A real estate investor has the opportunity to purchase land currently zoned residentiel. 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, d What is the expected profit? Expected profit - $ P(H)- a. If the probability that the rezoning will be approved is 0.5, what decision is recommended? Recommended decision - Purchase <- 0.53 P(L)-0.47 State of Nature EVSI = $ Rezoning Approved S₁ 550 0 190 ✓ thousands. 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: Rezoning Not Approved S₂ Let H = High resistance to rezoning L = Low resistance to rezoning P(S₁ | H) -0.15 P[S1L) - 0.00 -170 0 thousands. 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? High resistance: Do not purchase P(S₂1 H) - 0.85 P(Sz | L) - 0.12 Low resistance: Purchase c. If the option will cost the investor an additional $10,000, should the investor purchase the option? Yes, because the expected value of the option is more than the cost of the option. What is the maximum that the investor should be willing to pay for the option? Round your answer to three decimal places. Why or why not?
A real estate investor has the opportunity to purchase land currently zoned residentiel. 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, d What is the expected profit? Expected profit - $ P(H)- a. If the probability that the rezoning will be approved is 0.5, what decision is recommended? Recommended decision - Purchase <- 0.53 P(L)-0.47 State of Nature EVSI = $ Rezoning Approved S₁ 550 0 190 ✓ thousands. 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: Rezoning Not Approved S₂ Let H = High resistance to rezoning L = Low resistance to rezoning P(S₁ | H) -0.15 P[S1L) - 0.00 -170 0 thousands. 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? High resistance: Do not purchase P(S₂1 H) - 0.85 P(Sz | L) - 0.12 Low resistance: Purchase c. If the option will cost the investor an additional $10,000, should the investor purchase the option? Yes, because the expected value of the option is more than the cost of the option. What is the maximum that the investor should be willing to pay for the option? Round your answer to three decimal places. Why or why not?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:Problem 13-21 (Algorithmic)
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:
What is the expected profit?
Expected profit - $
F(H)
P(L)
Decision
Alternative
Purchase, d
Do not purchase, dz
- 0.53
-
EVSI = $
0.47
a. If the probability that the rezoning will be approved is 0.5, what decision is recommended?
Recommended decision - Purchase
190
thousands.
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:
Rezoning
Approved
S₁
State of Nature
550
0
X thousands.
Rezoning Not
Approved
Let H = High resistance to rezoning
L = Low resistance to rezoning
P(S₁ | H) - 0.15
P(S1L) - 0.88
S₂
-170
0
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?
High resistance: Do not purchase
Low resistance: Purchase
c. If the option will cost the investor an additional $10,000, should the investor purchase the option?
Yes, because the expected value of the option is more than the cost of the option.
F(Sz | H) - 0.85
P(S₂L) - 0.12
What is the maximum that the investor should be willing to pay for the option? Round your answer to three decimal places. Why or why
not?
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