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4. Pasha Entertainment, Inc. is expected to pay the following dividends over the next
four years: $6, $12, $17, and $3.25. Afterward, the company pledges to maintain
constant 5% growth rate in dividends, forever. If the required return on the stock
is 11%, what is the current share price?
D5 D = D x (1+g)
P = 5 4
4
(R – g)
$3.25 x (1.05)
=
= (.11 - .05)
P = $56.88
4
$6 $12 $17 $3.25 $56.88
P0 = + + + +
2 3 4 4
(1.11) (1.11) (1.11) (1.11) (1.11)
= $67.18
5. Suppose you know that a company’s stock currently sells for $67 per share and the
required return on the stock is 11.5%. You also know that the total return on the
stock is evenly divided between capital gains yield and dividend yield. If it is the
company’s policy to always maintain a constant growth rate in its dividends, what
is the current dividend per share?
R = Dividend yield + Capital gains yield = D1
+ g
P0
Dividend yield = Capital gains yield given from the problem
.115 = Dividend yield + Capital gains yield
.115 = 2x x x
D = D1
½ (.115) = x 0
(1 + g)
.0575 = x
D D = $3.85
Dividend yield = .0575 = 5.75% = 1 0
P 1.0575
D = .0575 x P 0
1 0
D = $3.64 Answer
D = .0575 x $67 0
1
D1 = $3.85
2
6. Take Time Corporation will pay a dividend of $3.65 per share next year. The
company pledges to increase its dividend by 5.1% per year, indefinitely. If you
require a return of 11% on your investment, how much will you pay for the
company’s stock today?
D1
P0 =
R - g
$3.65
=
(.11 - .051)
= $61.86
7. The next dividend payment by Dizzle, Inc. will be $2.48 per share. The dividends
are anticipated to maintain a growth rate of 4.5% forever. If the stock currently
sells for $39.85, what is the required return?
D1
R= + g
P0
$2.48
= + .045
$39.85
= .1072 or 10.72%
8. Mitchell, Inc. is expected to maintain a constant 4.6% growth rate in its dividend,
indefinitely. If the company has a dividend yield of 5.8%, what is the required
return on the company’s stock?
R = Dividend yield + Capital gains yield
= .058 + .046
= .1040 or 10.40%
3
9. Gontier Corporation stock currently sells for $53.95 per share. The market requires
a return of 10.3% on the firm’s stock. If the company maintains a constant 4.9%
growth rate in dividends, what was the most recent dividend per share paid on
the stock?
D x (1 + g)
P = 0
0
(R – g)
P x (R - g)
D = 0
0
(1 + g)
$53.95 x (.103 - .049)
D0 =
(1 + .049)
D0 = $2.78
10. Metallica Bearings, Inc. is a young start-up company. No dividends will be paid on
the stock over the next nine years because the firm needs to plow back its
earnings to fuel growth. The company will then pay a dividend of $19 per share 10
years from today and will increase the dividend by 5% per year thereafter. If the
required return on this stock is 13%, what is the current share price?
Find the stock price in Year 9:
D10
P =
9
(R – g)
$19.00
=
(.13 - .05)
= $237.50
$237.50
P =
0 (1.13)9
P0 = $79.06
4
Class Problems – Chapter 7C – Stock Valuation
1. Ushuaia, Inc. currently has an EPS of $4.13, and the benchmark PE ratio for the
company is 15. Earnings are expected to grow at 5% per year. What is your
estimate of the current stock price?
P0 = Benchmark PE ratio x EPS
= 15 x $4.13
= $61.95
2. What is the target stock price in one year?
EPS1 = EPS0 x (1 + g) P = Benchmark PE ratio x EPS
1 1
= $4.13 x (1 + .05) = 15 x $4.34
= $4.34 = $65.05
- or -
P = P x (1 + g)
1 0
= $61.95 x (1 + .05)
= $65.05
3. Assuming the company pays no dividends, what is the implied return on the
company’s stock over the next year?
(P - P ) Similar to:
1 0 D
R= 1
P =
P 0
0 R - g
($65.05 - $61.95) D
= R= 1 + g
$61.95
P0
= .05 = 5% This is 0 if no dividends
R = g (when no dividends)
So, if EPS is growing at 5% per year, there are no
dividends and the PE ratio is constant, then the
implied return is 5%.
5
4. The Sleeping Flower Co. has earnings of $2.65 per share. The benchmark PE for
the company is 18. What stock price would you consider appropriate? What if the
benchmark PE were 21?
P0 = Benchmark PE ratio x EPS
Benchmark PE ratio = 18
EPS = $2.65
P0 = 18 x $2.65
= $47.70
If Benchmark PE ratio = 21
P0 = 21 x $2.65
= $55.65
5. Davis, Inc. currently has an EPS of $2.75 and an earnings growth rate of 8%. If the
benchmark PE ratio is 21, what is the target share price five years from now?
EPS = EPS x (1 + g)5
5 0
= $2.75 x (1 + .08)5
= $4.04
P = Benchmark PE ratio x EPS
5 5
= 21 x $4.04
= $84.84
6. TwitterMe, Inc. is a new company and currently has negative earnings. Its sales are
$1.35 million and there are 130,000 shares outstanding. If the benchmark price-
sales ratio is 4.8, what is you estimate of the appropriate stock price?
Sales P = Benchmark PS ratio x Sales per share
Sales per share =
Shares outstanding
Benchmark PS ratio = 4.8
$1,350,000 Sales per share = $10.38
=
130,000 P = 4.8 x $10.38
= $10.38 = $49.85
6
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