principles of bond pricing

CSC Webinar Series Principles of Bond Pricing

CSC Webinar Series

Principles

CSI Global Education Inc.

Principles of Bond Pricing

Duration: 60 minutes


Agenda1. Presentation and reflective questions

2. Questions and answersAudio Mode: Mic & Speakers

CSI Global Education Inc. 2


PresenterScott Boniferro

CFP, FMA


CFP, FMA

3


Purpose

The purpose of this webinar is to help you develop a better understanding of:

principles of bond pricing, and;


principles of bond pricing, and;

how to calculate price and yield on a bond.


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:


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?


Webinar Topics

Bond Price Calculating the price of a bond

How changes in interest rates affect bond prices



Yield

Calculating the yield on a bond

6


Bond Price



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.



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?


Quoted Price Trading at:

102 Premium

100 Par

98 Discount


What is Bond Price?

102

P

r

i

c

e


Maturity100

98

P

r

i

c

e


ExampleBond A is trading at a premium to par.



A 5.5% 5 102.19 5.0%


Question



Calculating the Price of a Bond



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


3. Calculate the present value of the income stream4. Add the amounts from steps 2 and 3



Formula for Manual Calculation:

Bond Price = PV of the Principal + PV of the Income Stream

1


+ CPrincipal(1 + r)nr

1 - (1 + r)n1

=



Issuer Coupon Maturity Price Par Value Yield

Example:


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?




C 6% 8 ? $1000 5.25%


Step 1: Choose a discount rate

(The yield is the discount rate.)




C 6% 8 ? $1000 5.25%


Step 2: Calculate PV of the Principal

Principal

Discount Rate

Compounding Periods

Principal(1 + r)n=




C 6% 8 ? $1000 5.25%


Principal

Discount Rate

Compounding Periods

$1,000





C 6% 8 ? $1000 5.25%


Principal

Discount Rate

Compounding Periods

Semi-annual 5.25% 2 = 2.625%





C 6% 8 ? $1000 5.25%


Principal

Discount Rate

Compounding Periods8 2 = 16





C 6% 8 ? $1000 5.25%


= $1,000 (1 + 2.625%)16= $1,000 (1.02625)16= $1,000 1.5137= $660.6329

Calculation


Principal(1 + r)n=




C 6% 8 ? $1000 5.25%


Step 3: Calculate PV of the Income StreamCoupon Rate

Coupon Payment

Compounding Periods

Discount Rate

= Cr

1 - (1 + r)n1




C 6% 8 ? $1000 5.25%


Coupon Rate

Coupon Payment

Compounding Periods

Discount Rate

6% 2 = 3%

Step 3: Calculate PV of the Income Stream




C 6% 8 ? $1000 5.25%


Coupon Rate

Coupon Payment

Compounding Periods

Discount Rate

$1,000 3% = $30





C 6% 8 ? $1000 5.25%


Coupon Rate

Coupon Payment

Compounding Periods

Discount Rate

8 2 = 16





C 6% 8 ? $1000 5.25%


Coupon Rate

Coupon Payment

Compounding Periods

Discount Rate

Semi-annual 5.25% 2 = 2.625%





C 6% 8 ? $1000 5.25%


Calculation

$387.8671 (12.9289) 30 0.026255

0.3394 30

0.02625(1.02625)

1 - 1

30 16

==

=

=


= Cr

1 - (1 + r)n1




C 6% 8 ? $1000 5.25%


Step 4: Add the amounts from steps 2 and 3




C 6% 8 ? $1000 5.25%


Formula:Bond Price = PV of the Principal + PV of the Income Stream

660.6329 + 387.8671


30




C 6% 8 $1048.50 $1000 5.25%


1048.4999

Formula:Bond Price = PV of the Principal + PV of the Income Stream

660.6329 + 387.8671



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


3. Calculate the present value of the income stream

4. Add the amounts from steps 2 and 3


Calculating the Price of a Bond using a Financial Calculator

FV I/Y PMT PVN

Calculator Keys


FV I/Y PMT PVNN FV I/Y PVPMT



FV I/Y PMT PVN

Calculator Keys


Number of payments or years

N FV I/Y PVPMT

FV I/Y PMT PVN



FV I/Y PMT PVN

Calculator Keys


Future valueN FV I/Y PVPMT

FV I/Y PMT PVN



FV I/Y PMT PVN

Calculator Keys


Interest rateN FV I/Y PVPMT

FV I/Y PMT PVN



FV I/Y PMT PVN

Calculator Keys


Coupon paymentN FV I/Y PVPMT

FV I/Y PMT PVN



FV I/Y PMT PVN

Calculator Keys


Present valueN FV I/Y PVPMT

FV I/Y PMT PVN



FV I/Y PMT PVN

Calculator Keys


N FV I/Y PVPMT

FV I/Y PMT PVN



C 6% 8 ? $1000 5.25%



C 6% 8 ? $1000 5.25%

I/YFV PVPMTN



C 6% 8 ? $1000 5.25%



C 6% 8 ? $1000 5.25%

8 2 = 16

I/YFV PVPMTN



C 6% 8 ? $1000 5.25%



C 6% 8 ? $1000 5.25%

$1,000

I/YFV PVPMTN



C 6% 8 ? $1000 5.25%



C 6% 8 ? $1000 5.25%

5.25% 2 = 2.625%

I/YFV PVPMTN



C 6% 8 ? $1000 5.25%



C 6% 8 ? $1000 5.25%

(6% 1,000) 2 = $30

I/YFV PVPMTN



C 6% 8 $1048.48 $1000 5.25%



C 6% 8 $1048.48 $1000 5.25%

- $1,048.48

I/YFV PVPMTN


Relationship between Bond Prices and Market Interest Rates

Market Interest Rates


Interest Rates

Bond Prices


Type your questions in the Questions window Hit the Send button

What questions do you have?

Audio Mode: Mic & Speakers



Yield



What is Yield?Yield is the rate of return an investor can expect to receive on a bond.



Why is Yield Important?Yield is used to compare bonds that have similar characteristics.



Example


C 6% 8 1048.499 $1000 5.25%



Types of Yield

Yield-to-MaturityCurrent Yield



Types of Yield


The current yield:


is the income return on the investment, and

considers only coupon income and current price.


Types of Yield


The yield-to-maturity:


is the total income on investment, and

assumes bond income is reinvested and compounded.


Difference between Coupon and Yield


C 6% 8 1048.499 $1000 5.25%





C 6% 8 1048.499 $1000 5.25%


Fixed for the term of the bond.

Coupon

56




C 6% 8 1048.499 $1000 5.25%


Fixed for the term of the bond.

YieldCoupon

Can fluctuate due to changes in:Market interest ratesMarket conditions

57


Question



Calculating the Yield on a Bond




Formula for Manual Calculation:

Interest income Annual price change(Purchase price + 100) 2= x 100



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


4. Calculate the yield-to-maturity



Example:

Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 ?


D 5.5% 5 $1021.90 $1000 ?

What is the yield on Bond D?





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









Price change = $1,000 $1,021.90= 21.90Annual price change = 21.90 5= 4.38









= ($1,021.90 + $1,000) 2= $2,021.90 2= $1,010.95



Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 5.01%






= (55-4.38) 1,010.95 100= 50.62 1,010.95 100

= 5.0072= 5.01%


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


4. Calculate the yield-to-maturity


Calculating the Yield on a Bond using a Financial Calculator

FV PV PMT I/YN

Same Calculator Keys


FV PV PMT I/YNN FV I/YPV PMT





PVFV I/YPMTN





5 years

PVFV I/YPMTN





$1,000

PVFV I/YPMTN





- $1,021.90

PVFV I/YPMTN





$55 (5.5% 1,000)

PVFV I/YPMTN





4.9924% or 4.99%

PVFV I/YPMTN


Issuer Coupon Maturity Price Par Value YieldD 5.5% 5 $1021.90 $1000 4.99%



4.9924%

PVFV I/YPMTN


Summary



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


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.


Summary: Revisiting the client scenario


X 5.5% 10 years 107.98 4.5%



X 5.5% 10 years 107.98 4.5%

Y 4.5% 5 years 95.67 5.5%






X 5.5% 10 years 107.98 4.5%



X 5.5% 10 years 107.98 4.5%

Y 4.5% 5 years 95.67 5.5%




Bond Price Calculating the price of a bond


Summary: Topics covered today


Yield

Calculating the yield on a bond


Type your questions in the Questions window Hit the Send button

What questions do you have?

Audio Mode: Mic & Speakers



All the best!


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