**Dividend Discount Model** – It is a way of valuing a company based on the theory that a stock is worth the discounted sum of all of its future dividend payments. In other words, it is used to evaluate stocks based on the net present value of the future dividends.

Financial theory states that the value of a stock is the worth all of the future cash flows expected to be generated by the firm discounted by an appropriate risk-adjusted rate. We can use dividends as a measure of the cash flows returned to the shareholder.

Some examples of regular dividend paying companies are McDonalds, Procter & Gamble, Kimberly Clark, PepsiCo, 3M, CocaCola, Johnson & Johnson, AT&T, Walmart etc. We can use Dividend Discount Model to value these companies.

source: ycharts

This article is an in-depth article on Dividend Discount Model and covers the following –

- Dividend Discount Model – Foundation
- Types of Dividend Discount Model
- DDM Type #1 – Zero Growth Model
- DDM Type #2 – Constant Growth Rate DDM (Gordon Growth Model)
- DDM Type #3 – Variable Growth Rate DDM (Multi-stage DDM)
- Dividend Discount Model – Advantages
- Dividend Discount Model – Limitations

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**Dividend Discount Model – Foundation**

Intrinsic value of the stock is the present value all the future cash flow generated by the stock. For example, if you buy a stock and never intend to sell this stock (infinite time period). What is the future cash flows that you will receive from this stock. Dividends, right?

Here the CF = Dividends.

Dividend discount model prices a stock by adding its future cash flows discounted by the required rate of return that an investor demands for the risk of owning the stock.

However, this situation is a bit theoretical, as investors normally invest in stocks for dividends as well as capital appreciation. Capital appreciation is when you sell the stock at a higher price then you buy for. In such a case, there are two cash flows –

- Future Dividend Payments
- Future Selling Price

Find the present values of these cash flows and add them together :

**Intrinsic Value = Sum of Present Value of Dividends + Present Value of Stock Sale Price**

This Dividend Discount Model or DDM price is the **intrinsic value** of the stock.

If the stock pays no dividend, then the expected future cash flow will be the sale price of the stock. Let us take an example.

### Dividend Discount Model – Foundation Example

**Assume that you are considering the purchase of a stock which will pay dividends of $20 (Div 1) next year, and $21.6 (Div 2) the following year. After receiving the second dividend, you plan on selling the stock for $333.3 What is the intrinsic value of this stock if your required return is 15%? **

**Solution:**

This problem can be solved in 3 steps –

**Step 1 – Find the present value of Dividends for Year 1 and Year 2.**

- PV (year 1) = $20/((1.15)^1)
- PV(year 2) = $20/((1.15)^2)
- In this example, they come out to be $17.4 and $16.3 respectively for 1st and 2nd year dividend.

**Step 2 – Find the Present value of future selling price after two years.**

- PV(Selling Price) = $333.3 / (1.15^2)

**Step 3 – Add the Present Value of Dividends and present value of Selling Price**

- $17.4 + $16.3 + $252.0 = $285.8

## Types of Dividend Discount Models

Now that we have understood the very foundation of Dividend Discount Model, let us move forward and learn about three types of Dividend Discount Models.

**Zero Growth Dividend Discount Model –**This model assumes that all the dividends that are paid by the stock remain one and same forever until infinite.**Constant Growth Dividend Discount Model –**This dividend discount model assumes that dividends grow at a fixed percentage annually. They are not variable and are constant throughout.**Variable Growth Dividend Discount Model or Non Constant Growth –**This model may divide the growth into two or three phases. The first one will be a fast initial phase, then a slower transition phase an then ultimately ends with a lower rate for the infinite period.

We will discuss each one in greater detail now.

## #1 – Zero-growth Dividend Discount Model

Zero-growth model assumes that the dividend always stays the same i.e. there is no growth in dividends. Therefore, the stock price would be equal to the annual dividends divided by the required rate of return.

**Stock’s Intrinsic Value = Annual Dividends / Required Rate of Return**

This is basically the same formula used to calculate the **Present Value of Perpetuity**, and can be used to price preferred stock, which pays a dividend that is a specified percentage of its par value. A stock based on the zero-growth model can still change in price if the required rate changes when perceived risk changes, for instance.

**Zero Growth Dividend Discount Model – Example **

*If a preferred share of stock pays dividends of $1.80 per year, and the required rate of return for the stock is 8%, then what is its intrinsic value?*

**Solution:**

Here we use the formula for zero growth dividend,

**Intrinsic Value = Annual Dividends / Required Rate of Return**

Intrinsic Value = $1.80/0.08 = $22.50.

The shortcoming of the model above is that you’d expect most companies to grow over time.

## #2 – Constant-Growth Rate DDM (Gordon Growth Model)

The constant-growth Dividend Discount Modelor the Gordon Growth Model assumes that dividends grow by a specific percentage each year,

Can you value Google, Amazon, Facebook, Twitter using this method? Ofcourse not as these companies do not give dividends and more importantly are growing at a much faster rate. Constant growth models can be used to value companies that are mature whose dividends increase steadily over the years.

Let us look at Walmart’s Dividends paid in the last 30 years. Walmart is a mature company and we note that the dividends have steadily increased over this period. This company can be a candidate that can be valued using Gordon Growth Model.

source: ycharts

Please note that in Gordon Growth model, we do assume that the growth rate in dividends is **constant**, however, the **actual dividends outgo increases each year.**

Growth rates in dividends is generally denoted as g, and the required rate is denoted by Ke. Another important assumption that you should note is the the required rate or Ke also remains constant every year.

Constant growth Dividend Discount Model or DDM gives us the present value of an infinite stream of dividends that are growing at a constant rate.

Gordon Growth formula is as per below –

Where:

- D1 = Value of dividend to be received next year
- D0 = Value of dividend received this year
- g = Growth rate of dividend
- Ke = Discount rate

### Gordon Growth Model – Example#1

**If a stock pays a $4 dividend this year, and the dividend has been growing 6% annually, then what will be the intrinsic value of the stock , assuming a required rate of return of 12%?**

**Solution:**

D1 = $4 x 1.06 = $4.24

Ke = 12%

Growth rate or g = 6%

Intrinsic stock price = $4.24 / (0.12 – 0.06) = $4/0.06 = $70.66

### Gordon Growth Model – Example#2

**If a stock is selling at $315 and the current dividends is $20. What might the market assuming the growth rate of dividends for this stock if the rate of required return is 15%?**

**Solution:**

In this example, we will assume that the market price is the Intrinsic Value = $315

This implies,

$315 = $20 x (1+g) / (0.15 – g)

If we solve the above equation for g, we get the** implied growth rate as 8.13%**

## #3 – Variable-Growth Rate DDM (Multi-stage Dividend Discount Model)

Variable Growth rate Dividend Discount Model or DDM is much closer to reality as compared to the other two types of dividend dicount model. This model solves the problems related to unsteady dividends by assuming that the company will experience different growth phases.

Variable growth rates can take different forms, you can even assume that the growth rates are different for each year. However, the most common form is one that assumes 3 different rates of growth:

- an initial high rate of growth,
- a transition to slower growth, and
- lastly, a sustainable, steady rate of growth.

Primarily, the constant-growth rate model is extended, with each phase of growth calculated using the constant-growth method, but using different growth rates for the different phases. The present values of each stage are added together to derive the intrinsic value of the stock.

This can be applied as follows:

### #3.1 – Two stage Dividend Discount Model DDM

This model is designed to value the equity in a firm, with two stages of growth, an initial period of higher growth and a subsequent period of stable growth.

Two-stage Dividend Discount Model; best suited for firms paying residual cash in dividends while having moderate growth. For instance, it is more reasonable to assume that a firm growing at 12% in the high growth period will see its growth rate drops to 6% afterwards

My take is that the companies with a higher dividend payout ratios may fit such a model. As we note below such two companies – Coca-Cola and PepsiCo. Both companies continue to pay dividends regularly and their dividend payout ratio is between 70-80%. In addition, these two companies show relatively stable growth rates.

source: ycharts

**Assumptions **

- Higher growth rate is expected the first period.
- This higher growth rate will drop at the end of the first period to a stable growth rate.
- The dividend payout ratio is consistent with the expected growth rate.

### Two stage DDM model – Example

**Check Mate forecasts that its dividend will grow at 20% per year for the next four years before settling down at a constant 8% forever. Dividend (current year,2016) = $12; Expected rate of return = 15%. What is the value of the stock now?**

**Step 1** : **Calculate the dividends for each year till stable growth rate is reached**

The first component of value is the present value of the expected dividends during the high growth period. Based upon the current dividends ($12), the expected growth rate (15%) value of dividends (D1,D2,D3), can be computed for each year in the high growth period.

Stable growth rate is achieved after 4 years. Hence, we calculate the Dividend profile until 2010.

**Step 2: Apply Dividend Discount Model to calculate the Terminal Value (Price at the end of high growth phase)**

We can use the Dividend Discount Model at any point in time. Here, in this example the dividend growth is constant for first four years and then it decreases, so we can calculate the price that a stock should sell for in four years i.e. the terminal value at the end of the high growth phase (2020). This can be estimated using the Gordon Growth Formula –

We apply the formula in excel as seen below. TV or Terminal value at the end of year 2020.

Terminal value (2020) is $383.9

**Step 3: Find the present value of all the projected dividends **

Present value of dividends during the high growth period (2017-2020) is given below. Please note that in this example, required rate of return is 15%

**Step 4: Find the present value of Terminal Value.**

**Present value of Terminal value = $219.5**

**Step 5 : Find the Fair Value – the PV of Projeted Dividends and the PV of Terminal Value**

As we already know that Intrinsic value of the stock is the present value of its future cash flows. Since we have calculated the Present value of Dividends and Present value of Terminal Value, the sum total of both will reflect the Fair Value of the Stock.

Fair Value = PV(projected dividends) + PV(terminal value)

**Fair Value come to $273.0**

We can also find out the effect of changes in expected rate of return to the Fair Price of the stock. As we note from the graph below that the expected rate of return is extremely sensitive to the required rate of return. Due care should be taken to calculate the required rate of return. Required rate of return is professionally calculated using the CAPM Model.

### # 3.2 – Three stage Dividend Discount Model DDM

One improvement that we can make to the two-stage DDM is to allow the growth rate to change slowly rather than instantaneously.

The three-stage Dividend Discount Model or DDM is given by:

**First phase:**there is a constant dividend growth (g1) or with no dividend**Second phase:**there is a gradual dividend decline to the final level**Third phase:**there is a constant dividend growth again (g3), i.e. the growth company opportunities are over.

The logic that we applied to two-stage model can be applied to three-stage model in a similar fashion. Below is the formula for applying three stage.

My advise would be to not get intimidated by the formulas. Just try and apply the logic that we used in the two stage dividend discount model. Only change will be that there will one more growth rate in between the high growth phase and the stable phase. For this growth rate, you need to find out the respective dividends and its present values.

If you want to find more examples of dividend paying stocks, you can refer to Dividend Aristocrat List. This list contains 50 stocks with dividend paying history of 25+ years.

## Advantages of Dividend Discount Model

**Sound Logic –**The dividend discount model tries to value of the stock based on all the future cash flow profile. Here the future cash flows is nothing but the dividends. In addition, there is very less subjectivity in the mathematical model, and hence, many analyst show faith in this model.**Mature Business –**The regular payment of dividends does imply that the company has matured and there may not be much volatility associated with the growth rates and earnings. This is important for investors who prefer to invest in stocks that pay regular dividends.**Consistency –**Since dividends in most cases is paid by cash, companies tend to keep their dividend payments in sync with the business fundamentals. This implies that companies may not want to manipulate dividend payments as they can directly lead to stock price volatility.

## Limitations of Dividend Discount Model

For understanding the limitations of the Dividend Discount Model, let us take the example of Berkshire Hathaway.

CEO Warren Buffett mentions that dividends are almost a last resort for corporate management, suggesting companies should prefer to reinvest in their businesses and seek “projects to become more efficient, expand territorially, extend and improve product lines, or to otherwise widen the economic moat separating the company from its competitors.” By holding onto every dollar of cash possible, Berkshire has been able to reinvest it at better returns than most shareholders would have earned on their own.

Amazon, Google, Biogen are other examples that don’t pay dividends and have given some amazing returns to the shareholders.

**Can only be used to value Mature Companies –**This model is efficient in valuing companies that are mature and cannot value high growth companies like Facebook, Twitter, Amazon and others.**Sensitivity of Assumptions**– As we saw earlier, fair price is highly sensitive to growth rates and required rate of return. 1 percent change in these two can affect the valuation of the company by as much as 10-20%.**May not be related to earnings**– In theory, dividends should be correlated to the earnings of the company. On the contrary, companies, however, try to maintain a stable dividend payout instead of the variable payout based on earnings. In many cases companies have even borrowed cash to pay dividends.

## What next?

If you learned something new or enjoyed this Dividend Discount Model post, please leave a comment below. Let me know what you think. Many thanks and take care. Happy Learning!

Christiana Munzi says

Dear Dheeraj. I found this article really fantastic. My professor at University Tor Vergata (Rome) gave me and other students an assignment. Three days trying to understand what do I have to do and why. He gave us an assigment in an excel spreadsheet (Divided Discount Model -NYU Stern Excel spreadsheet-Aswath Damodaran) that I discovered referring to your explanation is the 3 DDM . I would like to invite you to teach us. Thank you very much. Christiana

Dheeraj Vaidya says

thanks Christiana! I look forward to engaging with your university in the near future.

Best,

Dheeraj

David says

I stormed your blog today and articles I have been seeing are really awesome. I have been searching for something like this for about 2 years now.

Thanks a bunch.

Dheeraj Vaidya says

Hey David, many thanks!

I am glad that you find these resources useful.

Best,

Dheeraj

Pintu Prasad says

hi dheeraj , you explained it really well, why don’t you make videos and upload, it will be much more helpful and aspirants from non-finance background will understand it better.

Dheeraj Vaidya says

Hello Pintu,

thanks for your feedback. Will checkout the viability of putting videos here. Just that it takes lot of time to prepare thos.

Best,

Dheeraj

Swagat Chavan says

Thanks Dheeraj, Appreciated.

Have been following your posts for quite some time.

You are a true master.

Dheeraj Vaidya says

thanks Swagat for the appreciation 🙂

mahmoud m mubaslat says

Thanks Dheeraj for the rich valuable model.

Myself i found it very helpful for me in real practice cases.

Appreciated

Mahmoud Mubaslat CPA

Dheeraj Vaidya says

Thank you Mahmoud! I am glad you found the article useful.

Rialdy Lokaputra says

Thanks for your kindness

Dheeraj Vaidya says

Thanks Rialdy!

George says

Thanks Dheeraj, wonderfully explained

Dheeraj Vaidya says

thank you George! 🙂