REAL ESTATE DEVELOPMENT A real estate developer has a bigbox

REAL ESTATE DEVELOPMENT

A real estate developer has a big-box store client who will pay him to lease a store if he can find the right property to build it on. He has found a property and has the opportunity to purchase it, but it is currently zoned as residential. A re-zoning request has been submitted, and the offering price for the property includes some premium reflecting the owner’s expectation of this being approved. However, if the zoning change is not approved, that premium will evaporate and the developer will have no use for the property and will have to sell it at a loss. The payoffs (profits, in thousands of dollars) are shown in the following table:

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 developer believes rezoning approval is 50-50 proposition, what decision is recommended? What is the expected profit?

b. There is also the possibility of purchasing an option to buy the land. In this case, the developer will have the right to purchase the land for the current offering price anytime during the next three months. If the developer chooses not to exercise the option, the cost of it is lost. These three months can be used to learn more about the degree of resistance to the rezoning proposal from area residents – which is expected to have some influence on the zoning board’s decision. (It is also possible that some well-placed campaign fund donations could have an effect, but we will ignore that for now!)

We will characterize resistance being either high (H) or low (L), and the following probabilities have been estimated:

P(H) = 0.55   P(s1 | H) = 0.18 P(s2 | H)=.82      

P(L) = 0.45   P(s1 | L) = 0.89 P(s2 | L)= 0.11                     

*State the optimal decision strategy if the developer buys the option.

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

Solution

a)

purchase 1

600*0.5 + 0*0.5 = 300

purchase 2

-200 * 0.5 + 0*0.5 = -100

I will recomend purchase 1

for the other literals I can gladly help you but you should post it in a new question