You must decide today whether to buy an office building that costs $1 billion immediately. If demand for office space is strong, you will receive $200 million a year in rent revenue forever. If demand is weak, you will receive $50 million a year in rent revenue forever. Costs to maintain the building are $20 million a year, no matter what demand is. As of today, both possibilities are equally likely. If demand is strong it will be strong forever, if it is weak it will be weak forever. The discount rate is 10%. The first revenue and cost cashflow will be realized in t=1.

a) What is the NPV if you buy the building now?

b) You must buy the building now, but you have the option convert the building to residential housing. If you do the conversion, at t=1 you will have no costs or revenues from renting. You will have a cost of $100 million at t=1. You will receive $200 million a year in rent revenue and have $20 million a year in costs at t=2 and each year after. What is the NPV?

c) The government decides to pay for any building conversions. Now the cost to convert in t=1 is $0. What is the NPV?

d) If the government does not pay for the conversion, how much would you be willing to pay now to have the option to convert the building to residential?