Chapter 04  Table 42  Notes
1/6
B
ACKGROUND
I
NFORMATION
For a coupon bond with face value
F
, yearly coupon rate
C
r
, the annual coupon payment
C
is determined by the face value and the
yearly coupon rate
r
C
F
C
, and
n
years to maturity.
The maximum price that investors are willing to pay for this coupon bond at the beginning of the current period is the sum of
discounted cash flows in the future,
n
n
i
F
i
C
i
C
i
C
P
)
1
(
)
1
(
...
)
1
(
)
1
(
2
(Equation 1).
There are two components embedded in the price of the coupon bond.
First, it is the discounted future coupon payments from the
current period until the bond matures in
n
years,
n
i
C
i
C
i
C
)
1
(
...
)
1
(
)
1
(
2
, note that even the coupon payment for the current
period will be discounted because the value of the bond (price) is evaluated at the beginning of the current period, but the annual
coupon payment will only be received in the end of each period.
Second, the discounted face value that the bond holder will receive when the bond matures
n
years from the current period,
n
i
F
)
1
(
.
A
PPLICATION TO
T
ABLE
42
Applying the above definition to a coupon bond with a face value
F
of 1000, yearly coupon rate
C
r
of 10%, the term to maturity
n
of 5
years.
The annual coupon payment
C
is 100, which is determined by the face value and the yearly coupon rate
r
C
F
C
.
The value of the coupon bond evaluated at the beginning of the current period
t
is the sum of the discounted future coupon payments
from year
t
until the bond matures in year
t+5
and the discounted face value that the bond holder will receive when the bond matures
in year
t+5
(with everything discounted using the current yield
i
c
of 10% because it is the relevant yield that investors expect to earn in
the next 5 years when it is assumed to remain unchanged until the bond matures),
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Chapter 04  Table 42  Notes
2/6
5
5
4
3
2
)
1
(
)
1
(
)
1
(
)
1
(
)
1
(
)
1
(
c
c
c
c
c
c
t
i
F
i
C
i
C
i
C
i
C
i
C
P
(Equation 2).
That is,
1000
621
62
68
75
83
91
)
1
.
0
1
(
1000
)
1
.
0
1
(
100
)
1
.
0
1
(
100
)
1
.
0
1
(
100
)
1
.
0
1
(
100
)
1
.
0
1
(
100
5
5
4
3
2
t
P
.
The timeline representation of the coupon bond is
1
2
3
4
5
Beginning of
the current
period
t
when the
coupon bond
is evaluated
End of each
period when
the coupon
payment is
received
End of the
period
t+5
when the
face value of
the bond is
received
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 Fall '09
 H
 1.7%, 8.3%, C C C C, C C C, 6 PT

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