CHAPTER 4
Bonds and Their Valuation




Key features of bonds
Bond valuation
Measuring yield
Assessing risk
6-1
Definition of a Bond

A bond is a security that obligates the
issuer to make specified interest and
principal payments to the holder on
specified dates.




Coupon rate
Face value (or par)
Maturity (or term)
Bonds are sometimes called fixed
income securities.
6-2
Valuation of Financial Assets: Bonds long term debt instruments
Key Terms


Principal Amount, Face Value, Maturity Value,
Par Value: The amount of money the firm
borrows and promises to repay at some
future date, often at maturity.
Coupon Payment: The specified number of
dollars of interest paid each period, generally
each six months, on a bond.
6-3
Key Terms


Coupon Interest Rate: The stated annual
rate of interest paid on a bond.
Maturity Date: A specified date on which the
par value of a bond must be repaid.
6-4
Types of Bonds



Pure Discount or Zero-Coupon Bonds
 Pay no coupons prior to maturity.
 Pay the bond’s face value at maturity.
Coupon Bonds
 Pay a stated coupon at periodic intervals
prior to maturity.
 Pay the bond’s face value at maturity.
Perpetual Bonds (Consols)
 No maturity date.
 Pay a stated coupon at periodic intervals. 6-5
Bond Issuers



Federal Government
Local Municipalities
Corporations
6-6
U.S. Government Bonds

Treasury Bills




No coupons (zero coupon security)
Face value paid at maturity
Maturities up to one year
Treasury Notes



Coupons paid semiannually
Face value paid at maturity
Maturities from 2-10 years
6-7
U.S. Government Bonds

Treasury Bonds





Coupons paid semiannually
Face value paid at maturity
Maturities over 10 years
The 30-year bond is called the long bond.
Treasury Strips


Zero-coupon bond
Created by “stripping” the coupons and
principal from Treasury bonds and notes.
6-8
Yield Curve
6-9
Municipal Bonds



Maturities from one month to 40 years.
Exempt from federal, state, and local
taxes.
Generally two types:



Revenue bonds
General Obligation bonds
Riskier than U.S. Government bonds.
6-10
Corporate Bonds

Secured Bonds (Asset-Backed)



Secured by real property
Ownership of the property reverts to the
bondholders upon default.
Debentures


General creditors
Have priority over stockholders, but are
subordinate to secured debt.
6-11
Basic Valuation
From “The Time Value of Money”
we realize that the value of
anything is based on the present
value of the cash flows the asset
is expected to produce in the
future.
6-12
Basic Valuation
^
CF
^
CF
Asset
1
2
 V 


1
2
value
1  k  1  k 
N

 1  k 
t 1

^
CF

^
CF
N
1  k 
N
^
CF = the cash flow expected to
t
t
t
be generated by the asset in
period t
k = the return investors consider appropriate for holding
such an asset--usually referred to as the required return-6-13
based on riskiness and economic conditions.
The Basic Bond
Valuation Model




kd = required rate of return on a debt
instrument
N = number of years before the bond
matures
INT = dollars of interest paid each year
(Coupon rate x Par value)
M = par or face, value of the bond to be
paid off at maturity
6-14
Bond Value
V
d

INT
INT

1  k d 1 1  k d 2
 
INT

M
1  k d N 1  k d N
INT
M
N

N
 
t
1 k
1 k
d
d
t 1




6-15
Value of a Bond
What is the value of a 10-year, 10%
semiannual coupon bond, if kd = 10%?
=PV(0.05,20,100,1000,0) = ?
INPUTS
OUTPUT
20
5
N
I/YR
PV
50
1000
PMT
FV
?
6-16
Value of a Bond
What is the value of a 10-year, 10%
semiannual coupon bond, if kd = 12%?
=PV
INPUTS
N
OUTPUT
I/YR
PV
PMT
FV
?
6-17
Value of a Bond
What is the value of a 10-year, 10%
semiannual coupon bond, if kd = 8%?
=PV
INPUTS
N
OUTPUT
I/YR
PV
PMT
FV
?
6-18
Changes in Bond Values Over
Time

Par Bond ($1,000):


Discount Bond (< $1,000):


A bond that sells at par value, which occurs whenever the
going rate of interest is equal to the coupon rate.
A bond that sells below its par value, which occurs
whenever the going rate of interest rises above the coupon
rate.
Premium Bond (>$1,000):

A bond that sells above its par value, which occurs
whenever the going rate of interest falls below the coupon
rate.
6-19
Yield-to-maturity (YTM)

What is the YTM of a 10-year, 10%
semiannual coupon bond, if the current
price is $1,000?
=RATE(20,50,-1000,1000,0) = ?
INPUTS
20
N
OUTPUT
I/YR
- 1,000
50
1000
PV
PMT
FV
?
6-20
Yield-to-maturity (YTM)

What is the YTM of a 10-year, 10%
semiannual coupon bond, if the
current price is $1,100?
=RATE
INPUTS
N
OUTPUT
I/YR
PV
PMT
FV
?
6-21
Yield-to-maturity (YTM)

What is the YTM of a 10-year, 10%
semiannual coupon bond, if the
current price is $900?
=RATE
INPUTS
N
OUTPUT
I/YR
PV
PMT
FV
?
6-22
Changes in Bond Values Over
Time



An increase in interest rates will cause the
price of an outstanding bond to fall.
A decrease in interest rates will cause the
price to rise.
The market value of a bond will always
approach its par value as its maturity date
approaches, provided the firm does not go
bankrupt.
6-23
Time path of
value of a 15%
Coupon,
$1000 par value
bond when
interest rates are
10%, 15%, and
20%
Year
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
k d = 10%
$1,380.30
$1,368.33
$1,355.17
$1,340.68
$1,324.75
$1,307.23
$1,287.95
$1,266.75
$1,243.42
$1,217.76
$1,189.54
$1,158.49
$1,124.34
$1,086.78
$1,045.45
$1,000.00
k d = 15% k d = 20%
$1,000.00
$766.23
$1,000.00
$769.47
$1,000.00
$773.37
$1,000.00
$778.04
$1,000.00
$783.65
$1,000.00
$790.38
$1,000.00
$798.45
$1,000.00
$808.14
$1,000.00
$819.77
$1,000.00
$833.72
$1,000.00
$850.47
$1,000.00
$870.56
$1,000.00
$894.68
$1,000.00
$923.61
$1,000.00
$958.33
$1,000.00 $1,000.00
6-24
Changes in Bond Values Over
Time

Time path of value of a 15% Coupon, $1000 par value
bond when interest rates are 10%, 15%, and 20%
Bond Value
$1,500
kd < Coupon Rate
$1,250
kd = Coupon Rate
$1,000
$750
kd > Coupon Rate
$500
$250
$0
1
3
5
7
9
11
13
15
Years
6-25
YTM = CY + CGY





YTM = Total return
Current Yield (CY) = Return from Interest
Capital Gains Yield (CGY) = Return from
the difference in purchase price and face
value
CY = Annual Int ($) / Price ($)
CGY = YTM - CY
6-26
An example:
Current and capital gains yield

Find the current yield and the capital gains
yield for a 10-year, 9% semiannual coupon
bond that sells for $887, and has a face
value of $1,000.
YTM = 10.88%
Current yield = $90 / $887 = 0.1015 = 10.15%
CGY= YTM – CY = 10.88% - 10.15% = 0.73%
6-27
Call provision (YTC)
A bond that sells for $950, has five years to
maturity, 10 percent semi-annual coupon,
and is callable in 2 years at a $50 call
premium. What is the yield-to-call?
 YTC = RATE(4,50,-950,1050) = ?
6-28
Call provision (YTC)
A bond that sells for $1075, has 14 years to
maturity, 8 percent semi-annual coupon,
and is callable in 5 years at a $50 call
premium. What is the yield-to-call?
 YTC = ?
6-29
Interest rate risk
6-30
Interest rate risk
6-31
Interest rate risk
6-32
Interest rate risk
6-33
Default risk


If an issuer defaults, investors receive
less than the promised return.
Therefore, the expected return on
corporate and municipal bonds is less
than the promised return.
Influenced by the issuer’s financial
strength and the terms of the bond
contract.
6-34
Bond Ratings
Moody’s
S&P
Quality of Issue
Aaa
AAA
Highest quality. Very small risk of default.
Aa
AA
A
A
Baa
BBB
Ba
BB
B
B
Caa
CCC
Ca
CC
High specullative quality. May be in default.
C
C
Lowest rated. Poor prospects of repayment.
D
-
In default.
High quality. Small risk of default.
High-Medium quality. Strong attributes, but potentially
vulnerable.
Medium quality. Currently adequate, but potentially
unreliable.
Some speculative element. Long-run prospects
questionable.
Able to pay currently, but at risk of default in the
future.
Poor quality. Clear danger of default .
6-35
Factors affecting default risk and
bond ratings

Financial performance




Debt ratio
TIE ratio
Current ratio
Bond contract provisions




Secured vs. Unsecured debt
Senior vs. subordinated debt
Guarantee and sinking fund provisions
Debt maturity
6-36