Valuing Common Stocks
Dividend Discount Model - Computation of today’s stock
price which states that share value equals the present
value of all expected future dividends.
1
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Dividend Discount Model - Computation of today’s stock
price which states that share value equals the present
value of all expected future dividends.
Div1
Div2
Div H  PH
P0 

...
1
2
H
(1  r ) (1  r )
(1  r )
H - Time horizon for your investment.
2
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay dividends
of $3, $3.24, and $3.50 over the next three years,
respectively. At the end of three years you anticipate
selling your stock at a market price of $94.48. What is the
price of the stock given a 12% expected return?
3
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and
$3.50 over the next three years, respectively. At the end of three years
you anticipate selling your stock at a market price of $94.48. What is the
price of the stock given a 12% expected return?
3.00
3.24
350
.  94.48
PV 


1
2
3
(1.12) (1.12)
(1.12)
PV  $75.00
4
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
If we forecast no growth, and plan to hold out stock
indefinitely, we will then value the stock as a
PERPETUITY.
5
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
If we forecast no growth, and plan to hold out stock
indefinitely, we will then value the stock as a
PERPETUITY.
Div1
EPS1
Perpetuity  P0 
or
r
r
Assumes all earnings are
paid to shareholders.
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Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Constant Growth DDM - A version of the dividend growth
model in which dividends grow at a constant rate
(Gordon Growth Model).
7
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example- continued
If the same stock is selling for $100 in the stock market,
what might the market be assuming about the growth in
dividends?
$3.00
$100 
.12  g
g .09
Answer
The market is
assuming the dividend
will grow at 9% per
year, indefinitely.
8
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
 If a firm elects to pay a lower dividend, and reinvest the
funds, the stock price may increase because future
dividends may be higher.
Payout Ratio - Fraction of earnings paid out as dividends
Plowback Ratio - Fraction of earnings retained by the firm.
9
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Growth can be derived from applying the
return on equity to the percentage of earnings
plowed back into operations.
g = return on equity X plowback ratio
10
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example
Our company forecasts to pay a $5.00
dividend next year, which represents 100%
of its earnings. This will provide investors
with a 12% expected return. Instead, we
decide to plow back 40% of the earnings at
the firm’s current return on equity of 20%.
What is the value of the stock before and
after the plowback decision?
11
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example
Our company forecasts to pay a $5.00 dividend next year, which
represents 100% of its earnings. This will provide investors with a 12%
expected return. Instead, we decide to blow back 40% of the earnings at
the firm’s current return on equity of 20%. What is the value of the stock
before and after the plowback decision?
No Growth
With Growth
5
P0 
 $41.67
.12
12
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example
Our company forecasts to pay a $5.00 dividend next year, which
represents 100% of its earnings. This will provide investors with a 12%
expected return. Instead, we decide to blow back 40% of the earnings at
the firm’s current return on equity of 20%. What is the value of the stock
before and after the plowback decision?
No Growth
5
P0 
 $41.67
.12
With Growth
g .20.40 .08
3
P0 
 $75.00
.12 .08
13
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Example - continued
If the company did not plowback some earnings, the stock
price would remain at $41.67. With the plowback, the
price rose to $75.00.
The difference between these two numbers (75.0041.67=33.33) is called the Present Value of Growth
Opportunities (PVGO).
14
Copyright 1996 by The McGraw-Hill Companies, Inc
Valuing Common Stocks
Present Value of Growth Opportunities (PVGO) Net present value of a firm’s future
investments.
Sustainable Growth Rate - Steady rate at which a
firm can grow: plowback ratio X return on
equity.
15
Copyright 1996 by The McGraw-Hill Companies, Inc
FCF and PV
 Free Cash Flows (FCF) should be the theoretical
basis for all PV calculations.
 FCF is a more accurate measurement of PV than
either Div or EPS.
 The market price does not always reflect the PV
of FCF.
 When valuing a business for purchase, always
use FCF.
16
Copyright 1996 by The McGraw-Hill Companies, Inc
FCF and PV
Valuing a Business
The value of a business is usually computed as the discounted
value of FCF out to a valuation horizon (H).
 The valuation horizon is sometimes called the terminal value and
is calculated like PVGO.
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
H
(1  r ) (1  r )
(1  r )
(1  r )
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Copyright 1996 by The McGraw-Hill Companies, Inc
FCF and PV
Valuing a Business
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
H
(1  r ) (1  r )
(1  r )
(1  r )
PV (free cash flows)
PV (horizon value)
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Copyright 1996 by The McGraw-Hill Companies, Inc
FCF and PV
Example
Given the cash flows for Concatenator Manufacturing Division,
calculate the PV of near term cash flows, PV (horizon value), and
the total value of the firm. r=10% and g= 6%
Year
1
Asset Value
2
3
4
5
6
10.00 12.00 14.40 17.28 20.74 23.43
7
8
9
10
26.47 28.05 29.73 31.51
Earnings
1.20
1.44
1.73
2.07
2.49
2.81
3.18
3.36
3.57
3.78
Investment
2.00
2.40
2.88
3.46
2.69
3.04
1.59
1.68
1.78
1.89
Free Cash Flow
- .80
- .96 - 1.15 - 1.39
- .20
- .23
1.59
1.68
1.79
1.89
6
6
6
.EPSgrowth (%) 20
20
20
20
20
13
13
19
Copyright 1996 by The McGraw-Hill Companies, Inc
FCF and PV
Example - continued
Given the cash flows for Concatenator Manufacturing Division,
calculate the PV of near term cash flows, PV (horizon value), and the
total value of the firm. r=10% and g= 6%
.
1  1.59 
PV(horizonvalue) 
  22.4
6 
1.1  .10  .06 
.80 .96
1.15 1.39
.20
.23
PV(FCF)  




2
3
4
5
1.1 1.1 1.1 1.1 1.1 1.16
 3.6
20
Copyright 1996 by The McGraw-Hill Companies, Inc
FCF and PV
Example - continued
Given the cash flows for Concatenator Manufacturing Division,
calculate the PV of near term cash flows, PV (horizon value), and the
total value of the firm. r=10% and g= 6%
.
PV(busines s)  PV(FCF)  PV(horizon value)
 -3.6  22.4
 $18.8
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Copyright 1996 by The McGraw-Hill Companies, Inc
WHAT DETERMINES THE REQUIRED RATE
OF RETURN ON AN INVESTMENT?
REQUIRED RETURN DEPENDS ON THE RISK
OF THE INVESTMENT
– GREATER THE RISK, GREATER THE RETURN
WHAT KIND OF RISK RESULTS IN A HIGHER RETURN?
LOOK AT THE HISTORY OF CAPITAL MARKETS.
– RETURNS FROM NONFINANCIAL INVESTMENTS
HAVE TO BE COMPARABLE WITH RETURNS FROM
FINANCIAL INVESTMENTS OF SIMILAR RISK
22
Copyright 1996 by The McGraw-Hill Companies, Inc
IBBOTSON ASSOCIATES
COMMON STOCKS
S&P500
SMALL STOCKS
SMALLEST 20% NYSE STOCKS
LONG-TERM CORPORATE BONDS
HIGH QUALITY
20-YEAR CURRENT MATURITY
LONG-TERM TREASURY BONDS
20-YEAR CURRENT MATURITY
US TREASURY BILLS
CURRENT MATURITY < 1 YEAR
23
Copyright 1996 by The McGraw-Hill Companies, Inc
VALUE AT END OF 1994
OF $1 INVESTMENT AT THE BEGINNING OF 1926
NOMINAL
REAL
SMALL CAP
$2,843
$340
S&P500
$811
$97
CORPORATE BONDS
$38
$4.5
TREASURY BONDS
$26
$3.1
T-BILLS
$12
$1.5
INFLATION
$7
– $7 AT THE END OF 1994 HAD THE SAME
PURCHASING POWER AS $1 AT THE
BEGINNING OF 1926
24
Copyright 1996 by The McGraw-Hill Companies, Inc
RISKS OF DIFFERENT ASSET CLASSES
SECURITY
RISK
TREASURY BILLS
NO RISK IN NOMINAL RETURN
BUT UNCERTAIN REAL RETURN
TREASURY BONDS
AND INTEREST RATE RISK
CORPORATE BONDS
AND DEFAULT RISK
AND EVENT RISK
COMMON STOCKS
AND MARKET RISK
AND UNSYSTEMATIC RISK
25
Copyright 1996 by The McGraw-Hill Companies, Inc
AVERAGE RETURNS AND STANDARD DEVIATIONS
1926 - 1994
Average
nominal
return
Portfolio
Treasury bills
bonds 5.2
5.7
2.7
2.1
8.9
8.4
13.9
Average Average
real
risk
return premium
3.7%
0.6%
1.4
2.0
0 % Government
Corporate bonds
Common stocks
12.2
Small-firm stocks
17.4
13.7
Source: Stocks, Bonds, Bills, and Inflation: 1995
Yearbook, Ibbotson Associates, Chicago, 1995
26
Copyright 1996 by The McGraw-Hill Companies, Inc
THE U.S. STOCK MARKET HAS BEEN A
PROFITABLE BUT VARIABLE INVESTMENT
Source: Ibbotson Associates (1989)
60
50
R
e
t
u
r
n
%
40
30
20
10
0
-10
-20
-30
-40
-50
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80 83 86
Year
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Copyright 1996 by The McGraw-Hill Companies, Inc
ANNUAL MARKET RETURNS IN THE US
1926 - 1994
SOURCE: IBBOTSON ASSOCIATES (1989)
14
13
12
N
u
m
b
e
r
o
f
11
10
y
e
a
r
s
9
8
9
8
6
4
4
2
3
2
1
2
1
0
-50
-40
-30
-20
-10
10
0
Return, percent
20
30
40
50
60
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Copyright 1996 by The McGraw-Hill Companies, Inc
STATISTICAL MEASURES OF SPREAD
VARIANCE, s2 = E(r - r)2
-UNITS ARE (RETURN)2
STANDARD DEVIATION,
s = VARIANCE(r)
-UNITS ARE RETURN
29
Copyright 1996 by The McGraw-Hill Companies, Inc
CALCULATING VARIANCE AND
STANDARD DEVIATION OF MERCK RETURNS
FROM PAST MONTHLY DATA
Month
Return
1
2
3
4
5
6
5.4%
1.7
- 3.6
13.6
- 3.5
3.2
Total
16.8
Mean:
Variance:
Standard deviation:
Annualized standard deviation
Deviation
from mean
return
2.6%
- 1.1
- 6.4
10.8
- 6.3
0.4
Squared
deviation
6.8
1.2
41.0
116.6
39.7
0.2
205.4
16.8/6 = 2.8%
205.4/6 = 34.2
 34.2 = 5.9% per month
5.9 x  (12) = 20.3%
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Copyright 1996 by The McGraw-Hill Companies, Inc
AVERAGE RETURNS AND STANDARD DEVIATIONS
1926 - 1994
Average
nominal
Portfolio
return
Treasury bills
3.7%
Government bonds 5.2
Corporate bonds
5.7
Common stocks
12.2
Small-firm stocks
17.4
Average Average Standard
real
risk
deviation
return premium of returns
0.6%
0%
3.3%
2.1
1.4
8.7
2.7
2.0
8.3
8.9
8.4
20.2
13.9
13.7
34.3
Source: Stocks, Bonds, Bills, and Inflation: 1995
Yearbook, Ibbotson Associates, Chicago, 1995
31
Copyright 1996 by The McGraw-Hill Companies, Inc
VARIABILITY IN STOCK MARKET RETURNS
BRIEF PERIODS OF EXTREMELY HIGH VOLATILITY
OCTOBER 19, 1987, MARKET FELL 23% IN ONE DAY
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Copyright 1996 by The McGraw-Hill Companies, Inc
VARIABILITY IN RETURNS OF
INDIVIDUAL STOCKS
CALCULATED OVER RECENT FIVE-YEAR PERIOD
– FIRM FACES CHANGING BUSINESS RISKS OVER 70-YEAR PERIOD
– CALCULATE MONTHLY VARIANCE AND MULTIPLY BY TWELVE,
ASSUMING SUCCESSIVE MONTHLY RETURNS ARE INDEPENDENT
– STANDARD DEVIATION INCREASES WITH THE SQUARE ROOT OF
THE LENGTH OF TIME OVER WHICH IT IS BEING MEASURED
MOST STOCKS MORE VARIABLE THAN MARKET
DIVERSIFICATION REDUCES VARIABILITY
– CHANGES IN THE PRICE OF DIFFERENT STOCKS ARE NOT
PERFECTLY CORRELATED
– TEND TO OFFSET EACH OTHER
33
Copyright 1996 by The McGraw-Hill Companies, Inc
DIVERSIFICATION ELIMINATES UNIQUE RISK
Portfolio
standard
deviation
UNIQUE RISK
MARKET RISK
5
10
Number of
securities
34
Copyright 1996 by The McGraw-Hill Companies, Inc
INDIVIDUAL STOCKS
HAVE TWO KINDS OF RISK:
MARKET RISK
– OR SYSTEMATIC RISK OR UNDIVERSIFIABLE RISK
– AFFECTS ALL STOCKS
UNIQUE RISK
– OR UNSYSTEMATIC RISK OR DIVERSIFIABLE RISK
OR SPECIFIC RISK OR RESIDUAL RISK
– AFFECTS INDIVIDUAL STOCKS OR SMALL
GROUPS OF STOCKS
– UNIQUE RISK OF DIFFERENT FIRMS UNRELATED
– ELIMINATED BY DIVERSIFICATION
35
Copyright 1996 by The McGraw-Hill Companies, Inc
UNIQUE OR UNSYSTEMATIC RISK
A DRUG TRIAL SHOWING THAT BETA BLOCKERS
INCREASE RISK OF CANCER IN OLDER PEOPLE WILL
AFFECT PFIZER’S STOCK
– BUT HAS NO AFFECT ON SHARES OF GM OR IBM
A STRIKE AT A SINGLE GM PLANT WILL AFFECT ONLY
GM AND PERHAPS ITS SUPPLIERS AND COMPETITORS
A HOT SUMMER WILL INCREASE DEMAND FOR AIR
CONDITIONERS
– BUT WON’T AFFECT THE DEMAND FOR COMPUTERS
36
Copyright 1996 by The McGraw-Hill Companies, Inc
MARKET OR SYSTEMATIC RISK
ALL FIRMS AFFECTED BY ECONOMY AND EXPOSED
TO MARKET RISK
– EXAMPLE: SURPRISE IN RATE OF GROWTH IN GNP
MARKET RISK CANNOT BE DIVERSIFIED AWAY
37
Copyright 1996 by The McGraw-Hill Companies, Inc
PORTFOLIO RISK
RISK OF A WELL-DIVERSIFIED PORTFOLIO
DEPENDS ONLY ON THE MARKET OR SYSTEMATIC
RISK OF THE SECURITIES IN THE PORTFOLIO
RISK OF A NON- DIVERSIFIED PORTFOLIO
DEPENDS ON THE MARKET RISK AND THE UNIQUE
RISK OF THE SECURITIES IN THE PORTFOLIO
38
Copyright 1996 by The McGraw-Hill Companies, Inc
SYSTEMATIC RISK OF A STOCK MEASURED
BY ITS BETA COEFFICIENT
b
THE MARKET OR AN AVERAGE STOCK HAS b =1
A STOCK WITH b =2 HAS TWICE AS MUCH
SYSTEMATIC RISK AS THE MARKET
AN INVESTOR IN A HIGH BETA STOCK WILL
EXPECT TO EARN A HIGHER RETURN THAN AN
INVESTOR IN A LOW BETA STOCK
39
Copyright 1996 by The McGraw-Hill Companies, Inc
MAJOR INVESTORS HOLD DIVERSIFIED PORTFOLIOS,
WITH LITTLE OR NO DIVERSIFIABLE OR UNIQUE RISK
THE RETURN ON A PORTFOLIO, DIVERSIFIED OR NOT,
DEPENDS ONLY ON THE MARKET RISK
OF THE PORTFOLIO
The market doesn’t reward us for taking unique risks we can
avoid at very little cost by diversification
– otherwise mutual funds would always sell at a premium to
the value of their underlying shares
40
Copyright 1996 by The McGraw-Hill Companies, Inc
MARKET RISK (BETA) FOR COMMON STOCKS
1989 - 1994
Stock
Beta
Stock
Beta
AT&T
Biogen
Bristol Myers Squib
Coca Cola
Compaq
.92.
2.20
.97
1.12
1.18
Exxon
Ford Motor Co.
General Electric
McDonald’s
Microsoft
.51
1.12
1.22
1.32
1.23
41
Copyright 1996 by The McGraw-Hill Companies, Inc
BIOGEN
b = 2.2
BIOGEN HAS 2.2 TIMES AS MUCH MARKET RISK AS
THE MARKET
RELATION BETWEEN b AND ACTUAL RETURNS NOT
PRECISE BECAUSE OF BIOGEN’S UNIQUE RISK
–
ACTUAL RETURNS SCATTERED ABOUT FITTED LINE
42
Copyright 1996 by The McGraw-Hill Companies, Inc
RISK OF INDIVIDUAL STOCKS
1. TOTAL RISK = DIVERSIFIABLE RISK + MARKET RISK
2. MARKET RISK IS MEASURED BY BETA, THE SENSITIVITY
TO MARKET CHANGES
EXPECTED
STOCK
RETURN
beta
EXPECTED
MARKET
RETURN
43
Copyright 1996 by The McGraw-Hill Companies, Inc
DIVERSIFICATION AND VALUE ADDITIVITY
DIVERSIFICATION MAKES SENSE FOR INVESTORS
DOES IT ALSO MAKE SENSE FOR A FIRM?
– IF DIVERSIFICATION MAKES SENSE FOR THE FIRM, EACH NEW
PROJECT HAS TO BE ANALYZED IN THE CONTEXT OF THE FIRM’S
PORTFOLIO OF EXISTING PROJECTS
– VALUE OF THE DIVERSIFIED PORTFOLIO OF PROJECTS WOULD BE
GREATER THAN THE SUM OF THE PROJECTS CONSIDERED
SEPARATELY
NO. INVESTORS CAN EASILY DIVERSIFY BY
HOLDING DIFFERENT SECURITIES; THEY WILL NOT
PAY MORE FOR FIRMS THAT DIVERSIFY
– IN COUNTRIES WITH EFFICIENT CAPITAL MARKETS,
DIVERSIFICATION DOES NOT INCREASE OR DECREASE A FIRM’S
VALUE
– TOTAL VALUE OF A FIRM IS THE SUM OF ITS PARTS
44
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SECURITY MARKET LINE
EXPECTED
RETURN
Expected
market
return
MARKET PORTFOLIO
Risk
free
rate
0
.5
1.0
BETA
r = rf + b (rm - rf)
45
Copyright 1996 by The McGraw-Hill Companies, Inc
MARKET RISK PREMIUM
rm - rf
– RATE OF RETURN ON MARKET - T-BILL RATE
HAS AVERAGED 8.4% OVER 69 YEARS
46
Copyright 1996 by The McGraw-Hill Companies, Inc
INVESTMENTS LYING BELOW THE SECURITY MARKET
LINE ARE DOMINATED BY A MIXTURE
OF THE MARKET PORTFOLIO AND THE RISKLESS ASSET
EXPECTED RETURN
rm
rf
k
k
1.0
BETA
47
Copyright 1996 by The McGraw-Hill Companies, Inc
EXPECTED RETURN ON AT&T STOCK
AT BEGINNING OF 1995
b = 0.92
INTEREST RATE ON T-BILLS rf = 6%
MARKET RISK PREMIUM rm - rf = 8.4%
EXPECTED RETURN ON AT&T
r = rf + b (rm - rf)
= 6 + .92 X 8.4 = 13.7%
48
Copyright 1996 by The McGraw-Hill Companies, Inc