Question

A real estate investor has the opportunity to purchase land currently zoned as 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:
State of Nature
Rezoning Approved Rezoning Not Approved
Decision Alternative s1 s2
Purchase, d1 650 -220
Do not purchase, d2 0 0
(a) If the probability that the rezoning will be approved is 0.5, what decision is recommended?
Recommended Decision:
What is the expected profit? Enter your answer in thousands dollars. For example, an answer of $200 thousands should be entered as 200,000.
$

(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) = 0.49 P(s1 | H) = 0.14 P(s2 | H) = 0.86
P(L) = 0.51 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?
High resistance:
Low resistance:

(c) If the option will cost the investor an additional $10,000, should the investor purchase the option? Enter your answer in thousands dollars. For example, an answer of $200 thousands should be entered as 200,000.

Why or why not?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.

What is the maximum that the investor should be willing to pay for the option?
EVSI = $

Answer 1

State the nature:2

	Rezoning Approved	Rezoing not Approved
Decision Alternative	S1	S2
Purchased D1	650	-220
Do not purchase D2	0	0

(a) If the probability that the rezoning will be approved is 0.5

Recommended Decision : Purchase:

Expected Profit:

Probability of rezoning will be approved is 0.5 so P(S1)= 0.5

Then probability of rezoning will not be approved is 1-0.5=0.5 so P(S2)=0.5

Expected profit for purchase:

=(D1S1)* P(S1)+(D1S2)*P(S2)

=(650*0.5)+(-220*0.5)

=325-110

=215

Expected profit for not purchase:

=(D2S1)* 9P(S1)+(D2S2)*P(S2)

=(0*0.5)+(0*0.5)

=0

As expected profit for purchase is greater than the expected profit for not purchase. The recommend purchase is D1

Therefore expected profit for recommended decision is 215000

b)

EV(D1 | H)=650*0.14+(-220*0.86)

=91-189.2

=(98.2)

EVP(D2 | H) =650*0.85+(-220*0.15)

=552.5-33

=519.5

EV with option= 519.5*0.15

=259.75

High resistance: -98.2 (do not purchase)

Low resistance: 519.5 (we will purchase)

C. If the option will cost the investor an additional $10000 then the expected profit of the recommended decision

= $215 thousands- $10000

=$205 thousands

As the expected profit is still greater than 0 the investor should purchase the option. The maximum that the investor should pay for the option is the expected profit of the recommended decision = 215 thousands of dollars.