Chapter 4 Topic Overview
Chapter 4
Bond Characteristics
‹ Annual and Semi-Annual Bond
Valuation
‹ Reading Bond Quotes
‹ Finding Returns on Bonds
‹ Bond Risk and Other Important Bond
Valuation Relationships
‹
Valuing Bonds
Characteristics of Bonds
Bond Characteristics
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Par (or Face) Value (F) = stated face value
that is the amount the issuer must repay,
usually $1,000
Coupon Interest Rate
Coupon (C) = Coupon Rate x Face Value
Maturity Date = when the face value is
repaid.
A legal contract called the bond indenture
specifies these values.
This makes a bond’s cash flows look like
this:
• Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every 6 months) and pay the par value
at maturity.
0
C/2 C/2
C/2 C/2
…
1
2
...
C/2+F
n
Bond Pricing
Bond Valuation
|
The price of a bond is the Present Value of
all cash flows generated by the bond (i.e.
coupons and face value) discounted at the
required rate of return.
Discount the bond’s cash flows at the
investor’s required rate of return.
z
z
z
PV =
(cpn + par )
cpn
cpn
+
+....+
1
2
(1 + r ) (1 + r )
(1 + r ) t
Bond Valuation Example #1
0
?
0
‹
‹
Duff’s Beer has $1,000 par value bonds
outstanding that make annual coupon
payments. These bonds have a 7.5%
annual coupon rate and 15 years left to
maturity. Bonds with similar risk have a
required return of 9%, and Moe Szyslak
thinks this required return is reasonable.
What’s the most that Moe is willing to pay
for a Duff’s Beer bond?
the coupon payment (C) stream (an
annuity).
the par (F) value payment (a lump sum).
PV = C (PVAF r, n) + F /(1+r)n
C
C
1
2
C+F
...
n
75
75
75
...
1000
75
1
2
3
...
15
r = 9%
Let’s Play with Example #1
?
0
‹ Homer
Simpson is interested in
buying a Duff Beer bond but
demands an 7.5 percent required
return.
‹ What is the most Homer would
pay for this bond?
Let’s Play with Example #1
some more.
‹ Barney
(belch!) Gumble is
interested in buying a Duff Beer
bond and demands on a 6
percent required return.
‹ What is the most Barney (belch!)
would pay for this bond?
75
75
75
...
1000
75
1
2
3
...
15
75
75
75
...
1000
75
1
2
3
...
15
r = 7.5%
?
0
r = 6%
Another Example 1 Lesson:
Bond Premiums and
Discounts
Lesson from Example 1: Bond
Prices and Interest Rates have an
inverse relationship!
($)M arket Value
Bond Values for 7.5% Annual Coupon Bond
1400
1200
1000
800
600
400
200
0
|
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
15-yr Bond
0%
2%
4%
6%
8%
10%
r > Coupon Interest Rate
P0 < par value
= DISCOUNT
r = Coupon Interest Rate
P0 = par value
=
r < Coupon Interest Rate
P0 > par value
= PREMIUM
PAR
Required Return
Bonds with Semiannual
Coupons
‹
Double the number of years, and
divide required return and annual
coupon by 2.
Semiannual Example
‹
P0 = C/2(PVFA
/2(PVFAr/2,2n) + F /(1+r/2)2n
‹
‹
Kwickee-Mart has an $1000 par value bond
with an annual coupon rate of 6% that pays
coupons semiannually with 20 years left to
maturity. What is the most you would be
willing to pay for this bond if your required
return is 7% APR?
Semiannual coupon = 6%/2($1000) = $30
20x2 = 40 remaining coupons
0
30
30
30
...
1000
30
1
2
3
...
40
Bond Yields
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Coupon (Current) Yield - Annual coupon
payments divided by bond price.
Yield To Maturity - Interest rate for which
the present value of the bond’s payments
equal the price. Also known as the market’s
required rate of return.
Yield To Maturity = total expected return =
coupon yield + expected capital gains yield
(change in price)
Bond Yields
Yield to Maturity Example
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond
(PV) and the coupon rate, the yield to
maturity can be found by solving for r.
‹
PV =
cpn
cpn
(cpn + par )
+
+....+
1
2
(1 + r ) (1 + r )
(1 + r ) t
Burns Power $1000 face value bond
with a 5% coupon rate paid annually
with 10 years left to maturity sells for
$890.
‹ What is this bond’s yield to maturity?
-890
0
50
50
50
...
1000
50
1
2
3
...
10
What is bond’s YTM?
U.S. Treasury Bond Quotations
RATE
MATURITY
MO/YR
8.875
Feb 19
BID
ASKED
Government Bonds & Notes
139:27
139:28
Par Value = $1000, semi-annual coupons
| Ask Price = 139.875%($1000) = $1398.75
| C/2 = 8.875%($1000)/2 = $44.375
| N = 2019-2006 = 13, 2N = 26
|
4.73
Bid price: the price traders receive if they
sell a bond to the dealer. Quoted in
increments of 32nds of a dollar
Bid prices
Ask prices
(percentage of
par value)
Ask price: the price traders pay to the
dealer to buy a bond
Bid-ask spread: difference between ask
and bid prices.
Yield to maturity on the ask price
Ask Yield
Verifying the T-bond’s YTM
(Ask Yld)
3
Coupon rate of 8.875%
Rate
What is the bond’s current yield?
ASK
YLD
CHG
Corporate Bond Quotations
Company
(Ticker)
Coupon
Maturity
Last
Price
Last Yield
Estimated
Spread
UST
Est $ Vol
(000s)
Ford
6.625
Feb15,20
28
68.25
10.298
565
30
110,064
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
The greater the default risk, the higher
the yield spread
Causes of Bond Price
Changes
Bond Value Changes Over
Time
Since a bond’s cash flows are fixed:
1. Changes in interest rates, and
2. Passage of time.
cause changes in a bond’s price.
‹
Interest Rate Risk
Interest Rate Risk Example
Measures Bond Price Sensitivity to
changes in interest rates.
| In general, long-term bonds have
more interest rate risk than short-term
bonds.
| Also, for bonds with same time to
maturity, lower coupon bonds have
more interest rate risk than higher
coupon bonds.
|
|
‹
|
Returning to the Duff’s Beer original
example #1, where k = 9%, N = 15, C
(PMT) = $75, par (FV) = $1000, & PV =
$879.09.
What is bond value one year later when N =
14 and r is still = 9%?
Recall from our earlier example (#1), the
15-year, 7.5% annual coupon bond has the
following values at kd = 6%, 7.5%, & 9%.
Let’s compare with a 2-yr, 7.5% annual
coupon bond.
15-year bond
2-year bond
r=6%: PV = $1,145.68
r=7.5%: PV = $1,000
r=9%: PV = $879.09
PV = $1,027.50
PV = $1,000
PV = $973.61
Interest Rate Risk: Bond
Price Sensitivity Graph
Bond Values for 7.5% Annual Coupon Bonds
2400
2150
1900
1650
1400
1150
900
650
400
2.0%
2-yr Bond
15-yr Bond
30-yr Bond
4.0%
6.0%
Moody' s
Aaa
AAA
Aa
AA
A
A
Baa
BBB
Ba
B
BB
B
Caa
Ca
C
CCC
CC
C
Credit risk
| Default premium
| Investment grade
| Speculative grade (Junk bonds)
|
8.0% 10.0% 12.0% 14.0%
Default Risk
Standard
& Poor's
Default Risk
Safety
The strongest rating; ability to repay interest and principal
is very strong.
Very strong likelihood that interest and principal will be
repaid
Strong ability to repay, but some vulnerability to changes in
circumstances
Adequate capacity to repay; more vulnerability to changes
in economic circumstances
Considerable uncertainty about ability to repay.
Likelihood of interest and principal payments over
sustained periods is questionable.
Bonds in the Caa/CCC and Ca/CC classes may already be
in default or in danger of imminent default
C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
Bonds by Issuer
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
• 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)
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
Bonds by Features
(Continued)
Zero-Coupon
Bonds
• Discount bonds or pure discount
bonds
• Sell below par value
• Treasury Bills (Tbills)
• Treasury STRIPs
Convertible
and
Exchangeable
Bonds
• 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