Vacant land has been zoned for either one 10,000- square-foot five-unit condominium or two single-family homes, each with 3,000 square feet. The cost of constructing the single-family homes is $100 per square foot and the cost of constructing the condominium is $120 per square foot. If the real estate market does well next year, the homes can be sold for $300 per square foot and the condominiums for $230 per square foot. If the market performs poorly, the homes can be sold for $200 per square foot and the condos for $140 per square foot. Today, comparable homes could be sold for $225 per square foot and comparable condos for $180 per square foot. First-year rental rates (paid at the end of the year) on the comparable condos and homes are 20 percent and 10 percent, respectively, of today's sales prices.
a. What is the implied risk-free rate, assuming that short selling is allowed?
b. What is the value of the vacant land, assuming that building construction will take place immediately or one year from now? What is the best building alternative?