The Dividend Discount Model is a valuation formula used to find the fair value of a dividend stock.

“Everything should be as simple as it can be, but not simpler”

– Attributed to Albert Einstein

The elegance of the dividend discount model is its simplicity. The dividend discount model requires only 3 inputs to find the fair value of a dividend paying stock.

- 1 year forward dividend
- Growth rate
- Discount rate

### Dividend Discount Model Formula

The formula for the dividend discount model is:

The dividend discount model is calculated as follows. It is next year’s expected dividend divided by an appropriate discount rate less the expected dividend growth rate.

This is abbreviated as:

### Alternate Names of the Dividend Discount Model

The dividend discount model is often referred to by 3 other names:

- Dividend Growth Model
- Gordon Growth Model
- Dividend Valuation Model

The Dividend Growth Model, Gordon Growth Model, and Dividend Valuation Model all refer to the Dividend Discount Model.

Myron Gordon and Eli Shapiro at created the dividend discount model at the University of Toronto in 1956.

### How The Dividend Discount Model Works

The dividend discount model works off the idea that the fair value of an asset is the sum of its future cash flows discounted back to fair value with an appropriate discount rate.

Dividends are future cash flows for investors.

Imagine a business were to pay $1.00 in dividends per year, forever. How much would you pay for this business if you wanted to make 10% return on your investment every year?

10% is your discount rate. The fair value of this business according to the dividend discount model is $10 ($1 divided by 10%).

We can see this is accurate. A $10 investment that pays $1 every year creates a return of 10% a year – exactly what you required.

The dividend discount model tells us how much we should pay for a stock for a given required rate of return.

### Estimating Required Return Using the CAPM

CAPM stands for capital asset pricing model. It is a critical financial concept to understand. Click here to see 101 important financial ratios and metrics.

The capital asset pricing model shows the inverse relationship between risk and return (in theory, not so much in practice) .

The required return for any given stock according to the CAPM is calculated with the formula below:

What is the current market risk premium?

The long-term inflation adjusted return of the market *not accounting for dividends* is 2.2%. Inflation is expected to be at 1.7% over the next decade. The current dividend yield on the S&P 500 is 2.2%. A fair estimate of market return to use in the CAPM formula is 6.1% (2.2% + 1.7% + 2.2%).

The current risk free rate is 0.3%. The risk-free rate is traditionally calculated as the yield on 3-month T-Bills.

All that is left to calculate the required return on any stock using the CAPM is beta. Beta over a 10 year period is calculated below for 3 Dividend Aristocrats:

- Aflac (AFL) has a beta of 1.5
- PepsiCo (PEP) has a beta of 0.5
- Archer-Daniels-Midland (ADM) has a beta of 1.0

These betas imply a required return of:

- Aflac has a required return of 9.5%
- PepsiCo has a required return of 3.4%
- Archer-Daniels-Midland has a required return of 6.4%

Beta has a significant effect on the required returns of different stocks. PepsiCo in particular has an exceptionally low required return. PepsiCo has a dividend yield of 2.8%. The CAPM implies that PepsiCo need only grow at 0.6% a year and pay its dividend to satisfy investors.

### The Importance of The Dividend Growth Rate

The dividend growth rate is critically important in determining the fair value of a stock with the dividend discount model.

The denominator of the dividend discount model is discount rate minus growth rate. *The growth rate must be less than the discount rate for the dividend discount model to function*. If the growth rate estimate is greater than the discount rate the dividend discount model will return a negative value.

There are no stocks worth *any* negative value. The lowest value a stock can have is $0 (bankruptcy with no sellable assets).

Changes in the estimated growth rate of a business change its value under the dividend discount model.

In the example below, next year’s dividend is expected to be $1 multiplied by 1 + the growth rate. The discount rate is 10%:

- $4.79 value at -9% growth rate
- $5.88 value at -6% growth rate
- $7.46 value at -3% growth rate
- $10.00 value at 0% growth rate
- $14.71 value at 3% growth rate
- $26.50 value at 6% growth rate
- $109.00 value at 9% growth rate

### Longer Growth Rates Push Value Out In Time

The closer the growth rate is to the discount rate, the more time it takes to approach the present value of discounted future cash flows.

The chart below shows the percentage of fair value reached through time for different growth rates. A discount rate of 10% and an expected dividend of $1 multiplied by $1 + the growth rate is used.

Businesses with a wide gap between the discount rate and the growth rate converge on their fair value faster. There is a hidden advantage here. *You don’t have to be right for as long*.

If you have a required return of 10% and estimate dividend growth at 0% a year (no growth) it would take 8 years for discounted cash flows to reach ~50% (53%, exactly) of fair value.

With a 9% growth rate, only 7% of fair value is reached after 8 years. The business will have to grow at 9% for… 75 years to reach 50% of its fair value. Growth rates are difficult to calculate over 1 year. How anyone can push growth rates out 50 or 75 years and have any confidence in them is beyond me.

It is impossible to have any idea what a business will be doing in 75 years, even in extremely stable industries. At best, we can say a business will probably exist in 75 years. Saying it will still be growing at 9% a year in 75 years is impractical.

### Estimating The Dividend Growth Rate

The dividend growth rate must approximate the growth rate of the business over long time periods. If dividend growth exceeded business growth for long dividends will be more than 100% of cash flows. This is impossible over any meaningful length of time.

Long-term earnings-per-share growth approximates long-term dividend per share growth.

Using earnings-per-share growth over dividend-per-share growth has a distinct advantage. Dividend growth can be inaccurate due to 1 time increases in payout ratio.

A company can raise its payout ratio from 35% to 70% and double its dividend. The company *cannot* repeat the same trick over the next period. The payout ratio cannot double again from 70% to 140% (at least, it can’t if it wants to stay in business).

Established businesses are easier to estimate future growth rates for. A business like Coca-Cola will probably grow around the same rate over the next decade as it has over the last decade.

Rapidly growing businesses like Amazon (AMZN) *cannot* grow at 15% or 20% a year indefinitely. If Amazon grew its market cap at 20% a year over the next 30 years it would be worth *more than $64 trillion*. To put that into perspective, the global GDP is currently around $73.5 trillion. Rapidly growing businesses’ growth rates should be reduced to more accurately reflect future growth.

### Dividend Discount Model Excel Spreadsheet Calculator

Download a free Excel Spreadsheet dividend discount model calculator at the link below:

**Dividend Discount Model Excel Spreadsheet Calculator**

The calculator has detailed instruction inside the spreadsheet on how to use it.

### The Implied Dividend Growth Rate

The dividend discount model can tell us the *implied* dividend growth rate of a business using:

- Current market price
- Beta
- Reasonable estimate of next year’s dividend.

To do so we need only rearrange the dividend discount model formula to solve for growth rather than price.

Let’s use Wal-Mart (WMT) as an example:

- Share price of $67.44
- Estimated dividend next year of $2.04
- 10 year Beta of .53

Using the Beta above with our previously calculated 6.1% expected market return and 0.3% risk-free rate gives us a CAPM required return of 3.5% to use for our discount rate.

Plugging these numbers into the implied dividend growth formula gives an implied dividend growth rate for Wal-Mart of just 0.5%.

While it’s true that Wal-Mart has struggled as of late, it is very likely the company grows at a faster clip than 0.5% a year.

Comparing the implied growth rate to reasonable growth expectations can turn up potentially undervalued securities.

We will run through the same example with Cummins (CMI).

- Share price of $105.12
- Estimated dividend next year of $4.28
- 10 year Beta of 1.58
- CAPM discount rate of 9.9%
- Implied dividend growth rate of 5.8% over the long run

Cummins has grown its earnings-per-share at 11% a year over the last decade. The company is currently struggling due to a global growth slowdown. However, long-term growth prospects remain bright. Again, Cummins appears undervalued when comparing historical growth numbers to market expectations.

Both Cummins and Wal-Mart are favorites of The 8 Rules of Dividend Investing thanks to their valuation, long-records of growth, and above average dividend yields.

Click the link below to download an implied growth rate dividend discount model calculator:

**Implied Growth Rate Excel Spreadsheet Calculator**

### Top 10 Dividend Aristocrats Using The Dividend Discount Model

In December of 2014 I published an article on the 10 cheapest Dividend Aristocrats using the dividend discount model.

The annualized return from each of the top 10 is shown below. The return of the S&P 500 ETF (SPY) and Dividend Aristocrats ETF (NOBL) are also show below for comparison:

- S&P 500 annualized total return of -0.4%
- Dividend Aristocrats annualized total return of 2.8%
- McDonald’s (MCD) annualized total return of 28.7%
- Clorox (CLX) annualized total return of 19.9%
- AT&T (T) annualized total return of 17.5%
- Kimberly-Clark (KMB) annualized total return of 15.3%
- Coca-Cola (KO) annualized total return of 7.5%
- PepsiCo (PEP) annualized total return of 6.3%
- Johnson & Johnson (JNJ) annualized total return of 4.9%
- Procter & Gamble (PG) annualized total return of -7.8%
- Abbot Laboratories (ABT) annualized total return of -8.3%
- Wal-Mart (WMT) annualized total return of -15.9%

Seven out of the top 10 Dividend Aristocrats using the dividend discount model outperformed the S&P 500 and the Dividend Aristocrats Index.

The chart below shows the value of $1 invested SPY, NOBL, and in an equal weighted portfolio of the Top 10 Dividend Aristocrats using the dividend discount model.

An equal weighted portfolio (with no rebalances) of the Top 10 Dividend Aristocrats using the dividend discount model has performed very well since late December 2014.

This outperformance is likely due to the tilt towards lower beta stocks that the dividend discount model has. The market has been essentially falt in the period above. Low beta, high quality dividend stocks tend to perform well in this environment.

The expected growth rates of many Dividend Aristocrats are higher than their CAPM discount rates. This makes using the dividend discount model ‘as is’ impractical in this case.

I have calculated the *implied *growth rate for all of the Dividend Aristocrats using the dividend discount model to account for this. I then subtract the implied growth rate from the expected growth rate. This shows which Dividend Aristocrats have the biggest difference between expected and implied growth.

The Top 10 Dividend Aristocrats using the dividend discount model now are:

- W. Grainger (GWW)
- Abbott Laboratories (ABT)
- Hormel (HRL)
- Becton Dickinson (BDX)
- Ecolab (ECL)
- Procter & Gamble (PG)
- Coca-Cola (KO)
- PepsiCo (PEP)
- VF Corporation (VFC)
- Walgreens Boots Alliance (WBA)

You can download a spreadsheet of all 50 Dividend Aristocrats ranked using the difference between expected and implied dividend growth from the dividend discount model at the link below:

**Dividend Discount Model Dividend Aristocrats Excel Spreadsheet**

### Shortcomings of the Dividend Discount Model

The dividend discount model values a stock *in perpetuity*. No business exists forever. The model ascribes a positive value (albeit negligible) to dividends paid 100+ years from now.

I am a firm believer in the efficacy of long-term investing. Making 100+ year forecasts is foolish, even for the longest of long-term investors.

The dividend discount model does not work on businesses that *do not pay dividends*. Google (GOOG) certainly has a positive value, even though it doesn’t pay dividends. This shortcoming makes the dividend discount model a useful tool *only for dividend paying stocks* (as the name implies).

The dividend discount model says the fair value of a business is the sum of its future cash flows discounted to present value.

The model fails to account for cash flows from *selling your shares*. Take Google again. The company invests its cash flows into growth, not paying dividends to shareholders. If the company can grow at 15% a year, its stock price should (in theory) grow at 15% a year as well. When investors sell the stock they will generate a very real cash flow. The dividend discount model does not account for this.

The model also does not take into account changing payout ratios. Some businesses will drastically hike their payout ratio. This meaningfully affects the fair value calculation of the dividend discount model.

Calculating the ‘fair’ discount rate is also a serious drawback to the dividend discount model. You can know *your* expected return, but not what the overall expected return of the market *should* be. The CAPM does a poor job of coming up with real world discount rates.

### Final Thoughts

The dividend discount model has serious flaws; but so does every other valuation metric. Investing is an art, not a science. There is no one perfect way to invest.

The dividend discount model is a useful tool to gauge assumptions about a dividend stock. It is not the final word on valuation, but it does provide a different way to look at and value dividend stocks.

This article contains 3 separate downloads. They are listed below as well for easy access: