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Textbook Notes
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Canada
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University of Guelph
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Economics
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ECON 2560
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Tahsin Mehdi
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Chapter 6

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Economics

ECON 2560

Tahsin Mehdi

Summer

Description

Chapter 6 ECON 2560
Valuing Bonds
BONDS & THE BOND MARKET
Governments & corporations borrow money by selling bonds to investors
Bond market is hug
They money governments or companies collect when bonds are issued is the amount of the debt
As borrowers, they promise to make interest payments & then repay debt at the maturity date
Coupon: The interest payment paid to the bondholder
Face Value: Payment at the maturity of the bond also called maturity value/par value
Bond Market Data
Coupon Rate: Annual interest payment as a percentage of face value
Prices for some government and corporate bonds are reported on the web sites of major newspapers, such as National post
& Globe & Mail, and are typically for the previous day’s trading activity
Price info for all bonds traded in Canada are available via subscription to financial data services such as GlobeInvestor Gold
or through a bond dealer such as TD Waterhouse
Bonds are traded by a network of bond dealers who quote bid and ask prices at which they are prepared to buy & sell
In the past, bonds were traded in an over-the-counter market, in which securities aren’t traded in one central place but
over the telephone
Development of electronic markets for bond trading such as CBID & CanDeal are changing the operation of the
Canadian bond market
Both these allow institutional investors, such as pensions fund, who trade larger dollar values of bonds, to see bond
quotes from multiple bond dealers at same time rather than having to call each dealer for a quote
Can execute a buy or sell order at the best price: increases competition & reduces the spread between bid & ask prices
If you a retail investor, wanted to buy a bond you would have to contact a bond dealer b/c they hold inventories of bonds
and are usually part of financial institutions such as banks or brokerage houses
When you buy a bond you’ll pay more than the ask price if you do not happen to buy the bond on a coupon payment date
The buyer has to compensate seller for the coupon interest earned from the last coupon payment to the settlement
date (date when buyer must pay the money for bond)
Settlement date is usually 3 days after the bond deal is executed
Extra payment is called accrued interest
Accrued interest = coupon payment x (# of days from last coupon to settlement date/ # of days in coupon period)
Accrued interest: Coupon interest earned from the last coupon payment to the purchase date of the bond
Clean Bond Price: Bond price excluding accrued interest
Dirty Bond Price: Bond price including accrued interest
INTEREST RATES & BOND PRICES
The value of the bond is the value of the bond’s cash flows so to find the value you need to identify the bonds cash flows
then calculate the PV of the cash flows using a discount rate that captures the bond’s opportunity cost of capital
Example
*3 year bond interest of $35 per year
*Opportunity cost = 2.15% bonds
Therefore PV = [$35/(1.0215)] + [$35/(1.0215) ] + [$1035/(1.0215) ] = $1038.82
PV (Bond) = PV (Coupons) + PV (Face value)
= (coupon x annuity factor) + (face value x discount factor)
= $35 x [(1/.0215) – (1/.0215(1.0215) )] + 1,000 x [1/(1.0215) ]
= $1038.82 How Bond Prices Vary W/ Interest Rates
As interest rates change so do bond prices
When discount rate is the same as the coupon rate, the bond sells for its face value
When cash flows are discounted at a rate higher than the bond’s coupon rate, the bond is worth less than its face value and
vice-versa
CURRENT YIELD & YIELD TO MATURITY
Current Yield: Annual coupon payment divided by current bond price
Premium Bond: A bond that sells for more than its face value
Discount Bond: A bond that sells for less than its face value
Yield to maturity: Interest rate for which the PV of the bond’s payments equals the price
A measure of the bond’s total return including both coupon income and capital gain
If investor buys bond today and holds it till maturity, his return will be the yield to maturity
Can calculate this by trail & error
Bond rates of Return
Rate of return: Total income per period per dollar invested
The yield to maturity is defined as the discount rate that equates the bond’s current price to the PVB of all its promised
future cash flows
Measures the rate of return that you will earn if you buy bond today and hold it till maturity
BUT interest rates fluctuate and the return you earn in the interim may be way different from the yield to maturity
Rate of Return = (coupon income + price change) / investment
Taxes & Rates of Return
Taxes reduce the rate of return on an investment
Tax on coupon = personal tax rate x coupon income
After-tax coupon income = coupon income = tax on coupon
Tax on capital gain = personal tax rate x .5 x capital gain
After-tax capital gain = capital gain – tax on capital gain
After-tax rate of return = (after-tax coupon income + after-tax capital gain) / investment
Multi-period rates of return
How to calculate the rate of return if investment lasts longer than 1 year…
Rate of Return = (coupon income + price change) / investment
The effective annual equivalent is (rate of retu-1 = annual rate of return (if this is a 2 year rate of return)
THE YIELD CURVE
The longer the maturity of bonds, the slightly higher the yield
Usually the case but SOMETIMES long-term bonds offer lower yields
Yield Curve/Term Structure of interest rates: Graph of the relationsh

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