AFM273 Chapter Notes - Chapter 6: Spot Contract, Net Present Value, Corporate Bond

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C6: Valuing Bonds
Bond Terminology
Bond: security sold by governments and corporations to raise money from investors today in exchange
for the promised future payment
Bond indenture: terms of the bond, indicates the amounts and dates of all payments to be made
Specifies applicable covenants which protects investors
Maturity date: last repayment date for a bond
Term: time remaining until the repayment date
Bonds make 2 types of payments
1. Coupons
o Promised interest repayments of a bond made at regular intervals up to and including the
maturity date
In NA, coupons are most often paid semi-annually
o Coupon payments CPN is determined from the bond's coupon rate and its face value
Ex. A bond with a face value of $1000 and a coupon rate of 6%, paid semiannually
CPN = 0.06 * 1000 / 2 = $30.0
2. Principal/Face Value
o Usually paid at maturity date, generally face value = $1000
Zero-Coupon Bonds
Zero-coupon bond: bond that does not make coupon payments, only cash payment investor receives
is the face value of the bond at maturity
Ex. Treasury Bills (Govt of Cad bonds) with a maturity date of up to 1 year
Investors in zero-coupon bonds are compensated for the time value of money by paying an initial
price lower than the face value (ex. investing $979.83 today for a $1000 face value bill maturing
in 1 year)
YTM/ IRR of a bond
To measure the rate of return earned by an investor in a bond, we use the IRR (discount rate
which makes the investment's NPV zero)
YTM: Return earned from holding the bond to maturity and receiving the promised face value
payment
Law of One Price implies that the risk-free interest rate for maturity is the YTM for a default-free
zero-coupon bond
o Competitive market risk-free interest rate is 3.5%, so all one year risk free investments must
earn 3.5%
Spot Rates of Interest
Law of One Price guarantees that the spot rate of interest (risk free interest rate)= YTM of a bond
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Coupon Bonds
Coupon bonds: pay investors their face value at maturity, and regular coupon interest payments
Normally issued with maturities of 2, 5, 10, 30 years by the GOC
Discounts and Premiums
Discount
(below par)
Investor who buys the bond will earn a return both from receiving the coupons
AND from receiving a face value that exceeds the price paid for the bond
YTM > coupon rate
Ex. zero coupon bonds are traded as a discount (prior to maturity, price < face
value)
Premium
(above par)
Investors return from the coupons is diminished from receiving a face value less
than the price paid for the bond
YTM < coupon rate
Par
Price = face value
YTM = coupon rate
Most issuers of coupon bonds choose a coupon rate so that bonds will INITIALLY trade at (close
to) par
Time and Bond Prices
Ex. Suppose you purchase a 10 year zero coupon bond with YTM of 4$ (EAR) and Face value of $100.
Initially trade for: 100/1.04^10 = $67.5564
If you sell the bond after 6 years and same TYM, Price is: 100/1.04^4 = $85.4804
o Bond price is higher, discount from face value is smaller when there is less time to maturity
Discount shrinks because the yield has not changed, but there is less time until the
face value will be received
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