Continued: Dividend Discount Model (DDM) - Part Due

Zero-Growth Rate DDM

Since the zero-growth model assumes that the dividend always stays the same, the stock price would be equal to the annual dividends divided by the required rate of return.

Stock’s Intrinsic Value = Annual Dividends / Required Rate of Return

This is basically the same formula used to calculate the value of a perpetuity, which is a bond that never matures, and can be used to price preferred stock, which pays a dividend that is a specified percentage of its par value. A stock based on the zero-growth model can still change in price if the capitalization rate changes, as it will if perceived risk changes, for instance.

Example—Intrinsic Value of Preferred Stock

 

If a preferred share of stock pays dividends of $1.80 per year, and the required rate of return for the stock is 8%, then what is its intrinsic value?

Intrinsic Value of Preferred Stock = $1.80/0.08 = $22.50.

Constant-Growth Rate DDM (Gordon Growth Model)

The constant-growth DDM (aka Gordon Growth model, because it was popularized by Myron J. Gordon) assumes that dividends grow by a specific percentage each year, and is usually denoted as g, and the capitalization rate is denoted by k.

Constant-Growth Rate DDM Formula

Intrinsic Value =	D1 ────── k - g	D1 = Next Year's Dividend k = Capitalization Rate g = Dividend Growth Rate

The constant-growth model is often used to value stocks of mature companies that have increased the dividend steadily over the years. Although the annual increase is not always the same, the constant-growth model can be used to approximate an intrinsic value of the stock using the average of the dividend growth and projecting that average to future dividend increases. 

Note that if both the capitalization rate and dividend growth rate remains the same every year, then the denominator doesn't change, so the stock’s intrinsic value will increase annually by the percentage of the dividend increase. In other words, both the stock price and the dividend amount will increase by the constant-growth factor, g.

Example—Calculating Next Year’s Stock Price Using the Constant-Growth DDM

 

If a stock pays a $4 dividend this year, and the dividend has been growing 6% annually, then what will be the price of the stock next year, assuming a required rate of return of 12%?

Next Year’s Stock Price = $4 x 1.06 / (12% - 6%) = 4.24 / 0.06 = $70.67

This Year’s Stock Price = $4 / 0.06 = 66.67

Growth Rate of Stock Price = $70.67 / $66.67 = 1.06 = Dividend Growth Rate

Note that both the zero-growth rate and the constant-growth rate dividend discount models both value stocks in terms of the dividends they pay and not on any capital gains in the stock price; the holding period for the stock is irrelevant; therefore the holding period return is equal either to the dividend rate of the zero-growth model or the constant-growth rate.