1
CHAPTER 8
81 DPS CALCULATION
WARR CORPORATION
just paid a dividend of $1.50 a share (i.e., D
0
=$1.50). The dividend
is expected to grow 5 percent a year for the next 3 years, and then 10 percent a year thereafter.
WHAT IS THE EXPECTED DIVIDEND PER SHARE FOR EACH OF THE NEXT 5
YEARS?
?%;10%;5;50.1$
51310
DthroughDggD
n
.
1011.2$)10.1()05.1(50.1$)1()1()1()1(.9101.1$)10.1()05.1(50.1$)1()1()1()1(.7364.1$)05.1(50.1$)
1()1()1(.6538.1$)05.1(50.1$)1()1(.5750.1$)05.1(50.1$)1(
2323210533210433210322102101
nn
ggggDDggggDD
gggDDggDDgDD
2
82 CONSTANT GROWTH VALUATION
THOMAS BROTHERS
is expected to pay a $0.50 per share dividend at the end of the year
(i.e., D
1
=$0.50). The dividend is expected to grow at a constant rate of 7 percent a year. The
required rate of return on the stock, k
s
, is 15 percent.
WHAT IS THE VALUE PER SHARE
OF THE COMPANY’S STOCK?
D
1
= $0.50 g = 7% k
s
= 15% ?
0
P
25.6$07.015.050.0$
10
gkDP
s
3
83 CONSTANT GROWTH VALUATION
HARRISON CLOTHIERS’
stock currently sells for $20 a share. The stock just paid a dividend
of $1.00 a share (i.e., D
0
=$1.00). The dividend is expected to grow at a constant rate of 10
percent a year.
WHAT STOCK PRICE IS EXPECTED 1 YEAR FROM NOW? WHAT IS
THE REQUIRED RATE OF RETURN ON THE COMPANY’S STOCK?
P
0
= $20 D
0
= $1.00 g = 10%
1
P
= ? k
s
= ? %50.15k
%.50.1510.020$10.1$10.020$10.100.1$gPDk22$10.120$g1PP
s01s01
4
84 PREFERRED STOCK VALUATION
FEE FOUNDERS
has preferred stock outstanding that pays a dividend of $5 at the end of each
year. The preferred stock sells for $60 a share.
WHAT IS THE PREFERRED STOCK’S
REQUIRED RATE OF RETURN?
D
p
= $5.00 V
p
= $60 K
p
= ? %33.800.60$00.5$
ppp
VDk
5
85 SUPERNORMAL GROWTH VALUATION
HART ENTERPRISES
recently paid a dividend, D
0
, of $1.25. The company expects to have
supernormal growth of 20 percent for 2 years before the dividend is expected to grow at a
constant rate of 5 percent. The firm’s cost of equity is 10 percent.
A. WHAT YEAR IS THE
TERMINAL, OR HORIZON, DATE? B. WHAT IS THE FIRM’S HORIZON, OR
TERMINAL, VALUE? C. WHAT IS THE FIRM’S INTRINSIC VALUE OF TODAY,
0
Pˆ
?
____________________________________________________________
a. Horizon Date:
The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at
the end of Year 2.
b. Horizon Value
:gkDPˆ
s1NN
= gkD
s3
gkg1DPˆ
s122
= gkD
s3
0 1 2 3
k
s
= 10%
g
s
= 20%
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s
= 20%
g
n
= 5%
1.25 1.50 1.80 1.89 The horizon, or terminal, value is the value at the horizon date of all
dividends expected thereafter. In this problem it is calculated as follows: 05.010.0)05.1(80.1$Pˆ
2
05.010.089.1Pˆ
2
80.37$Pˆ
2
6
c.
The firm’s intrinsic value is calculated as the sum of the present value of all dividends during
the supernormal growth period plus the present value of the terminal value. Using your financial
calculator, enter the following inputs: CF
0
= 0, CF
1
= 1.50, CF
2
= 1.80 + 37.80 = 39.60, I = 10,
and then solve for NPV = $34.09. 0 1 2 3
k
s
= 10%
g
s
= 20%
g
s
= 20%
g
n
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 Spring '09
 lindsay
 Net Present Value

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