CASE STUDY $-$ DECISION TREE

INTRODUCTION

A pharmaceutical drug is currently undergoing testing. The three$-$stage FDA approval process lays out the hurdles that have to be passed for this drug to be commercially sold, and failure at any of the three stages dooms the drug$$s chances.

BACKGROUND

This pharmaceutical drug treats Type I of a disease and has gone through pre$-$clinical testing and is about to enter Phase $1$ of the FDA approval process.

Phase $1$

$$ Phase $1$ is expected to cost $$50$ million and will involve $100$ volunteers to determine safety and dosage; it is expected to last $1$ year.

$$ There is a $70\%$ chance that the drug will successfully complete the first phase.

Phase $2$

$$ In Phase $2,$ the drug will be tested on $250$ volunteers for effectiveness in treating the disease over a two$-$year period.

$$ This phase will cost $$100$ million and the drug will have to show a statistically significant impact on the disease to move on to the next phase.

$$ There is only a $30\%$ chance that the drug will prove successful in treating Type I but there is a $10\%$ chance that it will be successful in treating both Type I and Type II$,$ and a $10\%$ chance that it will succeed only in treating Type II$.$

Phase $3$

$$ In Phase $3,$ the testing will expand to $4,000$ volunteers to determine the long$-$term consequences of taking the drug.

$$ If the drug is tested on only Type I or Type II patients, this phase will last $4$ years and cost $$250$ million; there is an $80\%$ chance of success.

$$ If it is tested on both types, the phase will last $4$ years and cost $$300$ million; there is a $75\%$ chance of success.

If the drug passes through all $3$ phases, the costs of developing the drug and the annual cash flows are provided below:

Cost of development and cash flows

Disease Treatment Cost of Development Annual Cash Flows

Type I $$500$ million $$300$ million for $15$ years

Type II $$500$ million $$125$ million for $15$ years

Type I and Type II $$600$ million $$400$ million for $15$ years

ASSUMPTIONS

Use the following assumptions in your decision analysis:

$$ The cost of capital is $10\%.$

$$ The cost of each phase is incurred in the beginning of each phase.

$$ Since these phases take time, you must consider time value of money. $($Hint: The payoff at each terminal node is the NPV of all revenues and costs associated with that particular path in the decision tree.$)$

ANALYSIS REQUIREMENTS

$$ Your spreadsheet must showcase a comprehensive decision analysis.

$$ You must set up the decision problem by clearly identifying the problem statement, decision alternatives, and states of nature.

$$ You must include an influence diagram.

$$ You must include a full $($unreduced$)$ decision tree that shows all of the following:

o the logical sequence of the decision problem,

o the payoff at every terminal node,

o the decision nodes,

o the chance nodes, and

o the probabilities.

$$ You must clearly walk through each backward induction step to reduce$/$fold back your decision tree.

$$ You must include a reduced decision tree at every single step$/$fold$.$ Each step of the decision tree should take up one full tab.

$$ You must show your work $-$ all calculations must be set up clearly using the correct Excel TVM functions.