Question

Problem 4-21 (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:

State of Nature

	Rezoning Approved	Rezoning Not Approved
Decision alternative	S1	S2
Purchase, d1	550	-190
Do not purchase, d2

If the probability that the rezoning will be approved is 0.5, what decision is recommended?

Recommended decision: Purchase or not Purchase

What is the expected profit?

Expected profit: $  

1. 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) = 0.51	P(S1 | H) = 0.18	P(S2 | H) = 0.82
   P(L) = 0.49	P(S1 | L) = 0.88	P(S2 | L) = 0.12

   
   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: Purchase or not Purchase
   
   Low resistance: Purchase or not Purchase
2. If the option will cost the investor an additional $10,000, should the investor purchase the option?
   
   
   
   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

	Rezoning Approved	Rezoning Not Approved
Decision alternative	S1	S2
Purchase, d1	550	-190
Do not purchase, d2	0	0

Expected Profit= 550*0.5+(-190)*0.5+0*0.5+0*0.5

=180,000+0=$180,000

a)

Let H = High resistance to rezoning
L = Low resistance to rezoning
P(H) = 0.51	P(S1 | H) = 0.18	P(S2 | H) = 0.82
P(L) = 0.49	P(S1 | L) = 0.88	P(S2 | L) = 0.12

Expected Profits / Loss in high resistance = (550 x 0.18) + (-190 x 0.82) = -$56,800 x 0.51 = -$28968

Expected Profits / Loss in low resistance = (550 x 0.88) + (-190 x 0.12) = $461,200 x 0.49 = $225,988

Optimal decision during high resistance is do not purchase and purchase during low resistance.

b)

The maximum the investor should be willing to pay for the option = $225,988 -$28968 = $197,020

EVSI = $197,020

If the option is available at $10,000 the investor should purchase the option as it is available at a lower value.