A piece of land that is currently designated for residential use is offered for sale and Richmond Investment Company (RIC) is presented with the opportunity to purchase it. If the local authority approves a plan to recategorize the property as commercial within the next year, then RIC will be able to lease the land to a large firm that wants to open a new store on the property. However, if the plan is not approved, RIC will have to sell the property at a loss. Profits (in 000s of s) are shown in the following payoff table: State of Nature Decision Alternatives Plan Approved s1 Plan Not Approved s2 Purchase, d1 500 -100 Do not purchase, d2 0 0 (a) If the probability that the recategorization plan will be approved is 0.75, what decision is recommended and what is the expected profit? (b) RIC can purchase an option to buy the land at an extra cost. Under the option, RIC maintains the rights to purchase the land anytime during the next three months while waiting to learn more about possible resistance to the recategorization proposal from local residents. Probabilities are as follows: P(H) = 0.45 P(s1 | H) = 0.82 P(s2 | H) = 0.18 P(L) = 0.55 P(s1 | L) = 0.11 P(s2 | L ) = 0.89 Where: H = High resistance to recategorization L = Low resistance to recategorization Determine the optimal decision strategy if the investor uses the option period to learn more about the resistance from local residents before making the purchase decision (c) If the option will cost RIC an additional 20,000, should they purchase the option? Why or why not? What is the maximum that RIC should be willing to pay for the option? Discuss your answer