## Wednesday, May 22, 2019

### Gordon Growth Model and Tradeoff between Dividends and Dividend Growth

Four companies have identical share prices but different initial dividends and different growth rates in dividends.   We make assumptions on cost of capital.   Find a dividend growth rate consistent with equal share prices across all four companies.

Question.   Company one is an established firm with a \$4.00 per share dividend, a 9 percent cost of capital, and a dividend growth rate of 1 percent per year. Company two has a \$1.00 annual dividend and a 9 percent cost of capital.   The cost of capital for the third and fourth companies are 10 percent higher or lower than the cost of capital for the first two companies.

What dividend growth rate leads to the same Gordon Growth model stock price estimate for the four firms?

Here is the situation in tabular form:

 Company 1 Company 2 Company 3 Company 4 D 4 1 1 1 R 0.09 0.09 0.099 0.081 G 0.01 \$ \$ \$ P=D/(R-G) 50 50 50 50

Analysis:  The problem specifies all four firms have the same Gordon Growth stock price as company one, which is \$50 per share.  For companies 2, 3 and 4 set stock price estimate of \$50 equal to D/(R-G).   As shown above, we have values of D and R.   Solve each equation for Dividend growth rate of G.     Calculations are shown below.

 Gordon Growth Dividend Calculations Company 1 Company 2 Company 3 Company 4 D 4 1 1 1 R 0.09 0.09 0.099 0.081 G 0.01 \$ \$ \$ P=D/(R-G) 50 50 50 50 Estimate of G (50 R- D)/50 NA 0.07 0.079 0.061 Check P=D/(R-G) 50 50 50

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.