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

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16 Oct 2016

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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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2

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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