Contents - Index

Dividend Model:  2-Stage Growth
©2009 OS Financial Trading System


FTS DJIA School Case:  Stock Recommendations and the Two Stage Dividend Growth Model


Question:  In the past Wall Street analysts have been accused of over estimating growth forecasts for stocks, but given market prices and a model of intrinsic value, you can assess what the market expectations are.  For the DJIA stocks apply the two stage abnormal dividend growth model to  compare analyst 5-year growth forecasts to implied market forecasts?  


Given your best estimate of the implied growth forecasts from the current stock price  and comparing  these estimates to consensus analyst forecasts,  would you recommend the stock as a "Strong Sell, Sell, Hold, Buy or Strong Buy" (and why)?


Background:  The constant dividend growth model constrains the growth forecast for a stock to be bound by the overall nominal growth for the economy as a whole.  Given long term averages this places an upper bound (including inflation) of around 4.5% for the US economy.  Clearly, many stocks have analyst growth forecasts that exceed this number.  However, given that that implied growth cannot be larger than economy forever, this implies that the "going concern" firm is expected to exhibit some finite period of abnormal growth followed by the simplifying assumption that thereafter it grows at some normal rate that is subject to economy wide bounds.   Applications of this approach often assume the stage 1 abnormal growth period to be between 5-10-years.   Clearly, the actual number of years depends upon the underlying economics that influence a firm's future earnings.  For example, Warren Buffet likes investing in firms that have some form of barrier to entry that protects future earnings and for this case his usual assumption is 10-years for stage 1 abnormal growth.  In this exercise we will work with 5-years so that we match the time period being forecast by the analysts.

Step 1:  How do we justify the above assumption that the upper bound for normal economy wide growth is 4.5%?

First, refer to the following Government report.  Long Term Growth in the US:  In a 2005 Report to Congress on Long Term Growth for the US economy.   The following quote was given:

<http://www.ftsmodules.com/public/modules/ftsRT/projects/longtermgrowth.pdf>


"We also observe over the last 100-year span that the rates of economic growth across the then emerging industrial nations were fairly tightly clustered around this 2.0% pace. At the high end was Japan with an annual rate of growth averaging about 2.7%, while at the low end was Great Britain with an annual growth rate averaging 1.4%. The United States, which grew at a 1.8% average annual rate, was slightly below average."


They also went on to observe:


"For the United States, the long-term growth of real GDP per capita over the last 125 years has revealed remarkable steadiness, advancing decade after decade with only modest and temporary variation from the observed 1.8% annual rate of increase."


Inflation has been a fact of life for the U.S. economy.   Inflation numbers suggest that inflation compounded from 1913 to 2008 resulted in a cumulative rate of 2071.23%  This, implies an annual constant compounded rate of approximately 3.24%. 

Combining the above we can make a reasonable estimate for one plus the long term nominal growth in the US, to be around 1.018*1.03 = 1.04854.  As a result, to be conservative we will use as an upper bound for economy wide growth for US stocks (i.e., the stage 2 growth rate) the rounded down number of 4.5%.  

Getting this number correct is most important to a 2-stage dividend growth model of intrinsic value.  This is because in stage 2 the simplifying assumption is that growth is constant in perpetuity.  Further, this simplifying assumption will usually drive the majority of most stock's intrinsic value estimate when using this model.  So as indicated earlier, nominal growth cannot exceed the overall rate for the economy as a whole in stage 2 and for some stocks a reasonable estimate may be lower.

Note:  In the internet boom the market was typically implying higher stage 2 growth rates for the economy as the "assessed dividend" from technology was revised upwards significantly.  Since this boom such assessments seem to have reverted back towards long term averages and lower.

FTS Real Time Trader Client Exercise

Recall, the specific question we will examine in this exercise is the following.

Question:  In the past Wall Street analysts have been accused of over estimating growth forecasts for stocks, but given market prices and a model of intrinsic value, you can assess what the market expectations are.  For the DJIA stocks apply the two stage abnormal dividend growth model to  compare analyst 5-year growth forecasts to implied market forecasts?  

The intrinsic value support system in the FTS Trader is designed around the 1- and 2-stage growth models using either "accounting" or "economic dividends" (i.e., the free cash flow dividend it could pay).  

Sample Analysis of the Above Question:     

To provide a sample answer to this question we will use a traditional dividend paying stock in the Dow Jones Industrial Index.  This stock is Coca-Cola which started in 1885 as a pharmacist's patent medicine.  It grew to become the biggest selling soft drink in the world and it's symbol became arguably most successful and widely recognized in the world.  

Additional Information:  The ticker symbol for Coca-Cola is KO.  Go to the web (e.g., Yahoo finance or MSN investor or equivalent site and identify for the companies you are working with the following inputs:

i.  Current Dividend Rate per share (e.g., For Coca-Cola this is $1.52 per share Feb 2009)
ii. Current analyst forecast for the "Next 5-years Earnings' growth rate" (e.g., For Coca-Cola from Yahoo Finance the analyst forecast for the next 5-years earnings growth is 8.29% Feb 2009 and at this same time MSN money was estimating 9.0%).
 
What is the implied abnormal growth rate from the 2-stage dividend model?  Assume the number of years in stage 1 equals 5 (see below under column Y1) to match the same horizon as the analyst forecasts and we will assume long term constant growth for KO equals the economy wide average 4.5% (see under Columns G1 (stage 1 abnormal growth) and G2 (stage 2 normal growth) respectively below).

We will first use the "Stocks: Dividend Model:  2 Stage" support for the DJIA School Case to obtain the implied growth supporting the constant dividend model.  

Inputs

First, the current CAPM estimate of ke  (Discount rates for stage 1 and stage 2 of the model ) for KO is provided in the "D1 (stage 1) and D2 (stage 2)" columns and is equal to 0.0747.  This is relatively low under CAPM to other DJIA stocks but it is because KO is a low beta stock 0.62.  

Note:  At the time of this example the cost of equity capital was estimated using a market premium equal to 0.075 in CAPM and the 10-year risk free rate was used.

To get the implied growth rate from the 2-stage dividend model requires entering the dividend for Coca-Cola to replace the FCF (Free cash flow dividend estimate).  In the above screen we have already overridden the default estimate of FCF (free cash flow) for Coca-Cola with the dividend rate = $1.52 per share (see under column FCF).  We describe next how this was done via the Parameters menu item in the FTS Real Time Client.  

Updating the Parameters with the Dividend for Coca-Cola

You do this by selecting from the main menu in the trader "Parameters" (see below):




By selecting Parameters then:

Step 1:  Click on "List All" and,
Step 2:   select from the Security drop down "Coca-Cola".
Step 3:  Below Security the drop down beside the label "Parameter Type" lets you select the model you are working with:



The model is Dividend Model:  2 Stage
Below this the dropdown contains the set of fields you have control over:
 


The inputs for the 2-Stage Dividend Model (2_) are:

Current Dividend (DIV2_D)
Number of years in stage 1:  DIV2_Y1
Abnormal growth stage 1:  DIV2_G1
Normal Growth stage 2:  DIV2_G2
Cost of equity capital stage 1:  DIV2_Ke1
Cost of equity capital stage 2:  DIV2_Ke2

This lets you override any of the intrinsic value parameters with your own estimates.  You do this as follows:
First pass enter the following:

Current Dividend (DIV2_D) = 1.52
Number of years in stage 1:  DIV2_Y1 = 5
Abnormal growth stage 1:  DIV2_G1 = 0.045
Normal Growth stage 2:  DIV2_G2 = 0.045
Cost of equity capital stage 1:  DIV2_Ke1 = 0.0747
Cost of equity capital stage 2:  DIV2_Ke2 = 0.0747



Tip:  You can toggle the check box "Use these values in my analytical support" to use this dividend value in your support (otherwise it reverts back to the default FCF number).  In the screen below the dividend value of 1.52 has now replace the original FTS estimate for FCF to equity (column FCF/Div).  



The above reveals that Coca-Cola when it is trading at $48.61 and we have entered economy wide long term average growth rates for both stage 1 and stage 2 then the benchmark intrinsic value is $53.48.  

From this model you can immediately draw several inferences.  First, the implied Dividend to support the current market price is 1.382 (see above screen).  As a result, the abnormal growth rate for Coca-Cola is currently below the consensus analyst forecast growth of between 8.29-9.0%.  That is, the market is pricing in lower implied growth estimates.  In fact the price is supported by a growth rate equal to around 0,042.

Conclusions from 1st Pass Intrinsic Value Analysis:  Implied Growth Estimates from Market Price

The above reveals a very conservative current market price.  When using a 2-stage abnormal growth model the above implied growth rates are as follows:

i. There is no (or slightly negative) abnormal growth being priced into KO current market price relative to the standard dividend model.
 
As a result, to answer the initial question asked in this project, the implied abnormal growth rates from the current market price is substantially below the analyst forecast.  

Suppose we change the question and ask the question what if the market accepted the consensus analyst forecast for growth over the next five years.  What is the implied normal growth (i.e., stage 2) rate?

To answer this question we need to update the stage 1 growth rate to 0.0829.  You do this again via the parameter support to change FCFGrowth1 to 0.0829 as provided below:

Abnormal growth stage 1:  DIV2_G1 = 0.0829
Normal Growth stage 2:  DIV2_G2 = 0.045
Now the implied intrinsic value for KO is around $63.33.

Of course at the time of this example the US economy was in a recession and as you can see the market is very pessimistic.  But from this initial analysis it would seem likely that the patient long term investor in KO who is buying at the beginning of February 2009 will be well rewarded for their patience!

Next we can check whether the dividend rate used is overly optimistic relative to reasonable current analyst and economy wide growth forecasts.

Implied Dividend from Analyst Consensus and Economy Wide Growth Forecasts:

If we check current consensus analyst forecast for earnings for the year ending 2009 we see that the consensus currently is:  +3.72% (2009).  Again, even though analysts are forecasting a slow down for Coca-Cola there is nothing here to support a dramatic revision downwards of Coca-Cola's dividend.

Conclusion:  The market appears to be pricing KO with very conservative implied growth forecasts.  From the above analysis the stock price does not appear to be consistent with analyst 5-year forecasts.  If you were taking a long term investor view of Coca-Cola then the growth forecasts appear to be very conservative for a company like Coca-Cola.  As a result, from a long term investors' perspective we would rate Coca-Cola as a strong buy currently given the implied values from a two stage abnormal growth model.  The major reason is that over the next five years it may be true that a conservative growth estimate is a reasonable growth estimate, but ultimately we would expect Coca-Cola to perform at least at long term economy wide growth averages, or even better.  It is a well managed company, that manages intangible assets extremely well plus it has survived the long term with conservative business practices.  

Recommendation:  Strong Buy for a long term investor.