H
AAS
S
CHOOL
OF
B
USINESS
U
NIVERSITY
OF
C
ALIFORNIA
AT
B
ERKELEY
UGBA 103 S
UMMER
2008
A
VINASH
V
ERMA
P
RICE
E
ARNINGS
R
ATIOS
AND
G
ROWTH
O
PPORTUNITIES
: A
N
E
XAMPLE
The common stock of XYZ Inc. is expected to pay a dividend of $12.00 for each
share exactly one year from now. Given the risk of the stock, the market requires
a rate of return of 16%. The dividends are expected to grow in perpetuity at a
constant rate of 8%.
(i):
What is the current market price of stock of the firm?
$150.00
=

=

=
.
150
$
08
.
0
16
.
0
12
$
1
0
g
r
D
P
(ii):
Assume that the firm has a stable retention ratio of 40%. Given the
expected dividend of $12.00 next year, work out the earnings per share
that can be expected to occur at
t=1
.
Given that the retention ratio,
α
, is 40%, and since
)
1
(
1
1
α

=
E
D
, we
have:
20
$
6
.
0
12
$
1
1
1
=
=

=
α
D
E
.
(iii):
Now, suppose we are also given that the earnings retained in the business
generate a return of 20%. Assume that the retained earnings are used
entirely for new investments and that assets in place are replaced in
perpetuity by accumulated depreciation. What is the present value of
earnings per share from the assets in place?
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 Spring '08
 MCCULLOUGH
 Depreciation, Net Present Value, new projects, HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA

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