You currently own a vacant plot of land in Lantau. This plot of land can accommodate either 1 or 2 hotel buildings. If you build a single building, the construction cost today is $30 million. If you build two hotels at once on the plot, your total construction cost will be $90 million. If you wait a year, the construction cost of building a single hotel building will rise to $36 million and the construction cost for building two hotel buildings will rise to $100 million. You must decide both the scale and timing of construction. Since you have no desire to run hotels, assume that you will SELL the hotels after construction is completed. To help you in making your decision, you have looked into

local hotel prices. The current market price of a similar hotel building is $80 million. You have also noted that similar hotels can be leased for $2.4 million per year, with the lease payment made at year end. The price at which hotels will sell next year is random. If the air travel picks up and real estate market is strong, hotel prices will rise by 20%. If the real estate market is weak, house prices will fall by 25%. The risk-free rate is 5%. You can either build NOW or ONE YEAR FROM NOW. If you build now, you will be able to sell the hotel building(s) for $80 million. If you choose to wait and build one year from now, you can vary the scale of the project depending on the observed FUTURE market price.

a) First compare the following two strategies: Build 1 hotel building now versus 2 hotel buildings now. Which of these two strategies gives you higher profits?

b) Suppose that you WAIT. What is your optimal building strategy?

c) Solve for the probability of an increase in hotel prices, call it "Pi", that rationalizes the current $80 million price of a hotel building. If you cannot find probabilities, assume it is 50/50 and continue to the next question.

d) Referring to parts B and C, what is the value of your claim if you choose the WAIT strategy?

e) Should you wait or should you build now? Justify your answer using numbers, not verbiage.