### Two-stage dividend discount model (DDM-2)

The dividend discount model (DDM) works best for evaluating stable dividend payers that grow slowly. A perfect example is AT&T (T) that pays good dividend (Y = 6% in early 2011) but the dividend growth is just g = 2%. This type of growth just matches the inflation and can be sustained forever even with no real growth in business. Using the DDM, the expected annual return for AT&T is r = Y + g = 8%. This is nothing to sneer at in comparison to expected market return rate (SP500) of 7%. Moreover, AT&T will return half of its value in dividends in just 12 years compared to the market half return time of 37 years.

A problem with investing in companies like AT&T is that there are few of them and they are consentrated in a small sectors of economy. A robust portfolio should have 10-20 companies diversified across multiple sectors. To do achieve this, one needs widen the search into companies that have a lower yield but a higher yield growth rate. As an example candidate, we will analyze the medical manufacturer Medronix (MDT) that in early 2011 has dividend yield of Y = 2% but has been growing the dividends at g = 19% for the last five years. The simple DDM would give total return of r = Y + g = 22% but this is unrealistic as the 19% dividend growth rate cannot be sustained forever.

The 2-stage dividend discount model (DDM2) solves the problem of unrealistically high long term dividend growth by assuming that the initial how growth period followed by a sustained terminal growth rate. Assuming the high dividend growth lasts N years, the value of the next N years is

In Equation (1), D0 is the current dividend, r is the discount rate (the desired rate of return for the investment), g1 is the initial high growth rate, and N is the number of years that the high growth rate is sustained.

Next, we will analyze the value of the dividends after the initial high growth rate. After N years, the dividend has risen to DN = (1+g1)ND0 and the dividends will continue to rise at a rate g2. Using the DMM, the net future value (NFV) of these dividends N years into the future is

Equation (2) gives the value of all remaining dividends N years into the future; however, since we don' have this money today the net present value will be lower as is illustrated in Figure 1.

Figure 1. The value of future dividends in the terminal dividend growth period needs to be discounted to the present.

The discounting the NFV of divideds given by Equation (2), the net present value of the future dividends after N years is

By combing Equations (1) and (3), the net present value of all (both the the high growth and terminal growth periods) divideds is

We now how three new variables that needs to be guessed/estimated: the high growth rate g1, terminal growth rate g2 and the length of the high growth period N. Depending our assumptions, the DDM2 can give widely different outcomes. The trick, therefore, is to be conservative. If DDM2 still gives a value below the current stock price, the purchase is likely to be a good bet.

As an example for the MDT, we could start with a low ball estimate that dividends would continue to grow at rate g1 = 19% for the next N = 5 years followed by a terminal growth rate of g2 = 3%. We note that g1 = 19% for the next N = 5 years would mean that the dividend doubles in the next five years. The current payout ratio is 30% so even with no earnings growth, the doubling of the dividend is sustainable. For the discount rate, we use r = 8.5% which is the relatively safe return that we can get from investing in AT&T (recall, the total return is yield plus growth, r = Y+g). The current dividend for MDT is D0 = \$0.90.  Plugging all these into the DMM2 in the Table 1, we obtain NPV =  \$33.60 which is well below the market price of \$41.40 (as of 2/18/2011). Clearly the market is much more optimistic on MDT.

By keeping the other factors intact but changing the length of the high growth period to N = 7, we get NPV = \$42 which matches the present price. However, this would also result in dividend tripling which is not sustainable without earnings growth. The assumptions are therefore more risky and investor is better of sticking to AT&T gives the same return r=8.5% with minimal growth g=2%.

An optimistic investor could increase the length of the high growth period to N = 10 to give NPV = \$58.80. With these assumptions, MDT is undervalued but the investor is also betting that the dividends will grow at a really fast rate for a decade. This is more speculation than investing.

As a second example, we will consider Intel (INTC) that has dividend D0 = \$0.72, payout ratio 31% and has been growing dividends at g1 = 14.5% per year for the last five years. Assuming the length of the high growth period to be N = 5 years and the terminal growth rate g = 3%, we obtain NPV = \$22.60 which is close to stock price of P = \$22.10 (as of 2/18/2011). Thus, INTC seems to be a relative bargain as there is a room for the dividends to grow longer than just the five years if Intel manages to show even modest real earnings growth – not an unlikely scenario given the strong dominant position that Intel has in computer microprocessor business.

Table 1. Two stage dividend discount model (DMM2) for MDT and INTZ. You can modify this Google spreadsheet for your own analysis.