Chapter 13 - Equity Valuation
CHAPTER 13
EQUITY VALUATION
1. Theoretically, dividend discount models can be used to value the stock of rapidly
growing companies that do not currently pay dividends; in this scenario, we would be
valuing expected dividends in the relatively more distant future. However, as a practical
matter, such estimates of payments to be made in the more distant future are
notoriously inaccurate, rendering dividend discount models problematic for valuation
of such companies; free cash flow models are more likely to be appropriate. At the
other extreme, one would be more likely to choose a dividend discount model to value
a mature firm paying a relatively stable dividend.
2. It is most important to use multi-stage dividend discount models when valuing
companies with temporarily high growth rates. These companies tend to be companies
in the early phases of their life cycles, when they have numerous opportunities for
reinvestment, resulting in relatively rapid growth and relatively low dividends (or, in
many cases, no dividends at all). As these firms mature, attractive investment
opportunities are less numerous so that growth rates slow.
3. The intrinsic value of a share of stock is the individual investor’s assessment of the true
worth of the stock. The market capitalization rate is the market consensus for the
required rate of return for the stock. If the intrinsic value of the stock is equal to its
price, then the market capitalization rate is equal to the expected rate of return. On the
other hand, if the individual investor believes the stock is underpriced (i.e., intrinsic
value > price), then that investor’s expected rate of return is greater than the market
capitalization rate.
D1 D2 DH + PH
4. Intrinsic value = V0 = + +…+
1+ k (1 + k )2 (1 + k )H
$1 × 1 .2 $1 × 1 .2 2
= + +
1 + 0.085 (1 + 0.0 85 )2
$1 × 1 .22 × 1.04
(0.0 85 － 0.0 4) × ( 1 + 0.0 85 ) 2
= $30.60
D 0× (1 + g )
5. Intrinsic value = V0 = :
k－ g
$1.22 × 1 .05
$32.03 = k = 0.089994 or 8.9994%
k － 0.0 5
D 0× (1 + g )
6. Intrinsic value = V0 = :
k－ g
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
,Chapter 13 - Equity Valuation
$1 × 1 .05
$35 = k = 0.08 or 8%
k － 0.0 5
E1 $3.64
7. Price = $41 = + PVGO = + PVGO PVGO = $0.56
k 0.0 9
8. Market value of the firm
= Market value of assets – Market value of debts
= ($10 million + $90 million) – $50 million = $50 million
Book value of the firm
= Book value of assets – Book value of debts
= ($10 million + $60 million) – $40 million = $30 million
Market-to-book ratio = = 1.6667
9. g = ROE b = 0.10 0.6 = 0.06 or 6%
1 －b 1 － 0.6
P/E = = = 20
k－ g 0.0 8 － 0.0 6
10. Market capitalization rate = k = rf + β [E(rM) – rf ]
= 0.04 + 0.75 (0.12 – 0.04) = 0.10
D1 $4
Intrinsic value = V0 = = = $66.67
k－ g 0. 10 － 0.0 4
11. Given EPS = $6, ROE = 15%, plowback ratio = 0.6, and k = 10%, we first calculate the
price with the constant dividend growth model:
D1 EPS × (1－ b ) $ 6 × (1 － 0.6 )
P0 = == = =
k－ g k － ROE × b 0. 10 － 0. 15 × 0.6
$ 2. 4
= $240
0. 10 － 0.0 9
Then, knowing that the price is equal to the price with no growth plus the present value
of the growth opportunity, we can solve the following equation:
E1 $6
Price = $240 = + PVGO = + PVGO PVGO = $240 –$60 =
k 0.10
$180
12. FCFF = EBIT(1 – tc) + Depreciation – Capital expenditures – Increase in NWC
= $300 (1 – 0.35) + $20 – $60 – $30 = $125
13. FCFE1 = FCFF – Interest expenses(1 – tc) + Increases in net debt
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
, Chapter 13 - Equity Valuation
= $205 – $22 (1 – 0.35) + $3 = $193.70 (million)
FCFE1 $ 193.7
Market value of equity = = = $2,152.22 (million)
k－ g 0. 12 － 0.0 3
14. Cost of equity = rf + E(Risk premium) = 7% + 4% = 11%
Because the dividends are expected to be constant every year, the price can be
calculated as the no-growth-value per share:
D $2.10
P0 = = = $19.09
ke 0. 11
15. k = rf + β [E(rM) – rf ] = 0.05 + 1.5 (0.10 – 0.05) = 0.125 or 12.5%
Therefore:
D1 $2.5
P0 = = = $29.41
k－ g 0. 125 － 0.0 4
16.
a
.Fa lse.
Higherbet
ame anst
hattheri
skoft
hefir mi shigherandt
hediscountr
ate
appli
edtovaluecas
hflo wsi shi
gher
.Foranyexpe
c t
edpa t
hofearnin
gsa ndc
ash
flo ws ,
thepres
entval
ueofthecashflo ws,a
ndtherefor
e,t
hepriceofthefirm
willbelowerwhenris
kishigher
.Thust
her a
ti
oofpricetoearni
ngswillbe
l
o wer.
b
.Tr
ue.Hi
ghe
rROEme
ansmor
eva
lua
blegr
owt
hoppor
tuni
ti
es.
c. Uncertain. The answer depends on a comparison of the expected rate of return
on reinvested earnings with the market capitalization rate. If the expected rate of
return on the firm's projects is higher than the market capitalization rate, then
P/E will increase as the plowback ratio increases.
17.
D1
a. Using the constant-growth DDM, P0 = :
k－ g
$2
$50 = g = 0.12 or 12%
0. 16 － g
D1 $2
b. P0 = = 0. 16 － 0.05 = $18.18
k－ g
c. The price falls in response to the more pessimistic forecast of dividend growth.
The forecast for current earnings, however, is unchanged. Therefore, the P/E
ratio decreases. The lower P/E ratio is evidence of the diminished optimism
concerning the firm's growth prospects.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
CHAPTER 13
EQUITY VALUATION
1. Theoretically, dividend discount models can be used to value the stock of rapidly
growing companies that do not currently pay dividends; in this scenario, we would be
valuing expected dividends in the relatively more distant future. However, as a practical
matter, such estimates of payments to be made in the more distant future are
notoriously inaccurate, rendering dividend discount models problematic for valuation
of such companies; free cash flow models are more likely to be appropriate. At the
other extreme, one would be more likely to choose a dividend discount model to value
a mature firm paying a relatively stable dividend.
2. It is most important to use multi-stage dividend discount models when valuing
companies with temporarily high growth rates. These companies tend to be companies
in the early phases of their life cycles, when they have numerous opportunities for
reinvestment, resulting in relatively rapid growth and relatively low dividends (or, in
many cases, no dividends at all). As these firms mature, attractive investment
opportunities are less numerous so that growth rates slow.
3. The intrinsic value of a share of stock is the individual investor’s assessment of the true
worth of the stock. The market capitalization rate is the market consensus for the
required rate of return for the stock. If the intrinsic value of the stock is equal to its
price, then the market capitalization rate is equal to the expected rate of return. On the
other hand, if the individual investor believes the stock is underpriced (i.e., intrinsic
value > price), then that investor’s expected rate of return is greater than the market
capitalization rate.
D1 D2 DH + PH
4. Intrinsic value = V0 = + +…+
1+ k (1 + k )2 (1 + k )H
$1 × 1 .2 $1 × 1 .2 2
= + +
1 + 0.085 (1 + 0.0 85 )2
$1 × 1 .22 × 1.04
(0.0 85 － 0.0 4) × ( 1 + 0.0 85 ) 2
= $30.60
D 0× (1 + g )
5. Intrinsic value = V0 = :
k－ g
$1.22 × 1 .05
$32.03 = k = 0.089994 or 8.9994%
k － 0.0 5
D 0× (1 + g )
6. Intrinsic value = V0 = :
k－ g
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
,Chapter 13 - Equity Valuation
$1 × 1 .05
$35 = k = 0.08 or 8%
k － 0.0 5
E1 $3.64
7. Price = $41 = + PVGO = + PVGO PVGO = $0.56
k 0.0 9
8. Market value of the firm
= Market value of assets – Market value of debts
= ($10 million + $90 million) – $50 million = $50 million
Book value of the firm
= Book value of assets – Book value of debts
= ($10 million + $60 million) – $40 million = $30 million
Market-to-book ratio = = 1.6667
9. g = ROE b = 0.10 0.6 = 0.06 or 6%
1 －b 1 － 0.6
P/E = = = 20
k－ g 0.0 8 － 0.0 6
10. Market capitalization rate = k = rf + β [E(rM) – rf ]
= 0.04 + 0.75 (0.12 – 0.04) = 0.10
D1 $4
Intrinsic value = V0 = = = $66.67
k－ g 0. 10 － 0.0 4
11. Given EPS = $6, ROE = 15%, plowback ratio = 0.6, and k = 10%, we first calculate the
price with the constant dividend growth model:
D1 EPS × (1－ b ) $ 6 × (1 － 0.6 )
P0 = == = =
k－ g k － ROE × b 0. 10 － 0. 15 × 0.6
$ 2. 4
= $240
0. 10 － 0.0 9
Then, knowing that the price is equal to the price with no growth plus the present value
of the growth opportunity, we can solve the following equation:
E1 $6
Price = $240 = + PVGO = + PVGO PVGO = $240 –$60 =
k 0.10
$180
12. FCFF = EBIT(1 – tc) + Depreciation – Capital expenditures – Increase in NWC
= $300 (1 – 0.35) + $20 – $60 – $30 = $125
13. FCFE1 = FCFF – Interest expenses(1 – tc) + Increases in net debt
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
, Chapter 13 - Equity Valuation
= $205 – $22 (1 – 0.35) + $3 = $193.70 (million)
FCFE1 $ 193.7
Market value of equity = = = $2,152.22 (million)
k－ g 0. 12 － 0.0 3
14. Cost of equity = rf + E(Risk premium) = 7% + 4% = 11%
Because the dividends are expected to be constant every year, the price can be
calculated as the no-growth-value per share:
D $2.10
P0 = = = $19.09
ke 0. 11
15. k = rf + β [E(rM) – rf ] = 0.05 + 1.5 (0.10 – 0.05) = 0.125 or 12.5%
Therefore:
D1 $2.5
P0 = = = $29.41
k－ g 0. 125 － 0.0 4
16.
a
.Fa lse.
Higherbet
ame anst
hattheri
skoft
hefir mi shigherandt
hediscountr
ate
appli
edtovaluecas
hflo wsi shi
gher
.Foranyexpe
c t
edpa t
hofearnin
gsa ndc
ash
flo ws ,
thepres
entval
ueofthecashflo ws,a
ndtherefor
e,t
hepriceofthefirm
willbelowerwhenris
kishigher
.Thust
her a
ti
oofpricetoearni
ngswillbe
l
o wer.
b
.Tr
ue.Hi
ghe
rROEme
ansmor
eva
lua
blegr
owt
hoppor
tuni
ti
es.
c. Uncertain. The answer depends on a comparison of the expected rate of return
on reinvested earnings with the market capitalization rate. If the expected rate of
return on the firm's projects is higher than the market capitalization rate, then
P/E will increase as the plowback ratio increases.
17.
D1
a. Using the constant-growth DDM, P0 = :
k－ g
$2
$50 = g = 0.12 or 12%
0. 16 － g
D1 $2
b. P0 = = 0. 16 － 0.05 = $18.18
k－ g
c. The price falls in response to the more pessimistic forecast of dividend growth.
The forecast for current earnings, however, is unchanged. Therefore, the P/E
ratio decreases. The lower P/E ratio is evidence of the diminished optimism
concerning the firm's growth prospects.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
