Valuation Concept
Part II – Equity Valuation
Valuation of Financial Assets –
Equity (Stock)
• Types of Stock:
 Common Stock
 Preferred Stock
Common Stock and Bond Hybrid
Definition of Terms Used in the
Stock Valuation Models
A stock’s value is calculated in the same manner as
other financial assets; it is determined by the
expected cash flows generated.
For Equity issues, the expected cash flow consists of
two components:
 Dividend stream
 Future Value of the stock when the investor sells it,
which includes the original value (purchase price) plus
and capital gains or loss.
Definitions
Dividends
^
Dt
D0
^
D1
Dividend expected by the investor in
Year t.
Most recently paid dividend.
Next dividend to be paid.
^ - denotes expected value.
Definitions
Price
^
Pt
P0
P0
^
^
P^ 1
Expected stock price at the end of Year t.
Current market price.
The theoretical (intrinsic) value of the
stock as calculated by a particular
investor today.
The theoretical value expected at the end
of year one.
Definitions
Rates & Yields
g
k^s
^
D
P
1
0
^
P1  P 0
P0
Expected dividend growth rate. When
the dividend growth rate is constant, it
will equal the stocks prices growth rate.
Required rate of return given the
riskiness and available rates.
Expected dividend yield.
Expected capital gains yield on the stock
over the next year
Definitions
Rates & Yields
g
k^s
^
ks
_
ks
Expected dividend growth rate. When
the dividend growth rate is constant, it
will equal the stocks prices growth rate.
Required rate of return given the
riskiness and available rates.
Expected rate of return.
Actual (Realized) Rate of Return
^
ks 
^
D
P
1
0
^

P1  P 0
P0
›
CF1
CF2
CFn-1 CFn
1
2
n-1
n
›
›
n
›
n-1
›
2
›
1
›
› › › ›
Basic Valuation 0
Formula
›
Expected Dividends as the Basis
for Stock Values
D1
D2
Dn-1
Dn
PV of CF1
PV of CF2
PV of CFn-1
PV of CFn
Value
› › › ›
Stock Valuation 0
Formula
PV of D1
PV of D2
PV of Dn-1
PV of Dn
Stock Value
Expected Dividends as the Basis
for Stock Values
 1 
PV  FV 

n
 (1  k ) 
Present Value
Formula
Stock Value
^
^
Vs  P 0 
^
D1
1
(1  ks )



Dt
 
t
(
1

k
s
)
t 1
D2
 ... 
2
(1  ks )
^
D

(1  ks )
The value of a firm is determined by
the expected dividend payments over
the life of the firm.
Valuing Stocks with Zero Growth
• Zero-Growth Stocks are stocks where
dividends are not expected to grow (ie g=0)
• Zero-Growth stock is a perpetuity.

D
P0 
ks
Valuing Stocks with Constant
Growth
Constant (Normal) Growth is the rate of growth
which is expected to continue into the future at, or
near the same rate as the economy as a whole.
D 0(1  g )1
P0 

1
(1  ks )

D 0(1  g )

ks  g
Requires that ks is
greater than g
D (1 g )
(1 k )
0
2
 ... 
s


D (1 g )
(1 k )

2
D1
ks  g
0

s
Constant Growth
Model (or the
Gordon Model)
Valuing Stocks with Constant
Growth
Div
Growth
Earnings
Growth
Inflation
Div./Reinvest.
Return on Equity
Expected Returns of Constant
Growth Stocks
Given that:

P0
And that:
Results in:
Expected
Rate of
Return

=
ks 

D1

ks  g
Expected
Dividend
Yield

D1
P0
+
Expected growth
(or Capital Gains
Yield)

g
Nonconstant Growth Stocks
Dividend Growth Rate
Nonconstant Growth
Normal Growth
Zero Growth
Declining Growth
1.6
1.4
Dividend ($)
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
Year
4
5
Valuing Stocks with Nonconstant
Growth
Nonconstant growth is that portion of a firm’s life cycle
during which its growth rate is either faster or slower
than the economy as a whole.
Three Step Approach for Nonconstant Growth:
 Calculate the PV of the dividends during the
nonconstant growth period.
 Calculate the expected price at the beginning of the
constant growth period and discount to PV.
 Add PV from Step 1 to PV from Step 2 to calculate
the intrinsic value.
Examples
Zero-Growth Stock
What is the value of a stock which is expected to
pay dividends of $0.75 per share and has a
required rate of return of 15%?

P0
D0

ks
$0.75

 $5.00
.15
Examples
Zero-Growth Rate of Return
What is the expected growth rate of a stock paying
a $0.75 dividend and currently selling at $5.00?

ks
D

P0
$0.75

$5.00
 15%
Examples
Constant Growth Stock
What is the value of a stock that is expected to pay
dividends of $0.75 per share with an expected constant
growth rate of 6% and has a required rate of return of
15%?

P0
D 0(1  g )

ks  g
$0.75(1.06)

 $8.83
.15  .06
Examples
Constant Growth Rate of Return
What is the expected growth rate of a stock paying a $0.75
dividend that is expected to grow 6% and is currently
selling for $5.00?

ks

D1

g
P0
$0.75(1.06)

 .06  21.9%
$5.00
Additional Formulas

D1  D 0(1  g )
Capital Gains Yield g
=

Pnew  Pold
Pold
Examples
Nonconstant Growth Stock
What is the value of a stock that is expected to pay
dividends of $0.75 per share with an expected growth rate
of 20% for the next 3 years and then a constant growth rate
of 6%, and has a required rate of return of 15%?
k
Ns
gs
gn
D0
15%
3
20%
6%
$0.75
Examples
Nonconstant Growth Stock
STEP 1: Calculate the PV of the dividends during
nonconstant growth period.
Year
1
2
3
4
Ps=$2.4514
Div
$0.90
$1.08
$1.30
$1.37
PV
$0.78
$0.82
$0.85
Examples
Nonconstant Growth Stock
STEP 2: Calculate the Price of the stock at the beginning
of the constant growth period.

D4
P3 
ks gn

P3

1.37

15%  6%
P3  $15.2640
Examples
Nonconstant Growth Stock
STEP 3: Combine PV from Step 1 and Step 2.
Ps =$2.4514
P3 =$15.2640
P0 =$17.7154 = $17.72
Examples
Nonconstant Growth Stock
gs=6%
gs=20%
0
1
2
3
4
.75 .90 1.08 1.30 1.37
.78
.82
.85
2.45 + 15.26
17.71

Stock Market Equilibrium
Equilibrium, term used to describe the condition
during which the expected return is equal to the
required return and the price is stable.

k
 k

P0  P0
Stock Market Equilibrium
Required Rate of Return (k) can be
found along the Security Market
Line (SML).
k
 kRF
 (kM  kRF ) b
Where:
k
Required Rate of Return
kRF Risk Free Rate (as estimated by
LT US T-Bonds)
kM Rate of Return on Market
Portfolio
b Beta coefficient of stock
Security Market Line: Line which
illustrates the relationship between
risk (beta) and return rates for
individual securities.
Beta Coefficient:Measure which
shows the correlation between the
overall market and the stock being
evaluated.
Stock Market Equilibrium
k
 kRF
 (kM  kRF ) b
b
k
kRF
0
6%
kLow
kM
kHigh
0.5
1
2
10%
14%
22%
Efficient Market Hypothesis
Efficient Markets Hypothesis (EMH), hypothesis that
security prices reflect all available public
information, and are therefore fairly priced and in
equilibrium.
Levels of Market Efficiency:



Weak Form
Semistrong Form
Strong Form
Efficient Market Hypothesis
Weak Form
The weak form level of efficiency dictates that
current market prices reflect all information in
past price movements.
Recent price shifts do not provide near term
predictability.
Efficient Market Hypothesis
Semistrong Form
The semistrong form level of efficiency perscribes
that all publicly available information is reflected
in current market prices.
Efficient Market Hypothesis
Strong Form
The strong form level of efficiency dictates that all
pertinent information (public and private) is
reflected in current market prices.