CHAPTER 18: EQUITY VALUATION MODELS
CHAPTER 18: EQUITY VALUATION MODELS
PROBLEM SETS
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 multistage 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.
4. First estimate the amount of each of the next two dividends and the terminal
value. The current value is the sum of the present value of these cash flows,
discounted at 8.5%.
$1.22 (1.05)
5. The required return is 9%. k = + 0.05 = .09, or 9%
$32.03
6. The Gordon DDM uses the dividend for period (t+1) which would be 1.05.
18-1
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
,CHAPTER 18: EQUITY VALUATION MODELS
$1.05
$35 =
(k − 0.05)
$1.05
k= + 0.05 = 0.08 = 8%
$35
7. The PVGO is $0.56:
$3.64
PVGO = $41 − = $0.56
0.09
8. a. D1
k= +g
P0
$2
0.16 = + g g = 0.12, or 12%
$50
D1 $2
b. P0 = = = $18.18
k − g 0.16 − 0.05
c. The price falls in response to the more pessimistic dividend forecast. The
forecast for current year earnings, however, is unchanged. Therefore, the
P/E ratio falls. The lower P/E ratio is evidence of the diminished
optimism concerning the firm's growth prospects.
9. a. g = ROE b = 16% 0.5 = 8%
D1 = $2 (1 – b) = $2 (1 – 0.5) = $1
D1 $1
P0 = = = $25.00
k − g 0.12 − 0.08
b. P3 = P0(1 + g)3 = $25(1.08)3 = $31.49
10. a. k = rf + [ E (rm ) − rf ] = 6% + 1.25 (14% − 6%) = 16%
2
g= 9% = 6%
3
1
D1 = E0 (1 + g ) (1 − b) = $3 (1.06) = $1.06
3
D1 $1.06
P0 = = = $10.60
k − g 0.16 − 0.06
b. Leading P0/E1 = $10.60/$3.18 = 3.33
Trailing P0/E0 = $10.60/$3.00 = 3.53
18-2
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
, CHAPTER 18: EQUITY VALUATION MODELS
E1 $3.18
c. PVGO = P0 − = $10.60 − = −$9.275
k 0.16
The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is
less than the market capitalization rate (16%).
d. Now, you revise b to 1/3, g to 1/3 9% = 3%, and D1 to:
E0 (1 + g) (2/3)
$3 1.03 (2/3) = $2.06
Thus:
V0 = $2.06/(0.16 – 0.03) = $15.85
V0 increases because the firm pays out more earnings instead of reinvesting
a poor ROE. This information is not yet known to the rest of the market.
D1 $6 (1 − .60)
P0 = = = $240
k − g 0.10 − 0.6 .15
11.
EPS
PVGO = P0 − = $240 − $60 = $180
.1
FCFF = ( EBIT − Dep) (1 − t ) + Dep − Cap − NWC
12. = ($300 − $20) (.79) + $20 − $60 − $30
= $151.2
FCFE = FCFF − Interest Expense (1 − t ) + Increases in net debt
= $205 − $22 (1 − .21) + $3
13. = $190.62
FCFE1 $190.62 (1.03)
V= =
kE − g .12 − .03
= $2,181.54
18-3
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
CHAPTER 18: EQUITY VALUATION MODELS
PROBLEM SETS
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 multistage 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.
4. First estimate the amount of each of the next two dividends and the terminal
value. The current value is the sum of the present value of these cash flows,
discounted at 8.5%.
$1.22 (1.05)
5. The required return is 9%. k = + 0.05 = .09, or 9%
$32.03
6. The Gordon DDM uses the dividend for period (t+1) which would be 1.05.
18-1
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
,CHAPTER 18: EQUITY VALUATION MODELS
$1.05
$35 =
(k − 0.05)
$1.05
k= + 0.05 = 0.08 = 8%
$35
7. The PVGO is $0.56:
$3.64
PVGO = $41 − = $0.56
0.09
8. a. D1
k= +g
P0
$2
0.16 = + g g = 0.12, or 12%
$50
D1 $2
b. P0 = = = $18.18
k − g 0.16 − 0.05
c. The price falls in response to the more pessimistic dividend forecast. The
forecast for current year earnings, however, is unchanged. Therefore, the
P/E ratio falls. The lower P/E ratio is evidence of the diminished
optimism concerning the firm's growth prospects.
9. a. g = ROE b = 16% 0.5 = 8%
D1 = $2 (1 – b) = $2 (1 – 0.5) = $1
D1 $1
P0 = = = $25.00
k − g 0.12 − 0.08
b. P3 = P0(1 + g)3 = $25(1.08)3 = $31.49
10. a. k = rf + [ E (rm ) − rf ] = 6% + 1.25 (14% − 6%) = 16%
2
g= 9% = 6%
3
1
D1 = E0 (1 + g ) (1 − b) = $3 (1.06) = $1.06
3
D1 $1.06
P0 = = = $10.60
k − g 0.16 − 0.06
b. Leading P0/E1 = $10.60/$3.18 = 3.33
Trailing P0/E0 = $10.60/$3.00 = 3.53
18-2
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
, CHAPTER 18: EQUITY VALUATION MODELS
E1 $3.18
c. PVGO = P0 − = $10.60 − = −$9.275
k 0.16
The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is
less than the market capitalization rate (16%).
d. Now, you revise b to 1/3, g to 1/3 9% = 3%, and D1 to:
E0 (1 + g) (2/3)
$3 1.03 (2/3) = $2.06
Thus:
V0 = $2.06/(0.16 – 0.03) = $15.85
V0 increases because the firm pays out more earnings instead of reinvesting
a poor ROE. This information is not yet known to the rest of the market.
D1 $6 (1 − .60)
P0 = = = $240
k − g 0.10 − 0.6 .15
11.
EPS
PVGO = P0 − = $240 − $60 = $180
.1
FCFF = ( EBIT − Dep) (1 − t ) + Dep − Cap − NWC
12. = ($300 − $20) (.79) + $20 − $60 − $30
= $151.2
FCFE = FCFF − Interest Expense (1 − t ) + Increases in net debt
= $205 − $22 (1 − .21) + $3
13. = $190.62
FCFE1 $190.62 (1.03)
V= =
kE − g .12 − .03
= $2,181.54
18-3
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
