principles of bond pricing
DESCRIPTION
Short presentation from on calculating bond prices.TRANSCRIPT
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CSC Webinar Series Principles of Bond Pricing
CSC Webinar Series
Principles
CSI Global Education Inc.
Principles of Bond Pricing
Duration: 60 minutes
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CSC Webinar Series Principles of Bond Pricing
Agenda1. Presentation and reflective questions
2. Questions and answersAudio Mode: Mic & Speakers
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CSC Webinar Series Principles of Bond Pricing
PresenterScott Boniferro
CFP, FMA
CSI Global Education Inc.
CFP, FMA
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CSC Webinar Series Principles of Bond Pricing
Purpose
The purpose of this webinar is to help you develop a better understanding of:
principles of bond pricing, and;
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principles of bond pricing, and;
how to calculate price and yield on a bond.
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CSC Webinar Series Principles of Bond Pricing
A Common Scenario
Issuer Coupon Maturity Price Yield
X 5.5% 10 years 107.98 4.5%
Im looking at these two bonds: A client says:
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X 5.5% 10 years 107.98 4.5%
Y 4.5% 5 years 95.67 5.5%
Im leaning toward purchasing Bond X because its coupon rate is higher.
As my financial advisor, which bond would you recommend?
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CSC Webinar Series Principles of Bond Pricing
Webinar Topics
Bond Price Calculating the price of a bond
How changes in interest rates affect bond prices
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How changes in interest rates affect bond prices
Yield
Calculating the yield on a bond
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CSC Webinar Series Principles of Bond Pricing
Bond Price
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CSC Webinar Series Principles of Bond Pricing
What is Bond Price? The price at which someone is willing to buy or sell a
particular bond on the secondary market. It is quoted relative to a base value of 100.
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CSC Webinar Series Principles of Bond Pricing
The price at which someone is willing to buy or sell a particular bond on the secondary market.
It is quoted relative to a base value of 100.
What is Bond Price?
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Quoted Price Trading at:
102 Premium
100 Par
98 Discount
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CSC Webinar Series Principles of Bond Pricing
What is Bond Price?
102
P
r
i
c
e
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Maturity100
98
P
r
i
c
e
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CSC Webinar Series Principles of Bond Pricing
ExampleBond A is trading at a premium to par.
Issuer Coupon Maturity Price Yield
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A 5.5% 5 102.19 5.0%
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CSC Webinar Series Principles of Bond Pricing
Question
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond Steps for Manual Calculation:1. Choose a discount rate2. Calculate the present value of the principal3. Calculate the present value of the income stream
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3. Calculate the present value of the income stream4. Add the amounts from steps 2 and 3
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Formula for Manual Calculation:
Bond Price = PV of the Principal + PV of the Income Stream
1
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+ CPrincipal(1 + r)nr
1 - (1 + r)n1
=
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
Example:
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C 6% 8 ? $1000 5.25%
What would you pay today to invest in Bond C that offers you a guaranteed sum of $1,000 in eight years?
Would you pay $1,000 for it today?
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Step 1: Choose a discount rate
(The yield is the discount rate.)
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Step 2: Calculate PV of the Principal
Principal
Discount Rate
Compounding Periods
Principal(1 + r)n=
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Principal
Discount Rate
Compounding Periods
$1,000
Step 2: Calculate PV of the Principal
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Principal
Discount Rate
Compounding Periods
Semi-annual 5.25% 2 = 2.625%
Step 2: Calculate PV of the Principal
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Principal
Discount Rate
Compounding Periods8 2 = 16
Step 2: Calculate PV of the Principal
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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= $1,000 (1 + 2.625%)16= $1,000 (1.02625)16= $1,000 1.5137= $660.6329
Calculation
Step 2: Calculate PV of the Principal
Principal(1 + r)n=
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Step 3: Calculate PV of the Income StreamCoupon Rate
Coupon Payment
Compounding Periods
Discount Rate
= Cr
1 - (1 + r)n1
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Coupon Rate
Coupon Payment
Compounding Periods
Discount Rate
6% 2 = 3%
Step 3: Calculate PV of the Income Stream
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Coupon Rate
Coupon Payment
Compounding Periods
Discount Rate
$1,000 3% = $30
Step 3: Calculate PV of the Income Stream
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Coupon Rate
Coupon Payment
Compounding Periods
Discount Rate
8 2 = 16
Step 3: Calculate PV of the Income Stream
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Coupon Rate
Coupon Payment
Compounding Periods
Discount Rate
Semi-annual 5.25% 2 = 2.625%
Step 3: Calculate PV of the Income Stream
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Calculation
$387.8671 (12.9289) 30 0.026255
0.3394 30
0.02625(1.02625)
1 - 1
30 16
==
=
=
Step 3: Calculate PV of the Income Stream
= Cr
1 - (1 + r)n1
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Step 4: Add the amounts from steps 2 and 3
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
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Formula:Bond Price = PV of the Principal + PV of the Income Stream
660.6329 + 387.8671
Step 4: Add the amounts from steps 2 and 3
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 $1048.50 $1000 5.25%
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1048.4999
Formula:Bond Price = PV of the Principal + PV of the Income Stream
660.6329 + 387.8671
Step 4: Add the amounts from steps 2 and 3
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond Revisiting the Steps for Manual Calculation:1. Choose a discount rate2. Calculate the present value of the principal3. Calculate the present value of the income
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3. Calculate the present value of the income stream
4. Add the amounts from steps 2 and 3
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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FV I/Y PMT PVNN FV I/Y PVPMT
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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Number of payments or years
N FV I/Y PVPMT
FV I/Y PMT PVN
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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Future valueN FV I/Y PVPMT
FV I/Y PMT PVN
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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Interest rateN FV I/Y PVPMT
FV I/Y PMT PVN
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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Coupon paymentN FV I/Y PVPMT
FV I/Y PMT PVN
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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Present valueN FV I/Y PVPMT
FV I/Y PMT PVN
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CSC Webinar Series Principles of Bond Pricing
Calculating the Price of a Bond using a Financial Calculator
FV I/Y PMT PVN
Calculator Keys
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N FV I/Y PVPMT
FV I/Y PMT PVN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
Calculating the Price of a Bond using a Financial Calculator
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C 6% 8 ? $1000 5.25%
I/YFV PVPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
Calculating the Price of a Bond using a Financial Calculator
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C 6% 8 ? $1000 5.25%
8 2 = 16
I/YFV PVPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
Calculating the Price of a Bond using a Financial Calculator
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C 6% 8 ? $1000 5.25%
$1,000
I/YFV PVPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
Calculating the Price of a Bond using a Financial Calculator
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C 6% 8 ? $1000 5.25%
5.25% 2 = 2.625%
I/YFV PVPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 ? $1000 5.25%
Calculating the Price of a Bond using a Financial Calculator
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C 6% 8 ? $1000 5.25%
(6% 1,000) 2 = $30
I/YFV PVPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 $1048.48 $1000 5.25%
Calculating the Price of a Bond using a Financial Calculator
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C 6% 8 $1048.48 $1000 5.25%
- $1,048.48
I/YFV PVPMTN
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CSC Webinar Series Principles of Bond Pricing
Relationship between Bond Prices and Market Interest Rates
Market Interest Rates
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Interest Rates
Bond Prices
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CSC Webinar Series Principles of Bond Pricing
Type your questions in the Questions window Hit the Send button
What questions do you have?
Audio Mode: Mic & Speakers
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CSC Webinar Series Principles of Bond Pricing
Yield
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CSC Webinar Series Principles of Bond Pricing
What is Yield?Yield is the rate of return an investor can expect to receive on a bond.
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CSC Webinar Series Principles of Bond Pricing
Why is Yield Important?Yield is used to compare bonds that have similar characteristics.
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CSC Webinar Series Principles of Bond Pricing
Example
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 1048.499 $1000 5.25%
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CSC Webinar Series Principles of Bond Pricing
Types of Yield
Yield-to-MaturityCurrent Yield
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CSC Webinar Series Principles of Bond Pricing
Types of Yield
Yield-to-MaturityCurrent Yield
The current yield:
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is the income return on the investment, and
considers only coupon income and current price.
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CSC Webinar Series Principles of Bond Pricing
Types of Yield
Yield-to-MaturityCurrent Yield
The yield-to-maturity:
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is the total income on investment, and
assumes bond income is reinvested and compounded.
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CSC Webinar Series Principles of Bond Pricing
Difference between Coupon and Yield
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 1048.499 $1000 5.25%
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CSC Webinar Series Principles of Bond Pricing
Difference between Coupon and Yield
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 1048.499 $1000 5.25%
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Fixed for the term of the bond.
Coupon
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CSC Webinar Series Principles of Bond Pricing
Difference between Coupon and Yield
Issuer Coupon Maturity Price Par Value Yield
C 6% 8 1048.499 $1000 5.25%
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Fixed for the term of the bond.
YieldCoupon
Can fluctuate due to changes in:Market interest ratesMarket conditions
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CSC Webinar Series Principles of Bond Pricing
Question
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Formula for Manual Calculation:
Interest income Annual price change(Purchase price + 100) 2= x 100
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond Steps for Manual Calculation:1. Calculate interest income 2. Calculate the annual price change3. Calculate the average bond price4. Calculate the yield-to-maturity
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4. Calculate the yield-to-maturity
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Example:
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
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D 5.5% 5 $1021.90 $1000 ?
What is the yield on Bond D?
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
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Calculate interest income
Calculate annual price change
Calculate average bond price
Calculate yield-to-maturity
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
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Calculate interest income
Calculate annual price change
Calculate average bond price
Calculate yield-to-maturity
= $1,000 5.5%= $1,000 0.055= $55.00
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
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Calculate interest income
Calculate annual price change
Calculate average bond price
Calculate yield-to-maturity
Price change = $1,000 $1,021.90= 21.90Annual price change = 21.90 5= 4.38
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
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Calculate interest income
Calculate annual price change
Calculate average bond price
Calculate yield-to-maturity
= ($1,021.90 + $1,000) 2= $2,021.90 2= $1,010.95
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 5.01%
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Calculate interest income
Calculate annual price change
Calculate average bond price
Calculate yield-to-maturity
= (55-4.38) 1,010.95 100= 50.62 1,010.95 100
= 5.0072= 5.01%
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond Revisiting the Step for Manual Calculation:1. Calculate interest income 2. Calculate the annual price change3. Calculate the average bond price4. Calculate the yield-to-maturity
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4. Calculate the yield-to-maturity
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CSC Webinar Series Principles of Bond Pricing
Calculating the Yield on a Bond using a Financial Calculator
FV PV PMT I/YN
Same Calculator Keys
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FV PV PMT I/YNN FV I/YPV PMT
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
Calculating the Yield on a Bond using a Financial Calculator
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PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
Calculating the Yield on a Bond using a Financial Calculator
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5 years
PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
Calculating the Yield on a Bond using a Financial Calculator
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$1,000
PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
Calculating the Yield on a Bond using a Financial Calculator
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- $1,021.90
PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
Calculating the Yield on a Bond using a Financial Calculator
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$55 (5.5% 1,000)
PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?
Calculating the Yield on a Bond using a Financial Calculator
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4.9924% or 4.99%
PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 4.99%
Calculating the Yield on a Bond using a Financial Calculator
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4.9924%
PVFV I/YPMTN
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CSC Webinar Series Principles of Bond Pricing
Summary
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CSC Webinar Series Principles of Bond Pricing
Bonds can trade at a discount, a premium or at par.Bonds always mature at their par value.When interest rates go up, bond prices go down, and
vice versa.
Summary: Key Learning
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vice versa.Yield is a measure of the return on a bond.Yield is used when comparing similar bonds.Yield-to-maturity shows the total return on the bond
between now and maturity.
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CSC Webinar Series Principles of Bond Pricing
Summary: Revisiting the client scenario
Issuer Coupon Maturity Price Yield
X 5.5% 10 years 107.98 4.5%
Im looking at these two bonds: A client says:
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X 5.5% 10 years 107.98 4.5%
Y 4.5% 5 years 95.67 5.5%
Im leaning toward purchasing Bond X because its coupon rate is higher.
As my financial advisor, which bond would you recommend?
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CSC Webinar Series Principles of Bond Pricing
Summary: Revisiting the client scenario
Issuer Coupon Maturity Price Yield
X 5.5% 10 years 107.98 4.5%
Im looking at these two bonds: A client says:
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X 5.5% 10 years 107.98 4.5%
Y 4.5% 5 years 95.67 5.5%
Im leaning toward purchasing Bond X because its coupon rate is higher.
As my financial advisor, which bond would you recommend?
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CSC Webinar Series Principles of Bond Pricing
Summary: Revisiting the client scenario
Issuer Coupon Maturity Price Yield
X 5.5% 10 years 107.98 4.5%
Im looking at these two bonds: A client says:
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X 5.5% 10 years 107.98 4.5%
Y 4.5% 5 years 95.67 5.5%
Im leaning toward purchasing Bond X because its coupon rate is higher.
As my financial advisor, which bond would you recommend?
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CSC Webinar Series Principles of Bond Pricing
Bond Price Calculating the price of a bond
How changes in interest rates affect bond prices
Summary: Topics covered today
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Yield
Calculating the yield on a bond
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CSC Webinar Series Principles of Bond Pricing
Type your questions in the Questions window Hit the Send button
What questions do you have?
Audio Mode: Mic & Speakers
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CSC Webinar Series Principles of Bond Pricing
All the best!
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