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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 = DPS
= 10
= 0.1
= 10%
VPS 100
VPS = DPS
= 10
= 100
kPS 0.1
Stocks
If require ROI = 12% = Kps
DPS = 10
VPS =
DPs = 10
= 83.3
kps 0.12
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 (%)
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 = ?
10%
PV = 100 n=1
FV = PV ( 1 + i )n
PV = FV
; ( 1 + i)n
Common Stock Valuation
Common Stock Valuation
N10%
INPUTS
I/YR FVPMTPV
OUTPUT
1 0-100
110
Common Stock Valuation
Example:
D1=10 P1 = 100
i=?%
PV = 100 1 yr
KS = 10 / 100 = 10%
Common Stock Valuation
N-100
INPUTS
I/YR FVPMTPV
OUTPUT
1 -10100
10%
Common Stock Valuation
Example:
D1=10 P1 = 100
KS = 10%
1 yr
P0= PV = ?
Common Stock Valuation
N100
INPUTS
I/YR FVPMTPV
OUTPUT
1 -1010%
100
Common Stock Valuation
P2
D1 D2
1 yr 2 yr
P0 = ?
P0 = D1
+ D2
+ P2
(1+k)1 (1+k)2 (1+k)2
Common Stock Valuation
P0
= D1 +
D2 + D3 +
+ Dn +
Pn
(1+k)1 (1+k)2 (1+k)3 (1+k)n (1+k)n
If n Example: Pn = 100/sh = FV,
n = 99
k = 15%
PV = ?
Common Stock Valuation
N-100
INPUTS
I/YR FVPMTPV
OUTPUT
99 015%
0.00009793
Common Stock Valuation
P0
= D1 +
D2 + D3 +
+ Dn +
Pn
(1+k)1 (1+k)2 (1+k)3 (1+k)n (1+k)n
If n Pn 0
(1+k)n
Therefore,
P0
= D1 +
D2 + D3 +
+ Dn
(1+k)1 (1+k)2 (1+k)3 (1+k)n
Common Stock Valuation
P0
= D1 +
D2 + D3 +
+ Dn
(1+k)1 (1+k)2 (1+k)3 (1+k)n
can be written as:
P0
= D0(1+g)1
+ D0(1+g)2
+ D0(1+g)3
(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+k)P0
=D0[1 +(1+g)1+(1+g)
2+ (1+g)
n-1 ](1+g) 1+k 1+k 1+k
(1+k)P0- P0= D0[1- (1+g)
n ]
1+g 1+k
Common Stock Valuation
If n and k > g,
(1+g)n
0
1+k
then, (1+k)P0 - P0= D0
1+g
P0[
1+k - 1] = D0
1+g
Common Stock Valuation
P0[
1+k-1-g ] = D0
1+g
P0[
k-g ] = D0
1+g
P0
= D0 (
1+g) =
D1 k-g 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?
P0 =
D1 = 10.5
= 80.77 = PV
k-g 0.18 - 0.05
Common Stock Valuation
If the stock is purchased at $90, K=?
90 = 10.5
P0 = D1 k-g
=
D1
k - 0.05 k-g P0
k =
D1 + g
P0
k = 17%
Dividend/Stock Price = Dividend Yield
Stock Markets and Stock ReportingI. Stock Markets
A. New York Stock Exchange (NYSE)
B. American Stock Exchange (AMEX)
C. Over-the-counter (OTC) markets
D. Smaller regional markets
II. Stock Market Reporting52 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
i=10%
PV = 100 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 P1
1 year
k%
Po
d1 P1
Po = (1+k)1 + (1+k)1
Appraisal Value of Stock
Common Stock Valuation
2 years: P2
D1 D2
1 k% 2
P0
P0 = D1
+ D2
+ P2
(1+k)1 (1+k)2 (1+k)2
Common Stock Valuation
P0
= D1 +
D2 + D3 +
+ Dn +
Pn
(1+k)1 (1+k)2 (1+k)3 (1+k)n (1+k)n
Make Assumptions:
1)If n Pn
(1+i)n 0
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 ValuationEquation :
(1+k)P0
=D0[1 +(1+g)1
+(1+g)2
+ (1+g)
n-1 ](1+g) 1+k 1+k 1+k
P0
= D0(1+g)1
+ D0(1+g)2
+ D0(1+g)3
(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)P0- P0= D0[1- (1+g)
n ]
1+g 1+k
Don’t Forget...
k = ROI (%) = Required Return on Investment
g = Dividend Growth
Common Stock Valuation
If n and k > g, then
(1+g)n
0
1+k
and, (1+k)P0 - P0= D0
1+g
P0[
1+k - 1] = D0
1+g
Common Stock Valuation
P0[
1+k-(1+g) ] = D0
1+g
P0[
k-g ] = D0
1+g
P0
= D0 (
1+g) =
D1 k-g 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 + (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 = KR - g = 0.1 - 0.05 = $105
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 ValuationKE = D1/ Po + g = Expected Return
(Po = Stock Price = $110)
Do (1+g) $5(1+0.05)
KE = + g = +0.05
Po $110
KE = 9.7% (Expected Return)
KR = 10% (Required Return)
Therefore, do not purchase
