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Chapter 7
Interest Rate and
Bond Valuation
•Homework: 15, 16 17 & 26
Lecture Organization
 Bonds and Bond Features
 Bond Valuation and Bond Return
 Bond Ratings
 Interest Rate Risk
 Real and Nominal Interest Rates
Bond Features
 Bond - evidence of debt issued by a corporation or a
governmental body. A bond represents a loan made by
investors to the issuer. The issuer promises to:
 Make regular coupon payments every period until the
bond matures, and
 Pay the face/par/maturity value of the bond when it
matures.
 Default - since the above-mentioned promises are
contractual obligations, an issuer who fails to keep
them is subject to legal action on behalf of the lenders
(bondholders).
Bond Features (continued)
 If a bond has five years to maturity, an $80 annual coupon,
and a $1000 face value, its cash flows would look like this:
Time
Coupons
Face Value
0
1
2
3
4
5
$80
$80
$80
$80
$80
$ 1000
$______
 How much is this bond worth? It depends on the level of
current market interest rates. If the going rate on bonds
like this one is 10%, then this bond is worth $924.18. Why?
Features of a May Department Stores Bond
Term
Explanation
Amount of issue
$200 million
The company issued $200 million worth
of bonds.
Date of issue
8/4/94
The bonds were sold on 8/4/94.
Maturity
8/1/24
The principal will be paid 30 years after
the issue date.
Face Value
$1,000
The denomination of the bonds is $1,000.
Annual coupon
8.375
Each bondholder will receive $83.75 per
bond per year (8.375% of the face value).
Offer price
100
The offer price will be 100% of the $1,000
face value per bond.
Features of a May Department Stores Bond (concluded)
Term
Explanation
Coupon payment dates
2/1, 8/1
Coupons of $83.75/2 = $41.875 will be
paid on these dates.
Security
None
The bonds are debentures.
Sinking fund
Annual
The firm will make annual payments
beginning 8/1/05 toward the sinking fund.
Call provision
Not callable
before 8/1/04
The bonds have a deferred call feature.
Call price
104.188 initially,
declining to 100
After 8/1/04, the company can buy back
the bonds for $1,041.88 per bond,
declining to $1,000 on 8/1/14.
Rating
Moody’s A2
This is one of Moody’s higher ratings.
The bonds have a low probability of
default.
The Bond Indenture
The Bond Indenture
 The bond indenture is a three-party contract between the
bond issuer, the bondholders, and the trustee. The
trustee is hired by the issuer to protect the bondholders’
interests.
 The indenture includes
 The basic terms of the bond issue
 The total amount of bonds issued
 A description of the security (if any)
 Repayment arrangements
 Call provisions
 Details of the protective covenants
Bond Prices and Yields
 The price of a bond (B) is determined by its face value (F),
the coupon payment per period (C), the number of
periods until maturity times the number of interest rate
periods in a year (T), and the underlying yield to maturity
(y):
T
C
F
B

t
T
(1  y )
t 1 (1  y )
Bond Price Sensitivity to YTM
Bond price
$1,800
Coupon = $100
20 years to maturity
$1,000 face value
$1,600
$1,400
$1,200
$1,000
$ 800
$ 600
Yields to maturity, YTM
4%
6%
8%
10%
12%
14%
16%
Bond Rates and Yields
 Suppose a bond currently sells for $932.90. It pays an
annual coupon of $70, and it matures in 10 years. It has a
face value of $1000. What are its coupon rate, current yield,
and yield to maturity (YTM)?

1. The coupon rate (or just “coupon”) is the annual
dollar coupon expressed as a percentage of the face
value:
Coupon rate =

2. The current yield is the annual coupon divided by
the current market price of the bond:
Current yield =
Under what conditions will the coupon rate and current
yield be the same?
Bond Rates and Yields (concluded)
The yield to maturity (or “YTM”) is the rate that makes the
price of the bond just equal to the present value of its future
cash flows. It is the unknown r in:
 3.
$932.90 = $_______
[1 - 1/(1 + r)10]/r + $_______ /(1 + r)10
To find the YTM is trial and error:
a. Try 10%:
b. Try 9%:
c. Try 8%:
( ) The yield to maturity is
Valuing a Bond
 Assume you have the following information.
Barnhart, Inc. bonds have a $1,000 face value
The promised annual coupon is $100
The bonds mature in 20 years
The market’s required return on similar bonds is 10%

1. Calculate the present value of the face value

2. Calculate the present value of the coupon payments

3. The value of each bond =
Example: A Discount Bond
 Assume you have the following information.
Barnhart, Inc. bonds have a $1,000 face value
The promised annual coupon is $100
The bonds mature in 20 years
The market’s required return on similar bonds is 12%

1. Calculate the present value of the face value

2. Calculate the present value of the coupon payments

3. The value of each bond =
Example: A Premium Bond
 Assume you have the following information.
Barnhart, Inc. bonds have a $1,000 face value
The promised annual coupon is $100
The bonds mature in 20 years
The market’s required return on similar bonds is 8%

1. Calculate the present value of the face value

2. Calculate the present value of the coupon payments

3. The value of each bond =
 Why do the bonds in this and the preceding example have prices
that are different from par?
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Bond Prices Over Time
1100
1050
1000
950
900
Semiannual Coupons
 In practice, bonds issued in Canada usually make coupon
payments twice a year.
 Bond yields are quoted like APRs. The quoted rate is
equal to the actual rate per period multiplied by the
number of periods.
 Suppose the coupon rate is 8%. With a 10% quoted yield
and semiannual coupon payments, the true yield is
________________. The bond matures in 7 years. What is
the bond’s price?
Sample Bond Quotations
Bonds
Supplied by RBC Dominion Securities Inc./
International from Reuters
Coupon
Mat. Date
Bid S
Yld%
6.500
7.750
10.500
7.250
8.200
5.100
Aug 01/99
Sep 01/99
Jul 01/00
Jun 01/07
Jun 30/00
Jun 02/03
101.36
102.87
109.96
113.80
105.42
99.04
5.23
5.25
5.27
5.29
5.35
5.32
6.900
4.500
9.875
6.650
11.000
8.650
Oct 16/01
Dec 06/99
Dec 15/99
Nov 08/27
Jan 11/02
Nov 10/25
104.16
98.73
106.12
107.69
117.46
133.29
5.51
5.41
1
5.53
6.08
5.53
6.13
Government
Canada
Canada
Canada
Canada
OMHC
OMHC
Corporate
Bank of Mont
Cdn Imp Bank
Imperial Oil
Loblaws Co.
Royal Bank
Union Gas
Source: The Financial Post, June 17, 1998, p.45. Used with permission.
Bond Returns
 Holding period return on a bond stems from
1.
2.
 Yield to maturity is internal return on bond but only relevant if
coupons reinvested at same rate up to maturity date
Bond Return Example
 Assume you have a 1-year investment horizon and are
choosing among three investment grade bonds with 10-years
to maturity: a zero-coupon bond, an 8% coupon bond, a 10%
coupon bond. Assume yield to maturity of 8%.
 If the yields on the three bonds are expected to be 8% next
year, what is their holding period return?
Default Risk
 Although all bonds are promises to repay the amount borrowed,
at times firms find themselves unable to pay. The risk that the
firm may not repay the issue is default risk.
 Several agencies quantitatively measure default risk through a
bond rating.

What determines ratings?

Why do firms get rated?
Bond Ratings
Investment-Quality Bond Ratings
Moody’s
DBRS (S&P)
Low Quality, speculative,
and/or “Junk”
High Grade
Medium Grade
Low Grade
Very Low Grade
Aaa
AAA
A
A
Ba
BB
Caa
CCC
Aa
AA
Baa
BBB
B
B
Ca C
CC C
D
D
Moody’s DBRS
Aaa
AAA
Debt rated Aaa and AAA has the highest rating. Capacity to pay
interest and principal is extremely strong.
Aa
AA
Debt rated Aa and AA has a very strong capacity to pay interest and
repay principal. Together with the highest rating, this group
comprises the high-grade bond class.
A
A
Debt rated A has a strong capacity to pay interest and repay
principal, although it is somewhat more susceptible to the adverse
effects of changes in circumstances and economic conditions than
debt in high rated categories.
Bond Ratings (concluded)
Baa
BBB
Debt rated Baa and BBB is regarded as having an
adequate capacity to pay interest and repay principal.
Whereas it normally exhibits adequate protection
parameters, adverse economic conditions or changing
circumstances are more likely to lead to a weakened
capacity to pay interest and repay principal for debt in
this category than in higher rated categories. These
bonds are medium-grade obligations.
Ba, B
Ca, C
BB, B
CC, C
Debt rated in these categories is regarded, on balance, as
predominantly speculative with respect to capacity to pay
interest and repay principal in accordance with the terms of
the obligation. BB and Ba indicate the lowest degree of
speculation, and CC and Ca the highest degree of
speculation. Although such debt will likely have some
quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures to
adverse conditions. Some issues may be in default.
D
D
Debt rated D is in default, and payment of interest and/or
repayment of principal is in arrears
Interest Rate Risk of Bonds
 Risk that the bond you own will change in value because interest
rates (e.g. YTM) have changed
 Review:
 As interest rates rise, PV _________ all else equal
 As interest rates fall, PV _________ all else equal
Determinants of the Interest Rate Risk of Bonds
 Time to Maturity:
 The longer the time to maturity, the greater the interest rate risk, all
else equal
Reason:

10% 1-year and 30-year bonds. Which bond’s price will change
more with a change in YTM?
Interest Rate Risk and Time to Maturity (Figure 7.2)
Bond values ($)
2,000
$1,768.62
30-year bond
Time to Maturity
1,500
Interest rate
5%
1,000
$1,047.62
1-year bond
$916.67
500
1 year
$1,047.62
$1,768.62
10
1,000.00
1,000.00
15
956.52
671.70
20
916.67
502.11
$502.11
Interest rates (%)
5
10
15
30 years
20
Value of a Bond with a 10% Coupon Rate for Different Interest Rates and Maturities
Determinants of the Interest Rate Risk of Bonds (Continued)
 Coupon Rate:
 The lower the coupon rate, the greater the interest rate risk, all else equal
Reason:

0% 8-year and 10% 8-year bonds. Which one has higher interest rate
sensitivity?
Bond Pricing Theorems
 The following statements about bond pricing are always true.

1. Bond prices and market interest rates move in _______
directions.

2. When a bond’s coupon rate is (greater than / equal to /
less than) the market’s required return, the bond’s
market value will be (greater than / equal to / less than)
its par value.

3. Given two bonds identical but for maturity, the price of
the longer-term bond will change _____ than that of the
shorter-term bond, for a given change in market
interest rates.

4. Given two bonds identical but for coupon, the price of
the lower-coupon bond will change _____ than that of
the higher-coupon bond, for a given change in market
interest rates.
Solution to Problem 7.17
 Bond J has a 4% coupon and Bond K a 10% coupon. Both
have 10 years to maturity, make semiannual payments, and
have 9% YTMs. If market rates rise by 2%, what is the
percentage price change of these bonds? If rates fall by 2%?
What does this say about the risk of lower-coupon bonds?
Current Prices:
Bond J:
Bond K:
Solution to Problem 7.17 (continued)
Prices if market rates rise by 2%:
Bond J:
Bond K:
Solution to Problem 7.17 (continued)
Prices if market rates fall by 2%:
Bond J:
Bond K:
Solution to Problem 7.17 (concluded)
 Percentage Changes in Bond Prices
Bond Prices and Market Rates
7%
9%
11%
_________________________________
Bond J
% chg.
Bond K
% chg.
(
%)
(
%)
(
%)
(
%)
_________________________________
The results above demonstrate that, all else equal, the
price of the ________________ changes more (in
percentage terms) than the price of the _____________
when market rates change.
Floaters and Inverse Floaters
 If interest rates rise:
- value of principal falls (normal).
- current coupon payment increases (floaters).
- current coupon payment falls (inverse floaters!!).
 If interest rates fall:
- value of principal rises (normal).
- current coupon payment falls (floaters).
- current coupon payment rises (inverse floaters!!).
Inverse Floaters
 Constant coupon bonds have ______ interest rate risk
 Floating coupon bonds have _________ interest rate risk.
 Inverse floaters have _________ interest rate risk.
Callable bonds and convertible bonds
 Callable bonds:
- When will issuers call?
- Yield-to-maturity compared with non-callables
 Convertible bonds:
- Why convertible?
What Do They Do on Bay Street and Wall Street
 Often Use Contingent claims pricing
 Important as bonds are risky. Two types of bond price risk:
 Basic Idea:
 Take into account changes in interest rate and probability of
default
Inflation and Returns
 Key issues:

What is the difference between a real and a
nominal return?

How can we convert from one to the other?
 Example:
Suppose we have $1,000, and Diet Coke costs $2.00 per six
pack. We can buy 500 six packs. Now suppose the rate of
inflation is 5%, so that the price rises to $2.10 in one year.
We invest the $1,000 and it grows to $1,100 in one year.
What’s our return in dollars? In six packs?
Inflation and Returns (continued)
 A. Dollars. Our return is
B. Six packs.
Inflation and Returns (continued)
 Real versus nominal returns:
Your nominal return is the percentage change in
______________________.
Your real return is the percentage change in
__________________________.
Inflation and Returns (concluded)
 The relationship between real and nominal returns is described by
the Fisher Effect. Let:
R
=
the nominal return
r
=
the real return
h
=
the inflation rate
 According to the Fisher Effect:
1 + R = (1 + r) x (1 + h)
 For example, the nominal return is 10%, the inflation rate is 5%, then
the real return is _______.
U.S. Interest Rates: 1800-1997
The Term Structure of Interest Rates (Fig. 7.4)
The Term Structure of Interest Rates (Fig. 7.4)
Solution to Problem 7.8
 Joe Kernan Corporation has bonds on the market with
10.5 years to maturity, a yield-to-maturity of 8 percent, and
a current price of $850. The bonds make semiannual
payments. What must the coupon rate be on the bonds?
Total number of coupon payments =
Yield to maturity per period
=
Maturity value
= F = $1000
Solution to Problem 7.8 (concluded)
 Substituting the values into the bond pricing equation:
Bond
Value
= C/2  [1 - 1/(1 + r )t] / r + F / (1 + r )t