A pharmaceutical firm is thinking of marketing a new drug, and they want to evaluate the...

  

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A pharmaceutical firm is thinking of marketing a new drug, and they want to evaluate the profitability of the project after 5 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 remaining 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 to (1-.05)^2 of the Year 1's value. There are 10 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 (fixed up-front cost); and $0.30 per year to operate one unit of capacity (fixed annual operating costs that are incurred whether or not the firm decides to produce the drug at full capacity). A pharmaceutical firm is thinking of marketing a new drug, and they want to evaluate the profitability of the project after 5 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 remaining 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 to (1-.05)^2 of the Year 1's value. There are 10 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 (fixed up-front cost); and $0.30 per year to operate one unit of capacity (fixed annual operating costs that are incurred whether or not the firm decides to produce the drug at full capacity).

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Let capacity level is x per year and unit produced y per year Fixed upfront cost35x Fixed operating ... View the full answer