Chapter 9
Stocks and Their Valuation
Features of Common Stock
Determining Common Stock Values
Preferred Stock
9-1
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Facts about Common Stock
•
•
•
•
•
Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the stock price
9-2
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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
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Determinants of Intrinsic Value and Stock Prices
Managerial Actions, the Economic Environment,
Taxes, and the Political Climate
“True” Investor
Cash Flows
“True” Risk
“Perceived” Investor
Cash Flows
Stock’s
Intrinsic Value
“Perceived”
Risk
Stock’s
Market Price
Market Equilibrium:
Intrinsic Value = Stock Price
9-4
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Different Approaches for Estimating the Intrinsic
Value of a Common Stock
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•
•
•
Discounted dividend model
Corporate valuation model
P/E multiple approach
EVA approach
9-5
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Discounted Dividend Model
•
Value of a stock is the present value of the future
dividends expected to be generated by the stock.
Pˆ0
D3
D1
D2
D
...
1
2
3
(1 rs ) (1 rs ) (1 rs )
(1 rs )
9-6
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Constant Growth Stock
•
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:
ˆP0 D0 (1 g) D1
rs g
rs g
9-7
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Future Dividends and Their Present Values
$
0.25
Dt D0 (1 g)t
PVDt
Dt
( 1 r )t
P0 PVDt
0
Years (t)
9-8
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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
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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
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Find the Expected Dividend Stream for the Next
3 Years and Their PVs
D0 = $2 and g is a constant 6%.
0
g = 6%
1
2
2.12
2.247
3
2.382
1.8761
1.7599
rs = 13%
1.6509
9-11
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What is the stock’s intrinsic value?
Using the constant growth model:
ˆP0 D1 $2.12
rs g 0.13 0.06
$2.12
0.07
$30.29
9-12
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What is the stock’s expected value, one year
from now?
•
D1 will have been paid out already. So, expected P1
is the present value (as of Year 1) of D2, D3, D4, etc.
ˆ1 D2 $ 2.247
P
rs g 0.13 0.06
$ 32.10
•
Could also find expected P1 as:
ˆ1 P0 (1.06) $32.10
P
9-13
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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
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What would the expected price today be,
if g = 0?
The dividend stream would be a perpetuity.
0
rs = 13%
1
2
3
2.00
2.00
2.00
ˆP0 PMT $2.00 $15.38
r
0.13
9-15
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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
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Valuing Common Stock with Nonconstant Growth
D0 = $2.00.
0 rs = 13%
g = 30%
1
2
g = 30%
2.600
2.301
2.647
3.045
46.114
ˆ0
54.107 = P
3
g = 30%
3.380
Pˆ3
4
g = 6%
4.394
4.658
4.658
$66.54
0.13 0.06
9-17
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Find Expected Dividend and Capital Gains Yields
During the First and Fourth Years
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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
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Nonconstant Growth: What if g = 0% for 3 years
before long-run growth of 6%?
D0 = $2.00.
0 r = 13%
s
g = 0%
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
2.12
1.77
1.57
1.39
20.99
ˆ0
25.72 = P
Pˆ3
2.12
$30.29
0.13 0.06
9-19
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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
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If the stock was expected to have negative growth (g = -6%),
would anyone buy the stock, and what is its value?
•
Yes. Even though the dividends are declining, the stock
is still producing cash flows and therefore has positive
value.
ˆP0 D1 D 0 (1 g)
rs g
rs g
$2.00(0.94) $1.88
$9.89
0.13 (-0.06) 0.19
9-21
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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
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Corporate Valuation Model
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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.
Depr.and Capital
FCF EBIT(1 T)
NOWC
amortization expenditures
9-23
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Applying the Corporate Valuation Model
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•
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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
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Issues Regarding the Corporate Valuation Model
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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
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Use the Corporate Valuation Model to Find the
Firm’s Intrinsic Value
Given: Long-Run gFCF = 6% and WACC = 10%
0
r = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
10
3
20
4
g = 6%
21.20
21.20
530
HV3
0.10 0.06
9-26
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What is the firm’s intrinsic value per share?
The firm has $40 million total in debt and
preferred stock and has 10 million shares of
common stock.
MV of equity MV of firm MV of debtandpreferred
$416.94 $40
$376.94 million
Valueper share MV of equity/#of shares
$376.94/10
$37.69
9-27
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Firm Multiples Method
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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
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EVA Approach
EVA = Equity capital(ROE – Cost of equity)
MVEquity = BVEquity + PV of all future EVAs
Value per share = MVEquity/# of shares
9-29
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Preferred Stock
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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
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If preferred stock with an annual dividend of $5 sells for
$50, what is the preferred stock’s expected return?
D
Vp
rp
$5
$50
rp
$5
$50
0.10 10%
rˆp
9-31
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