–
AAA, AA, A, and BBB are deemed “investment
grade”
–
Ratings below BBB are more “speculative”
FIN 300 - Bonds Pt. 1
9

Bond Math
•
Now to the mathematics of bonds
•
Just re-use the previous time-value of money
formulas: PV of the ordinary annuity & lump-
sum
•
For exams
–
There will be some qualitative, conceptual
questions – but, they will be focused less on
definitions/vocabulary and more on the intuition
of what causes the change in prices and rates of
return, or yields
FIN 300 - Bonds Pt. 1
10

Bond Math
•
In this class, we will keep it pretty simple and focus
on 2 basic types of bonds
–
Coupon-paying (or, “coupon”) bonds
–
Zero-coupon bonds
•
In our calculations, we will not be so concerned as to
whether the bond is a treasury, corporate, muni, etc.
•
Our basic bond math applies across many segments
of the bond market and covers the majority of bonds
–
Of course, there are many bonds that involve
quite complicated rules & math – we’ll leave that
alone
FIN 300 - Bonds Pt. 1
11

Coupon (Paying) Bond
•
A coupon bond pays both:
–
A series of repeated, identical
coupon payments
(think of this as a series of interest payments)
–
Plus a
large lump-sum payment made at the end
of the bond’s life – this is known as the face-value
(or par value) of the bond
•
You might think of this as a “balloon” payment due at
maturity, or the end of the life of the bond
FIN 300 - Bonds Pt. 1
12

Coupon Rate vs. YTM
•
Coupon Rate
–
Stated in the bond contract
–
Determines the size of the coupon payment relative to the
size of the par (or, face) value
–
It does not change – nor, is it determined by the market
•
Yield - aka. Yield-to-Maturity (YTM)
–
This is determined by the market and may fluctuate from
moment-to-moment
–
This is, in effect, the discount rate used by investors in the
market – to determine a fair market value (or, price)
FIN 300 - Bonds Pt. 1
13

Price a Coupon Bond
•
We will determine the price given:
–
Maturity
– length of time remaining on the bond’s life
–
Par (or, Face) value
– paid at maturity
–
Coupon Rate
– is the yearly sum of the coupon payments
stated as a percentage of par value
–
Yield-to-Maturity (YTM)
– market discount rate that
constantly changes and effects market price of the bond
–
Frequency of coupon
payment
•
Generally coupons are paid semi-annually or annually
•
There are some exceptions, though
•
We will focus on
semi-annual
coupons in this class
–
You will have
only semi-annual on exams!
FIN 300 - Bonds Pt. 1
14

Coupon Bond Diagram
(Semi-Annual)
FIN 300 - Bonds Pt. 1
15
PV = Bond Price
(at T=0, or today)
0.5 yr.
1.0 yr.
1.5yr.
6mths.
before
maturity
C
C
+
Face Value
maturity
C
C
C
We will calculate
an (ordinary
annuity) PV of
just the coupons
Separately we
will calculate
the PV of the
Face Value as
a lump-sum
Price = sum of these 2 PV’s

Semi-Annual Coupon Price
•
From previous slide
–
C = coupon pmt. = (coupon rate x face)/2
–
Face Value = FV = face value is given (not necessarily
the same as bond price)
–
Price (of bond) is the PV of the cash flows
•
PV of the coupon ordinary annuity + PV of the face-
value lump-sum
•
Also, you would be given the YTM & Maturity (in years)
–
Treat YTM as an APR with semi-annual compounding
•
Discount rate/coupon period = YTM/2
–
N = maturity in years x 2
FIN 300 - Bonds Pt. 1
16
Divide by 2,
since “semi”
annual
- if
annual, don’t
div. by 2
Mult. by 2, since “semi”
annual
- if annual,
don’t mult. by 2

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- Fall '08
- Olander
- Corporate Finance, Debt, YTM, Bond Markets, Bonds Pt.