# Dividend Discount Model (DDM) ## What is the Dividend Discount Model?

Dividend Discount Model, also known as DDM, in which stock price is calculated based on the probable dividends that will be paid and they will be discounted at the expected yearly rate. In simple words, 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 future dividends.

### Explained in Detail

The financial theory states that the value of a stock is 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 McDonald’s, Procter & Gamble, Kimberly Clark, PepsiCo, 3M, CocaCola, Johnson & Johnson, AT&T, Walmart, etc. We can use the Dividend Discount Model to value these companies.

source: ycharts

Learn Dividend Discount Valuation in Excel

The 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.

The 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. is when you sell the stock at a higher price then you buy for. In such a case, there are two cash flows –

1. Future Dividend Payments
2. Future Selling Price

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

### Formula

Dividend Discount Model = Intrinsic Value = Sum of Present Value of Dividends + Present Value of Stock Sale Price.

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

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

### Dividend Discount Model Example

Learn Dividend Discount Valuation in Excel

In this dividend discount model 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 dividend discount model example 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 the 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 the Dividend Discount Model let us move forward and learn about three types of Dividend Discount Models.

For eg:
Source: Dividend Discount Model (DDM) (wallstreetmojo.com)

1. Zero Growth Dividend Discount Model – This model assumes that all the dividends that are paid by the stock remain one and the same forever until infinite.
2. 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.
3. 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, a 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

The 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  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 dividend discount model formula for zero growth dividend,

Dividend Discount Model Formula = 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 Model

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

Can you value Google, Amazon, Facebook, Twitter using this method? Of course, 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 the constant-growth Dividend Discount Model.

source: ycharts

Please note that in the constant-growth Dividend Discount Model, we do assume that the growth rate in dividends is constant; however, the actual dividends outgo increases each year.

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

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

The Constant-growth Dividend Discount Model 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
##### Constant-growth Dividend Discount 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

##### Constant-growth Dividend Discount 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 Model (Multi-stage Dividend Discount Model)

Variable Growth rate Dividend Discount Model or DDM Model is much closer to reality as compared to the other two types of dividend discount 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:

1. an initial high rate of growth,
2. a transition to slower growth, and
3. 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 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% afterward.

My take is that the companies with a higher dividend payout ratio 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
1. The higher growth rate is expected in the first period.
2. This higher growth rate will drop at the end of the first period to a stable growth rate.
3. The is consistent with the expected growth rate.
##### Two-stage DDM model – Example

CheckMate 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 the 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.

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

Step 2: Apply the Dividend Discount Model to calculate the Terminal Value (Price at the end of the 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 the 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 Constant Growth Dividend Discount Model Formula –

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

Terminal value (2020) is \$383.9

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

The present value of dividends during the high growth period (2017-2020) is given below. Please note that in this example, the 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 Projected Dividends and the PV of Terminal Value

As we already know that the 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 , the sum total of both will reflect the Fair Value of the Stock.

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

Fair Value comes to \$273.0

We can also find out the effect of changes in the 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 . The 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 Model is to allow the growth rate to change slowly rather than instantaneously.

The three-stage Dividend Discount Model or DDM Model 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
• The third phase: there is a constant dividend growth again (g3), i.e., the growth company opportunities are over.

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

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

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

• Sound Logic – The dividend discount model tries to value 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 little subjectivity in the mathematical model, and hence, many analysts 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 are 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

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 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.
• The sensitivity of Assumptions – As we saw earlier, the fair price is highly sensitive to growth rates and the 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!

### Recommended Articles

This article has been a guide to what is the Dividend Discount Model. Here we discuss Dividend Discount model types (zero growth, constant growth, and variable growth – 2 stages and 3 stages), Dividend Model Formula with practical examples, and case studies.

1. Juliet Rita Adala says

i now get the better understanding of this models. Just last Saturday my lecturer took us through this topic and i needed something more. Thank you Dheeraj for dropping this. Keep teaching us and the good Lord will keep blessing you.

• Dheeraj Vaidya says

2. Charles says

Nice write up on DDM

3. Julia says

Thanks Dheeraj; found this tutorial quite useful

• Dheeraj Vaidya says

4. Sairam Chinni says

These are indeed good resource for my exam preparation. The way you explained is awesome. Thank you very much for dissemination of your knowledge.

• Dheeraj Vaidya says

5. 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

6. 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

7. 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

8. 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 :-)

9. 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.

10. Rialdy Lokaputra says

• Dheeraj Vaidya says
11. George says
• Dheeraj Vaidya says