## Saturday, May 11, 2019

### Some Simple Gordon Growth Model Calculations

This post uses the Gordon growth model to considers how one-time changes in the cost of capital or one-time changes in dividend payments impact share prices.   The example presented here assumes a constant growth rate in dividends.

Question:   Consider a firm with two possible cost of capital estimates – 7% percent and 9%.   The initial forward dividend is either \$3 dollars per share or \$4 per share.   Use the Gordon growth model to calculate the share price for the four combinations of dividend per share and cost of capital, assuming constant dividend growth of 3 percent.

Set up a spreadsheet so that share prices can be calculated for different values of forward dividends, the cost of capital and the dividend growth rate.

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.

Resource on Gordon Growth Model.

The spreadsheet used to calculate share prices for this application of the  Gordon growth model is presented below.

 Dividends Per Share Cost of Capital 3 4 % Increase in stock price due to increase in dividends per share 0.07 \$75.0 \$100.0 33.3% 0.09 \$50.0 \$66.7 33.3% % Decline in Stock Price given Increase in cost of capital -33.3% -33.3% Growth Rate of Dividends 0.03

The assumptions on cost of capital are places in the far left column.

The dividend per share assumptions are placed in the two center columns of the first row.

The assumption on the growth rate of dividends is places in the bottom row, second column.

The share price figures in the middle of the spread sheet are calculations based on the Gordon growth model from the formula P=D/(R-G).

Results:

An increase in dividend per share from 3% to 4% leads to a 33.3 % increase in share price

An increase in cost of capital from 7% to 9% leads to a 33.3% decrease in share price.

A simultaneous increase in the cost of capital and decrease in dividend payments leads to a decrease in share price from \$100 to \$50.

Question:   What happens if the cost of capital rises to 8 percent rather than 9 percent.

Comment:  Reader after constructing this spreadsheet can confirm increase in cost of capital will result in share price falling by 20 percent.

Concluding Remark:  This scenario involving a simultaneous increase in the cost of capital and dividend reductions is fairly realistic because increases in cost of capital could prompt management to reduce dividend payments.