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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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Nancy Bower
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Chapter 6

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Theory of Finance – Chapter 6
INTEREST RATES AND BOND PRICES
Bond: Government and corporations borrow money from investors by selling them
bonds
o The money governments or companies collect when bonds are issued is
the amount of their debt
o As borrowers, they promise to make a series of interest payments and
then to repay the debt at the maturity date
A bond is a debt security, under which the issuer (government or companies)
owes the holders (investors) a debt, and is obligated to pay them interest
(coupon) and to repay when the maturity level expires.
Coupon: Interest payment paid to the bondholder from the government or
corporations; coupon payments = interest payments
o At maturity, the debt is repaid, when the borrower pays the bond’s face
value to the bondholders
o Before computers, a typical bond had paper coupons that the investors
(bondholders) had to clip off and mail to the bond issuer to claim the
interest payment
Coupon Rate = Bond’s Coupon/Face Value
Face Value: Payment due at the bond’s maturity
Maturity: The date at which the loan will be paid off (when you will get your
interest payment)
Coupon Rate: The annual interest payment divided by the face value of the bond
o How much the interest the company is paying out
o Calculated as a percentage of face value
o Stays the same throughout the life of the bond
Example: Telus bond has a fixed coupon payment, based on its 5.05 percent coupon
rate, and the bond will mature in July 2020. Telus has to make coupon payments for 10
years and then has to repay the $1 billion face value.
Dividend: Your return of the money you invested in stock
o It is your payout from stock shares
Interest Rate (Discount Rate): The rate at which the cash flows from the bond are
discounted to determine its present value The coupon rate and the discount rate are NOT necessarily the same! When they
are not, the price of the bond is NOT the same as its face value
The price of a bond is the present value of all its future cash flows it is the
present value of the coupon payments and the face value of the bond. In
calculating the PV, the ‘appropriate’ opportunity cost has to be used
Buyer needs to compensate seller for interest earned between last coupon
payment and purchase date
Accrued Interest: Coupon interest earned from the last coupon payment to the
purchase date of the bond
Accrued Interest = Coupon Payment x # of days from last coupon to purchase
# of days in coupon period
Assume 180 days in a coupon period – every month has 30 days
Quoted bond prices are clean bond prices
o They do not include any interest accrued since last coupon payment
o Excluding accrued interest
When the coupon rate is equal to the required return, the bond sells at face
value (at par)
When the coupon rate is higher than the required return, the bond sells above
face value (at a premium)
When the coupon rate is lower than the required return, the bond sells below
face value (at a discount) when cash flows are discounted at a rate that is
higher than the bond’s coupon rate it is less than its face value
Bond is an annuity of coupon payments + repayment of face value at maturity
Calculating PV of Bonds
When you calculate the PV of bonds, remember that you are calculating the
PRICE OF THE BOND
o The price of the bond is the PV of all its future coupon payments that are
to be paid to the beholder, plus its face value
o Coupon payments are an annuity
PV = PV (coupon payments) + PV (face value):
t t
Price of a bond = C x [1/r – 1/r(1+r) ] + Face Value/(1+r)
o Use formula to calculate price of a bond or coupon rate Relationship Between: Coupon Rate, YTM, Current Yield, ROR
When the interest rate increases, the price of the bond decreases
When the coupon rate and the market rate are the same, the price of the bond is
face value
Coupon rate > interest rate; bond is selling at a premium
Coupon rate < interest rate; bond is selling at a discount
Semi – Annual Payments: Implies that the annual coupon payment is paid in two
equal installments, every 6 months
o This, the time line must be in six – month periods
o You need to compute the six – month required return
If they are semi – annual coupon payments:
1. Divide coupon payments by 2
2. Multiply the number of years by 2
3. Divide the discount rate by 2
Current Yield: Annual coupon payment divided by the bond price
o The return on one particular coupon payment of a bond
o If a bond sells at par, current yield = coupon rate
o If a bond sells at a premium, current yield < coupon rate (increase
denominator making it less for the coupon rate
o If a bond sell

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