In: Statistics and Probability
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:
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: $
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 |
|
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.