Interest Rate Risk. Consider two bonds, a 3-year bond paying an annual coupon of 5% and a 10-year bond also with an annual coupon of 5%. Both currently sell at face value. Now suppose interest rates rise to 10%. (LO6-3) a. What is the new price of the 3-year bonds? b. What is the new price of the 10-year bonds? c. Do you conclude that long-term or short-term bonds are more sensitive to a change in interest rates?

Question

Phoebe Blake

Business

7 October, 22:46

Interest Rate Risk. Consider two bonds, a 3-year bond paying an annual coupon of 5% and a 10-year bond also with an annual coupon of 5%. Both currently sell at face value. Now suppose interest rates rise to 10%. (LO6-3) a. What is the new price of the 3-year bonds? b. What is the new price of the 10-year bonds? c. Do you conclude that long-term or short-term bonds are more sensitive to a change in interest rates?

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Samir Berry · Answer 1

a. $875.66

b. $692.77

c. Long-term bonds are more sensitive to a change in interest rate in comparison to short-term bond.

Explanation:

a.

The new price will be equal to the present value of 03 annual coupon payments of $50 each (1,000 * 5%) plus the present value of principal repayment of $1,000 in three year time; discounted at 10% which is calculated as:

(50/0.1) * [ 1-1.1^ (-3) ] + 1,000/1.1^3 = $875.66

b.

The new price will be equal to the present value of 10 annual coupon payments of $50 each (1,000 * 5%) plus the present value of principal repayment of $1,000 in teen year time; discounted at 10% which is calculated as:

(50/0.1) * [ 1-1.1^ (-10) ] + 1,000/1.1^10 = $692.77

c.

As short-term bond's decrease its price less than long-term bond does, it can be concluded that Long-term bonds are more sensitive to a change in interest rate in comparison to short-term bond.