Question

1. A black box spews out $100 today and then every year, forever. The risk-free rate is currently 7% per year, and is not expected to change. What is the value of the black box today, before the first $100 are spewed out? 2. What is the value of the box from Q1, if the amount it spews out grows by 5% every year (i.e., it'll be $105 in 1 year, $110.25 in two years, ...)?

Answer 1

1.

This is a type of perpetuity,

Value of Black Box = 100/0.07

Value of Black Box = $1,428.57

2.

This is a type of Growing Perpetuity,

Value of Black Box = 100(1.05)/(0.07 - 0.05)

Value of Black Box = $5250.00