Dividends are the best friends an investor has. They are the gifts that keep on giving, and finding a company that pays them consistently over an extended period of time is a great way to build your wealth. Determining the intrinsic value of a dividend-paying company is paramount to investing with a margin of safety. This helps protect our investments and grow our wealth. Using the Dividend Discount model is an excellent way to find that intrinsic value, and the use of the Dividend Discount Two-Stage model is a fantastic way to get a more precise view of that value.

Our goal is to find the approximate value of a company, not to quibble about the minor details; we must remember that [G13] valuation is an art. What one investor sees as value, another might see as a liability; it can be seen as in the eye of the beholder.

The dividend discount two-stage model is a little more involved than the Gordon Growth model that we addressed last week, but it is doable on our part. We will walk through all the steps to help you calculate it on your own and give you examples to help illustrate what we are doing.

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**What’s the big deal with dividends, and why do we keep talking about them?**

To give you an example of the power of dividends, let’s take a look at our favorite guru, Warren Buffett (Trades, Portfolio). Over the years Buffett has grown his wealth by investing in and buying businesses with strong competitive advantages (moats) that have traded at fair or better prices.

His favorite company to invest in is one that pays him a dividend. Did you know that?

- Over 91% of his portfolio is invested in stocks that pay a dividend.
- His top four holdings, which make up over half of his holdings, pay a dividend yield of 2.9%.
- Best of all, most of his stocks have paid a rising dividend for decades.

This has helped lead to incredible wealth for him; he has used the compounding nature of stocks and their dividends to accumulate much of his wealth.

Consider this, his top four holdings which include **Wells Fargo** (NYSE:WFC), **Coca-Cola** (NYSE:KO), **Kraft Heinz** (NASDAQ:KHC) and **IBM** (NYSE:IBM) all pay handsome dividends, equating to a yield of 2.9%. Coke has paid a growing dividend for 55 years!

Another fact to consider is that over the last 10 years the Dividend Aristocrats have outperformed the market, the Standard & Poor's 500, by almost 2.64%. This makes dividends an incredibly powerful force to be reckoned with and why we focus a lot of our attention on them.

Dividends plus compounding over time equates to a powerful force that is hard to beat.

Because dividends are such a big deal we need a way to value these companies, and the answer is the Dividend Discount model.

**Dividend Discount Two-Stage model**

What is this model and how is it different from the Gordon Growth model I already know?

The Gordon Growth model is a simple but powerful way to value dividend-paying stocks, but it has one pretty big flaw: it takes it on faith that the growth rate for the company that you are valuing is going to continue growing at that same static growth rate forever.

And you and I know that this is simply not possible. The vagaries of the stock market and business lead to an incredible amount of volatility and cycles that all companies go through.

And so enter the two-stage model of the Dividend Discount model. It allows you to enter different growth rates as the company evolves and enables you to get a greater range of outcomes, which helps us in our valuations.

The remarkable part of this model is the ability to adjust the growth rates for some years, in essence giving you control of how you value that particular company. As the company goes through its growth spurt, no pun intended, you can adjust for a slower growth rate and a declining growth rate, if you wish.

**Dividend Discount Two-Stage model: formula and examples**

OK, on to the formula.

Intrinsic Value = DPS / ( 1 + Khg) + P / (1 + Kst).

Where P = DPS / kst - g.

So what does all that mean? Don't worry; I will lay it all out for you.

First, the variables are as follows:

- DPS = Expected dividends per share in year.
- Khg = Cost of equity during high growth rate.
- Kst = Cost of equity during stable growth rate.
- G = Extraordinary growth rate for the first number of years.

Now that we have some of the formula laid out we can start the process of working with a real company.

Let’s take **Procter & Gamble** (NYSE:PG) for a test run on this formula. Why would we do it? It has a reputation for paying a high dividend through the years and is a member of the Dividend Aristocrats.

Before we start, we need to gather a little background information. All this information will be collected from gurufocus.com, and it will be dated April 18.

- EPS = $3.69.
- Dividends per share = $2.66.
- Payout ratio 2016 = 72.08%.
- Return on Equity = 17.12%.

Now that we have these numbers we can next estimate the cost of equity for Procter & Gamble. To do this, we will use our formula that we discussed last week. [G44]

**Cost of equity = Risk-free rate + beta (risk premium)**

- Risk-free rate = 5.40%.
- Beta = 0.49.
- Risk premium = 2.23%.

For more on these numbers and how I arrived at them, please refer here.

- Cost of equity = .054 + 0.49(.0223).

So plugging in the numbers, we arrive at the cost of equity of 6.49%, and this will be for our growth period.

We will do the same calculation for the stable period, but we will raise the beta to reflect a more stable growth environment.

**Cost of equity = Risk-free rate + beta (risk premium)**

- Cost of equity = .054 + 0.6 (.0223).
- Cost of equity for our stable growth period will be 6.73%.

Next, we will calculate the expected growth rate during our growth period. To do this, we will use the following formula.

- Expected growth rate = retention rate * return on equity.

The retention rate is the payout ratio that we calculated earlier, which would be 72.08%, and our return on equity is 17.12%.

- Expected growth rate = .7208 * .1712.
- Expected growth rate = 12.34%.

The next number that we will calculate will be the retention ratio, a stable growth period. And to do this we will use the estimated growth rate of the economy which will be 3%, and the return on equity we will drop to 15%, which is lower than our current ratio, but it is higher than the cost of equity.

The formula for the retention ratio is:

- Retention ratio in stable growth = g / ROE.

Retention = .03/.15 would equate to 20%, which would mean that the payout ratio during our stable growth period would be 80%.

**First stage of formula**

Now that we have compiled some numbers we are ready to do the heavy lifting part of the formula. What we are going to do now is figure out the present value of future dividends. This is, in essence, a discounted cash flow of the dividends. Using numbers that we have calculated or gathered, we can do this.

What we will need to do first is calculate the future values of the dividends and then we can discount those back to the present values. To do this, we will have a couple of steps to go through. First, we will figure out our future dividends based on our current earnings per share (EPS) and our current payout ratio.

We will calculate our future earnings per share and the formula to do this is:

EPS * (1 + g) year one.

EPS1 * (1 + g) year two and so on.

- EPS1 = $3.69 * (1 + .1234) = $4.15.
- EPS2 = $4.15 * (1 + .1234) = $4.66.
- EPS3 = $4.66 * (1 + .1234) = $5.23.
- EPS4 = $5.23 * (1 + .1234) = $5.88.
- EPS5 = $5.88 * (1 + .1234) = $6.60.

Now to calculate our future dividends we just take our earnings per share and multiply that by our current payout ratio.

- DPS1 = $4.15 * .7208 = $2.99.
- DPS2 = $4.66 * .7208 = $3.36.
- DPS3 = $5.23 * .7208 = $3.77.
- DPS4 = $5.88 * .7208 = $4.24.
- DPS5 = $6.60 * .7208 = $4.76.

Next we will need to find the cumulative cost of equity to calculate the future dividends. To do this we will use our cost of equity for the growth period which we calculated earlier as 6.49%. So our formula to calculate this number will be:

(1 + COE ) * (1 + COE) = Cumulative cost of equity.

- COE1 = (1 + COE ) = 1.0649.
- COE2 = (1 + 0.0649) * (1 + 0.0649) = 1.1340.
- COE3 = 1.0649 * 1.0649 * 1.0649 = 1.2076.
- COE4 = 1.0649 * 1.0649 * 1.0649 * 1.0649 = 1.2859.
- COE5 = 1.0649 * 1.0649 * 1.0649 * 1.0649 * 1.0649 = 1.3694.

OK, we have gathered all the info that we need to calculate the present value of our future dividends. To do this we simply divide our future dividends by our cumulative cost of equity to arrive at our present value of the dividends.

- PV1 = $2.99 / 1.0649 = $2.81.
- PV2 = $3.36 / 1.1340 = $2.96.
- PV3 = $3.77 / 1.2076 = $3.12.
- PV4 = $4.24 / 1.2859 = $3.30.
- PV5 = $4.75 / 1.3694 = $3.47.

Now that we have the future dividends calculated based on our expected growth rate, we can then discount those back to the present value. The reason we do this is the dividend has a different value today than in the future; it is not worth as much today as in the future.

The cumulative present value of the dividends during high growth is figured by just adding up the value of the present value dividends we calculated for those five years.

**PV of dividends = $15.66**

That ends the calculations for the first stage of the formula.

**Second stage of formula**

What we will do now is calculate the terminal value at the end of the high growth phase. To do this, we will use the formula as follows:

Terminal price = expected dividends per share/stable cost of equity – growth rate of stable period.

To do this, we will need to calculate a few numbers. First will be:

Expected earnings per share = current EPS * (1 + high growth rate) * (1 + stable growth rate).

We will plug in some numbers.

Expected EPS = 3.69 * (1 + .1234) * (1 + .03) = $4.26

Next, we will need to calculate the expected dividends per share. Thus we will use this formula.

Expected DPS = expected EPS * stable period payout ratio

Expected DPS = 4.26 * .80 = $3.42

Now we can calculate the terminal price of Proctor & Gamble. To do this, we will plug in our numbers and calculate.

Terminal price = expected DPS / stable cost of equity – stable growth rate

Terminal price = 3.42 / .0673 - .03 = $91.69

Since this is the terminal price at the end of our growth period, we will need to discount it back to the present so that we can add it to our formula to find the present value of our company.

The formula for this is:

PV of terminal price = terminal price / (1 + high growth cost of equity).

PV = 91.69 / (1 + .0649) = $86.10.

And that brings us to the end of stage two.

**Putting it all together**

To put all this together, we simply add stage one's results to stage two's results, and we have our intrinsic value for the company that we just analyzed.

Proctor & Gamble value = Stage 1 + Stage 2.

$15.66 + $86.10.

Value = $101.76.

If we compare that the current price of $90.80 it appears that we are currently undervalued at the moment and would merit much more investigation as to why that would be.

Again this is just a tool and is only as good as the numbers that we plug into it. You must never buy a stock based on this calculation alone; it must be done with a more in-depth analysis before making that call.

As we have done this example I have been questioning the growth rate that we calculated for this particular company. To me, it is a little aggressive, and I wonder what would happen if we adjusted that down some. Would that get us closer to what I feel would be a better value?

No offense to Proctor & Gamble, but the price that we calculated is predicated on it hitting that growth number, and I am not confident that is possible. We should take a look at this with a different growth number that will give us a better number to work with.

Let's give it a try. I won't walk through the full example but will change the areas it would affect and go from there.

To refresh the numbers that we will use.

- EPS = $3.69.
- DPS = $2.66.
- Payout ratio = 72.08%.
- ROE = 17.12%.
- Cost of equity growth period = 6.49%.
- Cost of equity stable period = 6.73%.
- Growth rate = we will use 5%, which is quite a bit less but is more reasonable.
- Payout ratio during stable phase = 80%.
- Raise the beta to 1 for the stable period which will change the cost of equity for the stable period.

Now that we have all the numbers I will go through the process and calculate both stages of the formula and arrive at a different value.

Step 1:

The present value of the future dividends would be $12.75.

Step 2:

The terminal value of the stock price would be $64.69.

Putting them together gives us the price of $77.45

Now that number makes me feel like we are more in line with the financial status of the company. This would indicate that the company is overvalued; based on other calculations that appears to be the case.

Notice how changes to some variables can substantially alter the result.

**Using the formula for a growth company**

The Two-Stage Dividend Discount model is best suited for companies going through a growth period followed by a more stable growth period. Typically, the Dividend Aristocrats are going to be more stable, mature businesses and the Gordon Growth model would suit them better, but a company like **AbbVie** (NYSE:ABBV), a large pharmaceutical company that produces Humira, which is its best product, is a company that is going through a growth period right now. There is some question about that growth continuing for the long term based on its patent for Humira expiring recently.

Let's take a look at the financials, and we can go through the exercise of calculating its value.

**AbbVie**

- EPS = $3.63.
- DPS = $2.28.
- Payout ratio = 62.80%.
- Return on Equity = 20%.
- Risk-free rate = 5.40%.
- Risk premium = 2.23%.
- Beta = 1.47.

Cost of equity growth period = 5.43%.

Cost of equity stable period = 5.50%.

Growth rate = 15%.

Payout ratio during stable period = 80%.

Now that we have all of our numbers let's go ahead and run it through the process and see what we get.

Stage 1:

Present value of dividends = $12.79.

Stage 2:

Present value of stock = $133.88.

This would give us a price of $146.67. Comparing it to the price of $63.45 appears to make it undervalued and a possible buy.

Again this is a tool, not a final purchase decision.

**Potential limitations to the model**

The first limitation would be this model again only works on companies that pay a dividend; then it would not be of any benefit.

The second limitation is setting a limit on how long the company will be in a high-growth phase. Additionally we would be calculating how the decrease in growth would be assessed, and how long it would take before it is in the stable growth period.

The third limitation is the assumption that the growth rate will be high during the initial phase and then have a sudden overnight drop to the stable rate until the end of the period – meaning that defining the end of the growth period and the start of the stable period – and determining what to do with the drop down phase – is incredibly difficult.

**Final thoughts**

The Two-Stage Dividend Discount model offers some great flexibility to adjust the growth rates over a period to allow you to find a more realistic value according to the real-life examples of fluctuations in growth.

Again this is another tool we can use to help us determine intrinsic value and find a margin of safety, which is what we are all looking for.

In our search for the intrinsic value, we have tackled a few different models to help us determine a value. We started with the Benjamin Graham formula and some modifications. Next, we tackled a discounted-cash-flow and finally two separate versions of the Dividend Discount model.

All of these formulas are tools we can use in our toolbox to help us determine intrinsic value. None of the formulas requires hard math; it is mostly a matter of determining what values you need and then plugging them into the formulas.

We have seen that these formulas are sensitive to various inputs, so it is important to be cognizant of that when doing the calculations.

Also, remember that our goal is to be approximately right, meaning that the exact number is not important, more that we are close in our range of numbers to give us a picture of whether the company is overvalued or not.

That will do it for this week.

I hope you enjoyed our trip through this formula and that you found it of value to you. I know that I enjoyed working through the examples and find it helpful to me to follow the process. The more we do these calculations, the easier they will become.

If you have any questions or thoughts, please let me know.

As always thank you for taking the time to read this article, and I will see you next week.

Take care,

Dave

**Disclosure:** The author has no positions in the stocks mentioned or any plans to do so in the near future.

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**Dave Ahern**

Chilliwhiskey- 1 week ago Report SPAMhey! in the formula to calculate high growth rate, is the retention rate 72% or 28%, as 72% was calculated to be the payout ratio?