T7.1 Chapter Outline
Chapter 7
Interest Rates and Bond Valuation
Chapter Organization
 7.1 Bonds and Bond Valuation
 7.2 More on Bond Features
 7.3 Bond Ratings
 7.4 Some Different Types of Bonds
 7.5 Bond Markets
 7.6 Inflation and Interest Rates
 7.7 Determinants of Bond Yields
 7.8 Summary and Conclusions
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Bond Valuations
2 basic situations:
 For a given bond and a given interest rate – what is the bond
worth – what should I pay for this bond?
 For a given bond and a price for that bond – what is the yield to
maturity (YTM) I will earn?
 Basic premise – bonds are tradeable financial instruments that
change in value driven by a range of factors but in large part
by changing interest rates.
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Slide 2
T7.2 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. In return for his/her money, the investor receives a
legaI claim on future cash flows of the borrower. 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).
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Slide 3
T7.2 Bond Features (concluded)
 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
0
Coupons
Face Value
1
2
3
4
5
$80
$80
$80
$80
$80
$ 1000
Market Price $____
 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 has a market value of $924.18.
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Slide 4
T7.2 Bond Features (concluded)
 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
0
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
 Coupons - the stated interest payments made on the bond
 Face Value - (Par Value) - the principal amount of a bond that is
repaid at the end of the term
 Coupon rate - annual coupon divided by the face value
 Maturity - specified date at which the principal amount is paid
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Slide 5
T7.2 Bond Value
 A bond has five years to maturity, an $80 annual coupon, and a
$1000 face value, its cash flows would look like this:
Time
0
Coupons
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
Market Value = ‘s
PV of the coupon payments (annuity)
+
PV of the principal (PV of a single cash flow)
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Slide 6
T7.2 Bond Value
 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
0
Coupons
1
2
3
4
5
$80
$80
$80
$80
$80
Face Value
$ 1000
Market Value with r @ 10% = ?
PV of the coupon payments (annuity) - $303.26
PV of the principal (PV of a single cash flow) - $620.92
=‘s $924.18
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Slide 7
T7.3 Bond Rates and Yields
 Consider again our example bond. It sells for $924.18, pays an
annual coupon of $80, and it matures in 5 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 as a percentage of the face value:
Coupon rate = $80 /$1000 = 8%

2. The current yield is the annual coupon divided by
the current market price of the bond:
Current yield = $80 / 924.18 = 8.66%
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Slide 8
T7.2 Bond Yield to Maturity - YTM
 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
YTM - the market interest rate that equates a bond’s
present value of interest payments and principal
repayment with its price
If you paid $924.18 for this bond and received the above
cash flows - what is the YTM?
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Slide 9
T7.3 Bond Rates and Yields (concluded)
 3.
The yield to maturity (or “YTM”) is the rate that makes the
market price of the bond equal to the present value of its
future cash flows. It is the unknown r in the equation below:
$924.18 = $80  [1 - 1/(1 + r)5]/r + $1000/(1 + r)5
The only way to find the YTM is by trial and error:
a. Try 8%: $80  [1 - 1/(1.08)5]/.08 + $1000/(1.08)5 = $1000
b. Try 9%: $80  [1 - 1/(1.09)5]/.09 + $1000/(1.09)5 = $961.10
c. Try 10%: $80  [(1 - 1/(1.10)5]/.10 + $1000/(1.10)5 = $924.18
So, the yield to maturity is 10%.
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Slide 10
Bond Values and YTM
Let’s understand what has happened before going much
further........
• We have a 5 year bond that with a coupon of $80
• Face Value is $1000 - principal repayment in 5 years time
will be $1000
• Interest rates for 5 year bonds were about 8% when the
bond was issued - let’s assume this - so the bond would
have been issued at $1000
• interest rates change - 5 year interest rates move up to
the 10% level
The value of this bond has declined - because there are
competing products in the market place paying 10%
interest when this bond only pays 8% - to buy this bond
and still earn a 10% YTM I should only pay $924.18
What should we conclude? - bond values move up and
down in response to financial events - in this case a
change in interest rates
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Slide 11
Bond Values and Yields - what is the relationship?
 there is a relationship between the value of the bond and
rates of return (YTM) in market equilibrium

when interest rates change - we suddenly do not have market
equilibrium - to achieve equilibrium the values of existing
bonds in the marketplace need to shift to reflect the new
financial reality!

If interest rates move up - bond values decline
If interest rates move down - bond values increase

.....as the bond market strives for equilibrium in the face of
changes in the financial/business marketplace
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Slide 12
T7.4 Valuing a Bond
 Let’s do another one. Assume you have the following information.
Seagrams bonds have a $1000 face value.
The promised annual coupon is $100.
The bonds mature in 20 years.
The market’s required return on similar bonds is 10%
What is the bond’s value?

1. Calculate the present value of the face value
= $1000  [1/1.1020 ] = $1000  .14864 = $148.64

2. Calculate the present value of the coupon payments
= $100  [1 - (1/1.1020)]/.10 = $100  8.5136 = $851.36

3. The value of each bond = $148.64 + 851.36 = $1000
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Slide 13
T7.5 Example: A Discount Bond
 Assume you have the following information.
Seagrams bonds have a $1000 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
= $1000  [1/1.1220 ] = $1000  .10366 = $103.66

2. Calculate the present value of the coupon payments
= $100  [1 - (1/1.1220)]/.12 = $100  7.4694 = $746.94

3. The value of each bond = $103.66 + 746.94 = $850.60
Why is this bond selling at a discount to its face value?
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Slide 14
T7.6 Example: A Premium Bond

Now you have the following information.
Seagrams bonds have a $1000 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
= $1000  [1/1.0820 ] = $1000  .21455 = $214.55

2. Calculate the present value of the coupon payments
= $100  [1 - (1/1.0820)]/.08 = $100  9.8181 = $981.81

3. The value of each bond = $214.55 + 981.81 = $1,196.36
Why is this bond selling at a premium to par?
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Slide 15
T7.7 Bond Price Sensitivity to YTM
Bond price
$1,800
Coupon = $100
20 years to maturity
$1,000 face value
$1,600
Key Insight: Bond prices and
YTMs are inversely related.
$1,400
$1,200
$1,000
$ 800
$ 600
Yield to maturity, YTM
4%
6%
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8%
10%
12%
14%
16%
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Slide 16
T7.8 The Bond Pricing Equation
 Bond Value = Present Value of the Coupons
+ Present Value of the Face Value
= C  [1 - 1/(1 + r )t]/r + F  1/(1 + r )t
where:
C = Coupon paid each period
r = Rate per period
t = Number of periods
F = Bond’s face value
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Slide 17
T7.9 Interest Rate Risk and Time to Maturity (Figure 7.2)
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Slide 18
Interest Rate Risk
 the ‘risk that arises for bond owners from fluctuating interest
rates (market yields)’

the risk or sensitivity to interest rate changes is a function of
• time to maturity - the longer the time to maturity the greater
the interest rate risk
• coupon rate - the lower the coupon rate the greater the
interest rate risk

time to maturity - longer term bonds have greater interest rate risk
due to the timing of the the principal repayment - if it occurs in 30
years a small interest rate change can have a major impact on the
PV of that cash flow vs if the principal is due in one year
coupon rate - for a given YTM a higher coupon bond has larger
cash flows earlier than another bond with the same YTM but lower
coupon payments (more of the YTM is made up of the face amount
to be received at maturity)

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Slide 19
T7.10 Summary of Bond Valuation (Table 7.1)
I. Finding the value of a bond
Bond value = C [1 - 1/(1 + r )t]/r + F/(1 + r)t
where: C = Coupon paid each period
r = Rate per period
t = Number of periods
F = Bond’s face value
II. Finding the yield on a bond
Given a bond value, coupon, time to maturity, and face value, it is possible
to find the implicit discount rate, or yield to maturity, by trial and error only.
To do this, try different discount rates until the calculated bond value equals
the given bond value. Remember that increasing the rate decreases the
bond value.
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Slide 20
T7.11 Bond Pricing Theorems
 The following statements about bond pricing are always true.

1. Bond prices and market interest rates move in opposite
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 more (in percentage
terms) 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 more (in percentage
terms) than that of the higher-coupon bond, for a given
change in market interest rates.
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Slide 21
Bond characteristics & Features
 Debt vs. Equity
 debt is not an ownership interest in the firm - lenders or debt
holders stand in line ahead of common stock holders in terms of a
call on the firms cash flow
interest on debt must be paid before dividend or in the event of
bankruptcy debt holders are paid before any distribution is
made to equity holders
 interest on debt is tax deductible - it is considered a cost of doing
business - dividends paid to stockholders are not tax deductible
 unpaid debt is a liability of the firm - if it is not paid, creditors can
legally claim the assets possibly leading to bankruptcy
 the ideal combination is a debt security that is really equity in
that the firm receives the tax benefits of debt and the
bankruptcy benefits of equity.
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Slide 22
Bond Characteristics cont’d
 Bonds vs Debentures
 a bond is a form of secured debt - certain assets are pledged as
security
 a debenture is a form of unsecured debt - specific assets are not
pledged as security
However, typically the term ‘bond’ is used for all forms of debt
 Public vs Private Debt
 Public debt is offered to the public while private debt is where the
debt is placed with a single lender - often a pension fund,
insurance firm, etc.
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Slide 23
T7.12 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.
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 24
T7.12 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
beginning 8/1/05
The firm will make annual payments
toward the sinking fund.
Call provision
Not callable
before 8/1/04
The bonds have a deferred call feature.
(See Appendix 7C on Canada plus calls.)
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.
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Slide 25
7.13 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
The repayment arrangements
The call provisions
Details of the protective covenants
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Slide 26
Additional Bond Features
 registered vs bearer
 security
 bond
 debenture
 collateral
 mortgage securities
 seniority
 senior
 junior
 subordinated debt
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Slide 27
Additional Bond Features
 Repayment
 repaid at maturity
 early repayment
• sinking fund - an account managed by a bond trustee for the
purpose of repaying the bonds - the trustee uses the funds
and purchases the required amounts in the open market or
calling in a fraction of the outstanding bonds.
• value of a sinking fund to investors - reduces the risk that the
company will be unable to repay the principal at maturity thus
improving the marketability of the bonds
 call provisions
 protective covenants
• part of the loan agreement that limits actions of the borrowing
firm - e.g. restrictions on dividends and sales of major assets
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Slide 28
T7.14 Bond Ratings
Low Quality, speculative,
and/or “Junk”
Investment-Quality Bond Ratings
Moody’s
DBRS (S&P)
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.
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Slide 29
T7.14 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
BB, B
CC, C
Debt rated in these categories is regarded, on balance, as Ca, C
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 out-weighed 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
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Slide 30
Different Types of Bonds
 Stripped bonds - a bond that makes not coupon payments and
is initially priced at a deep discount


because all of the YTM is in the form of the principal repayment
interest is both deductible by the issuer and must be claimed by
the investor - even though there is no interest coupon payments
per se....it is imputed from discount
 Floating Rate Bonds (floaters) - the coupon payments are
adjustable (not fixed like a traditional bond)

were introduced by issuers to control the risk of price fluctuations
due to interest rate shifts.
 Income bond - coupon payments are dependent on company
income - only if that income is sufficient
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Slide 31
Different Types of Bonds Cont’d
 Real Return Bonds - coupons and principal are indexed to
inflation to provide a stated real return
 Convertible Bonds - can be ‘converted’ for a fixed number of
shares of the issuer’s stock - anytime before maturity and at the
holder’s option - are considered a ‘hybrid’ of debt and equity.
The convertible aspect provides the investor with additional
incentive to purchase the bond
 Retractable Bonds or ‘put’ bonds - allows the holder to ‘put’
the bonds back to the issuer or force the issuer to buy the
bonds back at a stated price - this effectively establishes a floor
price for the bonds
......issuers will combine various features at any given point in time to
encourage investors to buy a new bond issue!
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Slide 32
Bond Markets
 OTC (over the counter) market with dealers connected
electronically
 the bond market in trading volume is many times larger than
the trading volume in stocks

the U.S. Treasury market is the largest securities market in the
world in terms of trading volume
 Bond Price Reporting
 unlike stocks that are traded on an exchange - bonds do not have
that price ‘transparency’ - bonds prices are indications only and are
typically provided by bond dealers (not by the TSE for example)
 the Monday edition of the Globe & Mail is one of the best sources
for bond information
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Slide 33
Inflation and Interest Rates
 Real vs Nominal Rates of Return
 nominal rates - interest rates or rates of return that have not been
adjusted for inflation
 real rates - interest rates or rates of return that have been adjusted
for inflation


nominal rate on an investment is the % change in the number of
dollars you have
real rate on an investment is the % change in how much you can
purchase with your dollars or the % change in buying power
 Fisher Effect ( or theory)
 R = (r+h) +( r*h) where R is the Nominal rate, r is the real rate
and h is the rate of inflation
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Slide 34
T7.16 Inflation and Returns
 Key issues:

What is the difference between a real return and a nominal
return?

How can we convert from one to the other?
 Example:
Suppose we have $1000, and 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
$1000 and it grows to $1100 in one year. What’s our return in
dollars? In six packs?
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Slide 35
T7.16 Inflation and Returns (continued)
 A. Dollars. Our return is
($1,100 - $1,000)/$1,000 = $100/$1,000 = .10.
The percentage increase in our investment is 10%;
our return is 10%.
 B. Six packs. We can buy $1,100/$2.10 = 523.81 six packs,
so our return is
(523.81 - 500)/500 = 23.81/500 = 4.76%
The percentage increase in the amount of coke is
4.76%; our return is 4.76%.
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Slide 36
T7.16 Inflation and Returns (continued)
 Real versus nominal returns:
Your nominal return is the percentage change in the
amount of money you have.
Your real return is the percentage change in the
amount of stuff you can actually buy.
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Slide 37
T7.16 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)  (1 + h)
 From the example, the real return is 4.76%; the nominal return is 10%,
and the inflation rate is 5%:
(1 + R) = 1.10
(1 + r)  (1 + h) = 1.0476 x 1.05 = 1.10
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Slide 38
Factors Affecting Bond Yields
What factors affect observed bond yields?
Term Structure of Interest Rates
 The real rate of interest
 Expected future inflation
 Interest rate risk
Other factors
 Default risk premium
 Taxability premium
 Liquidity premium
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Slide 39
T7.17 U.S. Interest Rates: 1800-1997
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Slide 40
Term Structure of Interest Rates
 Term structure of interest rates is the relationship between short
and long term interest rates or
‘the relationship between nominal interest rates on default- free, pure
discount securities and the time to maturity
 What determines the shape of the term structure?
 Real rate of interest - pure time value of money
 rate of inflation
 interest rate risk
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Slide 41
Term Structure of Interest Rates
 Real rate of interest - basic component underlying every
interest rate - it is the ‘economic rent’ or compensation that
investors demand for forgoing the use of their money.

Tends to influence the overall level of rates moreso than the shape
of the structure
 Rate of Inflation - investor demand extra compensation or an
‘inflation premium’ for the expected erosion of the value of their
investment from inflation 
the key here is the expected inflation - if inflation is expected to
be higher in the future then long term rates will reflect this and be
higher than short term rates
 Interest Rate Risk - risk of interest rates changing and the
resulting impact on the value of the security

risk is greater over the longer term so this risk increases with the
length of maturity
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Slide 42
T7.18 The Term Structure of Interest Rates (Fig. 7.6)
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Slide 43
T7.18 The Term Structure of Interest Rates (Fig. 7.6)
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Slide 44
Factors Affecting Bond Yields
Other factors in addition to the Term Structure of Interest Rates
 Credit risk & the default risk premium
• if the risk of default is perceived to be higher - investors will
demand higher compensation - importance of bond ratings
 Taxation - is the return taxable and how is it taxed
 U.S. Vs Canada
 interest and capital gains
 Liquidity & liquidity premium - investors like ‘liquid’ issues
where there is high levels of trading of that issue - provides
confidence - low liquidity leads to higher yields - liquidity
premium demanded by investors increases
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 45
Yield Curve
 the ‘yield curve’ is a reflection of the term structure of interest
rates
 the ‘Canada Yield Curve’ reflecting Govt. of Canada bond
yields is essentially the same
 Corporate yield curves - however bring in these other factors
affecting yields - e.g. default risk premium, etc.
....what does the yield curve look like today?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 46