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Student File
Schulich School of Business
FINE 2000
AGENDA
Week 3
•
•
Students who don’t have a registered Mylab account will not be able to participate in the
quizzes, midterm or final exam. Please make sure that the account is setup.
Readings Chapter 6
In Class Problems
Chapter 6: Questions 2, 11, 22, 27, 28
Midterm Preparation
Start to plan for the midterm. Instructors will begin discussing the format in class. Use the study plan to
work on problems.
Next week
•
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Chapters 7 : Stock Valuations
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C O R P O R A T E
F I N A N C E
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COURSE OVERVIEW
AGENDA –
Week 3
• Group Reminder
Assignment
BONDS
IN CLASS QUESTIONS
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Corporate Finance
Student File
Fifth Canadian Edition
Chapter 6
Valuing Bonds
Ch.3.1 and 3.3
Ch.1
not present value
WC
D
E
LIQUIDITY
Bonds
NCA
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Chapter Outline
6.1 Bond Cash Flows, Prices, and Yields
6.2 Dynamic Behaviour of Bond Prices
6.3 The Yield Curve and Bond Arbitrage
6.4 Corporate Bonds
6.5 Sovereign Bonds
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6.1 Bond Cash Flows, Prices, and Yields (1 of 2)
• Bond Terminology
• Bond Certificate
• States the terms of the bond
• Maturity Date
• Final repayment date
• Term
• The time remaining until the repayment date
• Coupon
• Promised interest payments
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6.1 Bond Cash Flows, Prices, and Yields (2 of 2)
• Bond Terminology
• Face Value
EACH BOND IS WORTH THIS MUCH
• Notional amount used to compute the interest payments
• Coupon Rate
• Determines the amount of each coupon payment, expressed as
an APR
• Coupon Payment
Coupon Rate  Face Value
CPN =
Number of Coupon Payments per Year
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Zero-Coupon Bonds (1 of 7)
• Zero-Coupon Bonds
PMT WILL BE 0, THEY WONT PAY YOU ANYTHING
• Does not make coupon payments
• Always sells at a discount (a price lower than face value), so they are also
called pure discount bonds
• Treasury Bills are Government of Canada Bonds that are zero-coupon
bonds with a maturity of up to one year.
Pay $1,000 today and get back %1,000 plus interest after 10 years
No payments on an annual basis
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Zero-Coupon Bonds (2 of 7)
• Suppose that a one-year, risk-free, zero-coupon
bond with a $100,000 face value has an initial price
of $96,618.36. The cash flows would be:
Discount
• Although the bond pays no “interest,” your compensation
is the difference between the initial price and the face
value.
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Zero-Coupon Bonds (3 of 7)
• Yield to Maturity
• The discount rate that sets the present value of the
promised bond payments equal to the current market
price of the bond.
• Price of a Zero-Coupon bond
FV
P=
(1 + YTM n )n
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Zero-Coupon Bonds (4 of 7)
• Yield to Maturity
• For the one-year zero coupon bond:
$100, 000
$96, 618.36 =
(1 + YTM1 )
$100, 000
1 + YTM1 =
= 1.035
$96, 618.36
• Thus, the YTM is 3.5%.
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Zero-Coupon Bonds (5 of 7)
• Yield to Maturity
• Yield to Maturity of an n-Year Zero-Coupon Bond is:
1
 FV  n
YTM n = 
 −1
 P 
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Example 6.1 Yields for Different Maturities
Problem
Suppose the following zero-coupon bonds are trading at the
prices shown below per $100 face value. Determine the
corresponding yield to maturity for each bond.
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Zero-Coupon Bonds (6 of 7)
• Spot Rates of Interest
• The n-period rate of interest, rn, is the rate appropriate for
discounting a risk-free cash flow that occurs on date n, is
called the spot rate of interest.
• A default-free zero-coupon bond that matures on date n
provides a risk-free return over the same period. Thus, the
Law of One Price guarantees that the risk-free interest
rate equals the yield to maturity on such a bond.
• Risk-Free Interest Rate (Spot Rate) with Maturity n
rn = YTM n
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Zero-Coupon Bonds (7 of 7)
• Risk-Free Interest Rates
• Spot Interest Rate
• Another term for a default-free, zero-coupon yield
• Zero-Coupon Yield Curve
• A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity
date
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Coupon Bonds (1 of 3)
• Coupon Bonds
• Pay face value at maturity
• Pay regular coupon interest payments
• Government of Canada Bonds
• The Government of Canada Bonds are sold with maturities of 2, 5, 10, 20, or
30 years.
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Example 6.2 The Cash Flows of a Coupon
Bond (1 of 2)
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Problem
The Government of Canada has just issued a five-year, $1000 bond with a
5% coupon rate and semiannual coupons. What cash flows will you receive
if you hold this bond until maturity?
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Coupon Bonds (2 of 3)
• Yield to Maturity
• The YTM is the single discount rate that equates the
present value of the bond’s remaining cash flows to its
current price.
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Coupon Bonds (3 of 3)
• Yield to Maturity of a Coupon Bond
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Example 6.3 Computing the Yield to
Maturity of a Coupon Bond (1 of 2)
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Problem
Consider the five-year, $1000 bond with a 5% coupon rate and
semiannual coupons described in Example 6.2. If this bond is
currently trading for a price of $957.35, what is the bond’s yield to
maturity?
Discount bond because it is trading for below the par value
YTM (stands for the current interest rate) - Higher becasue trading for dscount to compesate for lower rate, menas annual rate
For this question the answer is 6%
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Example 6.4 Computing a Bond Price From
its Yield to Maturity (1 of 2)
Problem
Consider again the five-year, $1000 bond with a 5% coupon rate and semiannual
coupons in Example 6.3. Suppose you are told that its yield to maturity has increased to
6.30% (expressed as an APR with semiannual compounding). What price is the bond
trading for now?
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6.2 Dynamic Behaviour of Bond Prices
• Discount
YTM > Coupon Rate
• A bond is selling at a discount if the price is less than the face value.
• Par
• A bond is selling at par if the price is equal to the face value.
• Premium
• A bond is selling at a premium if the price is greater than the face value.
YTM < Coupon Rate
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Discounts and Premiums (1 of 3)
• If a coupon bond trades at a discount, an investor will earn a return
both from receiving the coupons and from receiving a face value
that exceeds the price paid for the bond.
Price paid right now is a lot lower
• If a bond trades at a discount, its yield to maturity will exceed its coupon
rate.
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Discounts and Premiums (2 of 3)
• If a coupon bond trades at a premium it will earn a return from
receiving the coupons but this return will be diminished by receiving
a face value less than the price paid for the bond.
• When a bond trades at a price equal to its face value, it is said to
trade at par.
Price will be higher
One increases value and one decreases in value
Premium
1000
Discount
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Maturity
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Discounts and Premiums (3 of 3)
TABLE 6.1 Bond Prices Immediately After a Coupon Payment
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When the bond
price is . . .
greater than the face
value
equal to the face
value
less than the face
value
We say the bond
trades . . .
“above par” or “at a
premium”
“at par”
“below par” or “at a
discount”
This occurs when
the . . .
Coupon Rate >
Yield to Maturity
Coupon Rate =
Yield to Maturity
Coupon Rate <
Yield to Maturity
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Example 6.5 Determining the Discount or
Premium of a Coupon Bond (1 of 2)
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Problem
Consider three 30-year Government of Canada bonds with annual coupon
payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one
has a 3% coupon rate. If the yield to maturity of each bond is 5% (EAR), what is
the price of each bond per $100 face value? Which bond trades at a premium,
which trades at a discount, and which trades at par?
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Time and Bond Prices
• Holding all other things constant, a bond’s yield to maturity will not
change over time.
• Holding all other things constant, the price of a discount or
premium bond will move towards par value over time.
• If a bond’s yield to maturity has not changed, then the IRR of an
investment in the bond equals its yield to maturity even if you sell
the bond early.
when looking at par value of bonds
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Example 6.6 The Effect of Time on the Price
of a Coupon Bond (1 of 4)
Problem
Consider a 30-year Government of Canada bond with a 10% coupon
rate (annual payments) and a $100 face value. What is the initial price
of this bond if it has a 5% (EAR) yield to maturity? If the yield to
maturity is unchanged, what will the price be immediately before
and after the first coupon is paid?
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Figure 6.1 The Effect of Time on Bond Prices
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YTM will stabilize
over time
price will move slowly and then they are smoothed
down with slight decline ebcase coupons are gone
The graph illustrates the effects of the passage of time on bond prices when the yield remains constant.
The price of a zero-coupon bond rises smoothly. The price of a coupon bond also rises between coupon
payments, but tumbles on the coupon date, reflecting the amount of the coupon payment. For each
coupon bond, the grey line shows the trend of the bond price just after each coupon is paid.
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Interest Rate Changes and Bond Prices (1 of 2)
• There is an inverse relationship between interest rates and bond
prices.
Sensitivity is imporatn
• As interest rates and bond yields rise, bond prices fall.
• As interest rates and bond yields fall, bond prices rise.
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Interest Rate Changes and Bond Prices (2 of 2)
• The sensitivity of a bond’s price to changes in interest rates is
measured by the bond’s duration.
• Bonds with high durations are highly sensitive to interest rate changes.
• Bonds with low durations are less sensitive to interest rate changes.
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Example 6.7 The Interest Rate Sensitivity of
Bonds (1 of 2)
Problem
Consider a 15-year zero-coupon bond and a 30-year coupon bond with 10%
annual coupons. Both bonds have a $100 face value. By what percentage will the
price of each bond change if its yield to maturity increases from 5% to 6%?
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Figure 6.2 Yield to Maturity and Bond Price
Fluctuations over Time
Student File
As Figure 6.2 demonstrates, prior to maturity the bond is exposed to interest rate risk. If an investor
chooses to sell and the bond’s yield to maturity has decreased, then the investor will receive a high
price and earn a high return. If the yield to maturity has increased, the bond price is low at the time of
sale and the investor will earn a low return. In the appendix to this chapter, we discuss one way
corporations
manage this type of risk. The graphs illustrate changes in price and yield for a 30-year zero-coupon
bond over its life. The top graph illustrates the changes in the bond’s yield to maturity over its life. In
the bottom graph, the actual bond price is shown in blue. Because the yield to maturity does not remain
constant over the bond’s life, the bond’s price fluctuates as it converges to the face value over time.
Also shown is the price if the yield to maturity remained fixed at 4%, 5%, or 6%.
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6.3 The Yield Curve and Bond Arbitrage
• Using the Law of One Price and the yields of default-free zerocoupon bonds, one can determine the price and yield of any other
default-free bond.
• The yield curve provides sufficient information to evaluate all such
bonds.
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Replicating a Coupon Bond (1 of 3)
• Replicating a three-year $1000 bond that pays 10%
annual coupon using three zero-coupon bonds:
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Replicating a Coupon Bond (2 of 3)
• Yields and Prices (per $100 Face Value) for Zero
Coupon Bonds
TABLE 6.2 Spot Rates and Prices (Per $100 Face Value) for Zero-Coupon Bonds
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Maturity
1 year
2 years
3 years
4 years
rn
3.50%
4.00%
4.50%
4.75%
Price
$96.62
$92.45
$87.63
$83.06
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Replicating a Coupon Bond (3 of 3)
• By the Law of One Price, the three-year coupon bond
must trade for a price of $1153.
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Valuing a Coupon Bond Using Zero-Coupon
Yields or Spot Rates
• The price of a coupon bond must equal the present
value of its coupon payments and face value.
• Price of a Coupon Bond
P = PV (Bond Cash Flows)
=
CPN
CPN
+
+
1 + r1 (1 + r2 ) 2
P=
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+
CPN + FV
(1 + rn ) n
$100 $100 $100 + $1000
+
+
= $1153
2
3
1.035 1.04
1.045
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Coupon Bond Yields
• Given the yields for zero-coupon bonds, we can price
a coupon bond.
100
100
100 + 1000
P = 1153 =
+
+
2
(1 + y) (1 + y)
(1 + y)3
P=
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100
100
100 + 1000
+
+
= $1153
2
3
1.0444 1.0444
1.0444
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Financial Calculator Solution (8 of 9)
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Example 6.8 Yields on Bonds with the Same
Maturity (1 of 3)
Problem
Given the following zero-coupon yields (i.e., spot rates),
compare the yield to maturity for a three-year, zero-coupon
bond; a three-year coupon bond with 4% annual coupons; and
a three-year coupon bond with 10% annual coupons. All of
these bonds are default free.
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6.4 Corporate Bonds
• Corporate Bonds
• Issued by corporations
• Credit Risk
• Risk of default
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Corporate Bond Yields (1 of 9)
• Investors pay less for bonds with credit risk than they would for an
otherwise identical default-free bond.
• The yield of bonds with credit risk will be higher than that of
otherwise identical default-free bonds.
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Corporate Bond Yields (2 of 9)
• No Default
• Consider a 1-year, zero coupon Treasury Bill with a YTM of
4%.
• What is the price?
$1000
$1000
P =
=
= $961.54
1 + YTM 1
1.04
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Corporate Bond Yields (3 of 9)
• Certain Default
• Suppose now bond issuer will pay 90% of the obligation.
• What is the price?
$900
$900
P =
=
= $865.38
1 + YTM 1
1.04
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Corporate Bond Yields (4 of 9)
• Certain Default
• When computing the yield to maturity for a bond with
certain default, the promised rather than the actual cash
flows are used.
FV
$1000
YTM =
−1 =
− 1 = 15.56%
P
865.38
900
= 1.04
865.38
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Corporate Bond Yields (5 of 9)
• Certain Default
• The yield to maturity of a certain default bond is not equal to the expected
return of investing in the bond. The yield to maturity will always be higher
than the expected return of investing in the bond.
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Corporate Bond Yields (6 of 9)
• Risk of Default
• Consider a one-year, $1000, zero-coupon bond issued. Assume that the
bond payoffs are uncertain.
• There is a 50% chance that the bond will repay its face value in full and a 50% chance
that the bond will default and you will receive $900. Thus, you would expect to receive
$950.
• Because of the uncertainty, the discount rate is 5.1%.
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Corporate Bond Yields (7 of 9)
• Risk of Default
• The price of the bond will be
950
P=
= $903.90
1.051
• The yield to maturity will be
FV
1000
YTM =
−1 =
− 1 = 0.1063
P
903.90
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Corporate Bond Yields (8 of 9)
• Risk of Default
• A bond’s expected return will be less than the yield to maturity if there is a
risk of default.
• A higher yield to maturity does not necessarily imply that a bond’s expected
return is higher.
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Corporate Bond Yields (9 of 9)
TABLE 6.3 Price, Expected Return, and Yield to Maturity of a
One-Year, Zero-Coupon Loblaw Bond With Different
Likelihoods of Default
Loblaw Bond (one-year, zero-coupon)
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Bond Price
Yield to Maturity
Expected Return
Default Free
$961.54
4.00%
4.0%
50% Chance of Default
$903.90
10.63%
5.1%
Certain Default
$865.38
15.56%
4.0%
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Bond Ratings (1 of 4)
• Investment Grade Bonds
• Speculative Bonds
• Also known as Junk Bonds or High-Yield Bonds
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Bond Ratings (2 of 5)
Is it ivnestable or non investable
political side is nasty
TABLE 6.4 Bond Ratings
Dominion Bond
Rating Service
(DBRS)
Moody’s
Standard
& Poor’s
Aaa
AAA
Description (Moody’s)
Investment Grade Debt
AAA
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Judged to be of the best quality. They carry the
smallest degree of investment risk and are generally
referred to as “gilt edged.” Interest payments are
protected by a large or an exceptionally stable
margin and principal is secure. While the various
protective elements are likely to change, such
changes as can be visualized are most unlikely to
impair the fundamentally strong position of such
issues.
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Bond Ratings (3 of 5)
TABLE 6.4 (continued)
Dominion Bond
Rating Service
(DBRS)
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Moody’s
Standard
& Poor’s
AA
Aa
AA
Judged to be of high quality by all standards.
Together with the Aaa group, they constitute what
are generally known as high-grade bonds. They are
rated lower than the best bonds because margins of
protection may not be as large as in Aaa securities or
fluctuation of protective elements may be of greater
amplitude or there may be other elements present
that make the long-term risk appear somewhat
larger than the Aaa securities.
A
A
A
Possess many favourable investment attributes and
are considered as upper-medium-grade obligations.
Factors giving security to principal and interest are
considered adequate, but elements may be present
that suggest a susceptibility to impairment some
time in the future.
Description (Moody’s)
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Bond Ratings (4 of 5)
TABLE 6.4 (continued)
Dominion Bond
Rating Service
(DBRS)
BBB
Moody’s
Standard
& Poor’s
Baa
BBB
Anything lowet than BBB is junk bonds, its speculative, its going to ahve a lot of issues in the future
ratings are important factor in investing
poor standing, issue, annual conference
Description (Moody’s)
Are considered as medium-grade obligations
(i.e., they are neither highly protected nor poorly
secured). Interest payments and principal security
appear adequate for the present but certain
protective elements may be lacking or may be
characteristically unreliable over any great length of
time. Such bonds lack outstanding investment
characteristics and, in fact, have speculative
characteristics as well.
Speculative Bonds
BB
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Ba
BB
Judged to have speculative elements; their future
cannot be considered as well assured. Often the
protection of interest and principal payments may
be very moderate, and thereby not well
safeguarded during both good and bad times over
the future. Uncertainty of position characterizes
bonds in this class.
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Bond Ratings (5 of 5)
TABLE 6.4 (continued)
Dominion Bond
Rating Service
(DBRS)
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Moody’s
Standard
& Poor’s
B
B
B
Generally lack characteristics of a desirable
investment. Assurance of interest and principal
payments of maintenance of other terms of the
contract over any long period of time may be small.
CCC
Caa
CCC
Are of poor standing. Such issues may be in default
or there may be present elements of danger with
respect to principal or interest.
CC
Ca
CC
Are speculative to a high degree. Such issues are
often in default or have other marked shortcomings.
C, D
C
C, D
Lowest-rated class of bonds, and issues so rated can
be regarded as having extremely poor prospects of
ever attaining any real investment standing.
Description (Moody’s)
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Corporate Yield Curves
• Default Spread
• Also known as Credit Spread
• The difference between the yield on corporate bonds and Treasury yields
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Figure 6.3 Corporate and Provincial
Yield Curves for January 22, 2020
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Corporate yield curves are higher than govt
can be downgraded because of speculation
This figure shows the coupon-paying yield curve for bonds from the Government of Canada, the
Province of Ontario, and Bell Canada on January 22, 2020. Note how the yield to maturity is higher for
lower-rated bonds, which have a higher probability of default.
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Figure 6.4 Yield Spreads and the
Financial Crisis
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2008 financial crisis
caused high rates
Panel A shows the yield spread between longterm (30-year) U.S. corporate and Treasury
bonds. Panel B shows the yield spread of shortterm loans to major international banks (LIBOR)
and U.S. Treasury bills (also referred to as the
Treasury-Eurodollar or “TED” spread). Note the
dramatic increase in these spreads beginning in
August 2007 and again in September 2008,
before beginning to decline in early 2009. While
spreads returned to pre-crisis levels by the end
of 2010, they increased sharply in the second
half of 2011 in response to the European debt
crisis. Spreads rose again in 2016, partly in
response to concerns about global economic
growth.
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6.5 Sovereign Bonds
• Bonds issued by national governments
• Government of Canada bonds are generally considered to be default free
• All sovereign bonds are not default free
• e.g. Greece defaulted on its outstanding debt in 2012
• Importance of inflation expectations
• Potential to “inflate away” the debt
• European sovereign debt, the EMU, and the ECB
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Figure 6.5 Percent of Debtor Countries in Default or
Restructuring Debt, 1800–2006
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The chart shows, for each five-year period, the average percentage of debtor countries per year that
were either in default or in the process of restructuring their debt. Recent peaks occurred around the
time of World War II and the Latin American, Asian, and Russian debt crises in the 1980s and 1990s.
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Figure 6.6 European Government Bond Yields, 1976–2018
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The plot shows the yield on government debt issued by six countries in the European Currency Union.
Prior to the euro’s introduction in 1999, yields varied in accordance with differing inflation expectations
and currency risk. Yields converged once the euro was introduced, but diverged again after the 2008
financial crisis as investors recognized the possibility of default.
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Q U E S T I O N S ?
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NEXT WEEK
• After completing this week you can work on the following problems
for practice
• Study Plan for Chapter
•7
• Continue working on the study plan questions working towards the
midterm
• At this stage we have completed bond valuation. Next week the
focus will be on stock valuation Chapter 7
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