Having gifted a large plot of vacant land as a graduation present, you decide to begin your career by constructing a warehouse on that land, which you intend to rent to Amazon. After charming your banker and engaging in careful research, you find that you can respectively finance the development with an interest only mortgage having an initial balance of $800 000 and that you can finish all this development and start renting its space in one month. You also know, from assiduous reading of the Financial Post, that there is a future contingency that will affect your return to this development: the market for warehouse space will either boom or bust next month, each alternative having a 0.5 probability of occurring. Based on your pro forma estimates, if the market booms, you will earn a monthly rent of $150 000 but if it busts, you will receive a monthly rent of $50 000. You know that one or the other event will happen, beginning one month after development with the respective rents lasting through the infinite future, but you don't know which one. The pressure is on, though, because you must decide what to do today. Suddenly, you remember your previous finance courses, especially the two in real estate, and you are confident that the skills you have acquired there will insure you make the right decision. Proceeding on both that belief and the assumption you have a per-period discount rate of ten percent, calculate:

a) the current (date 0) market value of your equity if you start development today

b) the current (date 0) market value of your equity if you postpone the start of development until a month from now, when the risk you face about the state of the market will resolved

c) how much would you willing to pay to postpone construction until a month from now?