__Gordon Growth Model:__The basic dividend discount model in its most simplest form is known as the Gordon Growth Model. You'll use the future value formula that we used in the discounted cash flow analysis and by taking the sum of all the discounted dividends the formula simplifies quite easily to:

Formula 1

*where P = fair price, D = next 12 months dividends, DR = discount rate, and GR = dividend growth rate*

Thank you math!

Let's run through an example. Say there's a company that will pay out $1.25 in dividends over the next 12 months and you think that a good conservative estimate of their dividend growth rate going forward is 6.50%. Since you want to make sure to get a good return you select a discount rate, or expected rate of return, of 10%.

I've created a spreadsheet that you can access to calculate the Gordon Growth Model fair value estimate for a company. As you can see, using the values from above the fair value estimate is calculated to be $35.71. This means if you pay $35.71 or less for the shares you will earn a 10% return from the dividends if you hold the company forever and they can grow the dividend at 6.50%. The spreadsheet will also calculate the fair value using a dividend growth rate and a discount rate that is plus and minus one from your target values.

The Gordon Growth Model is great because it's quick and easy. The biggest drawback to the Gordon Growth Model is that it assumes a constant dividend growth rate. This is a good estimate for companies such at AT&T or Verizon that are mature and already pay out most of their free cash as dividends; however, it's not quite as good of an estimate for faster growers. If a company has grown their dividend for 25% per year the past 5 years, can you realistically expect that continue going forward until the end of time?

Another flaw is that you can't account for different growth rates. A company like PG might be able to keep up a 10% growth rate for another 5 years, but I don't think they'd be able to continue at that rate for much longer. So how can we account for these shortcomings? Enter the dividend discount model.

__Dividend Discount Model:__The Dividend Discount Model is essentially the same as the Discounted Cash Flow except we're focusing on dividends. In theory as a buy/hold/monitor investor, a company's true value is based off of the cash that it spins off to you the shareholder in the form of dividends. Just as in the Discounted Cash Flow analysis, future dividends are worth less than their nominal value due to the time value of money. Once again, the formula that we'll base the calculations off of is:

Formula 1

*where FV = Future Value, PV = Present Value, GR = Growth Rate, and N = Number of Years*

Let's revisit the example from the Discounted Cash Flow post in case you forgot. If I offered to give you $1,000 a year from today, how much would you accept today so you had the same $1,000 in the future? If you assume that you can grow whatever dollar amount you receive by 10% in one year, then you would need me to give you at least $909.09 today to have $1,000 one year from now. How did I come up with the $909.09? Just rearrange the above formula to solve for PV.

Formula 2

Plugging in FV = $1,000, GR = 10% = 0.10 and N = 1 gives a PV of $909.09. In other words, if I were to give you at least $909.09 today and you could earn a 10% return in 1 year, you would be better off taking that money and investing now rather than waiting 1 year for me to give you $1,000.

If you assume a constant growth rate then the formulas simplify to that of the Gordon Growth Model above. However, we're wanting to calculate the Net Present Value (NPV) of the dividends using varying growth rates so we need to use the Dividend Discount Model. Using the Dividend Discount Model allows you to apply different growth rates at different stages of the company's lifespan. This is also known as a 2-stage Dividend Discount Model.

For example, I'd say it's safe to assume that Coca-Cola (KO) can grow their dividends by 9% per year for the next 2 years, although I do expect it to be longer than that, followed by a terminal growth rate of 3.5% which is about the long-term inflation rate. Going through the process you would apply the 9% growth rate to each year for the first 2 years and then switch to the 3.5% terminal growth rate, using Formula 1 from above. Now you have your estimate of KO's future dividends, but we need to figure out what the current value is by discounting the future payments to present day dollars, using Formula 3 below.

Just for the sake of clarity, we'll re-define Formula 2 from above as:

Formula 3

*where NPV = net present value, FV = future value, DR = discount rate (expected rate of return), and N = Number of years*

Formula 2 and 3 are the exact same except I've changed the names of some of the terms in order to make sure that the wrong growth rate is not used.

I'll run through the calculations from the KO scenario, although I have created a spreadsheet that will perform a 2-stage Dividend Discount Model for you to make everyone's life easier. Let's define the terms. GR = 9%, PV = $1.12 (current annualized dividend for KO), DR = 10%.

(1) Using Formula 1, FV = $1.12 * (1 + 0.09)^1 = $1.22

(2) Using Formula 3, NPV = $1.22 / (1 + 0.10)^1 = $1.11

(3) Using Formula 1, FV = $1.22 * (1 + 0.09)^1 = $1.33

(4) Using Formula 3, NPV = $1.33 / (1 + 0.10)^2 = $1.10

(5) Using Formula 1, FV = $1.33 * (1 + 0.035)^1 = $1.38 *Note switched to terminal growth rate

(6) Using Formula 3, NPV = $1.38 / (1 + 0.10)^2 = $1.03

...

Continue this on for at least three decades were of dividends, this is where a spreadsheet comes in handy. After calculating the NPV of all the future dividends, simply add them all together and this is the fair value estimate for company. In the KO example, the fair value becomes $19.72. In my actual analysis of KO, my DDM value was $20.96.

__Conclusions:__Once again the Dividend Discount Model is very sensitive to the inputs. Changing the discount rate from 10% to 9% increases the fair value price from $19.72 to $23.32, an 18% increase. My Dividend Discount Model spreadsheet will run through the process from above with your target discount rate as well as discounts rates of +/-1% and +/-2% giving you 5 different valuation prices. Small changes in the growth rate can also lead to vastly different results.

Some benefits of the Dividend Discount Model are that it allows a lot of flexibility in calculating the future dividends. If you wanted to you could go through a 3 stage or 4 stage analysis. I've even seen models that will use the starting dividend growth rate and then decrease it every year until it reaches the terminal growth rate. I'll put together a spreadsheet using this method rather than the constant growth method described in this post soon.

Once you have a spreadsheet to do the calculations for you, it's very easy to reverse engineer the required growth rate based on the current price. Just input the starting dividend, terminal growth rate, and discount rate and then guess different values for the growth rate until the fair value price equals the current price. Using a 4% terminal growth rate, 10% discount rate, and 10 years of growth, at KO's current price of around $42.50 they would need to be able to grow the dividend at 14.33% for 10 years to justify paying $42.50 per share.

As a dividend growth investor, I think the Dividend Discount Model is one of the better valuation methods since it is forward-looking and hits right to the core of DGI. Buy a company and hold it for the dividends. Of course the economy and each company can hit rough patches that can alter the future. While the Dividend Discount Model is more in depth than other methods, it's important to not become over-confident in your analysis and to revisit it when some thing changes for the company, for the better or worse.

As always, the Dividend Discount Model is just one valuation method and should not be relied on alone in order to determine a fair value for a potential investment. I use all the methods discussed so far in my Stock Valuation series and always compare across them to see where the company is currently trading in relation to each one.

Gordon Growth Model spreadsheet

2-stage Dividend Discount Model spreadsheet

Very solid write up on the DDM. Not my favorite valuation method but like you said it is one of many.

ReplyDeleteZach,

DeleteI think from a pure dividend play the DDM is probably the best valuation method, but it's not the best when you're trying to account for total return. I think it's very important to look at several different methods because each one has their strengths and weaknesses.

Thanks for stopping by!

Nice explanation of the Gordon Growth Model. It's amazing how sensitive these models become as the growth rate approaches the discount rate. It makes sense mathematically, but it's annoying when you're actually trying to value a stock.

ReplyDeleteMyFIJ,

DeleteI actually never use the Gordon Growth Model, rather I use the 2 stage DDM. Once you have a spreadsheet set up it's very easy to use and modify to your assumptions. It is crazy to see what happens if the growth rate approaches the discount rate. I know in one of the examples it was giving a value around $174 for PG. I think PG is a great company, but it's not $174 great. It's a pain when this situation arises but that's why I prefer the DDM over the Gordon Growth. Since you have a terminal rate that should be pretty low it helps to counter the higher growth rates. It's all a guess though, too bad there wasn't a fool-proof way to value stocks. Of course that's why there's a market.

Thanks for stopping by!