In this article, I will show you how to use dividend discount models to value dividend stocks in the stock market. Although the discounted cash flow (DCF) valuation model may provide a better means of determining a company's intrinsic value, dividend discount models remain a useful tool for estimating value, particularly with companies that regularly use much of their free cash flow (FCF) to pay out dividends. These dividend valuation methods are generally simpler as well, due to the fewer number of assumptions that need to be made.

It's important that investors know how to apply these dividend discount models, as dividends, although not obligatory, are the only forms of cash investors receive from directly investing in a company. Moreover, valuation methods like the DCF model are not always the most useful when valuing dividend stocks, which is when dividend discount models come in handy.

I will discuss six dividend valuation methods below, which are all similar, but have been developed based on different assumptions on future growth. I will also provide examples along the way that can be realistically applied to any company you may be looking to invest in.

Dividend Discount Model (DDM)

The dividend discount model (DDM) is a method of estimating the value of a stock as the present value of all expected future dividend payments.

The DDM formula is below:

V₀ = [D₁ / (1 + r)] + [D₂ / (1 + r)²] + [D₃ / (1 + r)³] + ... [D_n / (1 + r)ⁿ]

where:

• V₀ = stock's fair value
• D₁ = dividend (at year 1)
• n = number of years (for the final dividend payment)
• r = required rate of return (discount rate)

The DDM model suggests that the value of any asset is the present value of expected future cash flows, discounted at an appropriate rate depending on how risky future cash flows are. Much like any present value calculation, future cash flows are always discounted to account for the time value of money (TVM), which states that a dollar today is worth more than a dollar in the future due to its potential earning capacity. Unlike the discounted cash flow (DCF) model, future cash flows refer to future dividend payments instead of free cash flow (FCF) or owners earnings.

The DDM Model can be used if you are fairly certain on what companies are going to pay in dividends in the next 5, 10, or however many years. However, this is difficult to predict accurately without any sort of dividend growth rate in the formula, and because projections of dividends cannot be made into perpetuity (forever).

The next few dividend discount models therefore expand on the DDM formula by introducing dividend growth, both stable and/or unstable, which will be a lot more applicable when valuing dividend companies.

However, prior to covering these models, it's important that we quickly remind ourselves on how to calculate the discount rate (r) for any present value dividend discount calculation.

Discount Rate: CAPM

The required rate of return (aka cost of equity or the discount rate), is typically found from the Capital Asset Pricing Model (CAPM). This is used to determine the present value of expected future cash flows for all of the dividend discount models.

The CAPM attempts to illustrate the relationship between risk and return. According to the CAPM, the higher your risk, the higher your return.

The CAPM formula is below:

r_e = r_f + β*(r_m - r_f)

where:

• r_e = cost of equity
• r_f = risk-free rate
• β = beta
• r_m = expected market return

Solving for the cost of equity (r_e) will provide you with the required rate of return (discount rate) that you can then use in your present value dividend discount formulas. If you know your personal required rate of return, then you can use this instead.

• Related: How to Calculate and Interpret the Capital Asset Pricing Model (CAPM)

Put simply, the risk-free rate (r_f) is the interest rate on the 10-year Treasury Note (currently near 1%). The beta (β) is a measure of systematic risk, and can be found on Yahoo Finance after searching for a company (see: "Beta 5Y Monthly"). Finally, for the expected market return (r_m), you can use 10%, which is basically the average historical annual return of the market (aka S&P 500).

DDM Example

Company ABC expects to pay dividends of $2/share, $3/share, $5/share, $8/share, and $11/share in the next 5 years. The present value of the stock is calculated below with a discount rate of 10%:

V₀ = [$2 / (1 + .10)] + [$3 / (1 + .10)²] + [$5 / (1 + .10)³] + [$8 / (1 + .10)⁴] +[$11 / (1 + .10)⁵] --> $20.35/share

Gordon Growth Model

The Gordon Growth Model (GGM), or constant perpetual growth model, is a version of the dividend discount model (DDM) in which dividends grow forever at a constant rate.

The GGM formula is below:

V₀ = [D₀ * (1 + g) / r - g] = [D₁ / r - g]

where:

• V₀ = stock's fair value
• D₀ = dividend (over the past year)
• D₁ = dividend (at year 1)
• r = required rate of return (discount rate)
• g = annual dividend growth rate forever

With the GGM, applying the right dividend growth rate is essential, as the model is very sensitive to changes in growth and the required rate of return (discount rate). Therefore, it's important that we know how to best estimate this dividend growth.

How to Estimate the Dividend Growth Rate

To determine future (expected) dividends, which will grow into perpetuity, you can use one (or more) of the methods below:

Option #1: Use Past Average Dividend Growth Rates

This is probably the most intuitive approach, where you are simply calculating the historical growth rate of dividends paid out by the company. I'd recommend using 5-year or 10-year dividend growth rate data, as it's more reliable.

There are many sites where you can collect data on the amount of dividends paid over a period of time, which you can then use to determine the average dividend growth rate. However, you can also use sites like SeekingAlpha to search for a dividend-paying company and view its annual dividend growth rates, as shown below for Johnson & Johnson (JNJ):

Therefore, if we're using the 10-year dividend growth rate, this would be 6.55%.

If, for whatever reason, you cannot find this information, then you can opt into using the average annual historical dividend growth rates in the industry the company operates.

Option #2: Use Future Dividend Growth Rate Analyst Estimates

The second option is to just use what analysts estimate for future dividend growth. Although you don't really know how the analysts came up with their forecast, this is a quick way to estimate annual dividend growth.

Many times, this dividend growth can be hard to find, or hidden behind some kind of paywall or sign-up requirement. However, you can use SeekingAlpha, after searching for a dividend-paying company (again), to see what analysts predict for the next year's dividend. This is shown below for Johnson & Johnson (JNJ):

As you can see, 11 analysts estimate an average 2021 dividend of $4.24. This is a growth rate of about 5%, given a 2020 dividend of $4.04, which is fair given the 5-year dividend growth rate for the company is 6.17%.

Option #3: Estimate the Sustainable Dividend Growth Rate

The sustainable growth rate is the rate at which a company can continue to grow its dividend without any additional funding. Although it's more involved, this method is particularly useful when projecting dividends into perpetuity, as the GGM requires.

The sustainable dividend growth rate formula is below:

Sustainable dividend growth rate = ROE * (1 - (D / EPS))

where:

• ROE = return on equity (net income / average shareholders' equity)
• D = annual dividend
• EPS = earnings per share ((net income - preferred dividends) / weighted average outstanding shares)

For reference, the "D / EPS" calculation is also known as the dividend payout ratio. Again, we can use Johnson & Johnson (JNJ) for this example. For simplicity's sake, I will just provide the numbers needed to calculate the sustainable dividend growth rate, as it's rather intuitive and because the formulas are listed above.

The completed sustainable dividend growth rate formula for JNJ is below, using numbers from JNJ's FY 2020 on its 10-K annual report:

JNJ sustainable dividend growth rate = 25.36% * (1 - ($4.04 / $5.72)) --> 7.45%

This formula therefore suggests that JNJ can sustain a dividend growth rate of 7.45% forever.

Option #4: Estimate the "Augmented" Sustainable Dividend Growth Rate

This is an optional method that builds on the sustainable dividend growth rate method above. It can be used if a company issues a significant amount of stock buybacks, which is a common way companies use to return cash indirectly to shareholders. By applying this adjustment, we may be able to estimate a more accurate sustainable dividend growth rate, as we're now accounting for the cash returned to shareholders in the form of stock buybacks.

To make this adjustment, and to account for the potential increase in financial leverage, use the formula below:

Augmented dividend payout ratio = (Dividends + Stock buybacks - New long-term debt issued) / Net income

Repeating this calculation over a 3-5 year period and taking the average should reduce any skewed results due to stock buybacks not being issued one or more years, or from a very high (or very low) stock buyback issuance.

Then, you can use the formula below to calculate the augmented sustainable dividend growth rate:

Augmented sustainable dividend growth rate = ROE * (1 - Augmented dividend payout ratio)

where:

• ROE = return on equity (net income / average shareholders' equity)

Important Considerations for the Dividend Growth Rate

An important rule with the Gordon Growth Model (GGM), is that the growth rate must be lower than the discount rate (g < r). If the dividend growth rate was higher than the discount rate, then the dividend would be divided by a negative number. This would mean the company would be valued at a negative value, hence implying the company is worthless. Similarly, if the dividend growth rate was the same as the discount rate, then you'd be dividing by zero, which would lead to an undefined value. Obviously, this is not feasible as well.

Another rule here is that the growth rate must be reasonable. In other words, the dividend growth rate must be roughly less than or equal to the growth rate of the economy in which the firm operates, because you are growing the dividend into perpetuity (forever). I say roughly, because the infinite growth rate can exceed the growth rate for the overall economy by more than a small amount (1-2%).

One approach would therefore be to constrain the growth so that it could not exceed the risk-free rate, which as you may know from the CAPM, is the interest rate on the 10-year Treasury Note. As of writing, this is near 1%. In this case, if I were valuing JNJ, which has an average dividend growth rate of 6% annually, then I'd likely stick with the long-term average risk-free rate (~4% at time of writing) instead.

Another approach is to take the long-term inflation rate and add it to average the growth rate of the overall economy. Currently, long-term inflation rate is over 3% and the long-term growth rate of the overall economy for the U.S. is between 2-3%. For multinational companies like JNJ, you'd use the long-term growth rate of the world economy, which is about 1% higher.

In short, if you ensure the dividend growth rate is reasonable in respect to the growth rate of the overall economy, this will typically make the figure lower than the discount rate as well. You can use the approaches discussed above as a ballpark figure to confirm that your dividend growth rate is not too high.

Assumptions and Limitations of the Gordon Growth Model

The Gordon Growth Model (GGM) assumes the following:

• The company's business model is stable.
• The company grows at a constant, unchanging rate.
• The company has stable financial leverage.
• The company's free cash flow (FCF) is largely paid out as dividends.

As you can see, companies that do not closely follow these assumptions may result in misleading valuations. In specific, the GGM may underestimate the value of companies that consistently pay out less than they can afford to, and instead accumulate cash in the process.

Another limitation to the GGM, is that dividend growth rates must be constant forever. Obviously, this is a difficult assumption to meet, especially given how volatile earnings can be. Fortunately, this is not a huge downside as dividends are typically "smoothed out" overtime as they are less likely to be affected by changes in earnings growth. Moreover, if you were to use similar year-specific growth rates instead of a constant dividend growth rate like the GGM requires, there would likely be little difference in terms of the final present value dividend discount calculation.

These limitations/downsides to the Gordon Growth Model (GGM) are summarized below:

• The required rate of return (discount rate) cannot be smaller than the growth rate.
• The model excludes non-dividend factors.
• It's highly unlikely that most companies will increase their dividend at a constant rate.
• The model is highly sensitive to the growth rate and discount factor used.
• Not all dividend-players pay out a large portion of their earnings as dividends.

Despite these limitations or downsides of using the GGM, the model is still useful in determining the relationship between growth rates, discount rates, and fair value, and can provide you with a reasonable intrinsic value buy price range for a company.

Best Use for the Gordon Growth Model

To recap, with the Gordon Growth Model (GGM), one of the main assumptions is that the company you're valuing can continue to grow its dividend at its respective growth in perpetuity (forever). This alone can filter out many dividend players. Regardless, the GGM can still be very useful when applied to the right companies and/or industries.

To elaborate, the GGM works well for these companies/industries:

• Stable blue-chip dividend-paying companies: Large blue-chip companies typically have a proven track record of paying and growing its dividend over the long-term at a relatively consistent rate.
• Real estate investment trusts (REITs): REITs are required to pay out 90% of their net income as unqualified dividends to shareholders. They are also limited in terms of investment policy and typically do not grow at high rates.
• Regulated companies: Regulated companies in the utilities and energy industry, for example, generally have high stable leverage, pay high dividends already, and have limited growth because they can only service those in their geographical area.
• Large financial service companies: These companies are relatively predictable, pay high dividends, are limited in the amount of leverage they can change, and likely will not experience high growth.
• Companies that follow dividend payout policies: Any company that has a well-established dividend payout policy that has actually been followed in the past, may be a good candidate for a GGM. However, this only applies if the company promises (and practices) consistent dividend increases.

As you can see, the GGM works best for dividend players that follow the assumptions the model lays out.

GGM Example

Company ABC recently paid a dividend of $3/share and it's expected to grow at a constant rate of 6%. The present value with a discount rate of 10% is calculated below:

V₀ = [$3 * (1 + 0.06) / 0.10 - 0.06] --> $79.50/share

Non-Constant Growth in the First Stage

The non-constant growth in the first stage model is when the dividend grows at an erratic rate in the first stage, subsequently followed by a steady dividend growth rate into perpetuity (forever). In other words, this is basically when you merge the dividend discount model (DDM) and the Gordon Growth Model (aka constant perpetual growth model or GGM).

V₀ = DDM + (GGM / (1 + r)ⁿ)

OR... (written out):

V₀ = [D₁ / (1 + r)] + [D₂ / (1 + r)²] + [D₃ / (1 + r)³] + ... [D_n / (1 + r)ⁿ] + [(D_n * (1 + g) / r - g) / (1 + r)ⁿ)]

where:

• V₀ = stock's fair value
• DDM = Dividend Discount Model (shown before)
• GGM = Gordon Growth Model (shown before)
• r = required rate of return (discount rate)
• n = date/year when initial dividend growth period ends

The same assumptions, limitations/downsides, and rules apply here for both the DDM and the GGM. This model can be useful when you are fairly certain of the dividends a company will issue in the next 1+ years, and when a dividend-paying company is expected to have a stable dividend growth rate in the future. However, this is difficult to determine, so this model may not be used as often.

Non-Constant Growth in the First Stage Example

Company ABC expects to pay a dividend of $1/share, $3/share, and $4/share over the next three years. After the third year, it will grow at a constant rate of 4% into perpetuity. The stock's fair value is calculated below with a discount rate of 10%:

V₀ = [$1 / (1 + 0.10)] + [$3 / (1 + 0.10)²] + [$4 / (1 + 0.10)³] + [$4 * (1 + 0.04) / 0.10 - 0.04) / (1 + 0.10)³] --> $58.26/share

Two-Stage Dividend Growth Model

The two-stage dividend growth model applies when a firm will grow its dividend at an unstable growth rate for some period of time, subsequently followed by a steady dividend growth rate into perpetuity (forever).

Typically, the initial unstable growth rate period is higher than the stable growth rate into perpetuity, but a slower or negative dividend growth rate can be applied in the initial phase as well. Naturally, if the initial growth rate is the same as the second period of growth, then you'd just use the Gordon Growth Model (GGM) discussed in the previous section.

The two-stage dividend growth model formula is below:

V₀ = [D₀ * (1 + g₁) / (r - g₁)] * [1 - ((1 + g₁) / (1 + r))ⁿ] + [(1 + g1) / (1 + r)]ⁿ * [D₀ * (1 + g₂) / (r - g₂)]

where:

• V₀ = stock's fair value
• D₀ = dividend (over the past year)
• n = date/year when dividend growth rate changes from g₁ to g₂
• r = required rate of return (aka discount rate)
• g₁ = annual dividend growth rate for first stage
• g₂ = annual dividend growth rate for second stage

You can use the same methods to estimate dividend growth, as shown in the Gordon Growth Model (GGM) section. For the two-stage dividend growth model, I'd recommend calculating the sustainable or augmented growth rate for g₂, which will grow forever, or to use the "normal" dividend growth rate the company typically grows at. Then, although it depends on the company's unstable high growth period, using the historical average annual growth rate over the 1-yr or 3-yr period should provide you with the high growth figure you can use for g₁.

Once again, the growth rate of the second dividend must be lower than the discount rate (g₂ < r), and it must be less than or equal to the growth rate of the economy in which it operates, much like the GGM discussed in the previous section. However, the growth rate of the first dividend (g₁) can be above or equal to the discount rate (r), and can grow at a rate higher than the growth rate of the economy, because it's not growing to infinity.

After the initial high-growth period, the company should expect the following:

• Higher dividend payout ratio: Stable companies are able to pay out more of its earnings in dividends than growing companies.
• Beta close to 1: The company's levered beta should be between 0.8 - 1.2 as the company becomes stable.
• ROE should decrease: The return on equity (ROE) should decrease.

More or less, this information is just for your reference.

Limitations of the Two-Stage Dividend Growth Model

The main limitations/downsides to the two-stage dividend growth model are as follow:

• Defining the length of the initial growth period is difficult.
• Dividend growth rates are not transformed overnight into a stable growth rate at the end of the period. In reality, it's more gradual.
• Like the GGM, you may underestimate the value of firms that accumulate cash and pay out too little in dividends.

Future dividend discount models covered in this article, although more involved, do help to limit or eliminate these downsides.

Best Use for the Two-Stage Dividend Growth Model

As the model suggests, the two-stage dividend growth model works best for companies that are currently in a high-growth phase, and expect to maintain this growth for a specific period time until they return to "normal" growth. It may also work well for companies where the dividend growth rate is not yet stable, but is expected to be in the near future.

Below is a list of examples of companies and scenarios this may apply to:

• Companies with an important patent.
• Companies that have developed some kind of big (likely short-term) competitive advantage.
• Companies that are industries with high barriers to entry, perhaps due to short-term economic conditions.
• Companies that have a policy to pay out residual cash flows (i.e., from debt repayments) as dividends.
• Companies that pay out dividends that are roughly equal to FCFE, or when FCFE is hard to estimate accurately.

This should provide you with a better understanding of when the two-stage dividend growth model is most applicable. The most important parts to get right, however, are the length of the high dividend growth period and the growth rates of both periods. Typically, the easier it is to estimate this period of high dividend growth, the more accurate your present value discounted dividend model will be.

Two-Stage Dividend Growth Model Example

Company ABC recently paid a dividend of $2/share. Analysts predict a 3-year period of high dividend growth of 12%, and then a stable dividend growth into perpetuity of 5%. The stock value calculation is below with a discount rate of 15%:

V₀ = [$2 * (1 + 0.12) / (0.15 - 0.12)] * [1 - ((1 + 0.12) / (1 + 0.15))³] + [(1 + 0.12) / (1 + 0.15)]³ * [$2 * (1 + 0.05) / (0.15 - 0.05)] --> $25.10/share

H-Model for Valuing Growth

The H-model dividend discount formula is another two-stage dividend model, but differs as the growth in the initial phase gradually increases or decreases at a constant rate overtime to reach the next stable growth phase into perpetuity (forever).

The H-model dividend discount formula is below:

V₀ = [D₀ * (1 + g₂) / (r - g₂)] + [D₀ * H * (g₁ - g₂) / (r - g₂)]

where:

• V₀ = stock's fair value
• D₀ = dividend (over the past year)
• H = half life of anticipated transition period
• r = required rate of return (aka discount rate)
• g₁ = increasing/declining dividend growth rate for first stage
• g₂ = annual dividend growth rate for second stage

The first stage declining growth rate in the H-model (g₁) can be estimated based on historical averages and/or analyst estimates. For instance, if a company's dividend growth rate was 14%, and this is expected to decline by 2% each year over the next 6 years, then the input for "g1" would be 14%, and the input for "H" (half-life) would be 3 years.

The second stage dividend growth rate (g₂) in the H-model is the same as the Gordon Growth Model (GGM) or the second stage of the two-stage dividend growth model, where the dividend grows at a constant rate into perpetuity. Its growth rate can therefore be estimated in the same way, which must be below the discount rate and growth rate of the overall economy.

Limitations and Best Use for the H-Model

The H-Model may be the preferred two-stage dividend growth model, as it's more realistic that a dividend's growth rate gradually increases/decreases over time instead of increasing/decreasing suddenly overnight, as the two-stage dividend growth model implies. However, the model does not come without any faults.

The limitations/downsides to this model begins with the H-Model assuming that the dividend payout ratio and required rate of return (discount rate) are constant overtime, and are not affected by shifting growth rates. Although this may reduce valuation uncertainty, it's inconsistent, because as the growth rate declines, the dividend payout ratio usually increases.

The second limitation/downside to using this model is that any significant deviations from what is expected in the initial dividend growth rate, in particular, can cause problems in your valuation. This is because the initial dividend growth rate must be constant in this model.

In short, you can apply the H-Model to companies that may be growing rapidly now, but growth is expected to decline gradually overtime as the company reaches its maturity stage or as the firm begins to lose its economic moat to competitors.

H-Model Example

Company ABC recently paid a dividend of $2/share. Analysts predict the company to gradually decrease its dividend growth rate from 15% to 5% over the next 6 years. The stock's fair value calculation is below with a discount rate of 10%:

V₀ = [$2 * (1 + 0.05) / (0.10 - 0.05)] + [$2 * 3 * (0.15 - 0.05) / (0.10 - 0.05)] --> $54/share

Three-Stage Dividend Discount Model

The three-stage dividend discount model combines features of the Dividend Discount Model (DDM) and the H-Model. This model has an initial period of high growth, a transitional period where growth declines, and a final stable growth period to perpetuity.

The three-stage dividend discount formula is below:

V₀ = [D₁ / (1 + r)] + [D₂ / (1 + r)²] + [D₃ / (1 + r)³] + ... + [D_n / (1 + r)ⁿ] + [(D_n * (1 + g₂) + D_n * H * (g₁ - g₂)) / ((r - g₂) / (1 + r)ⁿ)]

where:

• V₀ = stock's fair value
• n = number of years of initial high dividend growth
• D₁ = dividend (at year 1)
• H = half life of anticipated transition period
• r = required rate of return (aka discount rate)
• g₁ = dividend growth rate for first stage
• g₂ = annual dividend growth rate for final stable stage

As you can see, this is the most complex model, but removes many of the constraints imposed by other versions of the dividend discount model. There are also no restrictions on the payout ratio, making it the most general of the models. In general, the three-stage dividend discount model, when used correctly, is likely the most accurate model to use to reflect the value of a stock.

This model is also more appropriate for companies whose earnings are growing at high rates, which are expected to decline gradually to a stable rate as the firm becomes larger and perhaps loses some of its competitive advantages. In short, this model is rather flexible, and is particularly useful for companies that expect growth but also change in their payout policies and risk.

Three-Stage Dividend Discount Model Example

Company ABC dividend growth rates prior to the current transition period have grown at average rate of 16% over 3 years. Afterwards, the growth gradually declined by 3% per year for 4 additional years until stabilizing at 4%. D₁, D₂, and D₃, are $2.50, $3.10, and $4 respectively before considering the initial high growth. The stock's fair value calculation is below with a discount rate of 10%:

V₀ = [$2.50 * 1.16 / (1 + 0.10)] + [$3.10 * 1.16 / (1 + 0.10)²] + [$4 / (1 + 0.10)³] + [($4 * (1 + 0.04) + $4 * 2 * (0.16 - 0.04)) / ((0.10 - 0.04) / (1 + 0.10)³)] --> $72.73/share

Dividend Discount Model Criticisms

Although dividend discount models have been criticized as being of limited value by analysts, they have been proven to be surprisingly adaptable and useful when valuing dividend-paying companies. To keep it short, I will only cover a few pointers here.

To begin, some say the model is too conservative. In response, if investors are worried about this they can use the augmented growth rate calculation, which as you know, factors in stock buybacks. Moreover, if investors build a model with varying growth rates, this will make the model more accurate and useful in determining the fair value of the stock.

It's also said that dividend discount models will uncover fewer undervalued stocks in bullish/inflated markets. However, this is naturally the case in a bullish environment and with models like the DCF. Moreover, this is not true because dividend discount models should increase an equivalent amount, only if the market increase is due to economic fundamentals (i.e., higher expected growth in the economy and/or lower interest rates).

Finally, although these dividend discount models are most applicable to companies that have a history of paying dividends, they can still be used to value companies that expect to issue dividends in the near future. This is a misconception many investors have.

In short, dividend discount models should not be ignored, and at the every least, are useful models investors can build out and analyze to better understand the fair/intrinsic value price of a dividend stock.

The Bottom Line

Now that you're aware of the different dividend discount models, the many assumptions, upsides, and downsides to the models, and which may be more applicable depending on the company you're analyzing, the next step is to apply a margin of safety to your fair value calculation, much like you'd do in a discounted cash flow (DCF) model.

Similarly, it would be wise to build a model where you cant test low, medium, and high dividend growth rate expectations, to best determine when to purchase the stock. This, along with an appropriate discount rate using the CAPM, or with your own personal required rate of return, should provide you with a good understanding on whether the stock is undervalued or overvalued.

Finally, you can use the stock's fair value, along with your understanding of the dividend company and its growth potential to make a decision on whether to purchase the stock or not.