6.11  Tutor Break: One Stage Dividend Model

Let’s apply our estimates to IBM.  The current annual dividend for IBM is 2.191.  What should we use as the growth rate?  Currently, analyst forecasts for IBM’s earnings growth are 5.53%.  If we use this number, we get:

Besides the calculated value, Valuation Tutor provides two other calculations: the “implied expected return” and the “implied growth rate.”    The implied expected return is the k_e that would make the intrinsic value equal to the market price.  The implied growth rate is the growth rate that would make the intrinsic value equal to the market price.  In this example, you can think of it as saying either that the “market is pricing IBM as if it has a cost of capital or discount rate of 7.338%” or as saying that the “market is pricing IBM as if it had a growth rate of 6.085%.”  This inference is very important in making judgments about the value of the stock; if the implied growth rate is too high to be plausible, then you may feel that the market price is too high relative to the intrinsic value.

Let’s go back to the historical growth rate of dividends we calculated earlier.  We had found that over the last 50 years, IBM’s dividend has grown by about 8%.  What if we use g=8%? 

The model would not work so well.  The growth rate would be greater than k_e, and so the value would actually be infinite.  Valuation Tutor would actually report a negative value; it calculates d₁/(k_e-g) and if k_e < g while d₁>0, the answer is negative.

You could argue that the discount rate is too low, perhaps because we are using the low end of consensus estimates for the equity premium. If we used 5.7% and the 7% growth estimate, we would get:

This is much higher than the market price.  However, let us work a little longer with CAPM.  One observation about beta’s is that over time, betas tend to drift towards 1.  So if a beta is low, it tends to become high, if a beta is greater than 1, it tends to adjust downwards  The Blume adjustment accounts for this; it replaces beta by

If we use this in the IBM example, we get

This obviously brings down the intrinsic value, and also gives you some insight into how sensitive the model is to the inputs.

Finally, we mention some other consistency checks you can perform.  For example, since stockholders only get paid after bondholders, IBM’s stock must be riskier than IBM’s bonds.   Therefore, k_e for IBM must be at least as great as the yield on IBM’s bonds.  This yield depends on IBM’s debt rating, and you can typically find information about the rating in their 10-K (Part 2, Item 7):

The major rating agencies’ ratings on the company’s debt securities at December 31, 2009 appear in the table below and remain unchanged from December 31, 2008. The company’s debt securities do not contain any acceleration clauses which could change the scheduled maturities of the obligation. In addition, the company does not have “ratings trigger” provisions in its debt covenants or documentation, which would allow the holders to declare an event of default and seek to accelerate payments thereunder in the event of a change in credit rating. The company’s contractual agreements governing derivative instruments contain standard market clauses which can trigger the termination of the agreement if the company’s credit rating were to fall below investment grade. At December 31, 2009, the fair value of those instruments that were in a liability position was $1,555 million, before any applicable netting, and this position is subject to fluctuations in fair value period to period based on the level of the company’s outstanding instruments and market conditions. The company has no other contractual arrangements that, in the event of a change in credit rating, would result in a material adverse effect on its financial position or liquidity.

In addition, they provide the following table:

If the information is not available in the 10-K, you can look up the current rating of the debt using the Bonds link in the information system::

On the resulting screen, enter the ticker (say IBM) and you will see a list of bonds issues by the company, their yields, as well as their Fitch ratings.   If bonds are not listed, you can simply enter the ticker and “credit rating” into your search engine; when we did this for IBM, we found various reports that it had been upgraded to A+.

What is the yield on an A+ rated corporate bond?  Various bond rating sites give you this information; a free source is the US Federal Reserve Board, which each provides Moody’s seasoned rates for both Aaa and Baa bonds of a 10 year maturity.  At the time of this example these were:

Aaa = 4.89%

Baa = 6.28%

You can linearly interpolate to get:

Aaa = 4.89%

Aa = 5.35%

A = 5.82%

Baa = 6.28%

We will need to add a small “spread” to this to adjust for the fact that we are using a 30-year Treasury yield (since we are discounting over the long term).  If we add 1% (the Treasury 30 year yield at this time is 0.92%, or 92 basis points, above the 10-year treasury yield), we get 5.82 + 1.00 = 6.82%.  This would be a lower bound for k_e.  An upper bound is 9.28% = 4.18% + 5.1%, which is CAPM applied to a firm with beta equal to 1 and since IBM’s beta is less than 1.  This gives you a reasonable range for the k_e.  At the lower rate, with a growth estimate of 5.53%, the value comes out to 179.24; at the high discount rate, it comes out to 61.65.  You can see the interplay between the growth rate and the discount rate; if we use the 8% growth rate and the high discount rate, the calculated value is 184.  If you think the growth rate is somewhere between the analysts forecast of 5.53% and the historical growth rate of 8%, then you can see that market price is consistent with a discount rate somewhat higher than the CAPM.

Criticism of the One Stage Model

The one-stage model is obviously quite simple. For example, it assumes that IBM’s dividend grows forever at a constant rate.  In reality we observe that firms go through a life cycle, and so the growth rate over the near term may be quite different from the long run growth rate.  This idea is captured by the two stage growth model, which was also first analyzed by Williams in 1938.  The idea can be extended to multi-stage models, e.g. a three stage model.