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/(RG)

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/(RG). 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/(RG)

50

50

50

50

Estimate
of G (50 R D)/50

NA

0.07

0.079

0.061

Check
P=D/(RG)

50

50

50

Check your answer by plugging
your estimate of G into the Gordon growth model formula.
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.
No comments:
Post a Comment