## Thursday, June 20, 2019

### The Dividend Growth Rate Assumption and the Cost of Capital

This note examines how assumptions on the dividend growth rate impact the estimates of Gordon Growth Model share prices for  fixed assumptions on the annual dividend and the required cost of capital.  I discuss how uncertainty in the growth of dividends impacts valuation outcomes from the use of the Gordon Growth Model.

Question:   Consider a stock with dividend per share of \$3.00 and a cost of capital equal to 8 %.   What is the estimated share price from the Gordon Growth Model for assumed dividend growth rates of 2%, 3%, 4%, 5% 6%, and 7%?  How do changes in the growth rate of dividends impact the Gordon Growth Model share price estimate?

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.

Analysis:   The Gordon Growth model estimates for this situation are outlined in the table below.

 Gordon Growth Model -- Dividend Growth and Cost of Capital D Dividend Payout 3 3 3 3 3 3 R Cost of Capital 0.08 0.08 0.08 0.08 0.08 0.08 G Dividend Growth Rate 0.02 0.03 0.04 0.05 0.06 0.07 P =D/(R-G) Gordon Growth Price Estimate 50 60 75 100 150 300

Observations

When G increases but remains less than R the denominator (G-R) becomes smaller and P the estimated share price increases.

The change in estimated share price increases in magnitude as G approaches R.   For example, a change in G from 2% to 3% leads to an increase in estimated share price from \$50 to \$60, an increase of 20% while an increase in g from 6% to 7% leads to an increase in estimated price from \$150 to \$300, which is a 100% price increase.

Discussion:  The current dividend level is known with certainty.   There is some uncertainty about the cost of capital but there are a lot of papers about how to get reasonable estimates.   An analyst can plug in a  published value of the cost of capital for the industry generated by an expert.  There are also published cost of capital estimates that account for the leverage or risk of the firm.

There is more uncertainty and less guidance about the dividend growth rate.   The key factor influencing changes in dividends is corporate earnings and as any CNBC watcher knows earnings can be extremely difficult to predict.    The simple one-stage Gordon Growth model assumes constant growth of dividends or earnings forever.   This assumption is almost always invalid.   Analysts respond by using a multi-stage Gordon Growth model or some other combination of valuation methods.