## Sunday, May 26, 2019

### Gordon growth model and the initiation of dividend payments

Post uses Gordon growth model to evaluate how timing of the initiation of dividend payments affects Gordon growth model firm valuations.

Question:   A firm with an 11 percent cost of capital currently does not pay any dividends.   What is the Gordon Growth model estimate of firm value if the firm initiates a \$3.00 dividend and an annual dividend growth rate of either 2% or 4.0% annual increase in dividends in 2, 3, or 4 years?

What is the estimated Gordon Growth valuation in these situations when the cost of capital is 12 percent?

Analysis:  Two steps.  First find the value of the stock on the day dividends are initiated.  This is P/(D-G).   Second, discount the value of P back to current time.   This is P/(1+R)t where t is the number of years to initiation of dividends.

Here are the calculations.

 Company 1 Company 2 Company 3 Company 4 D \$3.00 \$3.00 \$3.00 \$3.00 R 0.11 0.11 0.12 0.12 G 0.04 0.02 0.04 0.02 Undiscounted Valuation \$42.86 \$33.33 \$37.50 \$30.00 Year Dividends are initiated Discounted Values 2 \$34.78 \$27.05 \$29.89 \$23.92 3 \$31.34 \$24.37 \$26.69 \$21.35 4 \$28.23 \$21.96 \$23.83 \$19.07 Impact of two year delay for four scenarios -18.84% -18.84% -20.28% -20.28%

Background:   The Gordon Dividend Growth Model treats the value of a stock as the discounted value of all future dividends.

The formula for the value of the stock can be written as

P=D/(R-G)

P is the value of the stock,
D is the annual dividend,
R is the required cost of equity,
G is the growth rate of dividends.

Note that with R-G in the denominator the estimated share price will become quite large when G becomes almost as large as R.   The price will be negative, a nonsensical result, if G>R.

Resource on Gordon Growth Model.