Assume that you are the owner of an empty lot. You have decided that, at some point over the next three years, you will build on the lot. Assume that the value of the building if you were to build today is $2,000,000 (this value accounts for the cost of building). Each year, this value either goes up by a factor of 1.06 or goes down by a factor of 1/1.06. Assume that the probability of the value going up each year is 52%. You can decide to build at the following times: today, and receive today's value of the building of $2,000,000; in one year and receive either $2,000,000 times 1.06 or $2,000,000/1.06; in two years and receive either $2,000,000 times 1.06^2, $2,000,000, or $2,000,000/1.06^2; in three years and receive either $2,000,000 times 1.06^3 or $2,000,000 times 1.06 or $2,000,000/1.06 or $2,000,000/1.06^3. You can only build once; i.e., after building you stop. Assume that if you have not already built by the end of year 3, you will always build then. Also, assume that you can ignore the time-value of money; i.e., don't worry about discounting. You are trying to maximize the expected value of your lot. a. What is your optimal building strategy; i.e., Do you build today? For what values of the building do you build at the end of each year? b. What is the value of your lot today? c. For this part, assume that the lot is not currently empty, but that you are using it as a parking lot, which generates $50,000 per year. Assume that you receive the $50,000 at the end of each year, as long as you have not already used the lot to build. Report the value of your lot today, and the optimal building strategy.