Vacant land has been zoned for either a condominium (10,000 sqft) or a single-family home (6,000 sqft).

The construction cost of the condominium is $100 per sqft while that of the family home is $120 per sqft.

There are two possible market states next year which determine the sales prices of the condominium and the family homes as follows: Good state: the condominium and the family home are sold at $230 per sqft and $300 per sqft, respectively. Bad state: the condominium and the family home are sold at $140 per sqft and $200 per sqft, respectively.

The current price of a comparable condominium is $180 per sqft and that of a comparable family home is $225 per sqft. First-year rental rates (paid at the end of the year) on the comparable condos and homes are 20% and 10% of the current sales prices, respectively.

Answer the following questions.

1) Calculate the cash ows that a condominium and a family rm generates (i.e., the sum of the sales price and the rental revenue) in each state next year, respectively.

2) What is the implied risk-free rate? (Hint: Construct a mimicking portfolio of a risk-free asset using the cash ows from a condominium and a family home.)

3) Now suppose that you wait one year (i.e., until the realization of the states) before building a condominium or a family rm. Which building will you construct in each state?

4) What is the value of the lot if you wait one year as above?