Ch07 Solutions - Chapter 7 Stocks Stock Valuation and Stock...

r
s
= 13% g
n
= 6% g
2
= 25% g
1
= 50%
g = 50% g = 8%
r
s
= 15%
g = 5% r = 12% g = 15% g = 5%
Stocks, Stock Valuation, and Stock Market
Equilibrium
7-1 D
0
= $1.50; g
1-3
= 5%; g
n
= 10%; D
1
through D
5
= ?
D
1
= D
0
(1 + g
1
) = $1.50(1.05) = $1.5750.
D
2
= D
0
(1 + g
1
)(1 + g
2
) = $1.50(1.05) 2 = $1.6538.
D
3
= D
0
(1 + g
1
)(1 + g
2
)(1 + g
3
) = $1.50(1.05) 3 = $1.7364.
D
4
= D
0
(1 + g
1
)(1 + g
2
)(1 + g
3
)(1 + g
n
) = $1.50(1.05) 3 (1.10) = $1.9101.
D
5
= D
0
(1 + g
1
)(1 + g
2
)(1 + g
3
)(1 + g
n
)
2
= $1.50(1.05)
3
(1.10)
2
= $2.1011.
7-2 D
1
= $1.50; g = 7%; r
s
= 15%; = ?
= = = $18.75.
7-3 P
0
= $20; D
0
= $1.00; g = 10%; = ?;
s
= ?
= P
0
(1 + g) = $20(1.10) = $22.
s
= + g = + 0.10
= + 0.10 = 15.50%.
s
= 15.50%.
7-4 D
ps
= $5.00; V
ps
= $50; r
ps
= ?
Chapter 7
SOLUTIONS TO END-OF-CHAPTER PROBLEMS

r
ps
= = = 10%.
7-5 0 1 2 3
| | | |
D
0
= 2.00 D
1
D
2
D
3
Step 1: Calculate the required rate of return on the stock:
r
s
= r
RF
+ (r
M
- r
RF
)b = 7.5% + (4%)1.2 = 12.3%.
Step 2: Calculate the expected dividends:
D
0
= $2.00
D
1
= $2.00(1.20) = $2.40
D
2
= $2.00(1.20) 2 = $2.88
D
3
= $2.88(1.07) = $3.08
Step 3: Calculate the PV of the expected dividends:
PV
Div
= $2.40/(1.123) + $2.88/(1.123)
2
= $2.14 + $2.28 = $4.42.
Step 4: Calculate :
= D
3
/(r
s
– g) = $3.08/(0.123 – 0.07) = $58.11.
Step 5: Calculate the PV of :
PV = $58.11/(1.123)
2
= $46.08.
Step 6: Sum the PVs to obtain the stock’s price:

= $4.42 + $46.08 = $50.50.
Alternatively, using a financial calculator, input the following:
CF
0
= 0, CF
1
= 2.40, and CF
2
= 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve
for NPV = $50.50.
7-6 The problem asks you to determine the constant growth rate, given the following facts:
P
0
= $80, D
1
= $4, and r
s
= 14%. Use the constant growth rate formula to calculate g:
s
= + g
0.14 = + g
g = 0.09 = 9%.

7-7 The problem asks you to determine the value of , given the following facts: D
1
= $2, b =
0.9, r
RF
= 5.6%, RP
M
= 6%, and P
0
= $25. Proceed as follows:
Step 1: Calculate the required rate of return:
r
s
= r
RF
+ (r
M
– r
RF
)b = 5.6% + (6%)0.9 = 11%.
Step 2: Use the constant growth rate formula to calculate g:
s
= + g
0.11 = + g
g = 0.03 = 3%.
Step 3: Calculate :
= P
0
(1 + g) 3 = $25(1.03) 3 = $27.3182 ≈ $27.32.
Alternatively, you could calculate D
4
and then use the constant growth rate formula to
solve for :
D
4
= D
1
(1 + g)
3
= $2.00(1.03)
3
= $2.1855.
= $2.1855/(0.11 – 0.03) = $27.3188 ≈ $27.32.
7-8 V
ps
= D
ps
/r
ps
; therefore, r
ps
= D
ps
/V
ps
.
a. r
ps
= $8/$60 = 13.3%.
b. r
ps
= $8/$80 = 10%.

c. r
ps
= $8/$100 = 8%.
d. r
ps
= $8/$140 = 5.7%.
7-9 = = = = = $25.26.
7-10 a. r
i
= r
RF
+ (r
M
- r
RF
)b
i
.
r
C
= 9% + (13% – 9%)0.4 = 10.6%. r
D
= 9% + (13% – 9%)-0.5 = 7%.
Note that r
D
is below the risk-free rate. But since this stock is like an insurance policy
because it “pays off” when something bad happens (the market falls), the low return
is not unreasonable.