case?

5. [10 pts.] A vacant lot has been zoned to construct today either 50 offices or 50 apartments. Assume that:

Construction must occur immediately and cannot be delayed.

Construction takes no time. Therefore, the offices or the apartments we build today can be sold or rented out immediately.

Construction costs are $75 per office or $90 per apartment.

The current price of offices is $100 and the current price of the apartments is $105.

The rental rate is $10 per office and also $10 per apartment (net of expenses, to be received at the end of the year).

Next year,

o If the real estate market booms, offices will sell for $140 and apartments for $125.

o If the real estate market does poorly, offices will sell for $85 and apartments for $100.

The risk-free interest rate is 12%.

a. What is the value of the vacant lot?

b. Suppose now that, in addition to the previous information, a new construction technology becomes available. This technology allows us to build offices today that can be converted into apartments next year. The cost of converting each office unit into an apartment unit is $10 (to be paid next year, and only if an office is actually converted into an apartment). The opposite conversion is not possible (i.e., if we build apartments today, they cannot be converted into offices next year). Also, the conversion applies only to the particular offices we are thinking about building; it does not apply to existing offices traded in the market. Find the value of the lot now.

c. Suppose now that the cost of converting offices into apartments is $20 per unit (again, to be paid next year). What is the value of the lot now? Explain.