A real estate investor has the opportunity to purchase 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 and the investor will earn $600k. However, if the zoning change is not approved, the investor will have to sell the property at a loss of $200k. The investor feels that there is a 50% chance the zoning will be approved. The county board’s decision to approve or not to approve is highly dependent on whether the resistance to rezoning by local area residence is high or low. The investor believes that there is a 55% chance that the resistance will be high. Based on past county board history, there is a 89% chance the board will approve the rezoning given resistance is low. There is only an 18% chance the board will approve given resistance is high. The investor can also purchase an Option to buy the land for $10K. Under the Option, the investor maintains the rights to purchase the land anytime during the next 3 months while learning more about possible resistance to the rezoning proposal from area residents.
(a) Use a decision tree to determine what the investor should do to maximize expected profits.
(b) Provide a risk profile for the optimal decision.
(c) What is the maximum amount of money the investor should pay to guy the Option?
(d) What is the maximum amount of money the investor should pay to find out for sure if the board will approve the rezoning or not?