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/(RG)
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 RG 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/(RG)

Gordon
Growth Price Estimate

50

60

75

100

150

300

Observations
When G increases but remains less
than R the denominator (GR) 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 onestage Gordon
Growth model assumes constant growth of dividends or earnings forever. This assumption is almost always invalid. Analysts respond by using a multistage Gordon
Growth model or some other combination of valuation methods.
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