# Question

A pharmaceutical company is planning to develop a new drug. The development will take place in two phases. Phase I will cost $1 million and Phase II will cost $2 million. Any new drug has to be approved by the FDA (U.S. Federal Drug Administration) before it can be marketed. If the drug is approved by the FDA, then a profit contribution of $6,250,000 can be realized by marketing the drug. The only fixed costs to be subtracted from this contribution is the $3 million development cost. In other words, if the drug is approved, the profit would be $3,250,000. If the drug is not approved, then all the development cost has to be written off as a loss.

The managers estimate a 70% chance that the FDA will approve the drug. This still leaves a 30% chance of a $3 million loss. Because of the risk involved, one of the managers proposes a plan to conduct a test at the end of Phase I to determine the chances of FDA approval.

The test itself will cost $165,000. If the test result is positive, the company will continue with Phase II; otherwise, the project will be aborted. The motivation for the test is that in case the chances of FDA approval are slim, at least Phase II costs can be saved by aborting the project.

The manager has drawn the decision tree seen in Exhibit 1 to show possible outcomes. The tree shows the expenses and income along the relevant branches.

However, the manager has not been able to arrive at the probabilities for the branches from chance nodes. The researcher who conducts the test says that the test is not 100% accurate in predicting whether the FDA will approve the drug. He estimates the following probabilities:

P (Test positive | FDA will approve) = 0.90

P (Test negative | FDA will not approve) = 0.80

QUESTION CONTINUE TO NEXT PAGE

1. Given the above probabilities, compute the required probabilities for the decision tree.

2. Assuming that the company wants to maximize the expected monetary value, what is the best decision strategy?

3. The company assumed that if the test result is negative, the best decision is to abort the project. Prove that it is the best decision.

4. At what cost of the test will the company be indifferent between conducting and not conducting the test?

5. Is your answer to question 4 the same as the EVSI of the test information?

The managers estimate a 70% chance that the FDA will approve the drug. This still leaves a 30% chance of a $3 million loss. Because of the risk involved, one of the managers proposes a plan to conduct a test at the end of Phase I to determine the chances of FDA approval.

The test itself will cost $165,000. If the test result is positive, the company will continue with Phase II; otherwise, the project will be aborted. The motivation for the test is that in case the chances of FDA approval are slim, at least Phase II costs can be saved by aborting the project.

The manager has drawn the decision tree seen in Exhibit 1 to show possible outcomes. The tree shows the expenses and income along the relevant branches.

However, the manager has not been able to arrive at the probabilities for the branches from chance nodes. The researcher who conducts the test says that the test is not 100% accurate in predicting whether the FDA will approve the drug. He estimates the following probabilities:

P (Test positive | FDA will approve) = 0.90

P (Test negative | FDA will not approve) = 0.80

QUESTION CONTINUE TO NEXT PAGE

1. Given the above probabilities, compute the required probabilities for the decision tree.

2. Assuming that the company wants to maximize the expected monetary value, what is the best decision strategy?

3. The company assumed that if the test result is negative, the best decision is to abort the project. Prove that it is the best decision.

4. At what cost of the test will the company be indifferent between conducting and not conducting the test?

5. Is your answer to question 4 the same as the EVSI of the test information?

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