Chapter 7
Problems and Solutions
1. Murphy Motors, Inc. has just set the company dividend policy at $0.50 per year.
The company plans on being in business forever. What is the price of this stock if
a. An investor wants a 5% return?
b. An investor wants an 8% return?
c. An investor wants a 10% return?
d. An investor wants a 13% return?
e. An investor wants a 20% return?
SOLUTION: Use the constant dividend infinite dividend stream model:
Price = Dividend / r
a. Price = $0.50 / 0.05 = $10.00
b. Price = $0.50 / 0.08 = $6.25
c. Price = $0.50 / 0.10 = $5.00
d. Price = $0.50 / 0.13 = $3.85
e. Price = $0.50 / 0.20 = $2.50
2. Rice Electronics wants its shareholders to earn a 15% return on their investment
in the company. At what price would the stock need to be priced today if Rice
Electronics had the following cash dividend policy:
a. $0.25 constant annual dividend forever?
b. $1.00 constant annual dividend forever?
c. $1.75 constant annual dividend forever?
d. $2.50 constant annual dividend forever?
SOLUTION: Use the constant dividend infinite dividend stream model:
Price = Dividend / r
a. Price = $0.25 / 0.15 = $1.67
b. Price = $1.00 / 0.15 = $6.67
c. Price = $1.75 / 0.15 = $11.67
d. Price = $2.50 / 0.15 = $16.67
5. King Waterbeds has an annual cash dividend policy that raises the dividend each
year by 4%. Last year’s dividend was $0.40 per share. What is the price of this stock
if
a. An investor wants a 5% return?
b. An investor wants an 8% return?
c. An investor wants a 10% return?
d. An investor wants a 13% return?
e. An investor wants a 20% return?
SOLUTION: Use the constant growth dividend model with an infinite dividend
stream:
Price = Last Dividend x (1 + g) / (r – g)
a. Price = $0.40 x (1.04) / (0.05 – 0.04) = $0.4160 / 0.01 = $41.60
b. Price = $0.40 x (1.04) / (0.08 – 0.04) = $0.4160 / 0.04 = $10.40
c. Price = $0.40 x (1.04) / (0.10 – 0.04) = $0.4160 / 0.06 = $6.93
d. Price = $0.40 x (1.04) / (0.13 – 0.04) = $0.4160 / 0.09 = $4.62
e. Price = $0.40 x (1.04) / (0.20 – 0.04) = $0.4160 / 0.16 = $2.60
6. Seitz Glassware is trying to determine its growth rate for it’s an annual cash
dividend. Last year’s dividend was $0.25 per share. The target return rate for the
stock is 10%. What is the price of this stock if
a. The annual growth rate is 1%?
b. The annual growth rate is 3%?
c. The annual growth rate is 5%?
d. The annual growth rate is 7%?
e. The annual growth rate is 9%?
SOLUTION: Use the constant growth dividend model with an infinite dividend
stream:
Price = Last Dividend x (1 + g) / (r – g)
a. Price = $0.25 x (1.01) / (0.10 – 0.01) = $0.2525 / 0.09 = $2.81
b. Price = $0.25 x (1.03) / (0.10 – 0.03) = $0.2575 / 0.07 = $3.68
c. Price = $0.25 x (1.05) / (0.10 – 0.05) = $0.2625 / 0.05 = $5.25
d. Price = $0.25 x (1.07) / (0.10 – 0.07) = $0.2675 / 0.03 = $8.92
e. Price = $0.25 x (1.09) / (0.10 – 0.09) = $0.2725 / 0.01 = $27.25
9. Mulder Fashions expects the following dividend pattern over the next seven years:
Year 1
$1.00
Year 2
$1.10
Year 3
$1.21
Year 4
$1.33
Year 5
$1.46
Year 6
$1.61
Year 7
$1.77
Then the company will have a constant dividend of $2.00 forever. What is the price
of this stock today if an investor wants to earn
a. 15%?
b. 20%?
SOLUTION: This stock can be valued using a two-stage model. During the first
stage, we must find the present value of the dividends individually.
In the second stage, we can use the Gordon growth model (constant
growth model to find P7, which represents the cash flows in this stage. The first dividend
in the second stage is D8 ($2).
a. The price today for this stock with a required rate of return of 15% is
calculated in the following way:
In the second stage, dividends are $2 forever, therefore g = 0 and P7 is:
P7 
2
 13.33
0.15  0
Therefore, the price today is:
P0 
1
1.1
1.21
1.33
1.46
1.61
1.77
13.33







 10.36
2
3
4
5
6
7
(1.15) (1.15) (1.15) (1.15) (1.15) (1.15) (1.15) (1.15)7
b. The price today for this stock with a required rate of return of 20% is
calculated in the following way:
In the second stage, dividends are $2 forever, therefore g = 0 and P7 is:
P7 
2
 10.00
0.20  0
Therefore, the price today is:
P0 
1
1.1
1.21
1.33
1.46
1.61
1.77
10.00







 7.35
2
3
4
5
6
7
(1.20) (1.20) (1.20) (1.20) (1.20) (1.20) (1.20) (1.20)7
11. Huber Athletic Club is going to offer preferred stock to its members with the
following characteristics; par value is $100 and annual dividend rate of 6%. If a
member wants the following returns, what price should he be willing to pay:
a. Brad wants a 10% return.
b. Mike wants a 12% return
c. Rick wants a 15% return
d. Julius wants a 18% return
SOLUTION: Use the constant dividend model with finite horizon
Price = Dividend / r
a. Brad’s Price = $100 x 0.06 / 0.10 = $60.00
b. Mike’s Price = $100 x 0.06 / 0.12 = $50.00
c. Rick’s Price = $100 x 0.06 / 0.15 = $40.00
d. Julius’s Price = $100 x 0.06 / 0.18 = $33.33
14. Find the annual growth rate of the dividends for each of the firms listed in the
table below.
Year
ABC
EFG
HIJ
KLM
1999
$1.00
$1.00
$1.00
$0.00
2000
$1.05
$0.90
$1.00
$0.00
Dividend Payment per Year
2001
2002
$1.10
$1.16
$0.81
$0.73
$1.00
$2.00
$0.25
$0.50
2003
$1.22
$0.66
$2.00
$0.75
SOLUTION: Either find the change each year and then average the change or
g = (Dividend 2004 / Dividend 1999)1/5 – 1
ABC g = ($1.28 / $1.00)0.20 – 1 = 0.0506 = 5.06%
2004
$1.28
$0.59
$2.00
$1.00
EFG g = ($0.59 / $1.00)0.20 – 1 = -0.10 = negative 10%
HIJ g = ($2.00 / $1.00)0.20 – 1 = 0.1487 = 14.87%
KLM g = can only measure for the years 2001 to 2004, ($1.00 / $0.25)1/3 – 1 = 0.5874
= 58.74%
15. Find the equation for the Security Market Line given the following information:
a. Risk-free rate is 3% and the expected return of the market portfolio is 12%.
b. Risk-free rate is 5% and the expected return of the market portfolio is 18%.
c. Risk-free rate is 4% and the market risk premium is 8%.
d. Risk-free rate is 2% and the market risk premium is 6%.
e. The intercept is 3% and the slope of the line is 9%.
f. The intercept is 4% and the slope of the line is 7%.
SOLUTION: The Security Market Line equation is:
E(r) = rf + β (E(rm) - rf)
And the intercept is rf
The slope is E(rm) - rf
The market risk premium is E(rm) - rf
a. The SML is E(r) = 3% + β (12% - 3%) = 3% + β 9%
b. The SML is E(r) = 5% + β (18% - 5%) = 3% + β 13%
c. The SML is E(r) = 4% + β (8%)
d. The SML is E(r) = 2% + β (6%)
e. The SML is E(r) = 3% + β (9%)
f. The SML is E(r) = 4% + β (7%)
17. Fill in the missing expected returns for the following stocks if the current SML
equation is:
E(ri) = 3% + βi (12% - 3%)
a. TJB beta is 1.2
b. MAB beta is 0.6
c. PMF beta is 0.8
d. CNF beta is 1.4
e. SJN beta is 0.4
f. GFN beta is 1.6
g. JE beta is 1.0
h. PE beta is 0.0
SOLUTION
a. TJB expected return: E(rTJB) = 3% + 1.2 (9%) = 3% + 10.8% = 13.8%
b. MAB expected return: E(rMAB) = 3% + 0.6 (9%) = 3% + 5.4% = 8.4%
c. PMF expected return: E(rPMF) = 3% + 0.8 (9%) = 3% + 7.2% = 10.2%
d. CNF expected return: E(rCNF) = 3% + 1.4 (9%) = 3% + 12.6% = 15.6%
e. SJN expected return: E(rSJN) = 3% + 0.4 (9%) = 3% + 3.6% = 6.6%
f. GFN expected return: E(rGFN) = 3% + 1.6 (9%) = 3% + 14.4% = 17.4%
g. JE expected return: E(rJE) = 3% + 1.0 (9%) = 3% + 9% = 12%
h. PE expected return: E(rPE) = 3% + 0.0 (9%) = 3% + 0.0% = 3%
18. Fill in the missing betas for the following stocks if the current SML equation is:
E(ri) = 4% + βi (14% - 4%)
a. TJB’s expected return is 16%
b. MAB’s expected return is 10%
c. PMF’s expected return is 12%
d. CNF’s expected return is 18%
e. SJN’s expected return is 8%
f. GFN’s expected return is 20%
g. JE’s expected return is 14%
h. PE’s expected return is 4%
SOLUTION
a. TJB’s beta is: 16% = 4% + βTJB(10%), βTJB = (16% - 4%) / 10% = 1.2
b. MAB’s beta is: 10% = 4% + βMAB(10%), βMAB = (10% - 4%) / 10% = 0.6
c. PMF’s beta is: 12% = 4% + βPMF(10%), βPMF = (12% - 4%) / 10% = 0.8
d. CNF’s beta is: 18% = 4% + βCNF(10%), βCNF = (18% - 4%) / 10% = 1.4
e. SJN’s beta is: 8% = 4% + βSJN(10%), βSJN = (8% - 4%) / 10% = 0.4
f. GFN’s beta is: 20% = 4% + βGFN(10%), βGFN = (20% - 4%) / 10% = 1.6
g. JE’s beta is: 14% = 4% + βJE(10%), βJE = (14% - 4%) / 10% = 1.0
h. PE’s beta is: 4% = 4% + βPE(10%), βPE = (14% - 4%) / 10% = 0.0
19. The current Security Market Line is: E(ri) = 2.5% + βi (11.75% - 2.5%). Plot each
of the following assets and determine if they are over the line and thus underpriced
assets or under the line and thus overpriced assets (assume beta is correct for each
stock):
Company
TJB
MAB
PMF
CNF
SJN
Company Beta
1.2
0.6
0.8
1.4
0.4
Return
15.10%
10.55%
9.40%
14.45%
5.70%
Overpriced
?
?
?
?
?
Underpriced
?
?
?
?
?
1.6
1.0
0.0
GFN
JE
PE
18.80%
11.00%
3.0%
?
?
?
?
?
?
SOLUTION: First find the expected return for the stocks if the betas are correct.
Compare with the listed return. For stocks where the expected return is less than the
listed return, the stock is underpriced. For stocks where the expected return is greater
than the listed return, the stock is overpriced.
Company
TJB
MAB
PMF
CNF
SJN
GFN
JE
PE
Company
Beta
1.2
0.6
0.8
1.4
0.4
1.6
1.0
0.0
Listed
Return
15.10%
9.55%
9.60%
14.45%
5.70%
18.80%
11.00%
3.0%
Expected
Return
2.5% + 1.2 (9.25%) = 13.6%
2.5% + 0.6 (9.25%) = 8.05%
2.5% + 0.8 (9.25%) = 9.90%
2.5% + 1.4 (9.25%) = 15.45%
2.5% + 0.4 (9.25%) = 6.20%
2.5% + 1.6 (9.25%) = 17.30%
2.5% + 1.0 (9.25%) = 11.75%
2.5% + 0.0 (9.25%) = 2.50%
Underpriced or
Overpriced
Underpriced
Underpriced
Overpriced
Overpriced
Overpriced
Underpriced
Overpriced
Underpriced
20. Challenge Problem: Royal Seattle Investment Club is thinking of buying
100 shares of Sun-Dollar Coffee Company. The stock is currently selling for
$25.00 per share. The beta of Sun-Dollar Coffee is currently listed at 1.35 by
almost every rating agency and model available. If the current risk-free rate is
2.75% (yield on the one-year U.S. Treasury bill) and the market risk-premium
for the coming year is estimated at 8.25% by almost every financial service,
what price should Royal Seattle Investment Club expect for Sun-Dollar
Coffee at the end of the year?
SOLUTION: First find the expected return using the SML equation and then
multiply the current price by one plus the return to find the expected year-end
price.
Expected return of Sun-Dollar Company = 2.75% + 1.35 (8.25%) = 13.8875%
End of Year Price = $25.00 x 1.138875 = $28.47