Question

Given an interest rate of 6% per year compounded annually, what is the value at the date t = 0 of a perpetual stream of $2,000 annual payments that begin at date t = 10? (approx. to nearest integer value)

Select one:

a. $19730

b. $20914

c. $18613

d. $18000

Answer 1

This question has two parts:

1. First is to find the PV of the perpetuity at t=10
2. Second is to discount it back to t=0

Part 1:

PV of the perpetual stream of CFs is calculated by solving the below equation:

Part 2:

If 'now' is represented by t=0 implies the beginning of year 1 then by the same notation logic, t=10 represents beginning of year 11 or the end year 10, therefore the PV dount in part 1 has to be discounted back for 10 years to find the required PV and that can be done as follows:

So rounding off to nearest integer, the correct answer is 18613 as suggested by option C