Appendix 5A: The Term Structure of Interest Rates,
Spot Rates, and Yields to Maturity
5A.1
a.
The present value of any coupon bond is the present value of its coupon payments and
face value.
Match each cash flow with the appropriate spot rate.
For the cash flow that
occurs at the end of the first year, use the oneyear spot rate.
For the cash flow that
occurs at the end of the second year, use the twoyear spot rate.
P
= C
1
/ (1+r
1
) + (C
2
+F) / (1+r
2
)
2
= $60 / (1.1) + ($60 + $1,000) / (1.11)
2
= $54.55 + $860.32
=
$914.87
The price of the bond is $914.87.
b.
The yield to the maturity is the discount rate,
y
, which sets the cash flows equal to the
price of the bond.
P
= C
1
/ (1+
y
) + (C
2
+F) / (1+
y
)
2
$914.87 = $60 / (1+
y
) + ($60 + $1,000) / (1+
y
)
2
y
= .1097 =
10.97%
The yield to maturity is 10.97%.
5A.2
The present value of any coupon bond is the present value of its coupon payments and face value.
Match each cash flow with the appropriate spot rate.
P
= C
1
/ (1+r
1
) + (C
2
+F) / (1+r
2
)
2
= $50 / (1.10) + ($50 + $1,000) / (1.08)
2
= $45.45 + $900.21
=
$945.66
The price of the bond is $945.66.
5A.3
Apply the forward rate formula to calculate the oneyear rate over the second year.
(1+r
1
)
×
(1+
f
2
)
= (1+r
2
)
2
(1.09)
×
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 Spring '08
 NA
 Interest, Interest Rate, Forward rate, Forward contract, Forward price

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