Question

Problem III (12 Points) In their development of a new medical treatment, GSK plc would like to know how much profit it might expect to make. The development is currently in phase III clinical trials, awaiting the results of testing on 100 patients. The FDA will approve the treatment if it is effective in at least 85% of the patients. Based on similar trials conducted by other drug companies, GSK expects the number of patients in which the treatment will be effective to be distributed binomially, with the following parameters: • Number of trials = 100, • Probability of success = 0.88. The chart below visualizes the Binomial(100, 0.88) distribution. Note that x in the chart is the number (between 0 and 100) of the subjects in which the treatment is effective, and P(X=x) on the y-Axis is the probability of that outcome. If the treatment is approved, GSK will incur R&D expenses which will be uniformly distributed between $30 and $50 Million. If the treatment is not approved there are no expenses. Further, if the treatment is approved, the company expects to gain 8% of the $1 Billion market for that treatment (Assume a normal distribution for market share with a standard deviation of 2%. The probability of a negative market share is negligible and can be ignored in your calculations). Lastly, there is a 1-in-4 chance of a competitor entering the market, and if it does, GSK’s market share will be reduced by 25, 50 or 75 percent of the original market share, with equal probabilities. a) If the FDA approves the treatment, and the market share is exactly 8%, and the competitor does not enter the market, what is GSK’s expected profit? Answer this question without using simulation. (4 points) Use simulation to answer the following questions. To generate Binomial random numbers in Excel use binom.inv(X,Y,Z), where X and Y are the parameters of the binomial distribution and Z is the uniform(0,1) random number. Include the answers into your Word document. If your simulation approach is not clear from the Excel file, you can also describe your approach in words. b) What is GSK’s expected profit today (before FDA’s decision is known)? (6 points) c) Based on your simulation, what is the probability that GSK makes more than $50M in profit? (2 points)

Problem III (12 Points)

In their development of a new medical treatment, GSK plc would like to know how much profit it might expect to make. The development is currently in phase III clinical trials, awaiting the results of testing on 100 patients. The FDA will approve the treatment if it is effective in at least 85% of the patients. Based on similar trials conducted by other drug companies, GSK expects the number of patients in which the treatment will be effective to be distributed binomially, with the following parameters:

• Number of trials = 100,
• Probability of success = 0.88.

The chart below visualizes the Binomial(100, 0.88) distribution. Note that x in the chart is the number (between 0 and 100) of the subjects in which the treatment is effective, and P(X=x) on the y-Axis is the probability of that outcome.

If the treatment is approved, GSK will incur R&D expenses which will be uniformly distributed between $30 and $50 Million. If the treatment is not approved there are no expenses. Further, if the treatment is approved, the company expects to gain 8% of the $1 Billion market for that treatment (Assume a normal distribution for market share with a standard deviation of 2%. The probability of a negative market share is negligible and can be ignored in your calculations).

Lastly, there is a 1-in-4 chance of a competitor entering the market, and if it does, GSK’s market share will be reduced by 25, 50 or 75 percent of the original market share, with equal probabilities.

a) If the FDA approves the treatment, and the market share is exactly 8%, and the competitor does not enter the market, what is GSK’s expected profit? Answer this question without using simulation. (4 points)

Use simulation to answer the following questions. To generate Binomial random numbers in Excel use binom.inv(X,Y,Z), where X and Y are the parameters of the binomial distribution and Z is the uniform(0,1) random number. Include the answers into your Word document. If your simulation approach is not clear from the Excel file, you can also describe your approach in words.

b) What is GSK’s expected profit today (before FDA’s decision is known)? (6 points)

c) Based on your simulation, what is the probability that GSK makes more than $50M in profit? (2 points)

Problem III (12 Points)

In their development of a new medical treatment, GSK plc would like to know how much profit it might expect to make. The development is currently in phase III clinical trials, awaiting the results of testing on 100 patients. The FDA will approve the treatment if it is effective in at least 85% of the patients. Based on similar trials conducted by other drug companies, GSK expects the number of patients in which the treatment will be effective to be distributed binomially, with the following parameters:

• Number of trials = 100,
• Probability of success = 0.88.

The chart below visualizes the Binomial(100, 0.88) distribution. Note that x in the chart is the number (between 0 and 100) of the subjects in which the treatment is effective, and P(X=x) on the y-Axis is the probability of that outcome.

If the treatment is approved, GSK will incur R D expenses which will be uniformly distributed between 30 and50 Million. If the treatment is not approved there are no expenses. Further, if the treatment is approved, the company expects to gain 8% of the $1 Billion market for that treatment (Assume a normal distribution for market share with a standard deviation of 2%. The probability of a negative market share is negligible and can be ignored in your calculations).

Lastly, there is a 1-in-4 chance of a competitor entering the market, and if it does, GSK’s market share will be reduced by 25, 50 or 75 percent of the original market share, with equal probabilities.

a) If the FDA approves the treatment, and the market share is exactly 8%, and the competitor does not enter the market, what is GSK’s expected profit? Answer this question without using simulation. (4 points)

Use simulation to answer the following questions. To generate Binomial random numbers in Excel use binom.inv(X,Y,Z), where X and Y are the parameters of the binomial distribution and Z is the uniform(0,1) random number. Include the answers into your Word document. If your simulation approach is not clear from the Excel file, you can also describe your approach in words.

b) What is GSK’s expected profit today (before FDA’s decision is known)? (6 points)

c) Based on your simulation, what is the probability that GSK makes more than 50M in profit? (2 points)

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