Stocks (Equity)
Characteristics and Valuation
What is equity?
What factors affect stock prices?
How are stock prices determined?
How are stock returns determined?
What techniques do investors use to value
stocks?
1
Basic Types of Stock
Preferred stock: hybrid
Common stock
2
Preferred Stock Features
Par value
 The nominal or face value of a stock or bond
Dividends
 Generally fixed, like debt; based on the par value
Cumulative dividends
 Preferred dividends not paid in previous periods must be
paid before common dividends can be paid
Maturity
 No specific maturity date
Priority to assets and earnings
 Preferred stockholders are paid before common stockholders
3
Preferred Stock Features
Control of the Firm (Voting Rights)
 Most preferred stock is nonvoting, unless dividends are not
paid for a particular number of periods
Convertibility
 Can be converted to common stock
Call provision
 Firm has the right to call in preferred stock for redemption
Sinking fund
 A fund used to retire a given amount of the stock each year
Participating
 Shares earnings with common stockholders
4
Common Stock Features
Par value
 Stockholders’ minimum financial obligation
Dividends
 No legal obligation to pay dividends
Maturity
 No specific maturity date
Priority to assets and earnings
 Receive distributions last
Preemptive right
 Right to buy new issues
Control of the firm
 Vote on board of directors, stockholder proposals, etc.
5
Types of Common Stock
Classified Stock
 Special designations, such as Class A, Class B,
etc., used to meet special needs of the company
Founder’s Shares
 Classified stock
 A class of stock owned by the firm’s founders who
have sole voting rights for a particular time period
6
Equity Instruments in International
Markets
American Depository Receipts
 Certificates that represent ownership in stocks of
foreign companies
Foreign Equity
 Yankee stock—issued by foreign firm and traded
in the United States
 Euro stock—traded outside of “home” country,
excluding the United States
7
Stock Valuation
Stock value = Present value of the dividends
that the company is expected to pay during
its life.
If the stock never pays a dividend—whether
a regular dividend or a liquidating
dividend—then its value is $0.
8
Stock Valuation—Terms
D̂ t = dividend expected in Period t, such that
D̂ 1 = the dividend expected in Period 1
D0 = the most recently paid dividend
P̂t = stock price expected in Period t, such that
P̂1 = the price expected in Period 1
P0 = current market price
g = growth rate
rs = the rate of return investors require to
purchase the firm’s common stock
^ (hat) = an expected value—that is, a value that is
forecasted to occur in the future.
9
Stock Valuation
Stock ownership entitles the investor to the future cash
flows, called dividends, that are paid by the firm
0
PV of Dˆ 1
PV of Dˆ 2
PV of Dˆ 3
..
.
PV of Dˆ 

1
2
3
D̂ 1
D̂ 2
D̂ 3
…
∞
D̂ 
ˆ  Stock Value  Pˆ
PV of D
t
0
10
Stock Valuation
Stock value  Vs  Pˆ 0  PV of expected future dividends
Pˆ0 

Dˆ 1
1
(1  rs )


Dˆ 2
(1  rs )
2
 
Dˆ 
(1  rs ) 
Dˆ t
 (1  r ) t
t 1
s
rs = required return on stock
11
Stock Valuation
Constant Growth, g
If growth is constant such that g = g1 = g2 = … = g∞
Dˆ 1  D 0 (1  g)1
Pˆ0 
D0 (1  g)1
1
(1  rs )
D0 (1  g)1

rs - g

Dˆ 2  D 0 (1  g) 2
…
D0 (1  g)2
D0 (1  g) 
(1  rs )
Dˆ 1

rs - g
2

Dˆ   D 0 (1  g) 
(1  rs )




t 1
D0 (1  g) t
(1  rs ) t
Value of a constantgrowth stock
Required: g = constant
rs > g
12
Stock Valuation—Constant Growth, g
The most recent dividend paid (D0) by a firm was $2; the firm
is expected to grow at a constant rate (g) equal to 4 percent;
and the required rate of return (rs) on similar risk investments
is 12 percent.
1
1
$2.08
$2(1.04)
D
(1

g)
ˆP  0

 $26.00

0
0.08
0.12 - 0.04
rs - g
13
Stock Valuation—Constant Growth, g
D0 = $2; g = 4%; rs = 12%
Year
Dividend, D̂ t
D̂ t = $2.00(1.04)t
PV of D̂ t @ 12%
1
$2.0800
= $2.00(1.04)1
$1.8571
2
2.1632
= 2.00(1.04)2
1.7245
3
2.2497
= 2.00(1.04)3
1.6013
5
2.4333
= 2.00(1.04)5
1.3807
10
2.9605
= 2.00(1.04)10
0.9532
50
14.2134
= 2.00(1.04)50
0.0492
100
101.0099
= 2.00(1.04)100
0.0012
100

Dˆ t  25.9831  26.00
t 1
14
Stock Valuation—Constant Growth, g=0
Pˆ 0 
ˆ
D
1
(1 rs )
1
g=0
Pˆ 0 

ˆ
D
2
(1 rs )
2

ˆ
D

(1 rs )
ˆ D
ˆ D
ˆ D
D
1
2

D
D
D
D


 
1
2
(1  r s )
(1  rs )
(1  r s )
rs
15
Stock Valuation—Constant Growth, g=0
The preferred stock of a company pays a constant dollar
dividend equal to $4 per share. The required rate of return
on similar risk investments is 8 percent.
ˆP  D  $4  $50
0
rs
0.08
Relationship between value and rs
Required Return, rs
Stock Value
5.0%
$80.00
8.0
50.00
12.0
33.33
16
Stock Valuation—Nonconstant Growth
Pˆ0 

Dˆ 1

1
(1  rs )
D0 (1  g1 )
1
(1  rs )
Dˆ 2
(1  rs )

2

Dˆ 1 (1  g2 )
2
(1  rs )
ˆ (1  g
ˆ
D
)
D
N
norm
N1
PˆN 

rs - gnorm
rs - gnorm
Dˆ 
(1  rs ) 

Dˆ N11(1
(1 ggN)) PˆN
N
(1(1
 rs )r
)
s
gnorm = constant, or
normal, growth
17
Stock Valuation with Nonconstant
Growth—Example
D0
g1
g2
g3
g4
g5
=
=
=
=
=
=
$1.25
25%
20%
10%
-4%
5% = g6 = … = g∞
rs = 14%
18
Stock Valuation with Nonconstant
Growth—Example
D0 = $1.25; rs = 14%
Growth
Year rate, g Dividend, D̂ t
1
25%
2
Dˆ t  Dˆ t -1 (1  g t )
PV of D̂ t @ 14%
$1.5625
= $1.2500(1.25)
$1.3706
20
1.8750
= 1.5625(1.20)
3
10
2.0625
= 1.8750(1.10)
1.4428
1.3921
4
-4
1.9800
= 2.0625(0.96)
1.1723
S = 5.3778
19
Stock Valuation with Nonconstant
Growth—Example
Because the dividends grow at a constant rate after Year
4, we can apply the constant growth model such that:
ˆ
ˆ (1  g )
D
D
5
n
Pˆ4 
 4
rs - gn
rs - gn
$1.98(1.05) $2.0790


 $23.10
0.14 - 0.05
0.09
20
Valuation—Cash Flow Time Line
0
1
2
3
1.5625
1.8750
2.0625
14%
4
1.9800  D̂ t
5.3778
13.6771
19.0549
23.10
 P̂4
Pˆ 0  $19.05
21
Stock Valuation—Nonconstant Growth
The key to computing the value of a stock that exhibits
nonconstant growth is to assume constant growth occurs
at some point in the future—it might start in five years, 50
years, or 100 years:
 Apply the constant growth model to compute the value of the
expected dividends from that point forward.
 Compute the present value of the stock’s value at the point where
you assume constant growth begins.
Prior to the point where constant growth begins:
 Compute the dividend for each year
 Find the present value of each dividend
Sum the PV results.
22
Stock Return
r̂ s

Expected rate
=
of return
D̂1
P0
Expected
dividend
yield

g
+
Expected growth
rate (capital
gains yield)
23
Stock Return
P0 = $30.00; D0 = $1.50; g = 6.0%
ˆ
D
(1

g)
D
1
Pˆ0  0

rs - g
rs - g
ˆ
$1.50(1.06)
D
ˆrs  1  g 
 0.06
$30
Pˆ0
$1.59

 0.06  0.053  0.06  11.3%
$30
24
Stock Return
In one year, the price of the stock is expected to be:
Pˆ1 
Dˆ 2
1
(1  rs )

Dˆ 3
(1  rs )
2

Dˆ 
(1  rs ) -1
Dˆ 2

rs - g
$1.59(1.06) $1.6854


 $31.80
0.113 - 0.06
0.053
25
Stock Return
Because the value of the stock is expected to increase from
$30.00 to $31.80 during the year,
Ending value - Beginning value Pˆ1  P0


g
gains yield
Beginning value
P0
$31.80  $30.00

 0.06  6.0%
$30.00
^r = 11.3%
s
Dividend Dˆ 1
$1.59

 0.053  5.3%

$30.00
yield
P0
Capital
26
Valuation Using P/E Ratios
P/E ratio = Price ÷ EPS = price multiple
“Normal” P/E
Example: A firm’s P/E is normally 8.0x. If its
EPS = $7, then the value of its stock should
be $56 = $7 x 8
27
Valuation Using EVA
Economic Value Added = EVA
Earnings must be sufficient to pay those who
provide funds to the firm; otherwise the value of the
firm should decrease.
After  tax

  Cost of 
  

EVA  
 operating income   funds 
 EBIT(1  Tax rate)  (Dollar cost of funds)
28
Stocks (Equity)
Characteristics and Valuation
What is equity?
 Stock/ownership.
What factors affect stock prices?
 Investors change their expectations about the returns the
firm will generate in the future.
How are stock prices determined?
 The price is equal to the present value of the dividends
stockholders expect to receive during the company’s life.
29
Stocks (Equity)
Characteristics and Valuation
How are stock returns determined?
 Returns are based on the dividend the company
pays and the change in the market value of the
stock during the year
What techniques do investors use to value
stocks?
 P/E Ratio
 Economic Value Added (EVA)
30