You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 

1717 

years. You expect that the​ drug's profits will be 

​$44 

million in its first year and that this amount will grow at a rate of 

3 %3% 

per year for the next 

1717 

years. Once the patent​ expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 

10 %10% 

per​ year?

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Part 1

The present value of the new drug is 

​$enter your response here 

million. 

To solve for the present value (PV) of the profits from the drug over the next 1717 years, we will use the **present value of a growing annuity formula**. This formula is appropriate because the profits are growing at a constant rate, and we want to calculate their value in today's terms, discounted at the given interest rate.

The formula for the present value of a growing annuity is:

\[
PV = \frac{P_0}{r - g} \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right]
\]

Where:
- $P_0 = 44$ million (the initial profit in the first year),
- $r = 0.10$ (the interest rate or discount rate),
- $g = 0.03$ (the growth rate of the profits),
- $n = 1717$ years (the time period of profit generation before the patent expires).

Let's calculate the present value using this formula.The present value of the new drug's profits over the next 1717 years is approximately **$628.57 million**.

Would you like more details on the calculation? Here are 5 related questions for further exploration:

1. How does the interest rate affect the present value of the drug?
2. What would the present value be if the profit growth rate increased to 5%?
3. How would a decrease in the patent duration to 500 years change the present value?
4. Why does the present value approach a certain limit as time increases?
5. What are the implications of competition driving profits to zero after the patent expires?

**Tip**: In present value calculations, the higher the discount rate, the lower the present value of future cash flows.

You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 1717 years. You expect that the drug's profits will be $44 million in its first year and that this amount will grow at a rate of 3% per year for the next 1717 years. Once the patent expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 10% per year?

Calculate the present value of a pharmaceutical drug's profits over 1717 years, with profits growing at 3% annually and a 10% discount rate. This problem involves the present value of a growing annuity formula and demonstrates how financial mathematics applies to real-world business scenarios.

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