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 $ 2$2 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 nbsp 9 % 9% per​ year?

Answer 1

Answer: The present value of the new drug is $19.33 million

We follow these steps to arrive at the answer:

Expected Revenues from the drug in year 1(P)   $2 million

Growth Rate (g)                                                        2% p.a.

No. of years  (n)                                                      17 years  

Discount rate (r)                                                        9% p.a.

Since the revenues are expected to grow at a constant rate of 2% p.a, we can treat this series of cash flows as a growing annuity.

We calculate the Present Value of a growing annuity with the following formula:

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

Substituting the values we get,

$PV = \frac{2}{0.09-0.02}*\left [ 1- \left (\frac{1+0.02}{1+0.09}\right)^{17}\right]$

$PV = \frac{2}{0.07}*\left [1- 0.323558233\right]$

$PV = 28.57142857 * 0.676441767$

$PV = 19.32690763$