# Question

The Mutron Company is thinking of marketing a new drug used to make pigs healthier. At the beginning of the current year, there are 1,000,000 pigs that could use the product. Each pig will use Mutron’s drug or a competitor’s drug once a year. The number of pigs is forecast to grow by an average of 5% per year.

However, this growth rate is not a sure thing. Mutron assumes that each year’s growth rate is an independent draw from a normal distribution, with probability 0.95 that the growth rate will be between 3% and 7%. Assuming it enters the market, Mutron is not sure what its share of the market will be during year 1, so it models this with a triangular distribution. Its worstcase share is 20%, its most likely share is 40%, and its best-case share is 70%. In the absence of any new competitors entering this market (in addition to itself), Mutron believes its market share will remain the same in succeeding years. However, there are three potential entrants (in addition to Mutron).

At the beginning of each year, each entrant that has not already entered the market has a 40% chance of entering the market. The year after a competitor enters; Mutron’s market share will drop by 20% for each new competitor who entered. For example, if two competitors enter the market in year 1, Mutron’s market share in year 2 will be reduced by 40% from what it would have been with no entrants. Note that if all three entrants have entered, there will be no more entrants. Each unit of the drug sells for $2.20 and incurs a variable cost of $0.40. Profits are discounted by 10% annually.

a. Assuming that Mutron enters the market, use simulation to find its NPV for the next 10 years from the drug.

b. Again assuming that Mutron enters the market, it can be 95% certain that its actual NPV from the drug is between what two values?

However, this growth rate is not a sure thing. Mutron assumes that each year’s growth rate is an independent draw from a normal distribution, with probability 0.95 that the growth rate will be between 3% and 7%. Assuming it enters the market, Mutron is not sure what its share of the market will be during year 1, so it models this with a triangular distribution. Its worstcase share is 20%, its most likely share is 40%, and its best-case share is 70%. In the absence of any new competitors entering this market (in addition to itself), Mutron believes its market share will remain the same in succeeding years. However, there are three potential entrants (in addition to Mutron).

At the beginning of each year, each entrant that has not already entered the market has a 40% chance of entering the market. The year after a competitor enters; Mutron’s market share will drop by 20% for each new competitor who entered. For example, if two competitors enter the market in year 1, Mutron’s market share in year 2 will be reduced by 40% from what it would have been with no entrants. Note that if all three entrants have entered, there will be no more entrants. Each unit of the drug sells for $2.20 and incurs a variable cost of $0.40. Profits are discounted by 10% annually.

a. Assuming that Mutron enters the market, use simulation to find its NPV for the next 10 years from the drug.

b. Again assuming that Mutron enters the market, it can be 95% certain that its actual NPV from the drug is between what two values?

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