# Dividend Discount Model

*By John Del Vecchio*__
__The dividend discount model can be a worthwhile tool for equity valuation. Financial theory states that the value of a stock is the worth all of the future cash flows expected to be generated by the firm discounted by an appropriate risk-adjusted rate. We can use dividends as a measure of the cash flows returned to the shareholder.

There are several *dividend discount models (DDMs)*, and this article will address two of the more basic forms of the DDM -- the stable model and the two-stage model. As an illustration, both models will be used to value the stock of Caterpillar.

*Inputs Into the DDM
*

Several inputs are required to estimate the value of an equity using the DDM.

* DPS(1) = Dividends expected to be received in one year.

* Ks = The required rate of return for the investment. The required rate of return can be estimated using the following formula: Risk-free rate + (Market risk premium) * Beta

The rate on t-bills can be used to determine the risk-free rate. The market risk premium is the expected return of the market in excess of the risk-free rate. Beta can be thought of as the sensitivity of the stock compared with the market.

* g = Growth rate in dividends

*Stable Model
*

**Value of stock = DPS(1) / Ks-g
**

**Caveats:** The stable model is best suited for firms experiencing long-term stable growth. Generally, stable firms are assumed to grow at the rate equal to the long-term nominal growth rate of the economy (inflation plus real growth in GDP). In other words, the model assumes it is impossible to grow at 30% forever, otherwise, the company would be larger than the economy.

If the growth rate of the firm exceeded the required rate of return, you could not calculate the value of the stock. This is because if g>Ks, the result would be negative, and stocks do not have a negative value.

Another caveat is that models are often very sensitive to the assumptions made regarding growth rates, time frame, or the required rate of return.

Finally, the dividend discount model generally understates the intrinsic value of the firm. Important considerations such as the value of patents, brand name, and other intangible assets should be used in conjunction with the DDM to assess the value of a firm's equity. These intangibles should be added to the result of a DDM calculation to arrive at a more appropriate valuation.

*An Example:
*

DPS = Caterpillar has a dividend of $1.30 Ks = 6% + (6.8%) * 1.0 = 12.8% (we use a Beta of 1 because it should be the same as the market during the stable growth period) g = Because the stable model assumes a growth rate equal to the long-term nominal growth of the economy, we will use a growth rate of 6% (3% inflation + 3% GDP growth). V = 1.30 * (1.06) / (.1280-.06)

V = $20.26

Caterpillar's recent price of $38.63 per share shows that the dividend discount model suggests that Caterpillar is overvalued. However, Caterpillar for example, has a strong brand name, and customers will pay a premium price for its products. This is a good example of how the dividend discount model may understate the intrinsic value of the equity. Adjustments should be made to estimate the value of brand name or other value-enhancing traits that a company may possess.

*The Two-Stage Model** *

The two-stage model attempts to cross the chasm from theory to reality. The two-stage model assumes that the company will experience a period of high-growth followed by a decline to a stable growth period.

** Caveats:** The first issue to deal with when using the two-stage model is to estimate how long the high growth period should last. Should it be 5 years, 10 years, or maybe longer?

The next caveat is that the model makes an abrupt transition from high growth to low growth. In other words, the model assumes that the firm may be growing at 30% for five years only to then grow at 6% (stable growth) until eternity. Is this realistic? Probably not. Most firms experience a gradual decline in growth rates as their business matures (hence, using a three-stage dividend discount model may be more appropriate, yikes!).

Finally, just like the stable growth model, the two-stage dividend discount model is very sensitive to the inputs used to determine the value of the equity.

*An Example:**
*

High-growth phase (assuming **five years** for illustration purposes):

DPS = $1.30

Ks = 6% + (6.8%) * 0.94 = 12.39%

g = (1 - Payout Ratio ) * ROE = .506 * .1781 = 9%

DPS(1) = $1.30 * 1.09 = $1.42

DPS(2) = $1.42 * 1.09 = $1.54

DPS(3) = $1.54 * 1.09 = $1.68

DPS(4) = $1.68 * 1.09 = $1.84

DPS(5) = $1.84 * 1.09 = $2.00

*Now, we must discount the dividends by the appropriate rate to determine their present value.
*

$1.42 / (1.1239) = $1.26

$1.54 / (1.1239)2 = $1.22

$1.68 / (1.1239)3 = $1.19

$1.84 / (1.1239)4 = $1.15

$2.00 / (1.1239)5 = $1.12

*We add up the present value for the dividends during the high-growth stage and get $5.94.
*

*Next, we value the stable growth period:
*

DPS = $2.00 (1.06) = $2.12

Ks = 12.8%

g = 6%

$2.12 / (.128-0.06) = $31.18

*Next, we must calculate the present value of the dividends.
*

$31.18 / (1.1239)5 = $17.39

When calculating the present value of the dividends of the stable growth period, we use the same required rate of return as the high-growth phase and raise it to the fifth power for a five-year example like the one above.

Adding the two values, we get: $17.39 + $5.94 = $23.33 Again, our result is quite a bit lower than the current market price.

*Important Note**
*

Notice that most of the "value" of the equity is derived from the stable growth period (17.39 / 23.33 = 74.5%). This is an indication that the market views the value of equity from a long-term, not short-term perspective.

*What if the Stock Does Not Pay Dividends?
*

The DDM can still be used to value stocks that do not pay dividends. The analyst must make assumptions about what the dividend would be if the firm did pay dividends. Starting with free cash flow and estimating the dividend pay-out ratio based on comparable firms in the marketplace or industry can yield reasonable results for a non-dividend paying company.

*What Is the Usefulness of the DDM?**
*

It depends on how you apply the model. Since the model is highly sensitive to the assumptions made about growth rates and discount rates, performing a sensitivity analysis would be appropriate. Sensitivity analysis allows the investor to view how different assumptions change the valuation using the dividend discount model. Secondly, the dividend discount model is a good starting point to begin thinking about the valuation of an equity, but it is not the Holy Grail. **Infosys** has a substantial percentage of its value explained by intangible assets like the brainpower of its employees. Using the DDM may result in ridiculously low estimates of Infosysâ€™ value. Finally, the DDM is a good thinking exercise. It forces the investors to begin thinking about different scenarios in relation to how the market is pricing the stock.

*Do Professionals Use the DDM?
*

Yes. For example, **Merrill Lynch** uses the DDM model as a component of its market-beating Alpha Surprise Model. **JP Morgan** uses the DDM as an important input into the valuation and stock selection process. However, the DDM is only one of many valuation tools used in equity analysis.

The dividend discount model provides an excellent illustration of the difference between theory and reality. Plenty of assumptions must be made, the transition phases are often unrealistic, and a firm's intangibles, often a key driver in the growth rate of the company, are absent from the model. Yet, many analysts still use the DDM as a gauge for valuation. That's fine, just remember it is a model, after all, so use it carefully.