A real estate investor has the opportunity to purchase land currently zoned resi

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, 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 :

A) If the probability the the rezoning will be approved is 0.5. what decision is recomended? 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 3 months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows.

Let H = High Resistance to rezoning

Let L = Low resistance to rezoning

P (H) = 0.55 P(s1| H) = 0.18 P (s2 | H) = 0.82 P (L) = 0.45 P (s1| L) = 0.89 P (s2 | 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?

Decision alternative Rezoning Approved, s1 Rezoning not Approved, s2 Purchase, d1 600 200 Do not purchase, d2 0 0

Explanation / Answer

Solution

Part (A)

Expected profit for Decision Alternative, d1 (i.e., Purchase)

= {Profit if s1 (i.e., Rezoning Approved,) x P(s1)} + {Profit if s2 (i.e., Rezoning Not Approved,) x P(s2)}

= (600 x 0.5) + (200 x 0.5 ) = 400

Similarly, Expected profit for Decision Alternative, d2 (i.e.,Do Not Purchase)

= (0 x 0.5) + (0 x 0.5 ) = 0

Since 400 > 0, the decision is d1, i.e., Purchase ANSWER

Part (B)

Let us first evaluate probability of s1 and s2.

P(s1) ={P(s1/H) x P(H)} + {P(s1/L) x P(L)} = (0.18 x 0.55) + (0.89 x 0.45) = 0.4995

P(s2) = P(s2/H) x P(H) + P(s2/L) x P(L) = (0.82 x 0.55) + (0.11 x 0.45) = 0.5005

Now, following the same method as in Part (A),

Expected profit for Decision Alternative, d1 (i.e., Purchase)

= {Profit if s1 (i.e., Rezoning Approved,) x P(s1)} + {Profit if s2 (i.e., Rezoning Not Approved,) x P(s2)}

= (600 x 0.4995) + (200 x 0.5005 ) = 399.80

Similarly, Expected profit for Decision Alternative, d2 (i.e.,Do Not Purchase)

= (0 x 0.5) + (0 x 0.5 ) = 0

Since 399.80 > 0, the decision is d1, i.e., Purchase ANSWER

Part (C)

As seen in Part (B), the expected profit is $399.8 x 1000 = $399800 [because the pay-off figures are in thousands of dollars].

So, if the additional cost is less than the above expected profit, it is worthwhile hiring the option.

Since 10000 < 399800, it is worthwhile purchasing the option. ANSWER 1

Further, the maximum that can be paid for purchasing the option is S399800 ANSWER 2

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