicated by a minus sign.) million Expected value b. What is the expected value for the rezoned apartments, if the rezoning cost is included (but land cost is excluded)? (Do not round your intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Negative amounts should be indicated by a minus sign.) million Expected value b. What is the expected value for the rezoned apartments, if the rezoning cost is included (but land cost is excluded)? (Do not rout your intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Negative amounts should be indicated by a sign.) Expected value million c. If the land is rezoned, what should the contractor decide? O Build shopping center O Build apartments d. What is the expected revenue, if the land is not rezoned (excluding the land cost)? (Do not round your intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Negative amounts should be indicated by a minus sign.) Expected value million e. What is the expected net profit of entire project, including all applicable costs? (Do not round your intermediate calculations. Enter your answers in millions rounded to 2 decimal places, Negative amounts should be indicated by a minus sign.) Expected value million

To advise the builder on her decision, we need to calculate the expected values for the rezoned shopping center, rezoned apartments, revenue if the land is not rezoned, and the expected net profit of the entire project. The expected value for the rezoned shopping center is calculated based on the probabilities of selling to a department store chain or an insurance company.

a. To calculate the expected value for the rezoned shopping center, we multiply the probabilities of selling to a department store chain or an insurance company by their respective profits over construction cost:

Expected value = (0.80 * $6 million) + (0.20 * $3 million) - $1 million = $3.6 million - $0.2 million - $1 million = $2.4 million.

b. The expected value for the rezoned apartments is calculated by multiplying the probabilities of selling to a real estate investment corporation by their respective profits over construction cost:

Expected value = (0.60 * $2,300) + (0.40 * $2,250) - $1 million = $1,380 + $900 - $1 million = $280,000.

c. Comparing the expected values, the contractor should decide to build the shopping center since its expected value of $2.4 million is higher than the expected value of the apartments, which is $280,000.

d. If the land is not rezoned, the builder will construct 500 homes, with an expected profit of $4,200 per home:

Expected revenue = 500 * $4,200 = $2.1 million.

e. The expected net profit of the entire project can be calculated by subtracting the total costs (including the rezoning cost) from the expected revenue:

Expected net profit = Expected revenue - Rezoning cost = $2.1 million - $1 million = $1.1 million.

In conclusion, based on the analysis, if the land is rezoned, the builder should decide to construct the shopping center as it offers a higher expected value compared to the rezoned apartments. If the land is not rezoned, the builder will proceed with constructing 500 homes, resulting in an expected revenue of $2.1 million. The expected net profit of the entire project, including all applicable costs, is estimated to be $1.1 million. These calculations assist in evaluating the potential outcomes and guiding the builder's decision-making process.

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