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

Question

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

0

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

What is the expected profit?

If the option will cost the investor an additional $10,000, should the investor purchase the option?

What is the maximum that the investor should be willing to pay for the option?

State of Nature Rezoning Approved Rezoning Not Approved Decision Alternative s1 s2 Purchase, d1 600 -200 Do not purchase, d2 0

0

(a)

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

What is the expected profit?

(c)

If the option will cost the investor an additional $10,000, should the investor purchase the option?

What is the maximum that the investor should be willing to pay for the option?

Explanation / Answer

(a)

Probability that the rezoning will be approved is 0.5. So, P(s1) = 0.5

Then  probability that the rezoning will not be approved is 1 - 0.5 = 0.5. So, P(s2)= 0.5

Expected profit for Purchase = (d1,s1) * P(s1) + (d1,s2) * P(s2) = 600 * 0.5 - 200 * 0.5 = 200 thousands of dollars

Expected profit for not Purchase = (d2,s1) * P(s1) + (d2,s2) * P(s2) = 0 * 0.5 + 0 * 0.5 = 0

As, expected profit for Purchase is greater than expected profit for not Purchase, the recommended decision is Purchase, d1.

Expected profit of the recommended decision = 200 thousands of dollars

(c)

If the option will cost the investor an additional $10,000, then the expected profit of the recommended decision

= 200 thousands of dollars - $10,000

= 190 thousands of dollars

As, the expected profit is still greater than 0, the investor should purchase the option.

The maximum that the investor should be willing to pay for the option is the expected profit of the recommended decision = 200 thousands of dollars

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