Question

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 $ 5$5 million in its first year and that this amount will grow at a rate of 2 %2% 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?

Answer 1

Present value = $45,185,606

Step-by-step explanation:

Data:

number of periods(n) = 17 years

First-year profit = $5 million

Growth rate = 2%

Interest rate = 10%

Present value = ?

Solution:

The present value of the growing annuity can be calculated as follows

Formula:

Let's denote

annual interest rate = x

annual growth rate = y

Present value = First-year profit x
`((1-((1+y)/(1+x) )^(n) )/(x-y) )`

Present value = $5,000,000 x
`((1-((1+0.02)/(1+0.1) )^(17) )/(0.1-0.02) )`

Present value = $5,000,000 x 9.03

Present value = $45,185,606