Chapter 9

1. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Stocks and Their Valuation
Features of Common Stock
Determining Common Stock Values
Preferred Stock
Chapter 9
9-1

2. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Facts about Common Stock
• Represents ownership
• Ownership implies control
• Stockholders elect directors
• Directors elect management
• Management’s goal: Maximize the stock price
9-2

3. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Intrinsic Value and Stock Price
• Outside investors, corporate insiders, and analysts
use a variety of approaches to estimate a stock’s
intrinsic value (P0).
• In equilibrium we assume that a stock’s price
equals its intrinsic value.
– Outsiders estimate intrinsic value to help determine
which stocks are attractive to buy and/or sell.
– Stocks with a price below (above) its intrinsic value
are undervalued (overvalued).
9-3

4. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Determinants of Intrinsic Value and Stock Prices
“True”
Risk
“Perceived” Investor
Cash Flows
“Perceived”
Risk
Managerial Actions, the Economic Environment,
Taxes, and the Political Climate
Stock’s
Intrinsic Value
Stock’s
Market Price
Market Equilibrium:
Intrinsic Value = Stock Price
9-4

5. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Different Approaches for Estimating the Intrinsic
Value of a Common Stock
• Discounted dividend model
• Corporate valuation model
• P/E multiple approach
• EVA approach
9-5

6. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Discounted Dividend Model
• Value of a stock is the present value of the future
dividends expected to be generated by the stock.
∞
∞
+
++
+
+
+
+
+
=
)r(1
D
...
)r(1
D
)r(1
D
)r(1
D
Pˆ
s
3
s
3
2
s
2
1
s
1
0
9-6

7. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Constant Growth Stock
gr
D
gr
g)(1D
Pˆ
s
1
s
0
0
−
=
−
+
=
• A stock whose dividends are expected to grow
forever at a constant rate, g.
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = D0(1 + g)t
• If g is constant, the discounted dividend formula
converges to:
9-7

8. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Future Dividends and Their Present Values
t
t
t
)r1(
D
PVD
+
=
t0 PVDP ∑=
$
0.25
Years (t)0
t
0t )g1(DD +=
9-8

9. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
What happens if g > rs?
• If g > rs, the constant growth formula leads to a
negative stock price, which does not make sense.
• The constant growth model can only be used if:
– rs > g.
– g is expected to be constant forever.
9-9

10. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Use the SML to Calculate the Required
Rate of Return (rs)
• If rRF = 7%, rM = 12%, and b = 1.2, what is the required
rate of return on the firm’s stock?
rs = rRF + (rM – rRF)b
= 7% + (12% – 7%)1.2
= 13%
9-10

11. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Find the Expected Dividend Stream for the Next
3 Years and Their PVs
1.8761
1.7599
1.6509
rs = 13%
g = 6%
0 1
2.247
2
2.382
3
2.12
D0 = $2 and g is a constant 6%.
9-11

12. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Using the constant growth model:
What is the stock’s intrinsic value?
$30.29
0.07
$2.12
0.060.13
$2.12
gr
D
Pˆ
s
1
0
=
=
−
=
−
=
9-12

13. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
• D1 will have been paid out already. So, expected P1
is the present value (as of Year 1) of D2, D3, D4, etc.
• Could also find expected P1 as:
What is the stock’s expected value, one year
from now?
$32.10
0.060.13
$2.247
gr
D
Pˆ
s
2
1
=
−
=
−
=
$32.10(1.06)PPˆ 01 ==
9-13

14. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Find Expected Dividend Yield, Capital Gains Yield, and
Total Return During First Year
• Dividend yield
= D1/P0 = $2.12/$30.29 = 7.0%
• Capital gains yield
= (P1 – P0)/P0
= ($32.10 – $30.29)/$30.29 = 6.0%
• Total return (rs)
= Dividend yield + Capital gains yield
= 7.0% + 6.0% = 13.0%
9-14

15. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
The dividend stream would be a perpetuity.
What would the expected price today be,
if g = 0?
$15.38
0.13
$2.00
r
PMT
Pˆ0 ===
2.00 2.002.00
0 1 2 3rs = 13%
9-15

16. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Supernormal Growth: What if g = 30% for 3 years
before achieving long-run growth of 6%?
• Can no longer use just the constant growth model
to find stock value.
• However, the growth does become constant after 3
years.
9-16

17. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Valuing Common Stock with Nonconstant Growth
rs = 13%
g = 30% g = 30% g = 30% g = 6%
2.301
2.647
3.045
46.114
54.107 =
0 1 2 3 4
2.600 3.380 4.394 4.658
Pˆ0
$66.54
06.00.13
4.658
Pˆ3 =
−
=
9-17
D0 = $2.00.

18. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Find Expected Dividend and Capital Gains Yields
During the First and Fourth Years
• Dividend yield (first year)
= $2.60/$54.11 = 4.81%
• Capital gains yield (first year)
= 13.00% – 4.81% = 8.19%
• During nonconstant growth, dividend yield and
capital gains yield are not constant, and capital
gains yield ≠ g.
• After t = 3, the stock has constant growth and
dividend yield = 7%, while capital gains yield = 6%.
9-18

19. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Nonconstant Growth: What if g = 0% for 3 years
before long-run growth of 6%?
rs = 13%
g = 0% g = 0% g = 0% g = 6%
1.77
1.57
1.39
20.99
25.72 =
0 1 2 3 4
2.00 2.00 2.00 2.12
Pˆ0
$30.29
06.00.13
2.12
Pˆ3 =
−
=
9-19
D0 = $2.00.

20. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Find Expected Dividend and Capital Gains Yields
During the First and Fourth Years
• Dividend yield (first year)
= $2.00/$25.72 = 7.78%
• Capital gains yield (first year)
= 13.00% – 7.78% = 5.22%
• After t = 3, the stock has constant growth and
dividend yield = 7%, while capital gains yield = 6%.
9-20

21. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
• Yes. Even though the dividends are declining, the stock
is still producing cash flows and therefore has positive
value.
If the stock was expected to have negative growth (g =
-6%), would anyone buy the stock, and what is its value?
$9.89
0.19
$1.88
(-0.06)0.13
(0.94)$2.00
gr
)g(1D
gr
D
Pˆ
s
0
s
1
0
==
−
=
−
+
=
−
=
9-21

22. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Find Expected Annual Dividend and Capital
Gains Yields
• Capital gains yield
= g = -6.00%
• Dividend yield
= 13.00% – (-6.00%) = 19.00%
• Since the stock is experiencing constant growth,
dividend yield and capital gains yield are constant.
Dividend yield is sufficiently large (19%) to offset
negative capital gains.
9-22

23. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Corporate Valuation Model
• Also called the free cash flow method. Suggests
the value of the entire firm equals the present
value of the firm’s free cash flows.
• Remember, free cash flow is the firm’s after-tax
operating income less the net capital investment.
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 +−= NOWC
esexpenditur
Capital
onamortizati
andDepr.
T)EBIT(1FCF
9-23

24. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Applying the Corporate Valuation Model
• Find the market value (MV) of the firm, by finding
the PV of the firm’s future FCFs.
• Subtract MV of firm’s debt and preferred stock to
get MV of common stock.
• Divide MV of common stock by the number of
shares outstanding to get intrinsic stock price
(value).
9-24

25. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Issues Regarding the Corporate Valuation Model
• Often preferred to the discounted dividend model,
especially when considering number of firms that
don’t pay dividends or when dividends are hard to
forecast.
• Similar to discounted dividend model, assumes at
some point free cash flow will grow at a constant
rate.
• Horizon value (HVN) represents value of firm at the
point that growth becomes constant.
9-25

26. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
3HV
06.00.10
21.20
530 =
−
=
Use the Corporate Valuation Model to Find the
Firm’s Intrinsic Value
Given: Long-Run gFCF = 6% and WACC = 10%
r= 10%
g = 6%
-4.545
8.264
15.026
398.197
416.942
0 1 2 3 4
-5 21.2010 20
9-26

27. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
What is the firm’s intrinsic value per share?
9-27
The firm has $40 million total in debt and
preferred stock and has 10 million shares of
common stock.
million94.376$
40$94.416$
preferredanddebtofMVfirmofMVequityofMV
=
−=
−=
$37.69
/1094.376$
sharesofquity/#eofMVshareperValue
=
=
=

28. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Firm Multiples Method
• Analysts often use the following multiples to value
stocks.
– P/E
– P/CF
– P/Sales
• EXAMPLE: Based on comparable firms, estimate
the appropriate P/E. Multiply this by expected
earnings to back out an estimate of the stock price.
9-28

29. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
EVA Approach
EVA = Equity capital(ROE – Cost of equity)
MVEquity = BVEquity + PV of all future EVAs
Value per share = MVEquity/# of shares
9-29

30. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
Preferred Stock
• Hybrid security.
• Like bonds, preferred stockholders receive a fixed
dividend that must be paid before dividends are
paid to common stockholders.
• However, companies can omit preferred dividend
payments without fear of pushing the firm into
bankruptcy.
9-30

31. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
If preferred stock with an annual dividend of $5 sells for
$50, what is the preferred stock’s expected return?
10%0.10
$50
$5
rˆ
r
$5
$50
r
D
V
p
p
p
p
==
=
=
=
9-31