Security Valuation
FIN 461: Financial Cases & Modeling
George W. Gallinger
Associate Professor of Finance
W. P. Carey School of Business
Arizona State University
Valuation Fundamentals

Value of any financial asset is the PV of future
cash flows



Valuation is the process linking risk & return


Bonds: PV of promised interest & principal
payments
Stocks: PV of all future dividends
Output of process is asset’s expected market price
Key input is the expected return on an asset

Defined as the return an arms-length investor
would require for an asset of equivalent risk


Debt securities: risk-free rate plus risk premium(s)
Required return for stocks  using CAPM or other asset
pricing model.
W. P. Carey School of Business
Slide 2
Basic Valuation Model
CF 1
CF 2
CF n
+
+ . . .+
P0 =
1
2
n
(1 + r ) (1 + r )
(1 + r )
•
•
•
•
P0 = Price of asset at time 0 (today)
CFt = cash flow expected at time t
r = discount rate (reflecting asset’s risk)
n = number of discounting periods (usually years)
Model expresses the price of any asset at t = 0 mathematically.
W. P. Carey School of Business
Slide 3
Start with Bonds


Calculate price
Calculate yields



Current
Holding period
Yield to maturity.
W. P. Carey School of Business
Slide 4
How to Value Bonds


Identify the size and timing of cash
flows.
Discount at the correct discount rate.

If you know the price of a bond and the
size and timing of cash flows, the yield to
maturity is the discount rate.
W. P. Carey School of Business
Slide 5
Definition & Example of a
Bond

Consider a U.S. government bond listed as 63/8% of
December 2009




The par value of the bond = $1,000
Coupon payments are made semi-annually (June 30 and
December 31 for this particular bond)
Since the coupon rate is 63/8% the payment = $31.875
On January 1, 2002 the size and timing of cash flows are:
$31.875 $31.875
$31.875
$1,031.875
6 / 30 / 09
12 / 31 / 09

1 / 1 / 02
6 / 30 / 02
12 / 31 / 02
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Slide 6
Pure Discount Bonds
Information needed for valuing pure discount bonds:



Time to maturity (T) = Maturity date - today’s date
Face value (F)
Discount rate (r)
$0
$0
$0
$F
T 1
T

0
1
2
Present value of a pure discount bond at time 0:
F
PV 
T
(1  r )
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Slide 7
Pure Discount Bonds:
Example
Find the value of a 30-year zero-coupon bond
with a $1,000 par value and a YTM of 6%.
$0
$0
$0
$1,000
29
30

0
1
2
F
$1,000
PV 

 $174.11
T
30
(1  r )
(1.06)
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Slide 8
Level-Coupon Bonds
Information needed to value level-coupon bonds:



Coupon payment dates and time to maturity (T)
Coupon payment (C) per period and Face value (F)
Discount rate
$C
$C
$C
$C  $F
T 1
T

0
1
2
Value of a level-coupon bond
= PV of coupon payment annuity + PV of face value
C
1 
F
PV  1 

T 
T
r  (1  r )  (1  r )
W. P. Carey School of Business
Slide 9
Level-Coupon Bonds:
Example
Find the present value (as of January 1, 2002), of a 6-3/8 coupon Tbond with semi-annual payments, and a maturity date of
December 2009 if the YTM is 5%.
 On January 1, 2002 the size and timing of cash flows are:
$31.875 $31.875
$31.875
$1,031.875
6 / 30 / 09
12 / 31 / 09

1 / 1 / 02
6 / 30 / 02
12 / 31 / 02
 $1,000
$31.875 
1
PV 
1

 $1,049.30

16 
16
.05 2  (1.025)  (1.025)
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Slide 10
Current Yield
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Slide 11
Holding Period Rate of
Return
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Slide 12
Importance & Calculation of Yield
to Maturity

Yield to maturity (YTM)


YTM on a bond selling at par (P0 = Par) = coupon rate


Rate of return investors earn if they buy the bond at P0 and
hold it until maturity
When P0  Par, the YTM will differ from the coupon rate
YTM is the discount rate that equates the PV of a
bond’s cash flows with its price

Use T-Bond with n=2 years, 2n=4, C/2=$20, P0=$992.43
$992.43 
$20
$20
$20
$1,020



 r   r  2  r 3  r  4
1   1   1   1  
 2  2  2  2
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Slide 13
Price & Yield Relationships
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Slide 14
Semi-Annual Bond Interest
Payments


Most bonds pay interest semi-annually rather than annually
Can easily modify basic valuation formula; divide both coupon
payment (C) and discount rate (r) by 2:
C
C
C
C
 1,000
2
2
2
Price 


 ....  2
r
r
r
r
(1  )1 (1  ) 2 (1  ) 3
(1  ) 2 n
2
2
2
2
• C  annual coupon payment; C/2  semi-annual payment
• r  annual required return; r/2  semi-annual discount rate
• n  number of years; 2n semi-annual payments.
W. P. Carey School of Business
Slide 15
Semi-Annual Bond Interest
Payments …
An example....
Value a T-Bond
Par value = $1,000
Maturity = 2 years
Coupon pay = 4%
r = 4.4% per year
$40
$40
$40
$40
 1,000
2
2
2
2
P0 



1
2
3
4
 0.044   0.044   0.044   0.044 
1 
 1 
 1 
 1 

2
2
2
2

 
 
 

$20
$20
$20
$1,020
 $992.43




=
(1.022) (1.022) 2 (1.022)3 (1.022) 4
 $19.57  $19.15  $18.74  $934.97  $992.43
W. P. Carey School of Business
Slide 16
Characteristics of Bonds

Important factors can be stated using 5
bond theorems.
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Slide 17
Bond Theorem 1

Market rate >
coupon rate


Market rate <
coupon rate


Bond's price is
less than its
face value of
$1000
Bond's price
exceeds its face
value
Market rate =
coupon rate

Bond's price =
face value.
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Slide 18
Bond Theorem 2

The longer the maturity, the greater the
price change.
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Slide 19
Bond Theorem 3
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Slide 20
Bond Theorem 4



Maturity has no effect on
bond value, and thus gains
or losses, when the coupon
rate = market rate
If the market rate < coupon
rate, the bond's capital
gains--the price minus the
face value of $1000--become
smaller as maturity shortens
If the market rate > coupon
rate, the bond's capital
losses become smaller as
maturity shortens.
W. P. Carey School of Business
Slide 21
Bond Theorem 5

Maturity has no affect if coupon rate equals market rate.
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Slide 22
Bond Risk Premiums
February 97-November 98
600
500
400
High-yield Bond
Yields less yield
on 10-year
Treasurys in
basis points
300
200
100
0
97
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98
Slide 23
Term Structure of Rates


Term structure of interest rates compares YTMs of comparable risky securities
and maturities at a point in time
Provides info about market's forecast of rates and inflation
W. P. Carey School of Business
Slide 24
Some Historical Perspective
16
May 1981
14
Interest Rate %
12
10
January 1995
8
August 1996
6
October 1993
4
2
1
3
5
10
15
20
30
Years to Maturity
W. P. Carey School of Business
Slide 25
Shapes & Levels of Treasury
Yield Curve
October 1998
5.1
October 9
4.9
October 8
Yield %
4.7
October 2
4.5
4.3
4.1
3.9
3.7
1
5
10
30
Maturity in Years
W. P. Carey School of Business
Slide 26
YTM & Forward Rates
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Slide 27
Bond Duration
Coupon rate
= 8%;
market rate
= 8%
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Slide 28
Factors Influencing Duration


Duration increases with maturity
Decreases with higher yield, higher coupon rates, and higher payment
frequency.
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Slide 29
Discuss Common Stocks
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Slide 30
Valuation of Stocks

Value a function of expected future cash
flows



Capital gains
Dividends
Growth prospects



Zero
Constant
Differential.
W. P. Carey School of Business
Slide 31
Dividend Fundamentals

Relevant dates for dividend payments



Legal factors affecting dividend policy



Capital impairment constraint: Cannot pay out “legal capital”
Cannot accumulate earnings to escape taxes
Contractual constraints on dividend payments



Announcement, ex dividend, record and payment dates
Stock price should drop by about dividend amount on ex date
Loan covenants restrict, but don’t prevent, dividend payments
Establish a “pool” of earnings that can be paid out
Liquidity and ownership constraints



Must have cash on hand (cannot used borrowed funds)
High payout leads to potential dilution
Investment opportunity sets of investors.
W. P. Carey School of Business
Slide 32
Types of Dividends

Types of cash dividends



Types of dividend policies





Regular Cash Dividend
Special Cash Dividend
Constant payout policy (almost never observed)
Constant nominal payments (standard worldwide)
Low regular and extra dividend
Stock dividends and stock splits
Stock repurchase (3 methods)



Buying shares on the market
Tender Offer to Shareholders
Private Negotiation (Green Mail).
W. P. Carey School of Business
Slide 33
U.S. Firms Paying Dividends,
by Exchange
100
NYSE
Percent
80
60
AMEX
40
NASDAQ
20
0
1926
1936
1946
1956
1966
1976
1986
1996
Year
W. P. Carey School of Business
Slide 34
Aggregate Dividend Payout %,
U.S. Corporate Sector (1970-2000)
90
%
80
70
60
50
40
30
20
10
0
70
72
74
76
78
W. P. Carey School of Business
80
82
84
86
88
90
92
94
96
98
2000
Slide 35
Mkt. Value Share Repurchase
Announcements, (1980-1999)
250
$US
Bns
200
150
100
50
0
80
82
84
W. P. Carey School of Business
86
88
90
92
94
96
98
Slide 36
CUMULATIVE MEAN RATE OF RETURN
Market Reaction to Share
Repurchase Announcements
25%
20%
15%
10%
5%
0%
-5%
-10%
-60 -50 -40 -30 -20
-10
0
+10 +20 +30 +40 +50 +60
TRADING DAY
W. P. Carey School of Business
Slide 37
Patterns Observed in
Dividend Policies

Dividend policies show distinct national patterns


Dividend policies have pronounced industry patterns, and these
are the same worldwide


Profitable firms in mature industries tend to pay out much larger
fractions of their earnings
Within industries, dividend payout tends to be directly related to
asset intensity and the presence of regulation


Companies in common law countries tend to have higher payouts
than those from civil law countries
But payout is inversely related to growth rate
Almost all firms maintain constant nominal dividend payments
per share for long periods of time

Companies tend to "smooth" dividends, and these are far less
variable than are corporate profits.
W. P. Carey School of Business
Slide 38
Real-World Influences on
Dividends

Personal taxes on dividends should discourage payments




Security issuance costs should discourage dividends


But cost of selling shares for income has fallen steadily
Dividends might be a “residual” after funding investments


If costly to issue new stocks & bonds, firm should retain cash
Investor trading costs argue in favor of dividends


Empirical evidence is ambiguous
Dividends paid before 1936 (no taxes) and after
Some evidence of positive relation between payout and PS
But dividends are most stable of all cash flow series
May convey information in markets with info asymmetries


But what specific info & isn’t there a cheaper way to signal?
Latest empirical evidence: div signal the past, not the future.
W. P. Carey School of Business
Slide 39
How Do Corporations Really
Set Dividend Payments?

Dividends determined today as they were for Lintner (1956)






Managers believe investors value steady dividend payments
Managers have a target payout ratio, but only over time
Will allow payout to vary in the short term to keep $div same
Will only raise $div if permanent earnings increase
Will only cut $div if firm facing financial disaster
Managerial reluctance to change nominal dividend payment
gives rise to partial adjustment model





Assume target payout ratio = 0.50, profits initially $2.00/sh
Implies annual dividend of $1.00/sh; quarterly div of $0.25/sh
Suppose permanent earnings suddenly rise to $3.00/sh
Will not increase dividend to $1.50/year immediately. Instead,
May do so in $0.05 quarterly increments, over 2.5 yrs.
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Slide 40
Key Dividend Dates
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Slide 41
Calculating Intrinsic Price of a
Non-constant Dividend Stream
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Slide 42
Valuation of Perpetual
Dividend Streams
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Slide 43
Valuation of Two-Stage
Dividend Streams
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Slide 44
Estimates of Parameters in
the Dividend-Discount Model

The value of stock depends upon its
discount rate, r, and growth rate, g.


Where does r come from?
Where does g come from?
W. P. Carey School of Business
Slide 45
Where Does r Come From?

Best to use the CAPM

Discussed last lesson.
W. P. Carey School of Business
Slide 46
Formula for Stock’s Growth
Rate
g = (1 – EPS / DPS) × ROE / [1 – RR × ROE]
This is sustainable growth!
W. P. Carey School of Business
Slide 47
Other Approaches to
Common Stock Valuation

Book value:


Liquidation value:


More realistic than book value, but doesn’t consider firm’s
value as a going concern
Price/Earnings (P/E) multiples:





Assumes assets can be sold at book value
Reflects the amount investors will pay for each dollar of
earnings per share
P/E multiples differ between and within industries
May be helpful for privately-held firms
A “lazy person’s” approach to valuation
Discounting


Free cash flows
Economic value added (aka EVA).
W. P. Carey School of Business
Slide 48
Other Price Ratio Analysis

Many analysts frequently relate earnings per
share to variables other than price, e.g.:
 Price/Cash Flow Ratio


Price/Sales


Cash flow = Net income + depreciation = cash flow
from operations or operating cash flow
Current stock price divided by annual sales per share
Price/Book (aka market-to-book ratio)

Price divided by book value of equity, which is
measured as assets – liabilities.
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Slide 49
The End
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Slide 50