Understand Finance - Finance Tutorials and Finance How To's

So we’ve learned in our annuity tutorial that an annuity is just a series of equal cash flows, equally spaced out in
time. This tutorial will talk about a special kind of annuity called a
perpetuity. Simply put, a perpetuity is an annuity that goes on forever. This is
a really interesting type of investment, with a very easy to use formula.

This formula is just telling us that the value of our perpetuity at time 0 is the
annual payment divided by our required return. Let’s take a look at a problem and see how
this fits together.

Practice Problem 1.
How much would you be willing to pay today for an annuity that promises to pay $9,000 per
year forever? Assume your required rate of return is 8%.

Solution:
This couldn’t get easier, folks. They tell us the annual payment is $9,000 and that our
required rate is 8%. We just need to plug those two numbers in our trusty perpetuity
equation to get the value today! Just remember to use the decimal form for your interest
rate. Your formula should now look like this:

After doing that simple math, you found out that we would be willing to spend
$112,500 for that perpetuity today. These problems really are just that
easy!

Practice Problem 2.
While strolling down a dark alley, you’re approached by a man offering to give you $1,000
every year forever if you give him just $10,000 today. If your opportunity cost of funds
is 11%, is this a good deal?

Solution:
First of all, you probably don’t want to give money to anybody on the street. That having
been said, let’s find out what he’s offering. He will give you $1,000 payments and your
opportunity cost (or your required rate) is 11%. Plugging this into your equation, you
are left with the following:

Push a couple buttons and you’ll find out that this perpetuity is only worth
$9,090.90 to you today. He wanted to sell it to you for $10,000 so you’d
better keep on walking… quickly.

If you’re still a little hazy on perpetuities, post your questions below in the comments section and we’ll get you some answers!