Chapter 13 – Equity Valuation
CHAPTER 13
13-1
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whole or part.
Chapter 13 – Equity Valuation
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
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
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
4. Intrinsic value = V0 =
D1
1 + k
+
D2
(1 + k )2
+ … +
D H + P H
(1 + k )H
=
$1 × 1 .2
1 + 0.085
+
$1 × 1 .22
(1 + 0.0 85 )2
+
$1 × 1 .22 × 1.04
(0.0 85 － 0.0 4) × ( 1 + 0.0 85) 2
= $30.60
5. Intrinsic value = V0 =
D 0× (1 + g )
k － g
:
$1.22 × 1 .05
k － 0.05
6. Intrinsic value = V0 =
D 0× (1 + g )
k － g
:
$1 × 1 .05
k － 0.0 5
E1
k
$3.64
0.0 9
8. Market value of the firm
13-2
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 13 – Equity Valuation
9. g = ROE b = 0.10 0.6 = 0.06 or 6%
P/E =
1 － b
k － g
=
1 － 0.6
0.0 8 － 0.0 6
= 20
10. Market capitalization rate = k = rf + β [E(rM) – rf ]
= 0.04 + 0.75 (0.12 – 0.04) = 0.10
D1
k － g
$ 4
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:
P0 =
D1
k － g
= =
EPS × (1－ b)
k － ROE × b
=
$ 6 × (1 － 0.6 )
0. 10 － 0.15 × 0.6
=
$ 2. 4
0. 10 － 0.0 9
= $240
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
k
$6
0.10
$180
12. FCFF = EBIT(1 – tc) + Depreciation – Capital expenditures – Increase in NWC
13. FCFE1 = FCFF – Interest expenses(1 – tc) + Increases in net debt
FCFE1
k － g
$ 193.7
0. 12 － 0.0 3
Chapter 13 – Equity Valuation
k e
0. 11
15. k = rf + β [E(rM) – rf ] = 0.05 + 1.5 (0.10 – 0.05) = 0.125 or 12.5%
Therefore:
P0 =
D1
k － g
=
$2.5
0. 125 － 0.0 4
= $29.41
16.
a. False. Higher beta means that the risk of the firm is higher and the discount rate
b. True. Higher ROE means more valuable growth opportunities.
c. Uncertain. The answer depends on a comparison of the expected rate of return
a. Using the constant-growth DDM, P0 =
D1
k － g
:
$50 =
$2
0. 16 － g
g = 0.12 or 12%
b. P0 =
D1
k － g
=
$2
0. 16 － 0.05
= $18.18
c. P/E Ratio
We can calculate the P/E ratio by dividing the current price by the projected
earnings:
P0 =
D1
k － g
=
EPS × (1－ b)
k － ( ROE × b )
=
$ 2 × (1 － 0. 3 )
0. 12 － 0. 20 × 0.3
=
$1.4
0. 12 － 0.0 6
= $23.33
13-4
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
D
$2.10
Chapter 13 – Equity Valuation
E 1
k － (ROE × b )
0. 12 － 0. 20 × 0.3
d. Present Value of Growth Opportunities (PVGO)
g = ROE b = 0.20 0.3 = 0.6
PVGO = P0 –
E1
k
=
D1
k － g
–
E1
k
=
$1.4
0. 12 － 0.0 6
–
$2
0. 12
=
$6.67
e. Impacts of Reducing Plowback Ratio
g = ROE b = 0.20 0.2 = 0.04 = 4%
D1 = EPS (1 – b) = $2 (1 – 0.2) = $1.6
P0 =
D1
k － g
=
$1. 6
0. 12 － 0.0 4
= $20
P/E = $20/$2 = 10.0
PVGO = P0 –
E1
k
= $20.00 –
$2
0. 12
= $3.33
17. ROE = 16%, b = 0.5, EPS = $2, k = 12%
a. P0 =
D1
k － g
=
EPS × (1－ b)
k － ( ROE × b )
=
$ 2 × (1 － 0. 5 )
0. 12 － 0. 16 × 0.5
=
$1
0. 12 － 0.0 8
k － g
18.
a. k = rf + β [E(rM) – rf ] = 0.06 + 1.25 (0.14 – 0.06) = 0.16 or 16%
D1
k － g
0. 16 － 0.0 6
b. Leading P0/E1 = $10.60/$3.18 = 3.33
13-5
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 13 – Equity Valuation
c. PVGO = P0 –
E1
k
= $10.60 –
$3.18
0. 16
= $9.28
d. Now, you revise the plowback ratio in the calculation so that b = 1/3:
E1
k
0. 10
D1
P 0
Chapter 13 – Equity Valuation
c. Since k = ROE, the stock price would be unaffected if Nogro were to cut its
21. Xyrong Corporation
a. k = rf + β [E(rM) – rf ] = 0.08 + 1.2 (0.15 – 0.08) = 0.164 or 16.4%
Chapter 13 – Equity Valuation
24. The solutions derived from Spreadsheet 13.2 are as follows:
a.
b.
c.
25.
a. g = ROE b = 0.20 0.5 = 0.10 or 10%
D 0 × (1 + g)
$0.5 × (1 + 0.10)
Chapter 13 – Equity Valuation
1 $1.1000 $0.5500 $6.0500 g = 10%, plowback = 0.50
2 $1.2100 $0.7260 $6.5340
EPS has grown by 10% based on last year’s
earnings plowback and ROE; this year’s
earnings plowback ratio now falls to 0.40 and
payout ratio = 0.60
3 $0.9801 $0.5881 $6.9260
ROE has decrease to 15%, along with the
payout ratio of 0.6 gives the new growth rate of
15% (1 – 0.6) = 6% from next year.
Year Return
1
%0.15150.0
11$
55.0$)11$10.12($
2
%0.404.0
10.12$
726.0$)10.12$534.6($
3
%0.15150.0
534.6$
5881.0$)534.6$9260.6($
13-9
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.