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 2% 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

Solution :

The formula for calculating the present value of a growing annuity is

PV = [ A / ( r – g) ] * [ 1 – ( ( 1 + g ) / ( 1 + r ) ) ⁿ ]

Where

A = Annual profits or Annuity ;   r = rate of interest ;   g = growth rate   ; n = no. of years

PV = Present value of growing annuity

As per the information given in the question we have

A = $ 1,000,000   ;    r = 9 % = 0.09   ; g = 2 % = 0.02   ;   n = 17 years

Applying the above values in the formula we have

= [ $ 1,000,000 / ( 0.09 – 0.02 ) ] * [ 1 – ( ( 1 + 0.02 ) / ( 1 + 0.09 ) ) ¹⁷ ]

= [ $ 1,000,000 / ( 0.09 – 0.02 ) ] * [ 1 – ( ( 1.02 ) / ( 1.09 ) ) ¹⁷ ]

= [ $ 1,000,000 / ( 0.07 ) ] * [ 1 – ( 1.02 / 1.09 ) ¹⁷ ]

= [ $ 1,000,000 / ( 0.07 ) ] * [ 1 – ( 0.935780 ) ¹⁷ ]

= [ $ 1,000,000 / 0.07 ] * [ 1 – 0.323558 ]                    

= [ $ 1,000,000 / 0.07 ] * [ 0.676442]                            

= $ 14,285,714.285714 * 0.676442

= $ 9,663,453.814727

= $ 9,663,453.81 ( when rounded off to two decimal places )

= $ 9,663,454 ( when rounded off to the nearest whole number )

Thus the present value of the new drug if the interest rate is 9% per​ year = $ 9,663,454

Note: The value of ( 0.935780 ) ¹⁷   is calculated using the Excel formula =POWER(Number,Power)

=POWER(0.935780,17) = 0.323558