There are three bonds, each with a coupon of 6.00%, and maturity of 7, 16 and 25
ID: 2740839 • Letter: T
Question
There are three bonds, each with a coupon of 6.00%, and maturity of 7, 16 and 25 years. The market interest rate is 6.23% for all maturities. The par is $1,000.
. (a) Find the price of each bond.
. (b) Suppose the market interest rate now increases to 6.95%. For each bond, find the new price and percentage change in the price (which measures the price sensitivity). What is the relationship among the bonds in terms of bond price sensitivity, i.e. interest rate risk?
. (c) Suppose the market interest rate now decreases to 5.95%. For each bond, find the new price, and percentage change in the price as compared to the initial prices found in (a).
Explanation / Answer
a. Market value of bond with maturity of 7 years = 60 / (1.0623)1 + 60 / (1.0623)2 + 60 / (1.0623)3 + 60 / (1.0623)4 + 60 / (1.0623)5 + 60 / (1.0623)6 + 1060 / (1.0623)7
= 292.92 + 694.34
= $987.26
Similartly, market values of bond with maturity of 16 years = $977.12
Market values of bond with maturity of 25 years = $971.23
b. New market interest rate = 6.95%
New price of bond with 7 years to maturity =
60 / (1.0695)1 + 60 / (1.0695)2 + 60 / (1.0695)3 + 60 / (1.0695)4 + 60 / (1.0695)5 + 60 / (1.0695)6 + 1060 / (1.0695)7
= $948.71
Percentage change in price = [948.71-987.26] / 987.26 x 100 = -3.90%
Similarly, new price of bond with maturity of 16 years = $909.96
Percentage change in price = [909.96-977.12] / 977.12 x 100 = -6.87%
New price of bond with maturity of 25 years = $888.79
Percentage change in price = [888.79-971.23] / 971.23 x 100 = -8.49%
The relationship among the bonds in terms of bond price sensitivity is 'the greater the bond's term to maturity, the greater its price sensitivity to a given change in interest rates.'
c. New bond price with maturity of 7 years = 60 / (1.0595)1 + 60 / (1.0595)2 + 60 / (1.0595)3 + 60 / (1.0595)4 + 60 / (1.0595)5 + 60 / (1.0595)6 + 1060 / (1.0595)7
= $1002.80
Percentage change in price of bond = [1002.80 - 987.26] / 987.26 x 100 = 1.57%
New bond price with maturity of 16 years = $1005.07
Percentage change in price of bond = [1005.07 - 977.12] / 977.12 x 100 = 2.86%
New bond price with 25 years to maturity = $1006.42
Percentage change in price of bond = [1006.42 - 971.23] / 971.23 x 100 = 3.62%
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