Absolute Equity Valuation, Part III: Gordon Growth Model

Myron J. Gordon

Myron J. Gordon 1920 - 2010

Introduction:

In part-2 of this series we applied the concept of the present value of all future cash flows in the form of the dividend discount model. A variation of this is called the Gordon Growth Model 1 which deals with the infinite summation problem more directly.  

The Gordon Growth Model (GGM):  

The summation in the present value model is an infinite geometric series. It can be mathematically transformed 2 into what is known as the Gordon Growth Model, or GGM for short. Although cash flow can be represented by several measures, let’s use dividends for illustration purposes.  

Gordon Growth Model, formula 1

The GGM’s inputs are the next period’s cash flow (Div1), an appropriate required rate of return (r), and a dividend growth rate (g). By varying these inputs, we can calculate a minimum/maximum range for V0. 

Variations of the GGM can be constructed by simple substitution. Below are two examples. Et represents earnings, and k is the payout ratio k=Div/E. 

Gordon Growth Model, formula 2

Assumptions and Economic Rationale: 

When using any valuation model, its underlying assumptions, economic rationale, and intended application should be carefully understood. The assumptions behind the GGM include:  

  • The dividend is consistent with the firm’s profitability
  • The growth rate is constant and sustainable indefinitely 3
  • The required rate of return is greater than the growth rate (r > g)
  • Price tracks value over the long term Pt = Vt
  • Returns are approximately equal to the cost of capital
  • The payout ratio is constant, thus the dividend and earnings growth rates are equal
  • The growth rate of the firm is in line with or slower than that of GDP 4
  • The required return and growth rate reflect long term assumptions

The GGM is useful for valuing a mature firm expected to experience stable growth over the long term. The model is also useful in valuing broadly based equity indices. It is simple to use and easy to understand. The GGM is best applied as the mature stage of a multi-stage valuation model.  

A major drawback of the GGM is its extreme sensitivity to input data. Some underlying assumptions may unrealistic, such as a stable growth rate and constant payout ratio. The spread (r – g) is not necessarily constant. The required rate of return can vary over time independently from the growth rate.  

Application Notes:  

Rearranging the GGM explicitly shows that (r-g) represents the dividend yield. Solving for total return (r) reveals its two components: dividend yield  and capital appreciation.  

Total Return = Dividend Yield + Capital AppreciationGordon Growth Model, formula 3

The GGM can be used to explain or “justify” the popular Price-Earnings or PE ratio. Note that trailing PE is higher than leading PE by the growth rate, (1+g). The PE ratio is directly proportional to the payout ratio 5, and inversely proportional to (r-g). 

Gordon Growth Model, formula 4

  
Let’s Ty An Example: 

Your manager has asked you to determine, based on the GGM, the implied market discount rate for the S&P500 index (SPX) as of yearend 2009. You research data on the SPX and find that the long term SPX dividend growth rate has averaged 5.24% annually. The cash dividend in 2009 was $22.41, and the SPX closed at 1115.10. Rearranging the GGM and solving for required return 6

Gordon Growth Model, formula 5

Conclusion: 

The Gordon Growth Model is a variation of the basic dividend discount model. It deals directly with the infinite summation problem. The GGM is easy to understand and very versatile in application. But it requires calculating long term parameters to which it is extremely sensitive. 

Thank you for reading this article. Your comments are welcomed!

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Footnotes: 

  1. Also known as the constant growth model. Myron J. Gordon, and Eli Shapiro, 1956. Mr. Gordon, born October 15, 1920, passed away on July 5, 2010.
  2. Consult a math book for details. As for me, I will take it on faith.
  3. Sustainable growth rate can be approximated by g = ROE x (1-k)
  4. Since we are calculating the present value of all future dividends, the growth horizon is infinite. If a growth rate greater than that of the long term GDP were sustainable, the firm would eventually overtake the economy.
  5. The sustainable growth rate is a function of the payout ratio. A change in the payout ratio is partially offset by a change in the growth rate. Increasing k in the numerator decreases g, increasing the denominator.
  6. Your manager is busy working on your review, so you decide to go a step further and calculate the average implied required return for the past 30 years. I get 8.36% with a standard deviation of 1.41%.

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  1. Absolute Equity Valuation, Part II: Dividend Discount Model | Sargon Y. Zia, merging fundamental analysis with technical analysis — August 19, 2010 @ 6:31 pm

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