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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. 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 Alternative Purchase, d Do not purchase, d₂ Rezoning Approved $1 State of Nature 650 Rezoning Not Approved 5₂ -200 (a) If the probability that the rezoning will be approved is 0.5, what decision is recommended? O purchase O do not purchase What is the expected profit (in dollars)?

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. 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 Alternative Purchase, d Do not purchase, d₂ Rezoning Approved $1 State of Nature 650 Rezoning Not Approved 5₂ -200 (a) If the probability that the rezoning will be approved is 0.5, what decision is recommended? O purchase O do not purchase What is the expected profit (in dollars)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. 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 Alternative Purchase, d₁ Do not purchase, d₂ Rezoning Approved 5₁ 650 State of Nature 0 Rezoning Not Approved 52 -200 0 (a) If the probability that the rezoning will be approved is 0.5, what decision is recommended? O purchase O do not purchase What is the expected profit (in dollars)? $
Transcribed Image Text: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. 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 Alternative Purchase, d₁ Do not purchase, d₂ Rezoning Approved 5₁ 650 State of Nature 0 Rezoning Not Approved 52 -200 0 (a) If the probability that the rezoning will be approved is 0.5, what decision is recommended? O purchase O do not purchase What is the expected profit (in dollars)? $
(b) 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: Let H = High resistance to rezoning L = Low resistance to rezoning P(H) = 0.55 P(L) = 0.45 P(S₁ | H) = 0.14 P(S₁ | L) = 0.94 P(s₂ | H) = 0.86 P(S₂ | L) = 0.06 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? O If high resistance H, d₂ do not purchase. If low resistance L, d₂ do not purchase. O If high resistance H, d₁ purchase. If low resistance L, d₂ purchase. ○ If high resistance H, d₁ purchase. If low resistance L, d₂ do not purchase. O If high resistance H, d₂ do not purchase. If low resistance L, d₁ purchase. (c) If the option will cost the investor an additional $10,000, should the investor purchase the option? Why or why not? What is the maximum (in dollars) that the investor should be willing to pay for the option? The investor ---Select--- purchase this option, as the payoff of the investing in it is ---Select--- $10,000 dollars. In general, the cost of the option can be, at most, $ in order for its payoff to break even with its cost of investing in it.
Transcribed Image Text:(b) 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: Let H = High resistance to rezoning L = Low resistance to rezoning P(H) = 0.55 P(L) = 0.45 P(S₁ | H) = 0.14 P(S₁ | L) = 0.94 P(s₂ | H) = 0.86 P(S₂ | L) = 0.06 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? O If high resistance H, d₂ do not purchase. If low resistance L, d₂ do not purchase. O If high resistance H, d₁ purchase. If low resistance L, d₂ purchase. ○ If high resistance H, d₁ purchase. If low resistance L, d₂ do not purchase. O If high resistance H, d₂ do not purchase. If low resistance L, d₁ purchase. (c) If the option will cost the investor an additional $10,000, should the investor purchase the option? Why or why not? What is the maximum (in dollars) that the investor should be willing to pay for the option? The investor ---Select--- purchase this option, as the payoff of the investing in it is ---Select--- $10,000 dollars. In general, the cost of the option can be, at most, $ in order for its payoff to break even with its cost of investing in it.
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