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 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).
• The real estate market can evolve as follows: In one year:

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

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

Note: Probability of boom is not known; risk-free rate of return is not known.

1. What is the value of vacant lot?

2. Suppose now that, in addition to the previous information, a new construction technology becomes available. This technology allows building offices that can be converted into apartments by incurring in a $10 per unit (next year) if the office is actually converted into an apartment. Find the value of the lot now.

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