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1
FIN340
PRACTICE PROBLEM SET 6
BOND VALUATION
1.
Suppose that currently 5year government bonds are selling at a yield of four
percent. Please determine the value a 5year government bond with a 6 percent
coupon rate and a face value of 1,000.
a.
Start by assuming that the bond is issued by a continental
European government and makes annual coupon payments.
[Solution] With annual coupon payments of 0.06*1,000 = 60, the value of
the bond can be determined by the annuity formula plus discounting the
repayment of principal after 5 years:
1,089.04
(1.04)
1,000
(1.04)
0.04
1
0.04
1
60
PV
5
5
=
+
⎥
⎦
⎤
⎢
⎣
⎡
×
−
×
=
b.
Then rework your answer assuming that he bond is issued by the
U.S. Treasury, so that the bond pays semiannual coupons and the
semiannual yield for semiannually compounded US bonds is 2 percent.
[Solution] With semiannual coupon payments of 0.03*1,000 = 30:
1,089.83
(1.02)
1,000
(1.02)
0.02
1
0.02
1
30
PV
10
10
=
+
⎥
⎦
⎤
⎢
⎣
⎡
×
−
×
=
c.
How would your answers to a. and b. change if the annual
(semiannual) yield drops to 3% (1.5%)?
[Solution] With annual coupon payments:
1,137.39
(1.03)
1,000
(1.03)
0.03
1
0.03
1
60
PV
5
5
=
+
⎥
⎦
⎤
⎢
⎣
⎡
×
−
×
=
With semiannual coupon payments:
1,138.33
(1.015)
1,000
(1.015)
0.015
1
0.015
1
30
PV
10
10
=
+
⎥
⎦
⎤
⎢
⎣
⎡
×
−
×
=
2.
A 6year government bond makes annual coupon payments of 5 percent on a
par value of 1,000 and trades at a yield of 3 percent annually compounded.
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a.
Suppose that one year later the bond still yields three percent.
What return has the bondholder earned over this 12month period?
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 Spring '09
 Narg

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