Preferred Stock Valuation
• No ownership as with common stock
• Give higher return than bonds (debt)
VPS :Value of Preferred Stock, $100/sh
DPS : Preferred Stock Dividend, $10/sh
KPS : Return On Investment or
Required Return of Preferred
Stock investors, eg. 10%
(Risk Free Return + Risk)
Stocks
Calculation:
ROI = KPS =
VPS =
DPS
kPS
=
DPS
VPS
10
0.1
=
10
100
= 100
= 0.1 = 10%
Stocks
If require ROI = 12% = Kps
DPS = 10
VPS =
DPs
kps
=
10
0.12
= 83.3
Common Stock Valuation
Pt = Stock price at time t
Dt = Dividend at time t
D0 = Dividend at time t = 0 (just paid)
D1 = Dividend at time t = 1 (1 year
from today)
KS = Return on Investment on Common
Stock
Common Stock Valuation
D1 = D0 ( 1 + g )1
D2 = D0 ( 1 + g )2
where g : expected annual growth (or
increase) in dividend (%)
Common Stock Valuation
Example:
Find Dividend (given g = 5%)
D0 = $10
D1 = 10.5 = 10 (1 + 0.05)1 = D0 (1+g)t
D2 = 11.03 = 10 (1 + 0.05)2 or
10.5 (1 + 0.05)1
Common Stock Valuation
Example:
FV = ?
PV = 100
FV = PV ( 1 + i )
10%
n=1
n
;
PV =
FV
( 1 + i)n
Common Stock Valuation
INPUTS
1
10%
-100
0
N I/YR PV PMT FV
OUTPUT
110
Common Stock Valuation
Example:
D1=10
i=?%
PV = 100
1 yr
KS = 10 / 100 = 10%
P1 = 100
Common Stock Valuation
INPUTS
1
100
-10
-100
N I/YR PV PMT FV
OUTPUT
10%
Common Stock Valuation
Example:
D1=10
KS = 10%
1 yr
P0= PV = ?
P1 = 100
Common Stock Valuation
INPUTS
1
10%
-10
100
N I/YR PV PMT FV
OUTPUT
100
Common Stock Valuation
P2
D1
1 yr
D2
2 yr
P0 = ?
D1
D2
P2
P0 =
+
+
1
2
(1+k) (1+k)
(1+k)2
Common Stock Valuation
D1
D2
D3
P0 =
+
+
+
(1+k)1 (1+k)2 (1+k)3
Dn
Pn
+
+
(1+k)n (1+k)n
If n

Example: Pn = 100/sh = FV,
n = 99
k = 15%
PV = ?
Common Stock Valuation
INPUTS
99
15%
0
-100
N I/YR PV PMT FV
OUTPUT
0.00009793
Common Stock Valuation
D1
D2
D3
P0 =
+
+
+
(1+k)1 (1+k)2 (1+k)3
If n
, Pn
(1+k)n
Therefore,
D1
D2
D3
P0 =
+
+
+
(1+k)1 (1+k)2 (1+k)3
Dn
Pn
+
+
(1+k)n (1+k)n
0
Dn
+
(1+k)n
Common Stock Valuation
D1
D2
D3
Dn
P0 =
+
+
+ +
(1+k)1 (1+k)2 (1+k)3
(1+k)n
can be written as:
D0(1+g)1 D0(1+g)2
D0(1+g)3
P0 =
+
+
(1+k)1
(1+k)2
(1+k)3
D0(1+g)n
+
+
(1+k)n
Common Stock Valuation
P0 = D0 [
(1+g)1 + (1+g)2+ (1+g)3+ (1+g)n
(1+k)1
(1+k)2 (1+k)3 (1+k)
]
n
1 1+g 2
n-1
1+g
1+g
P0=D0[1 +(
) +( ) + ( ) ]
1+k
1+k
1+k
(1+g)
(1+k)
1+k
(
1+g
1+g
)P0- P0= D0[1- (
n
) ]
1+k
Common Stock Valuation
, and k > g,
If n
1+g n
( )
1+k
0
then, 1+k
( )P0 - P0= D0
1+g
1+k
P0[
- 1] = D0
1+g
Common Stock Valuation
P0[
1+k-1-g
] = D0
1+g
k-g =
P0[
] D0
1+g
P0
1+g
D
(
)
0
=
k-g
=
D1
k-g
Common Stock Valuation
Example:
g = 5%,
D0 = 10
D1 = 10.5 (10 x 1.05)
ks = 18%
What is the value of the stock?
D1
10.5
P0 =
=
= 80.77 = PV
k-g
0.18 - 0.05
Common Stock Valuation
If the stock is purchased at $90, K=?
10.5
D1
D1
90 =
P0 =
k-g =
k-g
P0
k - 0.05
D1
k=
+g
P0
k = 17%
Dividend/Stock Price = Dividend Yield
I. Stock Markets Stock Markets and Stock Reporting
A. New York Stock Exchange (NYSE)
B. American Stock Exchange (AMEX)
C. Over-the-counter (OTC) markets
D. Smaller regional markets
II. Stock Market Reporting
52 Weeks
Yld. P-E Sales
Net
High Low Stock Div. % Ratio 100s High Low Close Chg.
1757/8 102 IBM 4.40 3.8 16 27989 1181/4 1151/4 1171/4 +13/4
Dividend yield = D/P
= $4.40 / $117.25 = 3.8%
Common Stock Valuation
FV = 110
PV = 100
i=10%
n=1yr
FV = PV ( 1 + i )
n
Common Stock Valuation
PV(1+i)n = FV
100 (1+0.1) = 110
100 (1+0.1)2 = 121
100 (1+0.1)3 = 133
FV
PV = (1+i)n
Value of Stock
Common Stock Valuation
•
•
•
•
Discounted Valuation Approach
Know FV
Calculate PV (price you have to pay
now) or (value of stock or bond)
Bond debt - interest
Stock - dividend
Common Stock Valuation
Own stock one year:
d1
1 year
k%
Po
d1
Po =
(1+k)1
P1
+ (1+k)1
P1
Common Stock Valuation
2 years:
P2
D1
1
k%
D2
2
P0
D1
D2
P2
P0 =
+
+
1
2
(1+k) (1+k)
(1+k)2
Common Stock Valuation
D1
D2
D3
Dn
Pn
P0 =
+1
+2
+3 +
+
(1+k) (1+k) (1+k)
(1+k)n (1+k)n
Make Assumptions:
1)If n

Pn
0
n
(1+i)
2)If D1 = Do(1+g)1 Assume dividend
D2 = Do(1+g)2 rate increases at
Dn = Do(1+g)n g rate.
Common Stock Valuation
Example:
Do = $10
g = 5%
D1 =10 (1+0.05)
D1 = $10.5
Common Stock Valuation
Equation :
1 1+g 2
n-1
1+g
1+g
P0=D0[1 +(
) +( ) + ( ) ]
1+k
1+k
1+k
(1+g)
(1+k)
D0(1+g)1 D0(1+g)2
D0(1+g)3
P0 =
+
+
(1+k)1
(1+k)2
(1+k)3
D0(1+g)n
+
+
(1+k)n
Common Stock Valuation
Equation :
P0 = D0 [
(1+g)1 + (1+g)2+ (1+g)3+ (1+g)n
(1+k)1
(1+k)2 (1+k)3 (1+k)n
Equation :
1+k
(
1+g
)P0- P0= D0[1- (
1+g
n
) ]
1+k
]
Don’t Forget...
k = ROI (%) = Required Return on Investment
g = Dividend Growth
Common Stock Valuation
, and k > g, then
If n
1+g n
( )
1+k
0
and, 1+k
( )P0 - P0= D0
1+g
1+k
P0[
- 1] = D0
1+g
Common Stock Valuation
P0[
1+k-(1+g)
] = D0
1+g
k-g =
P0[
] D0
1+g
P0
1+g
D
(
)
0
=
k-g
=
D1
k-g
Common Stock Valuation
P0 =
D1
k-g
Only when n --  AND k>g
Gordon Model or
Constant Dividend Growth Model
k-g = D1/ Po
k = D1/ Po + g
Just a Reminder...
KR = risk free + risk premium
=
Rf
+ b (Rm - Rf)
market return
*use S&P 500
risk-free
index
*use T-Bill
Volatility
Rm - Rf = Market Risk Premium
Common Stock Valuation
Example:
Do=Paid Dividend=$5/share
g=Dividend Growth=5%
KR=Required Return=10%
pay for stock now
Do(1+g) $5(1+0.05)
Po = K - g = 0.1 - 0.05 = $105
R
Common Stock Valuation
Value of Stock = $105 (appraisal value)
Stock Price = $110
*Don’t buy the stock because the stock
is over valued. (too expensive)
Common Stock Valuation
KE = D1/ Po + g = Expected Return
(Po = Stock Price = $110)
KE =
Do (1+g)
+g =
$5(1+0.05)
Po
KE = 9.7% (Expected Return)
KR = 10% (Required Return)
Therefore, do not purchase
$110
+0.05