CHAPTER 4
The Value of Common Stocks
Answers to Practice Questions
1.
Newspaper exercise, answers will vary
2. The value of a share is the discounted value of all expected future dividends.
Even
if the investor plans to hold a stock for only 5 years, for example, then, at the time
that the investor plans to sell the stock, it will be worth the discounted value of all
expected dividends from that point on.
In fact, that is the value at which the
investor expects to sell the stock.
Therefore, the present value of the stock today
is the present value of the expected dividend payments from years one through
five plus the present value of the year five value of the stock.
This latter amount
is the present value today of all expected dividend payments after year five.
3. The market capitalization rate for a stock is the rate of return expected by the
investor.
Since all securities in an equivalent risk class must be priced to offer
the same expected return, the market capitalization rate must equal the
opportunity cost of capital of investing in the stock.
4.
Expected Future Values
Present Values
Horizon
Period
(H)
Dividend
(DIV
t
)
Price
(P
t
)
Cumulative
Dividends
Future
Price
Total
0
100.00
100.00
100.00
1
10.00
105.00
8.70
91.30
100.00
2
10.50
110.25
16.64
83.36
100.00
3
11.03
115.76
23.89
76.11
100.00
4
11.58
121.55
30.51
69.50
100.00
10
15.51
162.89
59.74
40.26
100.00
20
25.27
265.33
83.79
16.21
100.00
50
109.21
1,146.74
98.94
1.06
100.00
100
1,252.39
13,150.13
99.99
0.01
100.00
Assumptions
1.
Dividends increase by 5% per year compounded.
2.
The capitalization rate is 15%.
27
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
a.
Using the growing perpetuity formula, we have:
P
0
= Div
1
/(r – g)
73 = 1.68/(r  0.085)
r = 0.108 = 10.8%
b.
We know that:
Plowback ratio = 1.0 – payout ratio
Plowback ratio = 1.0  0.5 = 0.5
And, we also know that:
dividend growth rate = g = plowback ratio
×
ROE
g = 0.5
×
0.12 = 0.06 = 6.0%
Using this estimate of g, we have:
P
0
= Div
1
/(r – g)
73 = 1.68/(r  0.06)
r = 0.083 = 8.3%
6. Using the growing perpetuity formula, we have:
P
0
= Div
1
/(r – g) = 2/(0.12  0.04) = $25
7.
$100.00
0.10
$10
r
DIV
P
1
A
=
=
=
$83.33
.04
0
0.10
5
g
r
DIV
P
1
B
=

=

=
×
+
+
+
+
+
+
=
6
7
6
6
5
5
4
4
3
3
2
2
1
1
C
1.10
1
0.10
DIV
1.10
DIV
1.10
DIV
1.10
DIV
1.10
DIV
1.10
DIV
1.10
DIV
P
$104.50
1.10
1
0.10
12.44
1.10
12.44
1.10
10.37
1.10
8.64
1.10
7.20
1.10
6.00
1.10
5.00
P
6
6
5
4
3
2
1
C
=
×
+
+
+
+
+
+
=
At a capitalization rate of 10 percent, Stock C is the most valuable.
For a capitalization rate of 7 percent, the calculations are similar.
The results
are:
P
A
= $142.86
P
B
= $166.67
P
C
= $156.48
Therefore, Stock B is the most valuable.
28
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 myers
 Corporate Finance, Net Present Value, Dividend yield, P/E ratio

Click to edit the document details