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 3 % 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 nbsp 7 % per year?

$11,845,000

Explanation:

there are two ways to calculate the value, the first one is using an excel spreadsheet and the other one is by using the growing annuity formula:

the excel spreadsheet is relatively easy to use (use NPV function), so I'll focus on the growing annuity formula:

PV = [P / (r - g)] x {1 - [(1 + g) / (1 + r)]ⁿ}

PV = [$1,000,000 / (7% - 3%)] x {1 - [(1 + 3%) / (1 + 7%)]¹⁷}

PV = ($1,000,000 / 4%) x [1 - (1.03 / 1.07)¹⁷]

PV = $25,000,000 x (1 - 0.5232)

PV = $25,000,000 x 0.4738 = $11,845,000

the answer is a.

by: nicholas dooley