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 Decision Alternative Purchase, d, Do not purchase, d, 600 -200 a. If the probability that the rezoning will be approved is 0.5, what decision is recommended? What is the expected profit? 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) = 0.55 P(SH) = 0.18 P(82 H) = 0.82 P(L) = 0.45 Ps, L) = 0.89 Ps, L) = 0.11 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? c. If the option will cost the investor an additional $10,000, should the investor purchase the option? Why or why not? What is the maximum that the investor should be willing to pay for the option?

Answer 1

The decision tree is shown below :

pay off Profit 200 Rezone 606 Approved --200 - o (OO - 200 Rezoning Not Approved 57 ₂ o Decision Tree

Ev (node) = 0.18 (600) + 0.82 (-200) = -56 EU (node 7) = 0 Eu (node 8) = 0.89 (600) + 0.11 (-200) =512 EU( node 9) = 0 EV ( node 10) = 0.50(600) + 0.50 (-200) = 200 Ev ( node 11)= 0 Eu (node 3) = Max (- 56,0)= o dz EU (node 4)= Max (512, 0 ) - 512 di Ev (hade 5)= Max (200, o) = 200 di EU (node 2) = 0.55(0) + 0.45(512) = 230.4 without decision expected the option, the recommended is de purchase with an value of $ 200,000, decision with the Strategy 4 high low option, the best is : resistance H, d₂ resistance L, di don't purchase. purchase.

Expected value = $ 230,400 (C.) EVSI = $ 230,400 - $ 200,000 = $ 30, 400 since the cost is only $10,000 , hurchase the option. the investor Should