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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 4 % per year for the next 17 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?

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Answer:

PV=$10,593,984.88

Explanation:

This cash-flow described represents a growing annuity.

Present value of a growing ordinary annuity is calculated as follows:

PV=[tex]\frac{P}{i-g}*[1-[\frac{1+g}{1+i}]^n][/tex]

where P = the annuity payment in the first period

           i = interest rate per period that would be compounded for each period

          g = growth rate

          n = number of payment periods

from the question. P= $1,000,000; i=0.1; g= 0.04;n=18

PV=[tex]\frac{1,000,000}{0.1-0.4}*[1-[\frac{1+0.04}{1+0.1}]^1^8][/tex] =  $10,593,984.88

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