Chapter 7
Corporate Valuation and Stock Valuation
ANSWERS TO END-OF-CHAPTER QUESTIONS
7-1 a. A proxy is a document giving one person the authority to act for another, typically the
power to vote shares of common stock. If earnings are poor and stockholders are
dissatisfied, an outside group may solicit the proxies in an effort to overthrow
management and take control of the business, known as a proxy fight. The
preemptive right gives the current shareholders the right to purchase any new shares
b. The free cash flow model defines the total value of a company as the value of
operations plus the value of nonoperating assets.
The value of operations is the present value of all the future expected free cash
flows when discounted at the weighted average cost of capital:
.
WACC1
FCF
V
1t t
t
0)timeop(at
Nonoperating assets include investments in marketable securities and non-controlling interests in
the stock of other companies, and other financial securities.
c. Constant growth occurs when a firm’s earnings, dividends, and free cash flows grow
Vop (constant growth) =
L
1
gWACC
FCF
=
L
L0
gWACC
)g1(FCF
When applied to dividends, the model is:
7-4 The first step is to find the value of operations by discounting all expected future free
cash flows at the weighted average cost of capital. The second step is to find the total
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
7-1 D0 = $1.50; g1-3 = 5%; gn = 10%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.50(1.05) = $1.5750.
0
P
ˆ
0
P
ˆ
=
gr
D
s
1
=
06.013.0
50.1$
= $21.43.
7-3 P0 = $22; D0 = $1.20; g = 10%;
1
P
ˆ
= ?;
r
s= ?
1
P
ˆ
r
s=
0
1
P
D
+ g =
22$
)10.1(20.1$
+ 0.10
=
22$
32.1$
+ 0.10 = 16.00%.
r
s = 16.00%.
7-4 Dps = $5.00; Vps = $50; rps = ?
ps
ps
v
D
00.50$
00.5$
Step 2: Calculate the expected dividends:
D0 = $2.00
Step 3: Calculate the PV of the expected dividends:
Step 4: Calculate
2
P
ˆ
:
2
P
ˆ
Step 5: Calculate the PV of
2
P
ˆ
:
Step 6: Sum the PVs to obtain the stock’s price:
0
P
ˆ
Alternatively, using a financial calculator, input the following:
7-6 Value of operations = Vop = PV of expected future free cash flow
7-9 The problem asks you to determine the value of
3
P
ˆ
, given the following facts: D1 = $3, b
Step 1: Calculate the required rate of return:
Step 2: Use the constant growth rate formula to calculate g:
Step 3: Calculate
3
P
ˆ
:
3
P
ˆ
Alternatively, you could calculate D4 and then use the constant growth rate formula to
solve for
3
P
ˆ
:
3
P
ˆ
7-10 Vps = Dps/rps; therefore, rps = Dps/Vps.
a. rps = $3.5/$30 = 11.67%.
0
P
ˆ
gr
D
s
1
gr
)g1(D
s
0
)]04.0(14.0
)]04.0(1[6$
18.0
76.5$
0 1 2 3 4
| | | | |
P
| | | | | | |
0
P
ˆ
5
P
ˆ
of Year 5.
With these cash flows in the CFLO register, press NPV to get the value of the stock
today: NPV = $10.76.
rs = 13%
0
P
ˆ
05.013.0
)05.01(3$
18.0
85.2$
0
P
ˆ
0
P
ˆ
05.013.0
)05.1(3$
08.0
15.3$
0
P
ˆ
10.013.0
)10.1(3$
03.0
30.3$
0
P
ˆ
0
P
ˆ
These results show that the formula does not make sense if the required rate of return
is equal to or less than the expected growth rate.