A Simple Way To Apply The Discounted Dividend Model To Evaluate A Stock

Is a stock over- or undervalued? Let’s use a tool called the “Discounted Dividend Model” to find out.

The Gordon Shapiro formula, also known as the Gordon Growth Model or the Dividend Discount Model (DDM), is used to estimate the value of a stock based on its expected future dividends. The formula is usually presented in a way too complicated way and the abbreviations tend to confuse people. But let’s make it readable. The formula is as follows:

P=D⋅(1+g)/(r−g)

Where:

  • P is the current price of the stock.
  • D is the most recent dividend payment.
  • g is the expected constant growth rate of dividends.
  • r is the required rate of return or discount rate.

Great, so let’s apply it to an example:

Stock price: 21o USD

Dividend pay out ratio: 50%

Expected yield: 10%

Earnings growth: 8%

Should you buy the stock? (Is it under-valued?)

Well, let’s calculate: (10×50%)/(10%-8%) = $ 250

At $ 210, the share is under-valued. Yes, it’s that simple.

 

Let’s look at the details:

Calculate the current dividend per share (D): D=Dividend payout ratio×Earnings per share (EPS)

Assuming the earnings growth rate is applied to the EPS, you can calculate EPS as: EPS=Current stock price×Expected yield

So, this gives us:

D=Dividend payout ratio×(Current stock price×Expected yield)

We can determine the required rate of return (r), which is the sum of the expected yield and the earnings growth rate: r=Expected yield+Earnings growth rate

Then we play around and substitute the values into the Gordon Shapiro formula:

Substitute D, g, and r into the formula and solve for P.

Does it seem confusing? Don’t worry, let’s look at…

A Simpler Example

Suppose you are considering a stock that currently pays an annual dividend of $2 per share. You expect the dividend to grow at a constant rate of 5% per year, and your required rate of return, or discount rate, is 10%.

The Gordon Shapiro formula is:

P=D⋅(1+g)/(r−g)

Where:

  • P is the current price of the stock.
  • D is the most recent dividend payment.
  • g is the expected constant growth rate of dividends.
  • r is the required rate of return or discount rate.

Now, let’s calculate the fair value of the stock using the DDM:

  1. Calculate D: D = $2

  2. Determine r: r=10%

  3. Determine g:

  4. Substitute into the DDM: P=2⋅(1+0.05)/(0.10−0.05

In this example, the fair value of the stock according to the DDM would be the estimated price at which the stock is correctly priced. If the current market price is close to this calculated fair value, the stock may be considered fairly valued. If the market price is significantly lower than the fair value, the stock might be undervalued, and if it’s significantly higher, it might be overvalued.

DDM is a basic valuation model and has its limitations. If a stock doesn’t pay a dividend, then it’s of course not applicable. So other valuation methods and factors should of course be considered when making investment decisions. But the DDM is one of many useful tools that can help us compare stocks (businesses).

 

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