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Qualcomm has developed a groundbreaking new CPU chip. The patent on the chip will last 17 years. You expect that the chip’s profits to be $4 million in its first year and that this amount will grow at a rate of 5% per year for the next 17 years. Once the patent expires, Intel will be able to produce the same chip and competition will likely drive profits to zero. What is the present value of the new chip if the interest rate is 8% per year?

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Tundexi

Answer:

$50.74 million

Explanation:

Interest rate per annum = 8%

Number of years = 17

Number of compounding per annum = 1

Interest rate per period (r) = 8%/1 = 8%

Number of period (n) =17 * 1 = 17

Growth rate (g) = 5%

First payment (P) = 4 (

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million)

PV of the new Chip = p/(r-g) * [1 - [(1+g)/(1+r)]^n]

PV of the new Chip = 4/(8%-5%) * [1 - [(1+5%)/(1+8%)]^17]

PV of the new Chip = 4/0.03 * [1 - [1.05/1.08]^17]

PV of the new Chip = 4/0.03 * [1 - 0.972222^17]

PV of the new Chip = 133.333 * (1 - 0.6194589804)

PV of the new Chip = 133.333 * 0.3805410196

PV of the new Chip = 50.7386757663268

PV of the new Chip = $50.74 million

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