A firm is trying to decide whether to enter a highly uncertain market now or to wait to decide two years from now, when the size of the market will be less uncertain. If it enters now it must invest $3 billion, while if it waits to invest two years from now the costs will rise to $4 billion. The market size in units this year will be normally distributed with a mean of 5 million and a standard deviation of 1 million. The growth rate in subsequent years will be normally distributed with a mean of 10 percent and a standard deviation of 5 percent (whatever the growth rate turns out to be, it will be the same in all future years). Unit margins each year are normally distributed with a mean of $50 and a standard deviation of $10. The discount rate is 15 percent and the analysis should cover 15 years.
a. What is the expected NPV if the firm invests now?
b. What is the expected NPV if the firm invests in two years? c. Modify your model to implement a policy in which the firm will invest after two years only if the market size in year 2 exceeds a cutoff value. What is the optimal cutoff and the resulting expected NPV?