Your firm is thinking of expanding. If you invest​ today, the expansion will generate $12 million in FCF at the end of the​ year, and will have a continuation value of either $148 million​ (if the economy​ improves) or $47 million​ (if the economy does not​ improve). If you wait until next year to​ invest, you will lose the opportunity to make $12 million in FCF but you will know the continuation value of the investment in the following year​ (that is, in a year from now you will know what the investment continuation value will be in the following​ year). Suppose the​ risk-free rate is 5%​, and the​ risk-neutral probability that the economy improves is 42%. Assume the cost of expanding is the same this year or next year. a. If the cost of expanding is $81 ​million, should you do so​ today, or wait until next year to​ decide? b. At what cost of expanding would there be no difference between expanding now and​ waiting? To what profitability index does this​ correspond?