Understand Finance - Finance Tutorials and Finance How To's

When you are looking to find the value of a share of common stock, you have a very
easy solution as long as the dividends are growing at a constant rate. The
constant-growth model or Gordon Growth Model will do the trick! The equation to
find the value of a share of common stock is:

In this equation, V_cs is the value of a share of common stock.
D₁ is the next dividend to be paid, k_cs is the
required return, and g is the growth rate. If any of these terms seem a little
foreign to you, read our tutorials on the Cost of Equity or Three Ways To Find Growth
Rate. This equation is going to give us the value of a share of common
stock. You will see problems that ask for the intrinsic value or what the stock
is worth to us today. These all mean the same thing, so don’t get thrown off by
terms such as intrinsic value. So now that we understand all of the terms in
this simple equation, let’s put it to work in a problem!

Practice Problem 1
Marco Pollo is expected to pay a dividend next year of $2 and dividends will continue to
grow at 10% per year. If investors require a return of 15% for stocks of this level of
risk, what is the intrinsic value of a share of Marco Pollo common stock?

Solution
In the problem, we’re told that D₁, the next dividend to be paid, is
$2. We’re told that the growth rate is 10% and the required return,
k_cs is 15%. If we put this information into our equation, we get the
following:

"Practice Problem 1 Solution" />

So that’s it! We see that the value of Marco Pollo common stock is
$40 per share. This problem was pretty straight forward so let’s take it
a step further to make sure you have all of your bases covered.

Practice Problem 2
Peas & Carrots Produce recently paid a dividend of $3 per share and dividends are
expected to grow at a constant rate of 8% indefinitely. If the required rate for a share
of common stock is 18%, what is a share of Peas & Carrots common stock worth
today?

Solution
In this problem, we’re given a growth rate of 8% and a required return of 18%. But are we
given D₁? The problem tells us that the company recently
paid a dividend of $3. That dividend has already been paid! We’re looking for the
next dividend, D₁ so we must use our D₁
equation.

alt="Dividend Equation" />

alt="Dividend Equation" />

Now that we know that the next dividend will be $3.24, we can put all of our
information into the constant-growth equation to get a value for this stock.

"Practice Problem 2 Solution" />

That’s it! A share of Peas & Carrots common stock is worth
$34.20. Now that you have a good understanding of the constant-growth
model, try out a few of these problems!

Practice Problem 3
TennisTime recently paid a dividend of $2.25. Their return on equity is 18% and they
retain 40% of their net income and pay the remaining 60% in dividends. If investors
require 9% for stocks of this risk level, what is the intrinsic value of a share of
TennisTime common stock?

Solution
This problem is a lot tougher but you should get $134. In this problem,
you’ll need to use the growth equation from the tutorial Three Ways To Find Growth
Rate to find a growth rate of 7.2%. Then, use the D₁ equation to
get your dividend of $2.412. From there, you can plug the numbers into your
constant-growth equation for the end result!

Practice Problem 4
Sunshine State Umbrellas paid a dividend of $1.00 five years ago. Their recent dividend
was $1.61. If investors require 14% for a share of common stock, what is the intrinsic
value?

Did you get $44.17? If not, it could just be a rounding issue. But,
let’s look at what this one took. We know that D₀ is $1.61 but we need
D₁. You can use the time value of money to find the growth rate and
you will get 9.993%. From there you can get D₁ and then use the
constant-growth equation to get the final answer.

I know these practice problems were a bit harder than usual so if you have any
questions at all, please leave a comment and we’ll get everything sorted out!