## What is the 'Dividend Discount Model - DDM'

The dividend discount model (DDM) is a procedure for valuing a stock's price by discounting predicted dividends to the present value. If the value obtained from the DDM is higher than the current trading price of shares,Â then the stock is undervalued.

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## BREAKING DOWN 'Dividend Discount Model - DDM'

The dividend discount model is based on the idea that the intrinsic value of a stock can be estimated by the expected value of the cash flows it will generate in the future. The driving principle behind the model is the net present value (NPV) of the cash flows, which draws fromÂ the concept of the time value of money (TVM).

The DDMÂ isÂ derived from the formula for the present value of a perpetuity. Its variables include the dividend per share, the discount rate (also the required rate of return or cost of equity) and the expected rate of dividend growth. The model, therefore, does notÂ work for companies that don't pay out dividends. While not accurate for most companies, the simplest iteration of the dividend discount model assumes zero growth in the dividend, in which case the value of the stock is the value of the dividend divided by the required rate of return.

The required rate of return can vary due to investor discretion. Meanwhile, the dividend growth rate can be estimated by multiplying the return on equity (ROE) by the retention ratioÂ (the latter beingÂ the opposite of the payout ratio).

## Dividend Discount Model Variations and Calculation

The DDM has many variations that differ in complexity. The supernormal dividend growth model, for example, takes into account a period of high growth followed by a lower, constant growth period. For more on valuing a stock using this model, see: Valuing a Stock With Supernormal Growth Rates.

The most common and straightforward calculation of a DDM is known as the Gordon growth model (GGM), which assumes a stable dividend growth rate and was named in the 1960s after American economist Myron J. Gordon. To find the price of a dividend-paying stock, the GGM takes into account three variables:

• D1Â = the estimated value of next year's dividend
• r = the company's cost of equity capital
• g = the constant growth rate for dividends, in perpetuity

Using these variable, the equation for the GGM is:

• Price per Share = D1Â / (r - g)

## Examples of the DDM With Stable Growth

Assume Company X paid a dividend of \$1.80 per share this year. The company expects dividends to grow in perpetuity at 5% per year, and the company's cost of equity capital is 7%. The \$1.80 divided is the dividend for this year and needs to be adjusted by the growth rate to find D1, the estimated dividend for next year. This calculation is: D1 = D0 x (1 + g) = \$1.80 x (1 + 5%) = \$1.89. Next, using the GGM, Company X's price per share is found to be D(1) / (r - g) = \$1.89 / ( 7% - 5%) = \$94.50.

Now, take for exampleÂ the annual cash dividends paid out by Walmart Inc. between January 2014 and January 2018:Â \$1.92, \$1.96, \$2.00, \$2.04 andÂ \$2.08, in chronological order. Walmart's dividend has increased by \$0.04 each year, whichÂ equals average growth ofÂ about 2%. Assume an investor has a required rate of return of 5%. Using an estimated dividend of \$2.12 at the beginning of 2019, the investor would use the dividend discount model to calculate a per-share value of \$2.12/(.05Â - .02) = \$70.67.

## Shortcomings of the DDM

While the GGM method of DDM is widely used, it has two well-known shortcomings. The model assumes a constant dividend growth rate in perpetuity. This assumption is generally safe for very mature companies, but newer companies have fluctuating dividend growth rates in their beginning years.

The second flaw of this DDM is that the output is very sensitive to the inputs. For example, in the Company X example above, if the dividend growth rate is lowered 10% to 4.5%, the resulting stock price is \$75.24 (over a 20% reduction in the \$94.50 price).

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