Valuing Bonds
Chapter 4
© 2009 Cengage Learning/South-Western
Valuation Basics
Present Value of Future Cash Flows
Link Risk & Return
Expected Return
on Assets
Valuation
2
The Fundamental Valuation Model
CF 1
CF 2
CF n
+
+ . . .+
P0 =
1
2
(1 + r ) (1 + r )
(1 + r )n
P0
CFt
r
n
=
=
=
=
Price of asset at time 0 (today)
Cash flow expected at time t
Discount rate (reflecting asset’s risk)
Number of discounting periods (usually years)
This model can express the price of any asset at
t = 0 mathematically.
Marginal benefit of owning the asset: right to receive the
cash flows
3
Marginal cost: opportunity cost of owning the asset
Bond Vocabulary
Principal
• The amount of money on which interest is
paid.
Maturity date
• The date when a bond’s life ends and the
borrower must make the final interest
payment and repay the principal.
Par value
4
• The face value of a bond, which the
borrower repays at maturity.
Coupon
• A fixed amount of interest that a bond
promises to pay investors.
Indenture
• A legal document stating the conditions
under which a bond has been issued.
Bond Vocabulary
5
Coupon rate
• The rate derived by dividing the bond’s
annual coupon payment by its par value.
Coupon yield
• The amount obtained by dividing the
bond’s coupon by its current market price
(which does not always equal its par
value). Also called current yield.
Bond Valuation: The Basic Equation
• Bond Price = PV of coupons + PV of principal
Assuming annual interest:
C
C
C
M
+
+ . . .+
+
P0 =
1
2
n
(1 + r ) (1 + r )
(1 + r ) (1 + r )n
1

1  1  r n
=C
r


6


M
+
n
(1
+
r
)


Time Line for Bond Valuation
(Annual Interest Payments)
Worldwide United
9-1/8% Coupon,
$1,000 Par Value
Bond, Maturing at
End of 2019;
Required Return
Assumed To Be 8%
7
Yield to Maturity (YTM)
Estimate 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 rate.
YTM is the discount rate that equates the
PV of a bond’s cash flows with its price.
8
Bond Premiums and Discounts
What happens to bond values if the required
return is not equal to the coupon rate?
The bond's price will differ from its par value.
9
r > Coupon Interest Rate
P0 < par value
=
DISCOUNT
r < Coupon Interest Rate
P0 > par value
=
PREMIUM
On Discount Rates
• Generally,
• 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.
10
Semiannual Compounding
C
C
C
C
F
2 
2
2
Price 

 ....  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
Maturity = 2 years
Coupon rate = 4%
r = 4.4% per year
$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

 
 
 

= $992.43

11
$20
$20
$20
$1,020




(1.022) (1.022) 2 (1.022)3 (1.022) 4
Economic Forces Affecting Bond Prices
Time to maturity: bond prices converge to par
value (plus final coupon) with passage of time.
Interest rates: bond prices and interest rates
move in opposite directions.
Changes in interest rates have larger impact on
long-term bonds than on short-term bonds.
12
The Relationship Between
Bond Prices and Required Returns
6% coupon rate
for both
13
Interest Rate Risk
Interest Rate
Risk
• The risk that changes in market interest
rates will cause fluctuations in a bond’s
price. Also, the risk of suffering losses as a
result of unanticipated changes in market
interest rates.
Real return
• Approximately, the difference between an
investment’s stated or nominal return and
the inflation rate.
Nominal
return
14
• The stated return offered by an
investment unadjusted for the effects of
inflation.
Treasury Bond Yields and Inflation Rates
15
Primary versus Secondary Markets
Primary market: the initial sale of bonds by issuers
to large investors or syndicates
Secondary market: the market in which investors
trade with each other
Trades in the secondary market do not raise any
capital for issuing firms.
16
Types of Bonds: By Issuer
17
Corporate
Bonds
• Usually with par $1000 and semi-annual
coupon
• Bonds if maturity > 10 years; notes if
maturity < 10 years
Municipal
Bonds
• Issued by local and state government
• Interest on municipal bonds tax-free
Treasury
Bonds
• If maturity < 1 year: Treasury Bills
• If 1 year < maturity < 10 years: Treasury
Notes
• Maturity > 10 years: Treasury Bonds
• Used to fund budget deficits
Agency
Bonds
• Issued by government agencies: FHLB,
FNMA (Fannie Mae), GNMA (Ginnie Mae),
FHLMC (Freddie Mac)
Types of Bonds: By Features
Fixed vs.
Floating
Rates
Secured vs.
Unsecured
Bonds
18
• Floating-rate bonds: coupon tied to prime
rate, LIBOR, Treasury rate or other
interest rate
• Floating rate = benchmark rate + spread
• Floating rate can also be tied to the
inflation rate: TIPS, for example
• Unsecured bonds (debentures) are backed
only by general faith and credit of issuer
• Secured bonds are backed by specific
assets (collateral)
• Mortgage bonds, collateral trust bonds,
equipment trust certificates
Types of Bonds: By Features
Zero-Coupon
Bonds
Convertible
and
Exchangeable
Bonds
19
• Zero-coupon bonds pay no interest
• Also known as Discount bonds or pure
discount bonds
• Sell below par value
• Treasury Bills (Tbills)
• Treasury STRIPs
• Convertible bonds, in addition to paying
coupon, offers the right to convert the
bond into common stock of the issuer of
the bond
• Exchangeable bonds are convertible in
shares of a company other than the
issuer’s
Table 4.1 Zero-Coupon Bond Prices and
Taxable Income
20
Types of Bonds: By Features
21
Callable and
Putable
Bonds
• Callable bonds: bond issuer has the right
to repurchase the bonds at a specified
price (call price).
• Firms could retire and reissue debt if
interest rates fall.
• Putable bonds: the investors have the
right to sell the bonds to the issuer at the
put price.
Protection
from Default
Risk
• Sinking fund provisions: the issuer is
required to gradually repurchase
outstanding bonds.
• Protective covenants: requirements the
bond issuer must meet
• Positive and negative covenants
Types of Bonds: By Features
Treasury
InflationProtected
Securities
(TIPS)
22
• Notes and bonds issued by
the federal government that
make coupon payments that
vary with the inflation rate.
Bond Markets
The U.S bond market has grown from $250 billion
in 1950 to $22 trillion in 2004
Amount Oustanding in 2004
$1,900
$3,900
$3,700
Municipal Bonds
Treasury Bonds
Corporate Bonds
Federal Agency Bonds
Mortgage-related debt
$5,300
Other
$4,500
23
$2,700
U.S. Treasury Bond Quotations
MATURITY
RATE
MO/YR
BID
ASKED
CHG
ASK
YLD
Government Bonds & Notes
5.500
May 09n
Rate
Bid prices
Ask prices
(percentage of
par value)
107:13
107:14
3
3.83
Coupon rate of 5.5%
Bid price: the price traders receive if they
sell a bond to the dealer. Quoted in
increments of 32nds of a dollar
Ask price: the price traders pay to the
dealer to buy a bond
Bid-ask spread: difference between ask
and bid prices.
24
Ask Yield
Yield to maturity on the ask price
Corporate Bond Quotations
Company
(Ticker)
SBC Comm
(SBC)
Coupon
Maturity
Last Price
Last Yield
Estimated
Spread
UST
Est $ Vol
(000s)
5.875
Aug
15,2012
107.161
4.836
80
10
73,867
Corporate prices are quoted as percentage of par, without
the 32nds of a dollar quoting convention
Yield spread: the difference in yield-to-maturities between a
corporate bond and a Treasury bond with same maturity
25
The greater the default risk, the higher
the yield spread
Bond Ratings
Bond ratings: grades assigned to bond issues based
on degree of default risk
Investmentgrade bonds
Junk bonds
26
• Moody’s Aaa to Baa3 ratings
• S&P and Fitch AAA to BBBratings
• Moody’s Ba1 to Caa1 or lower
• S&P and Fitch BB to CCC+ or
lower
Figure 4.2 Bond Ratings
27
Table 4.3 The Relationship Between Bond Ratings and
Spreads at Different Maturities at a Point in Time
28
Term Structure of Interest Rates
• Relationship between yield and maturity is called
the Term Structure of Interest Rates
– Graphical depiction called a Yield Curve
– Usually, yields on long-term securities are higher than on shortterm securities.
– Generally look at risk-free Treasury debt securities
• Yield curves normally upwards-sloping
– Long yields > short yields
– Can be flat or even inverted during times of financial stress
What do you think a Yield Curve would look like
graphically?
29
Fig. 4-5 Yield Curves for U.S. Government
Bonds
30
The Expectations Hypothesis
31
Advanced Bond Valuation
Liquidity
Preference
Theory
Preferred
Habitat
Theory
32
• States that the slope of the yield curve is
influenced not only by expected interest
rate changes, but also by the liquidity
premium that investors require on longterm bonds.
• A theory that recognizes that the shape of
the yield curve may be influenced by
investors who prefer to purchase bonds
having a particular maturity regardless of
the returns those bonds offer compared to
returns available at other maturities.
Valuing Bonds
• Bond price = present value of coupons +
present value of principal
• Bond prices are inversely related to interest
rates.
• Bonds can have features like convertibility and
callability.
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