Question

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

Purchased d1 S1 (550) S2 (-190)

Do not purchase 0 0

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

Recommended decision: Purchase or do not purchase?

What is the expected profit? Expected profit: $ __________

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) = 0.53 P(S1 | H) = 0.16 P(S2 | H) = 0.84 P(L) = 0.47 P(S1 | L) = 0.86 P(S2 | L) = 0.14

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 Do not purchase?

Low resistance: Purchase or do not purchase?

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

a.

Expected Profit                     Expected Value                   Probability

Reazoning approved              550000                                  50%               275000

Reazoning not approved     -190000                                    50%               -95000

Expected Profit                         -                                            -                     180000

Recommend Decision=Purchase due to positive expected profit

b.

P(H) = 0.53 P(s1 | H) = 0.16 P(s2 | H) = 0.84

P(L) = 0.47 P(s1 | L) = 0.86 P(s2 | L) = 0.14

H High resistance

EV (550000*16%)+(-190000*.84)

=-71600, since negative ( not purchase)

L Low resistance

EV (550000*86%)+(-190000*.14)

=446400, Purchase

c. Expected profit

$180,000-$10,000= $170,000.00

Since the expected profit is positive, the investor should invest.

The maximum amount that the investor is willing to pay for the option equals to the expected profit of $180,000.