Chapter 4 Valuing Bonds
Professor Thomson
Fin 3013
Quote from Gyourko (UPenn)
• "Basically we've been growing rich people in the
U.S.," he said. In 1940, less than 1% of families
earned $100,000 in today's dollars. By 1970 that
income level applied to about 5% of families. By
2000 it applied to about 12% of families.
From Knowledge at Wharton
http://knowledge.wharton.upenn.edu/article/1498.cfm
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Bonds
• Bonds are debt instruments (i.e. loans)
• Government Bonds include:
– US Treasury
– Federal Agency
– Municipal (Government bonds issued by non
Federal entities such as States and Local
Governments
• Corporate Bonds – are private Bonds
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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
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$2,700
Bonds
• Bonds typically make “interest only”
payments, and repay the amount
borrowed at maturity.
– New bonds may be issue to repay an issue
that is maturing.
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Par Value or Face Value
• The Par or Face Value is the amount that
will be refunded at the maturity date.
• The par value is usually $1000 (especially
for corporate bonds).
• Assume $1000 par value unless another
value is provided.
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Coupon Rate
• The coupon rate is the annual rate of
interest (APR) paid on the bonds par
value. E.g. 6.125% or 6 1/8
• Bond coupons historically were in 1/8%
increments, but that is becoming less
common
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Coupon Payment
• The coupon payment is the periodic interest
payment made to bond holders.
CouponRate* FaceValue
CouponPm t
Num berOfPaym entsPerYear
• Payments per year, P/YR, is the number of
coupon payments per year
• P/YR = 2 for a typical (semiannual) bond
• If P/YR not stated, assume P/YR=2
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Show bond quote from WSJ
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Example 4.1: Semi Annual Coupon
Bond
• A 6% semi annual coupon bond has 10
years until maturity. The market
(discount) rate is 5%. What is its price?
• What would be the price of a similar
annual coupon bond?
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Example 4.2:
• Consider a 7% semiannual coupon bond
with 28 years until maturity. The market
rate = 8%. What is the price of the bond?
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Bond Price depends on the Market
rate (or discount rate or YTM)
Example 4.3: Consider 2 Bonds
A: 7% Bond with 28 years to maturity
B: 7% Bond with 4 years to maturity
Compute the market price of these bonds as
the market rate changes from 3-10%
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Example 4.4: What is the YTM of
the Wachovia Bond?
• The Wachovia Capital trust bond with a
5.800 coupon which matures Mar 15,
2011 has a price quote of 97.748. What is
its YTM? (Assume today is March 16,
2006)
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Example 4.5 Bond Prices
• You purchased a 5% semi annual coupon
bond, with 10 years until maturity, one
year ago when the market rate was 7%.
The market rate is now 6%. What price
did you pay for your bond, and what could
you sell it for today?
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Inflation
• What matters is not how many $ you
have, but what you can purchase with the
$ you have.
• Measures of inflation compute how many
$ it takes over time to purchase the same
basket of goods
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Inflation: Some Notation
• NR = Nominal Rate, which is the quoted
rate or yield on a bond
• RR = Real Rate, which measures your
increase in purchasing power over time
• IN = INflation rate, which is the rate at
which the cost of goods goes up
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Fisher Effect
17
• The Fisher effect shows the relationship
among the nominal rate [NR], the
inflation rate, [IN], and the real rate
[RR].
• Exact relationship is:
(1+NR) = (1+IN)*(1+RR)
• Approximate relationship (works best if
inflation rate is low) is:
NR = IN+RR
Example 4.5: Calculating the real rate
of return on a Treasury Bill
• If Treasury bills are currently paying 5
percent and the inflation rate is 3.4
percent, what is the approximate real
rate of interest? The exact real rate?
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What affects Bond Yields?
• Inflation – the higher the inflation rate,
the higher the bond yield (bond yields
were much higher in early 1980’s than
today because inflation was higher)
• Default risk – Riskier bonds have higher
yields (Thus, Treasury bonds have
lower yields than corporate bonds, and
investment grade bonds have lower
yields than “junk bonds”
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Bond Ratings
Bond ratings: grades assigned to bond issues based
on degree of default risk
Investmentgrade bonds
Junk bonds
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• 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
Bond Yields (continued)
• Liquidity – highly liquid bonds such as
Treasuries have lower yields than safe, but
less traded bonds.
• Taxes – Bonds that are tax free (most
Municipal Bonds) have lower yields than
taxable bonds
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Bond Yields (continued)
• Maturity – Other things equal, bonds
with a longer time until maturity usually
have a higher yield than bonds near
their maturity date (when this is not
true, we say we have an inverted yield
curve)
• The Treasury Yield Curve plots the yield
on Treasury Bonds versus their
maturity, and it is typically upward
sloping. (see Wall Street Journal)
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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 short-term 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
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What do you think a Yield Curve would look like
graphically?
Yield Curves U.S. Treasury
Securities
16
14
May 1981
Interest Rate %
12
10
8
January 1995
August 1996
6
October 1993
4
2
1
3
5
10
15
Years to Maturity
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20
30
See Smart Animation
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Example 4.7
• Example 4.7. Zero coupon Treasury strips
with 3 years until maturity have a yield of
5%, while similar 2-year strips yield 6%.
According to the expectations theory, what
yield will one year strips have two years
from now?
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Bond Indenture
• Are “the rules” I.e. is the bond contract
• It states the provisions of the bond
including the coupon rate and maturity
date
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Possible Bond Provisions
• Call Provision
– Allows bond to be refunded (I.e. called) prior
to its maturity date
• Put Provision
– Allows the bond purchaser to sell the bond
back to the issuer prior to its maturity date
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Possible Bond Provisions
• Convertible Bond
– Allows the bond to be swapped for stock
– This is an “option” as it gives you the right
but not the obligation to do the swap
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Covenants to Protect
Bondholders
• May have a limit on the dividends the firm
is allowed to pay, to keep cash in the firm
for paying bondholders coupons
• Seniority Rule
– Most senior (I.e. first issued) have their
coupon paid before junior issues, and has first
claim on firm assets in default
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Covenants to Protect
Bondholders
• Sinking Fund – various ways to ensure
that the bond will be repaid at maturity,
such as making deposits into a
dedicated account for this purpose, or
repurchasing some bonds over time
• Collateral – may be required to pledge
certain assets of the firm as surity
• Debenture – a bond where no collateral
is pledged. Most bonds are debentures
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Zero Coupon Bonds
• These bonds are bought at a deep
discount and redeemed for par
• A disadvantage is the you must pay taxes
each year on the imputed interest earned,
even though no coupon interest is paid to
you.
• More popular for tax sheltered
investments such as IRA or insurance
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Other Bond Types
• Variable Coupon – The coupon paid each
period depends on an interest rate index
– For example, the coupon on Series EE savings
bond is set to 90% of the yield on 5 year Treasury
Bonds
• TIPS (Treasury Inflation Protected Securities)
– These Treasury Bonds pay a real coupon rate, on
a Face Value that adjusts with inflation thus
providing a real rate of return for investors
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End of lecture notes
• The slides which follow are alternate ways
to state what has been covered thus far,
and some additional information for those
that may be interested.
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Corporate Bond Quotations
Company
(Ticker)
Coupon
Maturity
Last
Price
Last
Yield
Estimated
Spread
UST
Est $ Vol
(000s)
SBC
Comm
(SBC)
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
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The greater the default risk, the higher
the yield spread
U.S. Treasury Bond Quotations
MATURITY
MO/YR
RATE
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.
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Ask Yield
Yield to maturity on the ask price
Valuation Fundamentals
Present Value of Future Cash Flows
Link Risk & Return
Expected Return
on Assets
Valuation
38
The Basic Valuation Model
CF 1
CF 2
CF n
+
+ . . .+
P0 =
1
2
(1+ r ) (1+ r )
(1+ r )n
•
•
•
•
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.
Marginal benefit of owning the asset: right to receive the
cash flows
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Marginal cost: opportunity cost of owning the asset
Valuation Fundamentals: Example
Company issues a 5% coupon interest rate, 10-year
instrument with a $1,000 par value
– Assume annual interest payments
• Investors in company’s financial instrument
receive the contractual rights
– $50 coupon interest paid at the end of each
year
– $1,000 principal at the end of the 10th year
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P = $1,000
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.
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Bond Premiums and Discounts
What happens to bond values if required return is not equal to
the coupon rate?
The bond's price 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
Semi-Annual Interest Payments
C
C
C
C
F
2 
2
2  ....  2
Price 

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 rate = 4%
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r = 4.4% per year

$20
$20 = $992.43
$20
$1,020




2
3
4
(1.022) (1.022) (1.022) (1.022)
Factors that Affect 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.
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Interest Rate Risk
$1,500
$1,300
$1,100
$900
$700
$500
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Yield to maturity, %
2-year bond
10-year bond
What does this tell you about the relationship
between bond prices and yields for bonds with
different maturities?
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Primary vs. 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.
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Bonds by Issuer
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Corporate
Bonds
• Usually with par $1000 and semiannual 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)
Bonds by Features
Fixed vs.
Floating
Rates
Secured vs.
Unsecured
Bonds
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• 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
Bonds by Features (Continued)
Zero-Coupon
Bonds
Convertible
and
Exchangeable
Bonds
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• 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
Bonds by Features (Continued)
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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
Bond Valuation
 Bond price equals present value of its coupons
and principal.

Bond prices are inversely related to interest rates.

Bonds could have a number of features: such as
convertibility, callability.
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