Chapter 9
Valuing Stocks
Note:
A shaded box (
) indicates problems available in MyFinanceLab. An asterisk (*) indicates
problems with a higher level of difficulty.
All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems
with a higher level of difficulty.
1. Plan:
We can use Eq. (9.1) to solve for the price of the stock in one year given the current price
of $50.00, the $2 dividend and the 15% cost of capital.
Execute:
2
50
1.15
55.50
X
X
+
=
=
Evaluate:
At a current price of $50, we can expect Evco stock to sell for $55.50 immediately
after the firm pays the dividend in one year.
2. Plan:
We can rearrange Eq. (9.1) to find the cost of capital given the current stock price of $20,
the $1 and the expected stock price right after paying the dividend of $22. We can use Eq. (9.2)
to calculate the dividend yield and the capital gain.
Execute:
N
10
11
1
0
00
Capital Gain Rate
Dividend Yield
Div
Div
1
E
P
P
P
r
P
PP
−
+
+
=−
=
±²³
12
22
0
0.15 15%
20
20
E
r
−
=+
=
=
Dividend yield: 5% (1/20)
Capital gain: 10% (2/20).
Evaluate:
The cost of capital for Anle Corporation is 15% given the current stock price of $20
and the expected stock price of $22 after paying the dividend of $1 in one year. The cost of
capital is then split between the dividend yield at 5% and the capital gains yield at 10% which
together creates the 15% cost of capital.
3. Plan:
We can use Eq. (9.1) to solve for the beginning price we would pay now (
P
0
) given our
expectations about dividends ($2.80) and future price ($52.00) and the return we need to expect
to earn to be willing to invest (10%). We can use Eq. (9.1) to solve for the price you would
expect to be able to sell as share of Acap stock for in one year given our expectations about
dividends ($3.00) next year and future price ($52.00) and the return we need to expect to earn to
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Berk/DeMarzo/Harford •
Fundamentals of Corporate Finance
be willing to invest (10%). Given the price you would expect to be able to sell a share of Acap
stock for in one year, we can solve for the price you would be willing to pay for a share of Acap
stock today if you planned to hold the stock for only one year using the dividend of $2.80 and
the expected return of 10%.
Execute:
a.
P
(0)
=
2.80/1.10
+
(3.00
+
52.00)/1.10
2
=
$48.00
b.
P
(1)
=
(3.00
+
52.00)/1.10
=
$50.00
c.
P
(0)
=
(2.80
+
50.00)/1.10
=
$48.00
Evaluate:
The price you would be willing to pay for a share of Acap stock today if you held the
stock for two years or one is not affected by the amount of time you hold the stock for as can be
seen in Part (a) and (c).
4. Plan:
We can use Eq. (9.2) to calculate the dividend yield and the capital gain. We can then
compute the total expected return by adding the dividend yield to the capital gain.
Execute:
Dividend Yield
=
0.88/22.00
=
4%
Capital gain rate
=
(23.54
−
22.00)/22.00
=
7%
Total expected return
=
r
E
=
4%
+
7%
=
11%
Evaluate:
The stock’s dividend yield of 4% is the expected annual dividend of the stock
dividend by its current price. The dividend yield is the percentage return the investor expects to
earn from the dividend paid by the stock. The capital gain of 7% reflects the capital gain the
investors will earn on the stock, which is the difference between the expected sale price and the
original purchase price for the stock. The sum of the dividend yield and the capital gain rate is
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 Fall '10
 CelineSun
 Finance, Dividend, Dividend yield

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