INTRODUCTION TO
CORPORATE FINANCE
Laurence Booth • W. Sean Cleary
Prepared by
Ken Hartviksen and Robert Ironside
CHAPTER 6
Bond Valuation and Interest
Rates
Lecture Agenda
•
•
•
•
•
•
•
•
Learning Objectives
Important Terms
Basic Structure of Bonds
Bond Valuation
Bond Yields
Interest Rate Determinants
Other Types of Bonds/Debt Instruments
Summary and Conclusions
– Concept Review Questions
CHAPTER 6 – Bond Valuation and Interest Rates
6-3
Learning Objectives
• The basic features of different types of bonds
• How to value bonds given an appropriate discount rate
• How to determine the discount rate or yield given the
market value of a bond
• How market interest rates or yields affect bond investors
• How bond prices change over time
• The factors (both domestic and global) that affect interest
rates
CHAPTER 6 – Bond Valuation and Interest Rates
6-4
Important Chapter Terms
•
•
•
•
•
•
•
•
•
•
•
•
•
Balloon payment
Bills
Bond indenture
Bullet payment
Call prices
Callable bonds
Canada Savings Bonds
Collateral trust bonds
Coupons
Current yield
Debentures
Debt ratings
Default free
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Default risk
Discount (premium)
Duration
Equipment trust certificates
Expectations theory
Extendible bonds
Face value
Floating rate bonds
Interest payments
Interest rate parity (IRP) theory
Interest rate risk
Issue-specific premiums
Liquidity preference theory
Maturity value
CHAPTER 6 – Bond Valuation and Interest Rates
6-5
Important Chapter Terms
•
•
•
•
•
•
•
•
Mortgage bonds
Nominal interest rates
Notes
Paper
Par value
Protective covenants
Purchase fund provisions
Real return bonds
•
•
•
•
•
•
•
•
•
Retractable bonds
Risk-free rate
Sinking fund provisions
Spread
Term structure of interest
rates
Term to maturity
Yield curve
Yield to maturity
Zero coupon bond
CHAPTER 6 – Bond Valuation and Interest Rates
6-6
The Basic Structure of Bonds
• What is a bond?
• In its broadest sense, a bond is any debt
instrument that promises a fixed income stream
to the holder
• Fixed income securities are often classified
according to maturity, as follows:
– Less than one year – Bills or “Paper”
– 1 year < Maturity < 7 years – Notes
– < 7 years – Bonds
CHAPTER 6 – Bond Valuation and Interest Rates
6-7
The Basic Structure of Bonds
• A typical bond has the following characteristics:
– A fixed face or par value, paid to the holder of the
bond, at maturity
– A fixed coupon, which specifies the interest payable
over the life of the bond
• Coupons are usually paid either annually or semi-annually
– A fixed maturity date
CHAPTER 6 – Bond Valuation and Interest Rates
6-8
The Basic Structure of Bonds
• Bonds may be either:
– Bearer bonds
– Registered bonds
• Bond indenture - the contract between the
issuer of the bond and the investors who hold it
• The market price of a bond is equal to the
present value of the payments promised by the
bond
(See the basic pattern of cash flows from a traditional bond on the next slide)
CHAPTER 6 – Bond Valuation and Interest Rates
6-9
The Basic Structure of Bonds
Cash Flow Pattern for a Traditional Coupon-Paying Bond
FIGURE 6-1
0
1
I
2
I
…
3
I
I
n
I
F
I = interest payments, and F = principal repayment
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 10
Cash Flow Pattern of a Bond
0
1
Purchase Coupon
Price
Cash Outflows
to the Investor
2
3
4
n
Coupon
Coupon
Coupon
Coupon +
Face Value
Cash Inflows
to the Investor
The Purchase Price or Market Price of a bond is simply the present
value of the cash inflows, discounted at the bond’s yield-to-maturity
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 11
The Basic Structure of Bonds
• Bond indenture is the contract between the
issuer and the holder. It specifies:
–
–
–
–
–
Details regarding payment terms
Collateral
Positive and negative covenants
Par or face value (usually increments of $1,000)
Bond pricing – usually shown as the price per $100 of
par value, which is equal to the percentage of the
bond’s face value
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 12
The Basic Structure of Bonds
• Term-to-maturity – the time remaining to the
bond’s maturity date
• Coupon rate – the annual percentage interest
paid on the bond’s face value; to calculate the
dollar value of the annual coupon, multiply the
coupon rate by the face value
– If the coupon is paid twice a year, divide the annual
coupon by two
– Example: A $1,000 bond with an 8% coupon rate will
have an $80 coupon if paid annually or a $40 coupon
if paid semi-annually
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 13
Security and Protective Provisions
• Mortgage bonds – secured by real assets
• Debentures – either unsecured or secured with
a floating charge over the firm’s assets
• Collateral trust bonds – secured by a pledge of
financial assets, such as common stock, other
bonds or treasury bills
• Equipment trust certificates – secured by a
pledge of equipment, such as railway rolling
stock
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 14
Security and Protective Provisions
• Covenants
– Positive covenants – things the firm agrees to do
• Supply periodic financial statements
• Maintain certain ratios
– Negative covenants – things the firm agrees not to
do
• Restricts the amount of debt the firm can take on
• Prevents the firm from acquiring or disposing of
assets
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 15
More Bond Features
• Call feature – allows the issuer to redeem or pay
off the bond prior to maturity, usually at a
premium
• Retractable bonds – allows the holder to sell the
bonds back to the issuer before maturity
• Extendible bonds – allows the holder to extend
the maturity of the bond
• Sinking funds – funds set aside by the issuer to
ensure the firm is able to redeem the bond at
maturity
• Convertible bonds – can be converted into
common stock at a pre-determined conversion
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 16
price
Bond Valuation
• The value of a bond is a function of:
–
–
–
–
Par value
Term to maturity
Coupon rate
Investor’s required rate of return (discount rate is also
known as the bond’s yield to maturity)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 17
Bond Value
General Formula
[ 6-1]
1


1

 ( 1  k )n 
1
b
F
B  I 
n
k
(
1

k
)


b
b


Where:
I = interest (or coupon ) payments
kb = the bond discount rate (or market rate)
n = the term to maturity
F = Face (or par) value of the bond
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 18
Bond Valuation: Example
• What is the market price of a ten-year, $1,000 bond
with a 5% coupon, if the bond’s yield-to-maturity is 6%?
1  1  kb  n 
F
BI

n
k
1

k

 
b
b
1  1.06 10  1, 000
 50 

10
0.06

 1.06 
 $926.40
Calculator Approach:
1,000
50
10
I/Y
CPT PV 926.40
CHAPTER 6 – Bond Valuation and Interest Rates
FV
PMT
N
6
6 - 19
Factors Affecting Bond Prices
Bond Price-Yield Curve
When interest rates increase, bond prices fall
FIGURE 6-2
Price
($)
Market Yield (%)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 20
Factors Affecting Bond Prices
• The relationship between the coupon rate and the
bond’s yield-to-maturity (YTM) determines if the bond
will sell at a premium, at a discount, or at par
If
Then
Bond Sells at a:
Coupon < YTM
Market < Face
Discount
Coupon = YTM
Market = Face
Par
Coupon > YTM
Market > Face
Premium
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 21
Bond Valuation: Semi-Annual Coupons
• So far, we have assumed that all bonds have
annual pay coupons. While this is true for many
Eurobonds, it is not true for most domestic bond
issues, which have coupons that are paid semiannually
• To adjust for semi-annual coupons, we must
make three changes:
– Size of the coupon payment (divide by 2)
– Number of periods (multiply by 2)
– Yield-to-maturity (divide by 2)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 22
Bond Valuation: Semi-Annual Coupons
For example, suppose you want to value a five-year,
$10,000 Government of Canada bond with a 4%
coupon, paid twice a year, given a YTM of 6%.
  kb 2 n 
1  1   
I  
F
2 
B

kb
  kb 2 n
2

 1  
2
2

 
  .06 2 x 5 
1   1 
 
400  
10, 000
2  


0.06
  .06 2 x 5
2 

 1 

2
2 

 
Calculator Approach:
10,000
FV
400 ÷ 2 =
PMT
5x2=
N
6 ÷ 2 = I/Y
CPT PV 926.40
 $9,146.98
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 23
Factors Affecting Bond Prices
• There are three factors that affect the price
volatility of a bond
– Yield to maturity
– Time to maturity
– Size of coupon
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 24
Factors Affecting Bond Prices
• Yield to maturity
– Bond prices go down when the YTM goes up
– Bond prices go up when the YTM goes down
• Look at the graph on the next slide. It shows
how the price of a 25 year, 10% coupon bond
changes as the bond’s YTM varies from 1% to
30%
• Note that the graph is not linear – instead it is
said to be convex to the origin
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 25
Factors Affecting Bond Prices
Price and Yield: 25 Year Bond, 10% Coupon
Price per $100 of Face
Value
Price/Yield Relationship
350
300
250
200
150
100
50
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Percent YTM
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 26
Factors Affecting Bond Prices
Bond Convexity
• The convexity of the price/YTM graph reveals
two important insights:
– The price rise due to a fall in YTM is greater than the
price decline due to a rise in YTM, given an identical
change in the YTM
– For a given change in YTM, bond prices will change
more when interest rates are low than when they are
high
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 27
Factors Affecting Bond Prices
• Time to maturity
– Long bonds have greater price volatility than short
bonds
• The longer the bond, the longer the period for which the
cash flows are fixed
• Size of coupon
– Low coupon bonds have greater price volatility
than high coupon bonds
• High coupons act like a stabilizing device, since a greater
proportion of the bond’s total cash flows occur closer to
today & are therefore less affected by a change in YTM
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 28
Interest Rate Risk & Duration
• The sensitivity of bond prices to changes in
interest rates is a measure of the bond’s
interest rate risk
• A bond’s interest rate risk is affected by:
– Yield to maturity
– Term to maturity
– Size of coupon
• These three factors are all captured in one
number called duration
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 29
Duration
• Duration is a measure of interest rate risk
• The higher the duration, the more sensitive the
bond is to changes in interest rates
• A bond’s duration will be higher if its:
– YTM is lower
– Term to maturity is longer
– Coupon is lower
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 30
Bond Quotations
Issuer
Coupon
Maturity
Price
Yield
Canada
5.500
2009-Jun-01
103.79
4.16
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 31
Cash Versus Quoted Prices
• The quoted price is the price reported by the
media
• The cash price is the price paid by an investor
• The cash price includes both the quoted price
plus any interest that has accrued since the last
coupon payment date
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 32
Cash Versus Quoted Price: Example
• Assume you want to purchase a $1,000 bond with a 5%
coupon, paid semi-annually. Today is July 15th. The last
coupon was paid June 30th. If the quoted price is $902,
how much is the cash price?
• Solution: The cash price is equal to:
– Quoted price of $902
– Plus 15 days of interest
Cash price = Quoted Price+ Accrued Interest
 15 
 902  1, 000  0.05  

365


 902  2.05
 $904.05
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 33
Bond Yields
• Yield-to-maturity (YTM) – the discount rate used
to evaluate bonds
– The yield earned by a bond investor who:
• Purchases the bond at the current market price
• Held the bond to maturity
• Reinvested all of the coupons at the YTM
– Is the bond’s Internal Rate of Return (IRR)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 34
Bond Yield to Maturity
[ 6-2]
1

1

 ( 1  YTM) n
B  I 
YTM




1
F
n
(
1

YTM)


• The yield to maturity is that discount rate that causes the
sum of the present value of promised cash flows to
equal the current bond price.
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 35
Solving for YTM
• To solve for YTM, solve for YTM in the following
formula:
1  1  YTM  n 
F
BI

n
YTM

 1  YTM 
• Problem: can’t solve for YTM algebraically; therefore,
must either use a financial calculator, spreadsheet,
trial and error, or approximation formula.
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 36
Solving for YTM
• Example: What is the YTM on a 10 year, 5% coupon
bond (annual pay coupons) that is selling for $980?
1  1  YTM  n 
F
BI

n
YTM

 1  YTM 
1  1  YTM 10 
1, 000
980  50 

10
YTM

 1  YTM 
YTM  5.26%
CHAPTER 6 – Bond Valuation and Interest Rates
Financial Calculator
1,000 FV
980 +/- PV
50
PMT
10
N
I/Y
5.26%
6 - 37
Solving for YTM: Semi-annual Coupons
• When solving for YTM with a semi-annual pay
coupon, the yield obtained must be multiplied
by two to obtain the annual YTM
• Example: What is the YTM for a 20 year, $1,000
bond with a 6% coupon, paid semi-annually,
given a current market price of $1,030?
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 38
Solving for YTM: Semi-annual Coupons
1  1  YTM  n 
F
BI

n
YTM

 1  YTM 
1  1  YTM 40 
1, 000
1, 030  30 

40
YTM
1

YTM


 
YTM  2.87 x 2  5.74%
CHAPTER 6 – Bond Valuation and Interest Rates
Financial Calculator
1,000
FV
1,030 +/- PV
30
PMT
40
N
I/Y
2.87 x 2
= 5.746%
6 - 39
The Approximation Formula
Where
F = Face Value = Par Value = $1,000
B = Bond Price
I = the semi annual coupon interest
N = number of semi-annual periods left to maturity
F-B
I
Semi - annual Yield to Maturity  n
FB
2
YTM  2  semi - annual YTM
YTM  (1  semi - annual YTM) 2  1
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 40
Example
• Find the yield-to-maturity of a 5 year 6% coupon
bond that is currently priced at $850. (Always
assume the coupon interest is paid semiannually.)
• Therefore there is coupon interest of $30 paid
semi-annually
• There are 10 semi-annual periods left until maturity
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 41
Solution
$1,000  $850
F-B
 $30
I
$15  $30
10
n
Semi - annual Yield to Maturity 


 0.0486
FB
$1,850
$925
2
2
YTM  2  semi - annual YTM  0.0486  2  0.09273  9.3%
YTM  (1  semi - annual YTM) 2  1  (1.0486) 2  1  9.97%
The actual answer is 9.87%...so of course, the
approximation approach only gives us an approximate
answer…but that is just fine for tests and exams.
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 42
The Logic of the Equation
Approximation Formula for YTM
• The numerator simply represents the average semiannual returns on the investment; it is made up of two
components:
– The first component is the average capital gain (if it is a discount
bond) or capital loss (if it is a premium priced bond) per semiannual period.
– The second component is the semi-annual coupon interest
received.
• The denominator represents the average price of the
bond.
• Therefore the formula is basically, average semi-annual
return on average investment.
• Of course, we annualize the semi-annual return so that
we can compare this return to other returns on other
investments for comparison purposes.
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 43
Yield to Call
• If a bond has a call feature, the issuer can call
the bond prior to its stated maturity
• To calculate the yield to call, replace the
maturity date with the first call date
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 44
Yield to Call
[ 6-3]
1

1

 ( 1  YTC)n
B  I 
YTC




1
  CP 
n
(
1

YTC)


• The yield to call is that discount rate that causes the
present value of all promised cash flows including the
call price (CP) to equal the current bond price.
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 45
Solving for YTC: Semi-Annual Coupons
YTC on a 20-year 6 percent bond that is callable in five years at a call price of
$1,050. The bond pays semi-annual coupons and is selling for $1,030.
Financial Calculator
1,050
FV
1,030 +/- PV
30
PMT
10
N
I/Y
3.081 x 2
= 6.16%
1


1

 ( 1  YTC)n 
1
B  I 
  CP 
YTC
( 1  YTC)n




1


1

 ( 1  YTC)10 
$1,050
$1,030  $30 

10
YTC

 ( 1  YTC)


YTC  3.081% semi  annually
YTC  3.081%  2  6.16%
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 46
Current Yield
• The current yield is the yield on the bond’s current
market price provided by the annual coupon
– It is not a true measure of the return to the bondholder because it
does not consider potential capital gain or capital losses based
on the relationship between the purchase price of the bond and
it’s par value.
[ 6-4]
Annual interest
CY 
B
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 47
Current Yield
Example
• The current yield is the yield on the bond’s current
market price provided by the annual coupon
• Example: If a bond has a 5.5% annual pay coupon and
the current market price of the bond is $1,050, the
current yield is:
Annual Coupon
Current Market Price
55

1, 050
 5.24%
Current Yield =
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 48
Interest Rate Determinants
• Interest is the “price” of money
• Basis points – 1/100 of 1%
• Interest rates go:
– Up – when the demand for loanable funds rises
– Down – when the demand for loanable funds falls
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 49
Risk-free Interest Rate
• Usually use the yield on short federal
government treasury bills as a proxy for the riskfree rate (RF)
• The risk-free rate is comprised of two
components:
– Real rate – compensation for deferring consumption
– Expected inflation – compensation for the expected
loss in purchasing power
(See Figure 6-3 to see rates of inflation and yields on long Canada bonds since 1961)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 50
Inflation and Yields over Time
FIGURE 6-3
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 51
Fisher Equation
• If we call the risk-free rate the nominal rate, then the
relationship between the real rate, the nominal rate
and expected inflation is usually referred to as the
Fisher Equation (after Irving Fisher)
[ 6-5]
RF  Real rate  Expected inflation
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 52
Fisher Equation
• When inflation is low, can safely use the
approximation formula:
RNominal = RReal + Expected Inflation
• When inflation is high, use the exact form of the
Fisher Equation:
1  RNominal  = 1  RReal 1  Expected
CHAPTER 6 – Bond Valuation and Interest Rates
Inflation 
6 - 53
Fisher Equation
Example
• If the real rate is 3% and the nominal rate is 5.5%, what
is the approximate expected future inflation rate?
RNominal = RReal + Expected Inflation
5.5  3  Expected Inflation
Expected Inflation  2.5%
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 54
Global Influences on Interest Rates
• Canadian domestic interest rates are heavily
influenced by global interest rates
• Interest rate parity (IRP) theory states that FX
forward rates will be established that equalize
the yield an investor can earn, whether
investing domestically or in a foreign
jurisdiction
– A country with high inflation and high interest rates
will have a depreciating currency
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 55
Term Structure of Interest Rates
• Is that set of rates (YTM) for a given risk-class
of debt securities (for example, Government of
Canada Bonds) at a given point in time.
• When plotted on a graph, the line is called a
Yield Curve
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 56
Term Structure of Interest Rates
• The Yield Curve is the graph created by putting
term to maturity on the X axis, YTM on the Y axis
and then plotting the yield at each maturity.
• The four typical shapes of yield curves:
•
•
•
•
Upward sloping (the most common shape)
Downward sloping
Flat
Humped
(See Figure 6-4 for Yield curves that existed at various times in Canada)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 57
Historical Yield Curves
1990, 1994, 1998, 2004
FIGURE 6-4
16
14
12
Percent
10
8
6
4
2
0
1 mth
3 mths
6 mths
1 yr
2yrs
5 yrs
7 yrs
10 yrs
30 yrs
Term Left to Maturity
1990
1994
1998
CHAPTER 6 – Bond Valuation and Interest Rates
2004
6 - 58
Theories of the Term Structure
• Three theories are used to explain the shape of
the term structure
– Liquidity preference theory
• Investors must be paid a “liquidity premium” to hold less
liquid, long-term debt
– Expectations theory
• The long rate is the average of expected future short interest
rates
– Market segmentation theory
• Distinct markets exist for securities of different maturities
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 59
Term Structure of Interest Rates
Risk Premiums
• More risky bonds (i.e.. BBB rated Corporate Bonds) will
have their own yield curve and it will plot at higher YTM
at every term to maturity because of the default risk that
BBBs carry
• The difference between the YTM on a 10-year BBB
corporate bond and a 10-year Government of Canada
bond is called a yield spread and represents a defaultrisk premium investors demand for investing in more
risky securities.
• Spreads will increase when pessimism increases in the
economy
• Spreads will narrow during times of economic expansion
6 - 60
(confidence) CHAPTER 6 – Bond Valuation and Interest Rates
Yield Curves for Different Risk Classes
Risk Premiums (Yield Spreads)
16
14
12
Yield
Spread
Percent
10
8
6
4
2
0
1 mth
3 mths
6 mths
1 yr
2yrs
5 yrs
7 yrs
10 yrs
30 yrs
Term Left to Maturity
BBB Corporates
Government of Canada Bonds
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 61
Risk Premiums
• The YTM on a corporate bond is comprised of:
[ 6-6]
k b  YTM  RF  / - Maturity yield differenti al  Spread
• The maturity yield differential is explained by the term
structure
• Spread is the additional yield due to default risk
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 62
Debt Ratings
• All publicly traded bonds are assigned a “risk
rating” by a rating agency, such as Dominion
Bond Rating Service (DBRS), Standard & Poors
(S&P), Moodys, Fitch, etc.
• Bonds are categorized as
– Investment grade – top four rating categories (AAA,
AA, A & BBB)
– Junk or high yield – everything below investment
grade (BB, B, CCC, CC, D, Suspended)
CHAPTER 6 – Bond Valuation and Interest Rates
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Why Do Bonds Have Different Yields?
• Default risk – the higher the default risk, the
higher the required YTM
• Liquidity – the less liquid the bond, the higher
the required YTM
• Call features – increase required YTM
• Extendible feature – reduce required YTM
• Retractable feature – reduce required YTM
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 64
Treasury Bills
• Treasury bills are short-term obligations of government
with an initial term to maturity of one year or less
• Issued at a discount and mature at face value
• The difference between the issue price and the face
value is treated as interest income
• To calculate the price of a T-bill, use the following
formula
PT Bill 
F
n
1  BEY  
B
Where:
P = market price of the T Bill
F = face value of the T Bill
BEY = the bond equivalent yield
n = the number of days until maturity
B = the annual basis (365 days in Canada)
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 65
Treasury Bills: Example
• What is the price of a $1,000,000 Canadian T bill with 80
days to maturity and a BEY of 4.5%?
PT Bill 
F
n
1  BEY  
B
1, 000, 000

 80 
1  .045 

365


 $990, 233.32
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 66
Solving for Yield on a T Bill
• To solve for the yield on a T bill, rearrange the previous
formula and solve for BEY.
• Example: What is the yield on a $100,000 T bill with 180
days to maturity and a market price of $98,200?
BEY 
F PB
 
P n
100, 000  98, 200  365 



98, 200
 180 
 3.72%
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 67
Zero Coupon Bonds
• A zero coupon bond is a bond issued at a
discount that matures at par or face value
• A zero coupon bond has no reinvestment rate
risk, since there are no coupons to be
reinvested
• To calculate the price of a zero coupon bond,
solve for the PV of the face amount
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 68
Zero Coupon Bonds
• Example: What is the market price of a $50,000 zero
coupon bond with 25 years to maturity that is
currently yielding 6%?
B

F
1  kb 
n
50, 000
1.06 
25
 $11, 649.93
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 69
Floating Rate & Real Return Bonds
• Floating rate bonds have a coupon that floats
with some reference rate, such as the yield on T
bills
– Because the coupon floats, the market price will
typically be close to the bond’s face value
• Real return bonds are issued by the
Government of Canada to protect investors
against unexpected inflation
– Each period, the face value of the bond is grossed up
by the inflation rate. The coupon is then paid on the
grossed up face value.
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Canada Savings Bonds
• A Canada Savings Bond (CSB) is a special type
of bond issued by the Government of Canada
• It is issued in two forms:
– Regular interest – interest is paid annually
– Compound interest – interest compounds over the life
of the bond
• CSBs are redeemable at any chartered bank in
Canada at their face value
• There is no secondary market for CSBs
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 71
Summary and Conclusions
In this chapter you have learned:
– About the nature of bonds as an investment
– How to value a bond using discounted cash flow
concepts
– About the determinants of interest rates and theories
used to explain the term structure of interest rates
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 72
Copyright
Copyright © 2007 John Wiley & Sons Canada, Ltd. All rights
reserved. Reproduction or translation of this work beyond that
permitted by Access Copyright (the Canadian copyright licensing
agency) is unlawful. Requests for further information should be
addressed to the Permissions Department, John Wiley & Sons
Canada, Ltd. The purchaser may make back-up copies for his or her
own use only and not for distribution or resale. The author and the
publisher assume no responsibility for errors, omissions, or
damages caused by the use of these files or programs or from the
use of the information contained herein.
CHAPTER 6 – Bond Valuation and Interest Rates
6 - 73