Chapter 4
Stock & Bond Valuation
Professor XXXXX
Course Name / Number
© 2007 Thomson South-Western
Valuation Fundamentals
 The
greater the uncertainty about an
asset’s future benefits, the higher the
discount rate investors will apply when
discounting those benefits to the present.
 The valuation process links an asset’s risk
and return to determine its price.
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Valuation Fundamentals
Future Cash Flows
33
Risk
Valuation
Bond Valuation Fundamentals
Bonds are debt instruments used by business
and government to raise large sums of money
 Most bonds share certain basic characteristics

 First,
a bond promises to pay investors a fixed
amount of interest, called the bond’s coupon.
 Second, bonds typically have a limited life, or
maturity.
 Third, a bond’s coupon rate equals the bond’s annual
coupon payment divided by its par value.
 Fourth, a bond’s coupon yield equals the coupon
payment divided by the bond’s current market price
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Valuation Fundamentals
Present Value of Future Cash Flows
Link Risk & Return
Expected
Return on Assets
Valuation
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The Basic Valuation Model




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)
This model can express the price of any asset at t = 0
mathematically.
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Valuation Fundamentals
Bond Example
 Company
issues a 5% coupon interest rate,
10-year bond with a $1,000 par value on
01/30/04
 Assume
annual interest payments
 Investors
who buy company bonds receive
the contractual rights
 $50
coupon interest paid at the end of each
year
 $1,000 par value at the end of the 10th year
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Using the P0 equation, the bond would sell at a par value of $1,000.
Bonds: Premiums & Discounts
What Happens to Bond Values if the Required
Return Is Not Equal to the Coupon Rate?
The bond's value will differ from its par value
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R > Coupon Interest Rate
P0 < par value
=
DISCOUNT
R < Coupon Interest Rate
P0 > par value
=
PREMIUM
The Basic Equation (Assuming
Annual Interest)
 Cash
flows include two components:
the annual coupon, C, which equals the
stated coupon rate, i, multiplied by M, the
par value (that is, C i M), received for
each of the n years
 (2) the par value, M, received at maturity
in n years
 (1)
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Time Line for Bond: Valuation 91⁄8% Coupon,
$1,000 Par Bond, Maturing at End of 2017,
Required Return Assumed to be 8%
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10
Bonds
Semi-Annual Interest Payments
C
C
C
C
 1,000
2
2
2
Pr ice 


 ....  2
r 1
r 2
r 3
r 2n
(1  ) (1  )
(1  )
(1  )
2
2
2
2
An example....
Value a T-Bond
Par value = $1,000
$40
$40
$40
$40
 1,000
2
2
2
P0 


 2
1
2
3
4
0
.
044
0
.
044
0
.
044
0
.
044

 
 
 

1 
 1 
 1 
 1 

2
2
2
2

 
 
 

Maturity = 2 years
Coupon pay = 4%
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r = 4.4% per year

$20
$20
$20
$1,020
=
$992.43




2
3
4
(1.022) (1.022) (1.022) (1.022)
Yield to Maturity (YTM)
Rate of return investors earn if they buy
the bond at P0 and hold it until maturity.
The YTM on a bond selling at par will always equal
the coupon interest rate.
YTM is the discount rate that equates the
PV of a bond’s cash flows with its price.
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12
Risk-Free Bonds
A
risk-free bond is a bond that has no
chance of default by its issuer
 Zero-coupon
treasuries
 Coupon-paying treasuries
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Risky Bonds

Treasury bonds provide a known contractual stream of cash flows


if you can observe the market price of a bond, you can infer what the
market’s required return must be.
Valuing an ordinary corporate bond involves the same steps:
write down the cash flows
 determine an appropriate discount rate
 calculate the present value.


Discount rate on corporate bond should be higher than on Treasury
bond with the same maturity because corporate bonds carry default
risk


Yield spread between Treasury bonds and corporate bonds

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the risk that the corporation may not make all scheduled payments.
The difference in yield to maturity between two bonds or two classes of
bonds with similar maturities
Bond Issuers
 Bond
issuers
Corporate
bonds
Municipal bonds
Treasury bills
Treasury notes
Agency bonds
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Bond Ratings
 Bond
ratings
Moody’s
Standard
Fitch
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& Poor’s
Bond Ratings
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Bond Ratings and Spreads at Different
Maturities at a Given Point in Time
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Bond Price Behavior
 Bond
price quotations
 Bond
spreads reflect a direct relationship
with default risk
 Bond
price behavior
 Prices
change constantly
 Passage
of time
 Forces in the economy
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Bond Prices and Yields for Bonds with Differing
Times to Maturity, Same 6% Coupon Rate
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Bonds: Time to Maturity
Bond Price
$2,000
$1,500
$1,000
$500
$0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Yield to maturity, %
2-year bond
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10-year bond
What does this tell you about the relationship between
bond prices & yields for bonds with the equal coupon
rates, but different maturities?
Bonds: Yield to Maturity (YTM)
Rate of return investors earn if they buy the
bond at P0 and hold it until maturity.
The YTM on a bond selling at par will always
equal the coupon interest rate.
YTM is the discount rate that equates the PV of
a bond’s cash flows with its price.
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Evaluating the Yield Curve
Yields vary with maturity.
 Yields offered by bonds must be sufficient to
offer investors a positive real return.
 The real return on an investment approximately
equals the difference between its stated or
nominal return and the inflation rate.
 The shape of the yield curve can change over
time.
 Research shows the yield curve works well as a
predictor of economic activity, in the United
States and other large industrialized economies.

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Yield Curves for U.S. Government
Bonds
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Term Structure Theories
 Expectations
theory
 Liquidity preference theory
 Preferred habitat theory
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Expectations Theory
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Term Structure of Interest Rates

Relationship between yield and maturity is
called the Term Structure of Interest Rates
a Yield Curve
securities are higher
than on short-term securities
 Generally look at risk-free Treasury debt securities
 Graphical depiction is called
 Usually, yields on long-term

Yield curves normally upwards-sloping
 Long yields >
 Can be flat or
short yields
even inverted during times of
financial stress
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Stock Valuation: Preferred Stock
Preferred stock is an equity security that is expected to pay a fixed
annual dividend for its life
PS0 = Preferred stock’s value
DP = preferred dividend
rp = required rate of return
An example: A share of preferred stock pays $2.3 per share annual
dividend and with a required return of 11%
PS0=
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DP
rp
=
$2.30
0.11
= $20.90 / share
Valuation Fundamentals
Common Stock
Value of a Share
of Common Stock
P 0=
P1 + D1
(1+r)
P0 = Present value of the expected stock price at the end of period 1
D1 = Dividends received
r = discount rate
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Valuation Fundamentals:
Common Stock

But how is P1 determined?
 This
is the PV of expected stock price P2, plus
dividend at time 2
 P2 is the PV of P3 plus dividend at time 3, etc...

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Repeating this logic over and over, you find
that today’s price equals PV of the entire
dividend stream the stock will pay in the
future
Zero Growth Model
To value common stock, you must make
assumptions about the growth of future
dividends
 Zero growth model assumes a constant,
non-growing dividend stream:
D1 = D2 = ... = D


Plugging constant value D into the common
stock valuation formula reduces to simple
equation for a perpetuity:
P0 =
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D
r
Constant Growth Model


Assumes dividends will grow at a constant rate (g)
that is less than the required return (r)
If dividends grow at a constant rate forever, you can
value stock as a growing perpetuity, denoting next
year’s dividend as D1:
D1
P0=
r-g
Commonly called the Gordon Growth Model.
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Variable Growth
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Variable Growth Model
Example
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
Estimate the current value of Morris Industries'
common stock, P0 = P2003

Assume

The most recent annual dividend payment of Morris Industries
was $4 per share

The firm's financial manager expects that these dividends will
increase at an 8% annual rate over the next 3 years

At the end of the 3 years the firm's mature product line is
expected to result in a slowing of the dividend growth rate to
5% per year forever

The firm's required return, r , is 12%
Variable Growth Model
Valuation Steps #1 & #2

Compute the value of dividends in 2004, 2005, and
2006 as (1+g1)=1.08 times the previous year’s dividend
Div2004= Div2003 x (1+g1) = $4 x 1.08 = $4.32
Div2005= Div2004 x (1+g1) = $4.32 x 1.08 = $4.67
Div2006= Div2005 x (1+g1) = $4.67 x 1.08 = $5.04

Find the PV of these three dividend payments:
PV of Div2004= Div2004  (1+r) = $ 4.32  (1.12) = $3.86
PV of Div2005= Div2005  (1+r)2 = $ 4.67  (1.12)2 = $3.72
PV of Div2006= Div2006  (1+r)3 = $ 5.04  (1.12)3 = $3.59
Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17
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Variable Growth Model
Valuation Step #3
Find the value of the stock at the end of the
initial growth period using the constant growth
model
 Calculate next period dividend by multiplying
D2006 by 1+g2, the lower constant growth rate:

D2007 = D2006 x (1+ g2) = $ 5.04 x (1.05) = $5.292

Then use D2007=$5.292, g =0.05, r =0.12 in
Gordon model:
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$5.292
$5.292
D
2007
=
=
= $75.60
P2006 =
r - g 2 0.12 - 0.05 0.07
Variable Growth Model
Valuation Step #3

Find the present value
of this stock price by
discounting P(2006)
by (1+r)3
$75.60 $75.60
P
2006
PV =
=
=
=
$
53
.
81
3
3
(1  r ) (1.12)
1.405
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Variable Growth Model
Valuation Step #4
 Add
the PV of the initial dividend stream
(Step #2) to the PV of stock price at the
end of the initial growth period (P2006):
P2003 = $11.17 + $53.81 = $64.98
Current
(end of year 2003)
stock price
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Remember:
Because future growth rates might change, the variable growth model
allows for a changes in the dividend growth rate.
Time Line for Variable Growth
Valuation
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Free Cash Flow Approach
Begin by asking, what is the total operating
cash flow (OCF) generated by a firm?
 Next subtract from the firm’s operating cash
flow the amount needed to fund new
investments in both fixed assets and current
assets.
 The difference is total free cash flow (FCF).

 Represents
the cash amount a firm could distribute
to investors after meeting all its other obligations
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Common Stock Valuation:
Other Options
 Book
value
 Net
assets per share available to common
stockholders after liabilities are paid in full
 Liquidation
 Actual
value
net amount per share likely to be
realized upon liquidation & payment of
liabilities
 More realistic than book value, but doesn’t
consider firm’s value as a going concern
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Common Stock Valuation:
Other Options
 Price
/ Earnings (P / E) multiples
 Reflects
the amount investors will pay for
each dollar of earnings per share
 P / E multiples differ between & within
industries
 Especially helpful for privately-held firms
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