An investor has two bonds in his portfolio that have a face value of $1,000 and

Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year.

a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity ant that 15 more payments are to be made on Bond L.

b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change?

Explanation / Answer

At 5%

Price of Bond L = 100/1.05 +100/1.05^2 +100/1.05^3 .........1100/1.05^15

=1,518.98

Price of Bond S =1100/1.05^1=$1047.62

At 8%

Price of Bond L = 100/1.08 +100/1.08^2 +100/1.08^3 .........1100/1.08^15 =$1,171.19

Price of Bond S =1100/1.08^1=$1018.52

At 12%

Price of Bond L = 100/1.12 +100/1.12^2 +100/1.12^3 .........1100/1.12^15 =$863.78

Price of Bond S =1100/1.08^1=$982.14

b.There are two primary reasons why long-term bonds are subject to greaterinterest rate riskthan short-term bonds:

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