Chapter 03  Valuing Bonds
31
CHAPTER 3
Valuing Bonds
Answers to Problem Sets
1.
a.
Does not change
b.
Price falls
c.
Yield rises.
2.
a.
If the coupon rate is higher than the yield, then investors must be
expecting a decline in the capital value of the bond over its remaining life.
Thus, the bond’s price must be greater than its face value.
b.
Conversely, if the yield is greater than the coupon, the price will be below
face value and it will rise over the remaining life of the bond.
3.
The yield over 6 months is 3.965/2 = 1.79825%.
Therefore, PV = 3/1.0179825 + 3/1.0179825
2
+…. + 103/1.0179825
34
= 130.37
4.
Yields to maturity are about 4.3% for the 2% coupon, 4.2% for the 4% coupon,
and 3.9% for the 8% coupon. The 8% bond had the shortest duration (7.65
years), the 2% bond the longest (9.07 years).
5.
a.
Fall (e.g., 1year 10% bond is worth 110/1.1 5 100 if r 5 10% and is worth
110/1.15 = 95.65 if r = 15%).
b.
Less (e.g., See 5a).
c.
Less (e.g., with r = 5%, 1year 10% bond is worth 110/1.05 = 104.76).
d.
Higher (e.g., if r = 10%, 1year 10% bond is worth 110/1.1 = 100, while 1
year 8% bond is worth 108/1.1 = 98.18).
e.
No, lowcoupon bonds have longer durations (unless there is only one
period to maturity) and are therefore more volatile (e.g., if r falls from 10%
to 5%, the value of a 2year 10% bond rises from 100 to 109.3 (a rise of
9.3%). The value of a 2year 5% bond rises from 91.3 to 100 (a rise of
9.5%).
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 Spring '11
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