Problem
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 $0.12*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 $100 per square foot per month. Rents in this are are expected to increase in 5 years. There is a 50% chance that they will rise to $210 per square foot per month and stay there forever and a 50% chance that they will stay at $100 per square foot per month forever. The cost of capital is fixed at 12.3% per year.
I. Should you construct a building on the lot right away? If so how large should it be?
II. If you choose to delay the decision, how large a building should you construct in the $210/sq ft. state in five years?
III. If you choose to delay the decision, how large a building should you construct in the $100/sq ft. state in five years?
IV. If you wait, what is the expected value of the building today?
V. If you choose to delay the decision, how large a building will you construct in each possible state in five years?
VI. If you build today, how large a building should you construct?
VII. What is the NPV of the building today?
VIII. Should you invest today or wait five years?