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Chapter 19  Solutions
Overview:
Problem Length
Problem #’s
{S}
1, 2, 15,16,17
{M}
3,4,5, 7, 10,11,12, 14
{L}
6, 8, 9, 13
1.{S}The models should give identical results. Using 2003 expected
dividends of $4.50, a discount rate
r
of 20%, and growth rate
g
of 15%, we find that:
The dividend payout ratio for both 2002 ($4.05/$10.03 =
40.4%) and 2003 ($4.50/$11.40 = 39.5%) is approximately 40%.
The long term growth rates for earnings and dividends differ.
This is possible only if the payout rate will change over
time. Thus, in an earningsbased model using the earnings
growth rate of 14%, we must use another (higher than 40%)
estimate for the payout ratio. A payout ratio of 47.5% would
result in the same valuation:
Based on these models, Emfil shares are not attractive
at a price of $115, and should not be added to the
portfolio.
191
$90
=
.15

.20
$4.50
=
g

r
D
=
P
P =
kE
r  g
=
(.475)($11.40)
.20.14
= $90
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View Full Document 2.{S}a.
P/E
1
=
r
r
1
=
E
P
r
E
=
P
For a firm with a P/E ratio of 12
r
= 8.25%
b.
(i)
The increase of $3 is transitory. The market is
saying
that
the
price/earnings
ratio
should
reflect only the "normal" earnings of $10 per
share.
(ii) The increase of $3 is permanent and earnings in
the future are expected to remain at $13. The
market value is based on $13 per share of normal
earnings.
(iii)The increase of $3 implies not only permanence but
growth as future earnings are expected to increase
above the present level of $13.
192
3.{M}a.
The P/E ratio with a dividend payout of
k
, discount
rate of
r
and growth rate equal to
g
can be derived as:
For the Lo Company:
b.
Hi's P/E ratio must be identical to that of Lo (3.467)
as both firms have the same market value and earnings.
c.
Lo Company
2001
2002
2003
2004
2005
1) Earnings/share
2) Number of shares
3) Net income
4) Dividends paid
5) New investment
6) Firm value at
period end
7) Price per share
8) P/E ratio
$ 1.00
1,000
$1,000
200
800
3,467
3.47
3.467
$ 1.04
1,000
$1,040
208
832
3,605
3.61
3.467
$ 1.08
1,000
$1,082
216
865
3,750
3.75
3.467
$ 1.12
1,000
$1,125
225
900
3,900
3.90
3.467
$ 1.17
1,000
$1,170
234
936
4,056
4.06
3.467
Calculations:
1)
Given
2)
Since no new financing and no stock dividends or splits,
shares must remain constant over time.
3)
Earnings per share x number of shares
4)
Dividends per share (given) x number of shares
5)
Net income  dividends paid
6)
(.2 x next year's income)/(.10.04); 2005 value assumes
that net income continues to grow at 4% rate.
7)
Firm value/number of shares
8)
Firm value/current year net income
193
P =
kE(1+ g)
r  g
and
P
E
=
k(1+ g)
r  g
P
E
=
.2($1+.04)
.10.04
= 3.467
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View Full Document Hi Company
2001
2002
2003
2004
2005
1) Earnings/share
2) Number of shares
3) Net income
4) Dividends paid
5) New investment
6) New financing
7) Firm value at
period end
8) Price/share
before new issue
9) P/E ratio
10) Shares issued
11) Price/share at
new issue
$ 1.00
1,000
$1,000
1,000
800
800
3,467
3.47
3.467
300
$ 2.67
$ 0.80
1,300
$1,040
1,040
832
832
3,605
2.77
3.467
390
$ 2.13
$ 0.64
1,690
$1,082
1,082
865
865
3,750
2.22
3.467
507
$ 1.71
$ 0.51
2,197
$1,125
1,125
900
900
3,900
1.77
3.467
659
$ 1.37
$ 0.41
2,856
$1,170
1,170
936
936
4,056
1.42
3.467
857
$ 1.09
Calculations based on issuance of shares at end of year:
1)
Given
2)
2001 given; From 2001 on, previous year shares plus new
shares issued
3)
Earnings per share x number of shares
4)
Dividends per share (given) x number of shares
5)
Identical in amount to that computed for Lo Company
6)
Equal to (5)
7)
Identical to Lo Company [(.2 x next year's income)/
(.10.04)];
2001
value
assumes
that
net
income
continues to grow at 4% rate.
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This note was uploaded on 04/15/2009 for the course ACCOUNTING BUSI0027 taught by Professor Guan during the Spring '09 term at HKU.
 Spring '09
 GUAN
 Dividends

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