Question

Your uncle developed a new comic book franchise and left the rights to you. Under current copyright law, your intellectual property is protected for 85 years. You expect that the profits from the franchise will be $1 million in its first year and that this amount will grow at a rate of 3% per year during the life of the copyright. Assume each year’s profits are received at the end of the period. Further assume that once the copyright expires, imitations and knockoffs will drive the profits from the intellectual property to zero. What is the present value of the comic book franchise if the discount rate is 14% per year?

Answer 1

This is a problem of annuity with growth component. In the given problem, annual profit is $1 million and growing @3% per year. This is growing annuity.

Here, 3% or 0.03 is g

$1 million or $100,000 is A.

Life of the property is 85 years which is n

Discount rate is 14% or 0.14 which is r

Now, the present value of growing annuity can be calculated by using following formula:-

$\frac{A}{r-g}(1-\frac{(1+g)^{n}}{(1+r)^{n}})$

Now, put the above values in the formula as shown below:-

$\frac{1}{0.14-0.03}(1-\frac{(1+0.03)^{85}}{(1+0.14)^{85}})=9.09$

Thus, the present value of franchise will be $9.09 million when the profit is growing at 3%.