You own a piece of raw land in an up-and-coming area in Gotham City. The costs to construct a building increase disproportionately with the size of the building. A building of q square feet costs 0.1*q^2 to build. After you construct a building on the lot, it will last forever, but you are committed to it: You cannot put another building on the lot. Buildings currently rent at $ 97 per square foot per month. Rents in this area are expected to increase in five years. There is a 49 % chance that they will rise to $ 199 per square foot per month and stay there forever and a 51% chance that they will stay at $ 97 per square foot per month forever. The cost of capital is fixed at 11.9% per year.

a. Should you construct a building on the lot right away? If so, how large should the building be?

b. If you choose to delay the decision, how large a building will you construct in each possible state in five years?

(Make sure to state how big of a building you build if the rent is $199/sq ft and how big you build if rent is $97/sq ft)

(Also, make sure to give expected NPV of waiting and NPV of building today).