# Lang Drug needs to determine the proper capacity level for a new drug, Niagara. Its goal is

## Question:

Lang Drug needs to determine the proper capacity level for a new drug, Niagara. Its goal is to maximize the expected NPV earned from the drug during years 0-14, assuming a discount rate of 10 percent per year. It costs $10 to build enough capacity to produce one unit of drug per year. All construction cost is incurred during year 0. It costs$1 per year to maintain a unit of annual production capacity. In year 1, demand will be for 160,000 units of Niagara. The mean annual percentage growth of demand for Niagara is equally likely to assume any value between 10 percent and 20 percent. The actual growth rate of demand during any year is normally distributed with the given mean and a standard deviation of 6 percent. During year 1, each unit of Niagara sells for $8. The price of Niagara will almost surely grow at 5 percent per year. Unit variable cost is known to be 40 percent of the sales price. Suppose that Lang Drug has the additional opportunity to review demand during year 5 and, if desired, build additional capacity. This means that Lang Drug may not need to build as much capacity during year 1, because they can wait and see whether demand will be high. If demand is high, they can ramp up capacity during year 5 for future years; if not, they can stick with their year 1 capacity. To model this situation, assume that after observing year 5 demand, Lang Drug proceeds as follows: If the ratio of year 5 demand to capacity exceeds some cutoff point C, then Lang Drug will add capacity. If capacity is added, then Lang Drug will add enough capacity to bring total capacity to a multiple M of year 5 demand. We assume it costs$12 to build one unit of capacity at the end of year 5. Thus, Lang Drug's capacity strategy is defined by three decisions:
Initial capacity (year 1)
The cutoff value C, which determines whether capacity is added after year 5 (assume that capacity arrives in time for year 6)
The multiple M that defines how much capacity is added.
a. Assuming Lang Drug cannot build additional capacity in year 5, what capacity level will maximize expected discounted profit? Assume that all building costs are incurred during year 0 and that all cash flows occur at the beginning of the year.
b. With the additional opportunity to review demand and add capacity in year 5, what values would you recommend for the initial capacity, for C, and for M? What is the maximum expected discounted profit when these parameters are optimized?
Discount Rate
Depending upon the context, the discount rate has two different definitions and usages. First, the discount rate refers to the interest rate charged to the commercial banks and other financial institutions for the loans they take from the Federal...
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