423.10
10.Let’s say you’re Darth Vader and you’ve just occupied Cloud City. Lando Calrissian is offering you two tributes: Cloud City can afford to pay the Empire $10 million next year and increase the amount by 5% each year forever. Otherwise, you can accept no tribute for 9 years and then, starting 10 years from today, Cloud City will be able to afford to pay the Empire a flat tribute of $20 million every year forever. If your discount rate is 15% per year, which tribute should you take? (10)
There are two perpetuities here: one that starts next year and grows forever and another that is deferred, but does not grow.
The discount rate is 15%, and the growth rate for the first one is 5%, so the PV=$10M/(.15-.05)=$100M
The second one looks like this:
0 1.. 9 10 11 … 0 0 0 20 20
This is a deferred perpetuity and it is valued in 2 steps. First, find the value in the year before it starts (year 9) and then discount it back.