You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug’s profits will be $1 million in its first year and that this amount will grow at a rate of 5% per year for the next 16 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?
Question
You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug’s profits will be $1 million in its first year and that this amount will grow at a rate of 5% per year for the next 16 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?
Solution
To calculate the present value of the new drug, we need to discount each year's profits back to the present using the formula for the present value of a growing annuity:
PV = P / (r - g) * (1 - (1 + g / r) ^ -n)
where:
- P is the profit in the first year ($1 million),
- r is the interest rate (10% or 0.10),
- g is the growth rate of the profits (5% or 0.05),
- n is the number of years the profits are expected to last (17 years).
Substituting the given values into the formula, we get:
PV = $1,000,000 / (0.10 - 0.05) * (1 - (1 + 0.05 / 0.10) ^ -17)
Solving this equation will give us the present value of the new drug.
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