Question: Nancy holds an option to purchase a plot of land which will expire in one year. The option gives Nancy or anyone else holding the option the right to buy the plot of land for $1 million. The interest rate is zero. The price of condominium apartments is $500,000 and everyone believes correctly that the price of apartments will not change over the next five years. If Nancy exercises the option now she can build under current zoning any developer could build a condominium apartment building with 20 apartments at a cost of $8 million. . Zoning changes are under consideration. The plot will be either "upzoned" or "downzoned". If the plot is "upzoned" a 40 apartment building will be legal and would cost any developer $16 million to build. If the plot is "downzoned" no more than 2 apartments worth $500,000 can be built on the plot at a building cost of $1.5 million. The zoning board's decision will be known in six months All the other developers believe that the chance of upzoning is equal to the chance of downzoning.
i) What is Nancy's option to purchase the land worth now?
ii) Nancy's reading of the news convinces her that the chance of an upzoning is only 10% and the risk of a downzoning is 90%. Other developers reading the same news do not agree with her. What should she do?