Kenneth R. Szulczyk

value formula to include a dividend growth rate in Equation 18. Consequently, we can simplify
this infinite sequence into something similar to a perpetuity.

 

 

 

 

 

  r g

D

+

+r

D +g

+

+r

D +g

+

+r

D +g

P=



3 

3

2

2

0

1

1

1

1

1

1

( 18 )

For instance, you purchase stock as a long-term investment. Your rate of return equals 10%,
and you expect the corporation to pay $2 dividend that grows 5% per year. Thus, we compute a
market value of the stock of $40 per share in Equation 19.

40.00

0.10 0.05

2

0 =$

$

=

r g

D

P=

 

( 19 )

Using the same numbers, what would happen if dividends grow at a slower rate, such as 2%
per year? We calculate a market value of $25 per share because the dividend grows slowly in
Equation 20.

25.00

0.10 0.02

2

0 =$

$

=

r g

D

P=

 

( 20 )

Two forces reduce future cash flows. First, a greater discount rate lowers the future value of
cash flows. Second, a larger dividend growth rate increases the value of future cash flows,
causing the dividends to grow faster than the rate of return. Nevertheless, the dividend growth
rate must become lower than the discount rate, or g > r. Otherwise, the future cash flows become
more valuable over time, making the present value negative.
For example, you purchase stock as a long-term investment. Your rate of return is 12%, and
you expect the corporation to pay $5 at Time 1 with dividends growing at 5% per year. We
calculated a market value of this stock of $71.43 per share in Equation 21.

71.43

0.12 0.05

5

0 =$

$

=

r g

D

P=

 

( 21 )

Market value of stock for the second period does not equal $71.43 because the stock price
has grown 5% per year. Instead, we calculate the market value of $75 in Equation 22.

P 1 =P 0  1 +g=$71.43 1 +0.05=$75.00 ( 22 )

Using Equation 18, we can solve for different variables, depending what we know. For
example, the stock price equals $100 per share while dividends are $3 per share that grows 5%