A real estate invrr.1or has the opportunity to purchase Und committee zoned as r

Question

A real estate invrr.1or has the opportunity to purchase Und committee zoned as residential. If the county board approves a request to rezone the property as commercial within the next year, the investor we be able to lease the land to a large discount firm that wants to open a new strop 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: If the probability that the rezoning will be approved is 0.5, what decision is recommended? 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. Prcbabi Mles are as follows: What is the optimal decision strategy if the investor uses the period to learn mote about the resistance from area residents before making the purchase decision? If the option will cost the investor an additional $10,000. should the Investor purchase the option?

Explanation / Answer

(a)

Expected profit when purchased = 0.5*550 - 0.5*190 = $180,000

Expected profit when not purchased = 0.5*0 +0.5*0 = $0

Since expected profit when purchased is higher the right decision should be to purchase.

(b)

In case of high resistance to zoning, the expected profit will be,

P = 0.51(0.18*550 - 0.82*190) = -$28,968

Since the profit is negative the optimal decision would be to not purchase.

In case of low resistance to zoning , the expected profit will be,

P = 0.49(0.88*550-0.12*190) = $225,998

Since the expected profit is positive the optimal decision would be to purchase.

(c)

Net expected profit = $225,998 - $28,968 = $197,020>$10,000

SInce the net expected profit in case of purchasing exceed by more than $10,000 the investor should purchase the option.

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