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TO 513

WINTER 2018 EXAM…………………………

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TO 513 WINTER 2018 EXAM Due Sunday, 4/22 @ 11:59 pm Problem 1 (20 pts) A pharmaceutical firm is thinking of marketing a new drug, and they want to evaluate the profitability of the project after five years. At the beginning of the current year, there are 1,000,000 potential users (customers) of the product. Each customer will use the drug (or a competitor’s drug) at most once a year. The number of potential users is forecasted to grow by an average of 5% per year, and they are about 95% confident that the number of potential users will grow each year by between 3% and 7% (this variability can be modeled with a normal random variable). They are not sure what proportion of potential customers will use the drug during year 1, but their worst-case guess is 20%, most likely 40% and best case use is 70% (model this variability with a triangular random variable). In later years, they feel that the fraction of potential customers using their drug (or a competitor’s) will remain the same, but in the year after a competitor enters, they lose 5% of their share for each competitor who enters. Thus, if in Year 1 two competitors enter the market, in Year 2 the firm’s market share will be reduced by 10%. There are ten potential entrants (in addition to the firm). At the beginning of each year, each entrant who has not already entered the market has a 40% chance of entering the market. Each unit of the drug is sold for $2.20 and incurs a variable cost of $0.40. Profits are discounted by 10% (risk-adjusted rate) annually. Before marketing the drug, the firm needs to decide on their annual capacity level; that is, the maximum number of units of the drug they will be able to produce per year. Suppose it costs $3.50 to build one unit of annual capacity (up-front cost) and $0.30 per year to operate one unit of capacity (whether or not they use the capacity to produce the drug). a) Determine the capacity level that maximizes risk-adjusted NPV …

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