Post on 01-Jan-2016
McGraw-Hill Ryerson©
1515 1515Bonds
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Bonds
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15 - 1
McGraw-Hill Ryerson©
Chapter 15Chapter 15
McGraw-Hill Ryerson©
1515 1515Bonds
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Bonds
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15 - 2
Calculate
… the market price of a bond on any date
After completing this chapter, you will be able to:
… the yield to maturity of a bond on any interest payment date
Learning ObjectivesLearning Objectives
LO 1.LO 1.
LO 2.LO 2.
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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
Basic Concepts & Definitions of
Main CharacteristicsMain Characteristics
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Basic Concepts & Definitions of
… are fixed Income investments i.e. they have a fixed interest rate or coupon payable on the principal amount
Main CharacteristicsMain Characteristics
… the issue date is the date on which the loan was made and on which interest starts to accrue
… a bond is basically a loan used to raise funds for the organization or institution, e.g. CSB’s, Municipalities…
… borrower is required to make periodic payments of interest only
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Basic Concepts & Definitions of
Main CharacteristicsMain Characteristics
… on the maturity date of the bond,
the full principal amount is repaid along with the final interest payment
… issued with maturities ranging from 2 to 30 years
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Do Canada Savings Bonds have exactly the
same characteristics as Marketable Bonds?Canada Savings
Bonds
Canada Savings Bonds
Marketable Bonds
Marketable Bonds
You can cash in a CSB before its scheduled maturity date and
receive the full face value
plus accrued interest
You can cash in a CSB before its scheduled maturity date and
receive the full face value
plus accrued interest
You cannot do this with a M B
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”
If you want to cash in before it matures, you must do this through an investment
dealer in the “bond market”
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If the market rate falls below the coupon rate, the bond’s price rises above its face value
If the market rate falls below the coupon rate, the bond’s price rises above its face value
If the market rate rises above the coupon rate, the bond’s price falls below its face value
If the market rate rises above the coupon rate, the bond’s price falls below its face value
Market Rate
Market Rate
CouponRate
CouponRate
Bond Price
Bond Price
Face Value
Face Value
Market Rate
Market Rate
CouponRate
CouponRate
Bond Price
Bond Price
Face Value
Face Value
Effects of Interest Rate Changes on Bond Prices
Effects of Interest Rate Changes on Bond Prices
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2b = coupon rate (compounded semiannually)
FV = Face Value of the bond
2b = coupon rate (compounded semiannually)
FV = Face Value of the bond
Effects of Interest Rate Changes on Bond Prices
Effects of Interest Rate Changes on Bond Prices
Fair Market Value of a Bond
Present Value of the Interest Payments
Present Value of the Face Value
Formula Formula Bond Price = b(FV)1 – (1 + i)- n
i+ FV(1 + i)- n
ExampleExample
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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. 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?
The semi-annual interest paid on the bond isb(FV) = 0.033 ($5,000) = $165
The semi-annual interest paid on the bond isb(FV) = 0.033 ($5,000) = $165
FV = b = 6.6%/25000
September 1, 2002 = interest payment date
15.5 years remain until maturity
n = 15.5 * 2 = 31 n = 15.5 * 2 = 31
CalculationCalculation
LO 1.LO 1.
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31
2 6 165
Calculate the bond price before the market rate increase.
5000
$5,300.01 is the bond price before the rate increase
$5,300.01 is the bond price before the rate increase
PV = -5300.01
A $5,000 face value bond has a coupon rate
of 6.6% and a maturity date of March
1, 2018. 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?
A $5,000 face value
bond has a coupon rate of 6.6% and a
maturity date of March 1, 2018.
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?
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6.2
Calculate the bond price after the market rate increase.
$5,197.38 is the bond price after the rate
increase
$5,197.38 is the bond price after the rate
increase
PV = -5197.38
Bond price decreased by…
$5,300.01 – 5,197.38
= $128.51= $128.51
A $5,000 face value
bond has a coupon rate of 6.6% and a
maturity date of March 1, 2018.
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?
A $5,000 face value
bond has a coupon rate of 6.6% and a
maturity date of March 1, 2018.
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?
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The bond’s yield-to-maturity is the discount rate that makes the
combined…
Calculating the Yield-to-Maturity of a
Bond
Calculating the Yield-to-Maturity of a
Bond
PV of all remaining interest payments and the Face Value
equal to
the bond’s Market Value
LO 2.LO 2.
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Calculating the Yield-to-Maturity of a Bond
Calculating the Yield-to-Maturity of a Bond
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?
22922
1000972
P/Y = 2I/Y = 6.154
The bond’s YTM is 6.154% The bond’s YTM is 6.154%
PMT = 1000*5.8%/2
PMT = 1000*5.8%/2
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15 - 15 Pricing a Bond
between Interest Payment Dates
Pricing a Bond between
Interest Payment Dates
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 PV of the remaining payments on the preceding interest
payment date.
Calculate the FV of the Step 1 result on the date of sale.
Calculate the FV of the Step 1 result on the date of sale.
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Pricing a Bond between Interest Payment Dates
Pricing a Bond between Interest Payment Dates
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?
23036
10006.5
P/Y = 2P/V = -947.40
On August 15, 2002, the bond’s value is $947.40
On August 15, 2002, the bond’s value is $947.40
Most recent
interest payment date is
August 15, 2002
Most recent
interest payment date is
August 15, 2002
PMT = 1000*6.0%/2
PMT = 1000*6.0%/2
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Pricing a Bond between Interest Payment Dates
Pricing a Bond between Interest Payment Dates
P/Y = 2P/V = -947.40
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
We need to find: a) # of days between interest payment dates, and
b) # of days from Aug.15 to Nov.3
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?
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11.0302
Using… Texas Instruments BAII PLUS
i
Days Between DatesDays Between Dates
2nd
Enter
Date
CPT
Enter
08.1502
Calculate… the time from Aug.
15th to Nov. 3rd
DBD = 80
… the time from
Aug. 15th,2002 to Feb. 15th,2003
DBD = 184
02.1503
2nd
Date
CPT
Enter
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Pricing a Bond between Interest Payment Dates
Pricing a Bond between Interest Payment Dates
0.4348
947.40
P/Y = 2 .4348
The bond sold for $960.67 on Nov.3, 2002The bond sold for $960.67 on Nov.3, 2002
N = 80/184 N = 80/184FV= 960.67
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?
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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.
This site provides complete details on how bonds function. Just click on the areas that the site provides for information.
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