Debt Consolidation Loan

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:

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.

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.

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 ask in our forums. We'll be glad to help you!

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