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Mini Case: 7 - 30
m. What insight does the free cash flow valuation model give provide us about
possible reasons for market volatility? Hint: Look at the value of operations for
the combinations of ROIC and gL in the previous questions.
Answer: .
ROIC
gL
8.0%
8.8%
9.8%
10.8%
5%
$958
$1,191
$1,523
$1,756
6%
$933
$1,247
$1,694
$2,008
n. 1. Write out a formula that can be used to value any dividend-paying stock,
regardless of its dividend pattern
Answer: The value of any stock is the present value of its expected dividend stream:
0
P
ˆ
=
.
)r1(
D
)r1(
D
)r1(
D
)r1(
D
s
3
s
3
s
2
t
s
1
However, some stocks have dividend growth patterns which allow them to be valued
using short-cut formulas.
Mini Case: 7 - 31
or in part.
n. 2. What is a constant growth stock? How are constant growth stocks valued?
n. 3. What happens if a company has a constant gL that exceeds its rs? Will many
stocks have expected growth greater than the required rate of return in the short
run (i.e., for the next few years)? In the long run (i.e., forever)?
Answer: The model is derived mathematically, and the derivation requires that rs > gL. If gL is
o. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the
yield on T-bonds) is 7%, and that the market risk premium is 5%. What is the
required rate of return on the firm’s stock?
Answer: Here we use the SML to calculate temp force’s required rate of return:
p. Assume that Temp Force is a constant growth company whose last dividend (D0,
which was paid yesterday) was $2.00 and whose dividend is expected to grow
indefinitely at a 6% rate.
p. 1. What is the firm’s current stock price?
Answer: We could extend the time line on out forever, find the value of Temp Force’s
Mini Case: 7 - 33
or in part.
p. 2. What is the stock’s expected value one year from now?
Answer: After one year, D1 will have been paid, so the expected dividend stream will then be
D2, D3, D4, and so on. Thus, the expected value one year from now is $32.10:
1
P
ˆ
=
)gr(
D
Ls
2
D2 = D1 (1+gL) = $2.12(1.06) = 2.2472
1
P
ˆ
=
)gr(
D
Ls
2
=
)06.013.0(
2472.2$
=
07.0
2472.2$
= $32.10.
Mini Case: 7 - 34
p. 3. What are the expected dividend yield, the capital gains yield, and the total
return during the first year?
Answer: The expected dividend yield in any year n is
Dividend Yield =
1n
n
P
ˆ
D
06.013.0
12.2$
Expected Dividend Yield at Time 0 =
0
1
P
ˆ
D
=
29.30$
12.2$
= 7%
While the expected capital gains yield is
Capital Gains Yield =
1n
1nn
P
ˆ
)P
ˆ
P
ˆ
(
Expected Capital Gains Yield at Time 0 =
1n
1nn
P
ˆ
)P
ˆ
P
ˆ
(
=
29.30$
29.30$10.32$
=
29.30$
81.1$
= 6%
Alternatively,
Capital Gains Yield = rs – Dividend Yield = 13% − 7% = 6%
The total yield is comprised of the dividend yield and the capital gains yield.
Dividend yield = 7.0%
Capital gains yield = 6.0%
Total return = 13.0%
q. Now assume that the stock is currently selling at $30.29. What is its expected
rate of return?
Answer: The constant growth model can be rearranged to this form:
rs =
g
P
D
0
1
.
or in part.
Here the current price of the stock is known, and we solve for the expected return.
For Temp Force:
r. Now assume that Temp Force’s dividend is expected to experience nonconstant
growth of 30% from Year 0 to Year 1, 20% from Year 1 to Year 2, and 10%
from Year 2 to Year 3. After Year 3, dividends will grow at a constant rate of
6%. What is the stock’s intrinsic value under these conditions? What are the
expected dividend yield and capital gains yield during the first year? What are
the expected dividend yield and capital gains yield during the fourth year (from
Year 3 to Year 4)?
Answer: Temp Force is no longer a constant growth stock, so the constant growth model is not
applicable. Note, however, that the stock is expected to become a constant growth
stock in 3 years. Thus, it has a nonconstant growth period followed by constant
growth. The easiest way to value such nonconstant growth stocks is to set the
stock today, P
Mini Case: 7 - 36
or in part.
The dividend yield and the capital gains yield are:
600.2$
During the nonconstant growth period, the dividend yields and capital gains yields are
s. What is the market multiple method of valuation? What are its strengths and
weaknesses?
Answer: Analysts often use the P/E multiple (the price per share divided by the earnings per
share) or the P/CF multiple (price per share divided by cash flow per share, which is
the earnings per share plus the dividends per share) to value stocks. For example,
Mini Case: 7 - 37
or in part.
t. What are the advantages of the free cash flow valuation model relative to the
dividend growth model?
u. What is preferred stock? Suppose a share of preferred stock pays a dividend of
$2.10 and investors require a return of 7%. What is the estimated value of the
preferred stock?
Answer:
00.30$
07.0
10.2$
r
D
Vps
ps
ps
