Expected Value Topic

1. A real estate investor can purchase a piece of land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table:

Decision alternatives	States of Nature
Rezoning approved	Rezoning not approved
S1	S2
Purchase, d1	110	-65
Do not purchase, d2	0	0

1. If the probability that the rezoning will be approved is 0.35, what decision is recommended? What is the expected profit?
2. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows:

LetH_High resistance to rezoning

L_Low resistance to rezoning

P(H) = 0.6 P(S1 | H) = 0.25 P(S2 | H) = 0.75

P (L) = 0.4 P(S1 | L) = 0.85 P(S2 | L) = 0.15

What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision?

3. If the option will cost the investor an additional $8,000, should the investor purchase the option? Why or why not? What is the maximum value that the investor should be willing to pay for the option?