Question

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: 0.60.

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 1,150 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 $7 million over her construction cost (also excluding the land). If, instead of the shopping center, she decides to build the 1,150 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 $4,000 each over her construction cost; there is a 40 percent chance that she can get $2,200 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 650 homes, on which she expects to make $3,800 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? (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

b. What is the expected value for the rezoned apartments, if the rezoning cost is included? (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

c. If the land is rezoned, what should the contractor decide?

	Build shopping center
	Build apartments

d. What is the expected revenue, if the land is not rezoned? (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 revenue            $ million

e. What is the expected net profit of entire project? (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 net profit            $ million

Answer 1

Note: All amounts are in $ millions, unless written otherwise

Cost of land = 2

Probability of rezoning = 0.6

Rezoning costs = 1

If rezoned, options are as follows:

Option 1: Shopping Center

Probability of sale to department store = 0.5

Amount from department store = 5

Probability of sale to insurance company = 0.5

Amount from insurance company = 7

a. What is the expected value for the rezoned shopping center, if the rezoning cost is included?

Expected value = probability of rezoning * ($\sum$(probability * (amount - rezoning costs))

= 0.6 * (0.5 * (5 -1) + 0.5 * (7 - 1))

= 0.6 * (2 + 3) = 0.6 * 5

Expected value of rezoned shopping center = $3 million

Option 2: 1,150 apartments

Higher amount = $4,000

Probability of higher amount = 0.6

Lower amount = $2,200

Probability of lower amount = 0.4

b. What is the expected value for the rezoned apartments, if the rezoning cost is included?

Expected value = probability of rezoning * ($\sum$(probability * (amount - rezoning costs))

= 0.6 * (0.6 * ((1150 * 4000) - 1000000) + 0.4 * ((1150 * 2200) - 1000000))

= 0.6 * (0.6 * (4600000 - 1000000) + 0.4 * (2530000 - 1000000))

= 0.6 * (0.6 * 3600000 + 0.4 * 1530000)

= 0.6 * (2160000 + 612000)

= 1663200

Expected value of rezoned apartments = $1.66million

c. If land is rezoned (excluding land cost in both cases), expected value of rezoned shopping center is greater than expected value of rezoned apartments, therefore, contractor should build a Shopping Center

d. What is the expected revenue, if the land is not rezoned?

Probability of land not being rezoned = 1 - Probability of rezoning land

                                                      = 1 - 0.6 = 0.4

Number of apartments = 650

Amount per apartment = $3,800

Expected revenue = probability of not rezoning * (number of apartments * amount per apartment)

= 0.4 * (650 * 3800)

= 0.4 * 2470000

= 988000

Expected revenue in case of no rezoning = $0.99million