Question

2) 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 $4 million in its first year and that this amount will grow at a rate of 6% 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 9% per​ year?

Answer 1

Present value = Sum [ Cash flows * PVF(r%, n) ]

Particulars	Amount
Cash flow at Year 1	$ 4,000,000.00
Int Rate ( r )	9.00%
Growth Rate (g )	6.00%
No. of Years	17

PV of Growing Annuity = [ CF1 / ( r - g ) ] * [ 1 - [ ( 1 + g ) / ( 1 + r ) ] ^ n ]
= [ $ 4000000 / ( 0.09 - 0.06 ) ] * [ 1 - [ ( 1 + 0.06 ) / ( 1 + 0.09 ) ] ^ 17 ]
= [ $ 4000000 / ( 0.03 ) ] * [ 1 - [ (1.06 ) / ( 1.09 ) ] ^ 17 ]
= [ $ 133333333.33 ] * [ 1 - [ ( 0.9725 ) ] ^ 17 ]
= [ $ 133333333.33 ] * [ 1 - [ 0.6222 ] ]
= [ $ 133333333.33 ] * [ 0.3778 ]
= $ 50373333.33

PV of annuity is $ 50373333.33