19 8 20 constant growth stock valuation investors

19

8-20
CONSTANT
GROWTH STOCK
VALUATION
Investors require a 15 percent rate of return on LEVINE COMPANY’S stock (k
s
=
15%). We are asked to determine what Levine Company stock value ought to be if its
cost of equity capital (ks…also the required return for retained earnings) is 15% and a
most recent paid dividend of $2.00 (Do). We are to consider the various values for its
stock using four different growth rates (g) of
1. - 5 %
2. 0%
3. + 5 %
4. + 10%
a. WHAT WILL BE LEVINE’S STOCK VALUE IF THE PREVIOUS
DIVIDEND WAS D
0
= $2 AND IF INVESTORS EXPECT DIVIDENDS
TO GROW AT A CONSTANT COMPOUND ANNUAL RATE OF
(1) -5 %
(2) 0 %
(3) 5 %
(4) 10 %
b. Using the data from part a, what is the Gordon (constant growth) model value for
Levine’s stock if the required rate of return is 15 percent and the expected
growth rates is
(5) 15 %
(6) 20 %
ARE THESE REASONABLE RESULTS? EXPLAIN .
c. IS IT REASONABLE TO EXPECT THAT A CONSTANT GROWTH
STOCK WOULD HAVE G › K
s
?
20

a.
( 29
( 29
( 29
00 . 44 $
05 . 0
20 . 2 $
10 . 0 15 . 0
10 . 1 2 $
. 4
00 . 21 $
10 . 0
10 . 2 $
05 . 0 15 . 0
05 . 1 2 $
. 3
33 . 13 $ 15 . 0 / 2 $ . 2
50 . 9 $
20 . 0
90 . 1 $
05 . 0 15 . 0
05 . 0 1 2 $
. 1
0
0
0
0
= =
-
=
= =
-
=
= =
= =
+
-
=
∧
∧
∧
∧
P
P
P
P
b.
( 29
. , 48 $ 05 . 0 / 40 . 2 $ . 2
0 / 30 . 2 $ . 1
0
0
nonsense is which P
Undefined P
- = - =
= =
∧
∧
These results show that the formula does not make sense if the required rate of return is
equal to or less than the expected growth rate.
c.
No.
Revised 4-26-06
21