Your firm is thinking of expanding. If you invest today, the expansion will generate $10 million in FCF at the end of the year, and will have a continuation value of either $150 million (if the economy improves) or $50 million (if the economy does not improve). If you wait until next year to invest, you will lose the opportunity to make $10 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 45%. Assume the cost of expanding is the same this year or next year.
a. If the cost of expanding is $80 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?