MGM230 20Class 20 3 Bonds STUDENT 2 Essay

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Lecturer: Tanya Kirsch
Class #3: Bonds
Ross: Ch 7


Additional office hours for Quiz 1
Please check blackboard for additional TA office hours for Quiz 1


• Review of TVM lecture
• Real-life application – a mortgage example
• Objectives for today’s lecture
• Chapter 6: Bonds
• Suggested problems
• Wrap-up and forthcoming attractions


…The average Canadian home sold for $386,585 in June, which means monthly payments of
$1,865 if you assume a 3.39 per cent fixed five-year mortgage rate and a 5 per cent down payment. If prices fell 5 per cent and mortgage rates increased by half a percentage point, the monthly payment is pretty much the same…. To do:
1. Recalculate the monthly payment based on the current average price and mortgage rate (assume a 25 year amortization period)
2. Prove that if prices fell by 5% and mortgage rates increased by half a % cleNews/story/gam/20130716/GICARRICK0715ATL (i.e. to 3.89%), the monthly payment would be the same

TVM application:
You decide to buy an investment that has the following cash flows:
Semi-annual payments of $30 every six months, for 10 years (i.e. 20 payments)
A lumpsum payment of $1,000 at the end of 10 years
The relevant interest rate is 4% for a six month period.
You would like to use formulas to calculate the Present
Value of this investment. Look at the formula sheet, and write down what formula(s) you would use:

Objectives for today’s lecture
1. Apply principles learnt in TVM module to Bonds.
2. Calculate key variables in bond valuation problems
3. Identify the key interest rate and other risk factors for bonds, and explain how these impact the bond price
4. Calculate the yield to maturity and forward rates for a bond, given a set of zero coupon bonds
5. Illustrate an arbitrage opportunity when an implied forward rate differs from that offered by a bank


Chapter 6


Bond Characteristics
• Governments and corporations borrow money for the long term by issuing bonds.
• The bond indenture is the contract between issuer and holder, which specifies, e.g.:

Details regarding payment terms
Par value or face value (usually in increments of
• Bond pricing, usually shown as the price per $100 of par value which is equal to a percentage of the bond’s face value

Bond Characteristics
• Some terminology used with Bonds:

Face value / Principal / Par value
Discount rate / interest rate / required return
Bond price
Maturity date


The Basic Structure of Bonds
• The market price of a bond is the present value of the payments promised by the bond

Coupon Rate vs Discount Rate:
• Note that a coupon rate is not the same as a discount rate
• The coupon rate is the annual interest payment as a percentage of the face value of the bond.
• The interest rate (or discount rate or required return) is the rate at which the cash flows from the bond are discounted to determine its present value.
– This is determined by market-related interest rates

Factors Affecting Bond Prices
Interest rates are inversely related to bond prices:


Factors Affecting Bond Prices
• The relationship between the coupon rate and the bond’s yield to maturity (YTM) determines if the bond will sell at a premium, a discount, or at par
Coupon vs YTM

Price vs Face Value


Coupon Rate < YTM

Price < Face Value


Coupon Rate = YTM

Price = Face Value

At Par

Coupon Rate > YTM

Price > Face Value



The Price of a Bond

PV of annuity formula

B = price of bond
F = Face value
I = Coupon payment kb = discount rate, and for a semi-annual pay bond, is calculated as YTM/2 (i.e. kb is the IRR of the bond)

Yield to maturity

The yield-to-maturity (YTM) is the discount rate that causes the present value of the bond’s future cash flows to equal its current price •

For a bond with semiannual