Time:
0
1
2
3
D
t
$1.0000
$1.2500
$1.5625
$1.953125
g
25.0%
25.0%
25.0%
5.0%
a.
The dividend to be paid at the end of year 3 is the first installment of a
dividend stream that will increase indefinitely at the constant growth rate of
5%.
Therefore, we can use the constant growth model as of the end of year 2
in order to calculate intrinsic value by adding the present value of the first two
dividends plus the present value of the price of the stock at the end of year 2.
The expected price 2 years from now is:
P
2
= D
3
/(k – g) = $1.953125/(0.20 – 0.05) = $13.02
The PV of this expected price is: $13.02/1.20
2
= $9.04
The PV of expected dividends in years 1 and 2 is:
13
.
2
$
20
.
1
5625
.
1
$
20
.
1
25
.
1
$
2
=
+
Thus the current price should be: $9.04 + $2.13 = $11.17
b.
Expected dividend yield = D
1
/P
0
= $1.25/$11.17 = 0.112 = 11.2%
c.
The expected price one year from now is the PV at that time of P
2
and D
2
:
P
1
= (D
2
+ P
2
)/1.20 = ($1.5625 + $13.02)/1.20 = $12.15
The implied capital gain is:
(P
1
– P
0
)/P
0
= ($12.15 – $11.17)/$11.17 = 0.088 = 8.8%
The sum of the implied capital gains yield and the expected dividend yield
is equal to the market capitalization rate.
This is consistent with the DDM.
26.
Time:
0
1
4
5
E
t
$5.000
$6.000
$10.368
$12.4416
D
t
$0.000
$0.000
$0.000
$12.4416
Dividends = 0 for the next four years, so b = 1.0 (100% plowback ratio).
a.
944
.
82
$
15
.
0
4416
.
12
$
k
D
P
5
4
=
=
=
42
.
47
$
15
.
1
944
.
82
$
)
k
1
(
P
V
4
4
4
0
=
=
+
=
b.
Price should increase at a rate of 15% over the next year, so that the HPR
will equal k.
1816
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27.
Beforetax cash flow from operations
$2,100,000
Depreciation
210,000
Taxable Income
1,890,000
Taxes (@ 35%)
661,500
Aftertax unleveraged income
1,228,500
Aftertax cash flow from operations
(Aftertax unleveraged income + depreciation)
1,438,500
New investment (20% of cash flow from operations)
420,000
Free cash flow
(Aftertax cash flow from operations – new investment) $1,018,500
The value of the firm (i.e., debt plus equity) is:
000
,
550
,
14
$
05
.
0
12
.
0
500
,
018
,
1
$
1
0
=
−
=
−
=
g
k
C
V
Since the value of the debt is $4 million, the value of the equity is $10,550,000.
1817
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 Spring '13
 Ohk
 Dividend yield, P/E ratio, PEG ratio

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