Introduction to Finance

Cost of Retained Earnings: Constant Dividend Growth Model 
Chapter 10 
presented the constant dividend growth model to estimate a fi rm’s stock price:
p
=
D
1
r
cs
−
g
(18-4)
where,
P
= the stock’s price
g
= the expected (constant) dividend growth rate
D
1
= next year’s expected dividend (equal to the current dividend increased by 
g
percent)
 r
cs
= the shareholders’ required return on the stock
Rather than use the model to determine a price, however, we can substitute today’s stock price 
for 
P
and solve for the shareholders’ required rate of return, 
r
cs
:
k
re
=
r
cs
=
D
1
p
+
g
(18-5)
The shareholders’ required return represents the fi rm’s cost of retained earnings, 
k
re
. The 
ratio 
D
1
∕
P
represents the current income yield to shareholders from their investment of 
P
. 
From the fi rm’s perspective, this ratio represents the ratio of dividends it pays to its current 
market value. The growth rate, 
g
, represents shareholders’ expected capital gain, arising from 
dividend growth. From the fi rm’s perspective, 
g
can be viewed as an opportunity cost of rais-
ing equity today. It is expected to be able to sell equity at a 
g
percent higher price next year.
Cost of New Common Stock 
To estimate the cost of new equity, we must modify equation 18-5 to refl ect the extra cost to the 
fi rm of issuing securities in the primary market. The costs of issuing stock, or 
fl otation costs
, 
include the accounting, legal, and printing costs of off ering shares to the public, as well as the 
commission or fees earned by the investment bankers who market the new securities to investors.
If the fl otation cost is 
F
per share, the cost of issuing new common stock, or 
k
n
, is given 
by equation 18-6:
k
n
=
D
1
P
−
F
+
g
(18-6)
Suppose a fi rm has just paid a dividend of $2.50 a share. Its stock price is $50 a share, and 
the expected growth rate of dividends is 6 percent. The current dividend of $2.50 must be 
multiplied by a factor to refl ect the expected 6 percent growth for 
D
1
, next year’s dividend. 
Using equation 18-5, the cost of using retained earnings as a fi nancing source is the following:
k
cs
=
2.50(1 + 0.06)
$50
+ 0.06 =
$2.65
$50
+ 0.06
= 0.053 + 0.06 = 0.113, or 11.3 percent
If new common stock is to be issued to fi nance the project, and fl otation costs are expected 
to be $4 per share, we need to use equation 18-6 to estimate the cost of new common equity:
k
cs
=
2.50(1 + 0.06)
$50 − $4
+ 0.06 =
$2.65
$46
+ 0.06
= 0.058 + 0.06 = 0.118, or 11.8 percent
The cost of using new common stock is 11.8 percent.