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Answers and Solutions: 7- 1
or in part.
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
issued in proportion to their current holdings. The preemptive right may or may not
be required by state law. When granted, the preemptive right enables current owners
to maintain their proportionate share of ownership and control of the business. It also
prevents the sale of shares at low prices to new stockholders which would dilute the
value of the previously issued shares. Classified stock is sometimes created by a firm
to meet special needs and circumstances. Generally, when special classifications of
stock are used, one type is designated “Class A”, another as “Class B”, and so on.
Class A might be entitled to receive dividends before dividends can be paid on Class
B stock. Class B might have the exclusive right to vote. Founders’ shares are stock
owned by the firm’s founders that have sole voting rights but restricted dividends for
a specified number of years.
Vop (constant growth) =
L
1gWACC
FCF
=
L
L0 gWACC
)g1(FCF
When applied to dividends, the model is:
P
^0 =
Ls
1
Ls
L0 gr
D
gr
)g1(D
The horizon date is the last year in a cash flow forecast. Cash flows may grow
unevenly during the forecast period, but are assumed to grow at a constant rate for all
periods after the horizon date.
The horizon value is the value all cash flows beyond the horizon date when
discounted back to the horizon date.
When applied to free cash flows, the horizon value is the value of operations at
or in part.
Vop,0 =
T
T
T
1t t
t
)WACC1(
HV
)WACC1(
FCF
When applied to dividends, the present value of dividends is:
P
^0=
T
L
T
T
1t t
s
t
)r1(
P
ˆ
)r1(
D
e. Estimated value (
0
P
ˆ
) is the present value of the expected future cash flows. The
market price (P0) is the price at which an asset can be sold.
f. The required rate of return on common stock, denoted by rs, is the minimum
acceptable rate of return considering both its riskiness and the returns available on
other investments. The expected rate of return, denoted by ^
rs, is the rate of return
expected on a stockn given its current price and expected future cash flows. If the
stock is in equilibrium, the required rate of return will equal the expected rate of
constant growth stock, the capital gains yield is g, the constant growth rate. The
dividend yield on a stock can be defined as either the end-of-period dividend divided
by the beginning-of-period price, or the ratio of the current dividend to the current
price. Valuation formulas use the former definition. The expected total return, or
it without throwing the company into bankruptcy. So, although preferred stock has a
fixed payment like bonds, a failure to make this payment will not lead to bankruptcy.
Most preferred stocks entitle their owners to regular fixed dividend payments.
or in part.
7-2 True. The value of a share of stock is the PV of its expected future dividends. If the two
7-3 A perpetual bond is similar to a no-growth stock and to a share of preferred stock in the
2. All three are assumed to have indefinite lives with no maturity value (M) for the
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 = ?
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.05)3(1.10) = $1.9101.
7-2 D1 = $1.50; g = 6%; rs = 13%;
0
P
ˆ
= ?
0
P
ˆ
=
gr
D
s
1
=
06.013.0
50.1$
= $21.43.
ˆ
Answers and Solutions: 7 - 6
7-5 0 1 2 3
| | | |
D0 = 2.00 D1 D2 D3
2
P
ˆ
Step 1: Calculate the required rate of return on the stock:
rs = rRF + (rM - rRF)b = 7.5% + (4%)1.2 = 12.3%.
Step 2: Calculate the expected dividends:
D0 = $2.00
D1 = $2.00(1.20) = $2.40
Step 4: Calculate
2
P
ˆ
:
2
P
ˆ
= D3/(rs – g) = $3.08/(0.123 – 0.07) = $58.11.
Step 5: Calculate the PV of
2
P
ˆ
:
PV = $58.11/(1.123)2 = $46.08.
Step 6: Sum the PVs to obtain the stock’s price:
0
P
ˆ
= $4.42 + $46.08 = $50.50.
Alternatively, using a financial calculator, input the following:
CF0 = 0, CF1 = 2.40, and CF2 = 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve
for NPV = $50.50.
7-6 Value of operations = Vop = PV of expected future free cash flow
)g1( FCF
)05.1(000,400$
ˆ
Step 2: Use the constant growth rate formula to calculate g:
r
s =
0
1
P
D
+ g
0.10 =
40$
3$
+ g
g = 0.025 = 2.5%.
Step 3: Calculate
3
P
ˆ
:
3
P
ˆ
= P0(1 + g)3 = $40(1.025)3 = $43.076 ≈ $43.08.
Alternatively, you could calculate D4 and then use the constant growth rate formula to
solve for
3
P
ˆ
:
7-10 Vps = Dps/rps; therefore, rps = Dps/Vps.
d. rps = $3.5/$70 = 5.00%.
ˆ
D
1
)g1(D
0
)]04.0(1[6$
76.5$
7-12 D0 = $1, rS = 7% + 6% = 13%, g1 = 50%, g2 = 25%, gn = 6%.
= 30.268
23.704
7-13 Calculate the dividend stream and place them on a time line. Also, calculate the price of
the stock at the end of the nonconstant growth period, and include it, along with the
dividend to be paid at t = 5, as CF5. Then, enter the cash flows as shown on the time line
into the cash flow register, enter the required rate of return as I = 15, and then find the
rs = 13%
ps
D
10$
