Question

Given an interest rate of 5.5 percent per year, what is the value at date t=6 of a perpetual stream of $1,000 payments that begins at date t=16?

Answer 1

$9,095.44

Step-by-step explanation:

First and foremost, we need to compute the present value of the perpetual stream of payments at t=16 using the below formula:

present value(at t=16)=payment/interest rate

present value(at t=16)=$1000/5.5%

present value(at t=16)=$18,181.82

Then we discount it backward for 9 years. Note that $18,181.82 is at the beginning period 16 which is equivalent to the end of period 15, hence,15 minus 6 gives 9 years.

Value at t=6 is using the present value formula below:

PV=FV/(1+r)^n

PV=$18,181.82 /(1+8%)^9

PV=$9,095.44