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Lecture 14

BU473 Lecture Notes - Lecture 14: Dirty Price, Accrued Interest, Sinking Fund

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David Cimon

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BU-473 Lecture 14
Bond Characteristics
When bonds are issued, they have fundamental characteristics:
1. The face value is the value paid to holder at maturity
2. Coupon Rate, Rate multiplied by Face value in the form of coupons
3. Bond Indenture, actual contract agreed to by the bond issuer, contains any covenants that form
the bond
4. Yield, percentage rate which we discount bond’s Future value coupons and face value
International Bonds
Often, corporations may want to raise money in other jurisdictions than their operations
When corporations issue in foreign countries, they sometimes issue in foreign currency,
protecting foreign investors from exchange-rate risk
o Yankees (USA), Maples (Canada), Samurai Bonds (Japan), Bulldog Bonds (UK)
Other times they issue in their own currency: called Eurobonds
Special Bond Types
Callable Bonds
o After the call protection period, corporation can buy back the bond at a specific price
Convertible Bonds
o The option to convert the bonds into equity at a specified ratio
Extendable/Retractable Bonds
o Bondholders can extend or retract the maturity of the bond
Floating rate bonds
o Coupon payment adjusts based on some external factor
Problem with Regular Bond Formula
The regular bond formula assumes the coupon payment will be made 6 months from now, but
for most of the time this is not right
The price would rise until the coupon is made, then drop right after then rise progressively again
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Bond Pricing in Reality
Bond Prices in practice:
o Clean/Flat Price
o Dirty/invoice Price
Accrued Interest
Accrued interest accounts for the facts that the coupon becomes more valuable closer to the
date its paid
$100 FV Bond Formula:
 
c is the annual coupon rate, f is the number of coupons per year, DCS is the days between the
last coupon date and the trade settlement date, and DC is the number of days in the coupon
Clean vs. Dirty Price
Dirty price is the actual present value of the bond cash flows
$100 FV, T years left to maturity, c annual coupons:
 
Where y is the yield to maturity, DSC days from settlement date to next coupon, and DC
number of days in coupon period
Clean Price:
   
We have to adjust the formula if coupons are paid more frequently
Yield to Maturity
Bond’s yield is typically the YTM
YTM is the yield that sets the PV of cash flows to current price
We can classify bonds based on whether their coupon is above or below YTM
o Coupon above YTM equals premium, Coupon below YTM equals discount
Yield to Call
Callable bonds have a second yield based on the price they may be called at, YTC
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