Chapter 8 Stock Valuation
Overview
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Preferred Stock Characteristics and
Valuation
Common Stock Characteristics
Common Stock as a Financing Tool
Common Stock Valuation
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Dividend Discount Model
Preferred Stock Characteristics
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Unlike common stock, no ownership interest
Second to debt holders on claim on
company’s assets in the event of bankruptcy.
Annual dividend yield as a percentage of par
value
Preferred dividends must be paid before
common dividends
If cumulative preferred, all missed past
dividends must be paid before common
dividends can be paid.
Preferred Stock Valuation
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Promises to pay the same dividend year after
year forever, never matures.
A perpetuity.
Vps = D/kps
Example: GM preferred stock has a $25 par
value with a 8% dividend yield. What price
would you pay if your required return is 9%?
D = $25(0.08) = $2
Vps = $2/0.09 = $22.22
Expected Rate of
Return on Preferred

Just adjust the valuation model:
kps =
D
Po
Example

If we know the preferred stock
price is $40, and the preferred
dividend is $4.125, the expected
return is:
Example

kps
If we know the preferred stock
price is $40, and the preferred
dividend is $4.125, the expected
return is:
D
=
Po
4.125
=
=
40
Example

kps
If we know the preferred stock
price is $40, and the preferred
dividend is $4.125, the expected
return is:
D
=
Po
4.125
=
= .1031
40
The Financial Pages:
Preferred Stocks
52 weeks
Yld
Vol
Hi
Lo
Sym
Div % PE 100s
2788 2506 GM pfG 2.28 8.9 … 86

Close
25 53
Dividend: $2.28 on $25 par value
= 9.12% dividend rate.
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Expected return: 2.28 / 25.53 = 8.9%.
Facts about Common Stock:
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Claim on Income after interest and dividend
payments to creditors and preferred
stockholders.
Represents ownership.
Ownership implies control.
Limited liability.
Stockholders elect directors. = Voting Rights
Directors elect management.
Management’s goal: Maximize stock price.
Advantages of Financing with
Stock:
No required fixed payments.
 No maturity.
 Improves debt ratio, coverage.
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Disadvantages of Financing
with Stock:
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Controlling shareholders may lose some
ownership control.
 Preemptive Right
Future earnings shared with new
stockholders. Possible EPS Dilution.
Higher flotation costs vs. debt.
Higher component cost of capital.
Too little debt may encourage a takeover bid.
Common Stock Valuation
(Single Holding Period)
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You expect XYZ stock to pay a $5.50
dividend at the end of the year. The
stock price is expected to be $120 at
that time.
If you require a 15% rate of return,
what would you pay for the stock now?
Common Stock Valuation
(Single Holding Period)
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You expect XYZ stock to pay a $5.50
dividend at the end of the year. The
stock price is expected to be $120 at
that time.
If you require a 15% rate of return,
what would you pay for the stock now?
?
5.50 + 120
0
1
Common Stock Valuation
(Single Holding Period)
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Solution:
Vcs = (5.50/1.15) + (120/1.15)
= 4.783
+ 104.348
= $109.13
Common Stock Valuation
(Single Holding Period)
Financial Calculator solution:
P/Y =1, I = 15, n=1, FV= 125.50
CPT PV = -109.13
or:
P/Y =1, I = 15, n=1, FV= 120,
PMT = 5.50
CPT PV = -109.13
The Financial Pages:
Common Stocks
52 weeks
Hi Lo Sym
126 87 IBM
Div
.56
63 42 WalMart .28
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Yld
Vol
Net
% PE 100s Close Chg
0.6 23 77995 98.12 +0.29
0.5 47 119515 62.01 -0.24
IBMs Dividend Yield = $0.56/$98.12 = 0.6%
PE Ratio = Close Price/Earnings Per
Share(EPS)
IBMs Latest EPS = Close/PE = $98.12/23 =
$4.27
Stock Valuation
Multiple Holding Periods
Stock Value = PV of Future
Expected Dividends
D3
D1
D2
D
Vcs 


 ... 
1
2
3

1  kcs  1  kcs  1  kcs 
1  kcs 
Stock Valuation: Dividend
Patterns
For Valuation: we will assume stocks fall into
one of the following dividend growth
patterns.
 Constant growth rate in dividends
 Zero growth rate in dividends, like preferred
stock
 “Supernormal” (non-constant) growth rate in
dividends(see Chapter 8 notes in Syllabus
book)
Doh! Doughnuts Stock Valuation
Example: Basic Information
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We have found the following information for
Doh! Doughnuts:
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current dividend = $2,
beta of 0.9
T-bill (risk-free) rate = 1.75%
the market risk premium is 9.5%
Using the SML equation to find Doh!’s
required return = krf +(krp)b =
1.75% +(9.5%)0.9 = 10.3% = kcs
Analysts Estimates for Doh!
Doughnuts
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NEDFlanders predicts a constant annual growth rate in
dividends and earnings of zero percent (0%)
Barton Kruston Simpson predicts a constant annual
growth rate in dividends and earnings of 8 percent
(8%).
Moe Homer Simpson & Bernard expect a dramatic
growth phase of 20% annually for each of the next 3
years followed by a constant 8% growth rate in year 4
and beyond.
Our Task: Valuation Estimates
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What should be each analyst’s
estimated value of Doh! Doughnuts?
First Analyst: Zero Growth
Stock Valuation
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No growth in dividends, so Doh!
Doughnuts will remain at the current
dividend of $2 forever.
Estimated Value (Vcs)= PV(perpetuity) =
D0/kcs
Doh! Kcs = 10.3%
NEDFlanders Estimate P0 = $2/.103 =
$19.42
Constant Growth Stock
Valuation Model
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Dividends are expected to grow at an
annual constant rate, g, forever.
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D1 = D0(1+g)
Dt = D0(1+g)t
Vcs =
V
cs
=
D0(1+g) =
kcs – g
D0 (1 + g )
k
cs
-
g
D1
kcs – g
=
D
1
k
cs
-
g
Constant Growth Stock
Valuation Model Terms
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D0 = today’s (or current) dividend
D1 = expected dividend at the end of
this year(year 1)
kcs = stock’s required rate of return
g = the constant growth rate in
dividends
2nd Analyst: Constant Growth
in Dividends
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Current Dividend = $2
Projected Constant Growth Rate = 8% or
0.08
Kcs = 10.3%
What happens if g > kcs?
D1
Vcs 
requires kcs  g.
kcs  g
If kcs< g, get negative stock price, which is
nonsense.
 We can’t use model unless (1) kcs> g and (2)
g is expected to be constant forever.
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Doh! A good buy?
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Assume Doh! Doughnuts current stock price
is $100.
Required return = 1.75% + 9.5%(0.9) =
10.3%
Let’s assume the 2nd analyst is correct and
Doh! Has a constant growth rate of 8% and
its current dividend is $2.
What is the stock’s expected return?
Is Doh! Doughnuts’ current stock price in
equilibrium?
Expected Return of Constant
Growth Stocks
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Expected Rate of Return = Expected Dividend Yield +
Expected Capital Gains Yield
D1/P0 = D0(1+g)/P0 = Expected Dividend Yield
g = Expected Capital Gains Yield
From our example, D1=$2(1.08) = 2.16, P0=$100, g
= 8% or 0.08
D1
$2.16
k cs 
g 
 8%  2.16%  8%  10.16%
P0
$100
^
DOH! Doh! Doughnuts
Stock Market Equilibrium
The stock price when the stock’s
expected return = stock’s required
return (CAPM)
 D1/P0 + g = krf +(km - krf )b
Expected Return = Required Return
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The Effect On the Stock Price
Return
SML
1.75
0.9
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Beta
Expected Return needs to rise to the required return of
10.3%. This means the stock price must fall to the the
equilibrium price which yields the required return of
10.3%
New Price = D1/(kcs- g)=$2.16/(.103 - .08)= $93.91
At the current price of $100, Doh! has NPV of
$93.91 - $100 = -$6.09
“Supernormal” Growth Stock
Valuation
Framework: Assume Stock has period
of non-constant growth in dividends
and earnings and then eventually
settles into a normal constant growth
pattern(gc).
0 g1 1 g2 2 g3 3 gc 4 gc 5 gc…
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D1
D2
D3
“Supernormal” Growth Period
Constant Growth
Supernormal Growth Valuation
Process
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3 Step Process
Estimate Dividends during “supernormal”
growth period.
Estimate Price, which is the PV of the
constant growth dividends, at the end of
“supernormal” growth period which is also
the beginning of the constant growth period.
Find the PV of “supernormal” dividends and
constant growth price. The total of these PVs
= Today’s estimated stock value.
3rd Analyst:“Supernormal”
Growth Stock Valuation for Doh!
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“supernormal” growth rate g for years
1-3 = 20% or 0.2
After year 3, Doh! Has constant growth
rate gc = 8% or 0.08
D0 = $2.00
kcs = 10.3% or .103
Finally, the Answer!
0 g = 20% 1 g = 20% 2 g = 20% 3 gc = 8%
$2.40
$2.88
PV= P0
10.3%,1
2.17
10.3%,2
2.37
123.51
128.05 = $128.05 = P0
$3.46
Fin’l Calculator
$162.28 = P3 Solution:
$165.74
CF0=0,C01= 2.40
C02 = 2.88
10.3%,3
C03 = 165.74
I = 10.3
NPV=128.05 = P0
P0 = $2.40(PVIF10.3%,1)+$2.88(PVIF10.3%,2)+$3.46(PVIF10.3%,3)
+ $162.28(PVIF10.3%,3) = $128.05
Summary of Doh! Doughnuts
Stock Price Estimates
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NEDFlanders: 0% constant growth: P0 =
$19.42
Barton Kruston Simpson: 8% constant
growth: P0 = $93.91
Moe Homer Simpson & Bernard: 20%,
3-year supernormal growth followed by
8% constant growth: P0 = $128.05
Other Valuation Approaches
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Our dividend discount models are best for
established dividend paying companies, which
makes it difficult to apply to non-dividend
paying start-up companies.
PE Multiple Approach: Forecast a company’s
earnings per share and multiply this forecast
times the company’s PE ratio.
Value entire firm by finding PV of future
expected Free Cash Flows available to
stockholders, then divide by number of
shares. (Chapter 13)