15 - 1
Bonds
15
& SF
Chapter 15
McGraw-Hill Ryerson©
Bonds
15
Learning Objectives
& SF
After completing this chapter, you will be able to:
Calculate
LO 1.
… the market price of a bond on any date
LO 2.
… the yield to maturity of a bond on any
interest payment date
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Bonds
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& SF
… fixed Income investments
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Bonds
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Basic Concepts & Definitions of
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Main Characteristics
Face Value (or denomination)
… the principal amount that the issuer is
required to pay to the bond holder on
the maturity date
Coupon
… interest rate paid on face value
… rate normally fixed for life of bond
… paid semiannually
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Bonds
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Basic Concepts & Definitions of
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Main Characteristics
… a bond is basically a loan used to raise funds for the
organization or institution, e.g. CSB’s, Municipalities…
… the issue date is the date on which the loan was made
and on which interest starts to accrue
… are fixed Income investments i.e. they have a fixed interest
rate or coupon payable on the principal amount
… borrower is required to make periodic payments of interest only
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Bonds
15
Basic Concepts & Definitions of
& SF
Main Characteristics
… issued with maturities ranging from 2
… on the maturity
to 30 years
date of the bond,
the full principal amount is repaid
along with the final interest payment
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15 - 7
Bonds
15
& SF
Do Canada Savings Bonds have exactly the
same characteristics as Marketable Bonds?
Canada Savings
Bonds
You can cash in a CSB
before its scheduled
maturity date and
receive the
full face value
plus accrued interest
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Marketable
Bonds
You cannot do this
with a M B
If you want to cash in before
it matures, you must do this
through an investment
dealer in the “bond market”
Bonds
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& SF
Effects of Interest Rate
Changes on Bond Prices
15 - 8
Bond
Price
If the market rate falls
below the coupon rate,
the bond’s price rises
above its face value
Coupon
Rate
Market
Rate
Face
Value
If the market rate rises
above the coupon rate,
the bond’s price falls
below its face value
Coupon
Rate
Market
Rate
Face
Value
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Bond
Price
Bonds
15
Effects of Interest Rate
Changes on Bond Prices
& SF
Fair Market
Value of a Bond
Formula
15 - 9
=
+
Present Value of the
Interest Payments
Bond Price = b(FV)
1 – (1 + i)- n
Present Value of
the Face Value
+ FV(1 + i)- n
i
2b = coupon rate (compounded semiannually)
FV = Face Value of the bond
Example
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Bonds
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A $5,000 face value bond has a coupon rate
of 6.6% and a maturity date of March 1, 2018.
LO 1. Interest is paid semi-annually. On September 1, 2002, the
prevailing interest rate on long-term bonds abruptly
rose from 6% to 6.2% compounded semi-annually. What were
the bond's prices before and after the interest rate change?
& SF
FV = 5000
b = 6.6%/2
September 1, 2002 = interest payment date
15.5 years remain until maturity
n = 15.5 * 2 = 31
The semi-annual interest paid on the bond is
b(FV) = 0.033 ($5,000) = $165
Calculation
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Bonds
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& SF
A $5,000 face value
bond has a coupon rate
of 6.6% and a maturity
date of March 1, 2018.
Interest is paid semiannually. On September
1, 2002, the prevailing
interest rate on longterm bonds abruptly
rose from 6% to 6.2%
compounded semiannually. What were
the bond's prices before
and after the interest
rate change?
McGraw-Hill Ryerson©
Calculate the bond price before
the market rate increase.
PV =
2
-5300.01
6
165
31
5000
$5,300.01 is the bond price
before the rate increase
Bonds
15
& SF
A $5,000 face value
bond has a coupon rate
of 6.6% and a maturity
date of March 1, 2018.
Interest is paid semiannually. On September
1, 2002, the prevailing
interest rate on longterm bonds abruptly
rose from 6% to 6.2%
compounded semiannually. What were
the bond's prices before
and after the interest
rate change?
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15 - 12
Calculate the bond price after
the market rate increase.
PV =
-5197.38
6.2
$5,197.38 is the bond price
after the rate increase
Bond price decreased by…
$5,300.01 – 5,197.38
= $128.51
Bonds
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& SF
Calculating the
Yield-to-Maturity of a Bond
LO 2.
The bond’s yield-to-maturity is the
discount rate that makes the
combined…
PV of all remaining interest payments
and the Face Value
equal to
the bond’s Market Value
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Bonds
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Calculating the Yield-to-Maturity
of a Bond
& SF
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A $1,000 face value Province of Manitoba bond, bearing
interest at 5.8% payable semiannually, has 11 years
remaining until maturity. What is the bond’s yield to
maturity (YTM) at its current market price of $972?
I/Y
P/Y ==
2
22
972
6.1542
PMT =
1000*5.8%/2
29
1000
The bond’s YTM is 6.154%
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Bonds
Pricing a Bond
between
Interest Payment Dates
15
& SF
15 - 15
A $1,000, 20 year, 6% coupon bond was issued on
August 15, 2000. It was sold on Nov 3, 2002 to yield
the purchaser 6.5% compounded semiannually until
maturity. At what price did the bond sell?
Calculate the PV of the remaining
payments on the preceding interest
payment date.
Calculate the FV of the Step 1 result on
the date of sale.
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Bonds
15
Pricing a Bond between
Interest Payment Dates
& SF
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A $1,000, 20 year, 6% coupon bond was issued
on August 15, 2000. It was sold on Nov 3, 2002 to yield
the purchaser 6.5% compounded semiannually until
maturity. At what price did the bond sell?
P/V ==
P/Y
Most
recent
interest
payment
date is
August 15,
2002
McGraw-Hill Ryerson©
-947.40
2
2
36
30
6.5
1000
PMT =
1000*6.0%/2
On August 15, 2002, the bond’s value is
$947.40
Bonds
15
& SF
Pricing a Bond between
Interest Payment Dates
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A $1,000, 20 year, 6% coupon bond was issued
on August 15, 2000. It was sold on Nov 3, 2002 to yield
the purchaser 6.5% compounded semiannually until
maturity. At what price did the bond sell?
P/V
P/Y ==
-947.402
Calculate the FV of $947.40 on Nov.3, 2002
We need to find:
a) # of days between interest payment dates, and
b) # of days from Aug.15 to Nov.3
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Bonds
15
Using…
& SF
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i Texas Instruments
BAII PLUS
2nd
Calculate…
the time from
Aug. 15th to Nov. 3rd
Date 08.1502
2nd
Date
Enter
DBD = 80
11.0302
Enter
02.1503
Enter
… the time from
Aug. 15th,2002 to
CPT
CPT
Feb. 15th,2003
DBD = 184
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Days Between Dates
Bonds
15
Pricing a Bond between
Interest Payment Dates
& SF
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A $1,000, 20 year, 6% coupon bond was issued
on August 15, 2000. It was sold on Nov 3, 2002 to yield
the purchaser 6.5% compounded semiannually until
maturity. At what price did the bond sell?
FV=
P/Y =
.4348
960.67
.43482
N = 80/184
0
947.40
The bond sold for $960.67 on Nov.3, 2002
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Bonds
15
15 - 20
& SF
Click here: http://www.finpipe.com/fixed.htm
This site provides complete details on how bonds function.
Just click on the areas that the site provides for information.
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Bonds
15
15 - 21
& SF
This completes Chapter 15
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