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:

Explanation / Answer

(a) Expected Profit when purchased

= E(Profit | Purchased)

= 640*P ( Profit =640| d1) +(-200)* P(Profit = -200| d1)

= 640*P(s1) + (-200)*P(s2)

= 640*0.5 + (-200)*0.5

= 320 -100 = 220 (in thousand dollars)

Similarly, Expected Profit when Not Purchased

= 0*P(s1) + 0*P(s2)

= 0

Hence, Expected Profit when purchased is higher than when not purchased.

So, recommendation is: Do Purchase.

Expected Profit on Purhasing = $ 220,000

(b) Suppose Resistance is High. Then,

E(profit | d1) = 640*P(s1|H) - 200*P(s2|H) = 640*0.16 -200*0.84

= 102.4 - 168

= -65.6 which is less than 0, the value if not purchased.

Hence, Recomendation is: Do NOT Purchase if High Resitance.

For Low Resistance,

E(Profit | d1) = 600*P(s1|L)-200*P(s2|L)

= 600*0.85 - 200*0.15

= 510 - 30 = 480, which is greater than 0

Hence, Recomendation is: Do Purchase if Low Resitance.

Hence, Optimal Strategy is:

Purchase if Low Resistance. But, Do NOT Purchase if High Resistance.

Additionally, if Resistance is not known in advance, then

E(Profit | d1)

= E(Profit | d1 and High Resistance) * P(High Resistance) + E(Profit | d1 and Low Resistance) * P(Low Resistance)

= (-65.6)* 0.51 + 480*0.49

= 201.74400 (in thousands of dollars)

(c) In this case,

Option Cost = $10,000

As shown in (b) above,

if Resistance is not known in advance, then

E(Profit | d1)

= E(Profit | d1 and High Resistance) * P(High Resistance) + E(Profit | d1 and Low Resistance) * P(Low Resistance)

= (-65.6)* 0.51 + 480*0.49

= 201.74400 (in thousands of dollars)

So, Net Expected Profit if Resistance is not known in advance is

= -10000 + 201744

= 191744 which is more than 0

Hence, Yes. Option can be purchased.

Now, Maximum that the investor should be willing to pay for the option

= E(Profit if Resistance is not known)

= $ 201744

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