We are considering buying and developing a vacant lot that has been zoned for building either offices or apartments. We can construct a building with either 50 offices or 50 apartments today. Assume that:

1) Construction must occur immediately and cannot be delayed.

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

3) Construction costs are $75,000 per office or $90,000 per apartment.

4) The current price of similar offices is $100,000 and the current price of similar apartments is $105,000.

5) The rental rate is $10,000 per office and also $10,000 per apartment (net of expenses), to be received at the end of the year.

6) Next year,

a) If the real estate market booms, offices will sell for $140,000 and apartments for $125,000.

b) If the real estate market does poorly, offices will sell for $85,000 and apartments for $100,000.

7) The risk-free interest rate is 12%.

2a) (20 points) What is the value of the vacant lot?

2b) (10 points) Suppose now that we have access to a proprietary construction technology that allows any offices we build today to be converted into apartments next year. The cost of converting each office unit into an apartment unit is $10,000, to be paid next year if an office is actually converted into an apartment. The opposite conversion is not possible (i.e., if e build apartments today, they cannot be converted into offices next year). Also, the ability to convert applies only to offices that we build; it does not apply to existing offices traded in the market. Find the value of the lot now.

2c) (10 points) Suppose now that the cost of converting offices into apartments is $20,000 per unit (again, to be paid next year). What is the value of the lot now? Explain.