Asked by Lucia Callista on Jul 15, 2024

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ABC Corporation has 4-year, 5% annual coupon bonds outstanding. Given a 6.5% yield to maturity, determine the duration of these bonds.

A) 2.52
B) 3.02
C) 3.52
D) 4.02
E) 4.52

Annual Coupon Bonds

Bonds that pay interest to the bondholder yearly until maturity, at which point the face value is also repaid.

Yield To Maturity

The expected total yield from a bond when held until its maturity date.

Duration

A measure of the sensitivity of the price of a bond or other debt instrument to interest rate changes, representing the weighted average time until all cash flows are received.

  • Compute the bond duration and comprehend its impact on exposure to interest rate fluctuations.
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CH
Carla HoustonJul 16, 2024
Final Answer :
C
Explanation :
Duration measures the sensitivity of a bond's price to changes in interest rates, typically calculated as the weighted average time to receive the bond's cash flows. For a bond with a 4-year maturity, a 5% annual coupon, and a yield to maturity of 6.5%, the duration will be less than its maturity because the bond pays coupons before maturity, which means the investor receives some of the investment before the bond's final maturity. The correct duration of 3.52 years (option C) suggests that on average, the bond's cash flows are received in 3.52 years, taking into account the time value of money and the bond's coupon payments and final principal repayment. Calculating the exact duration involves a present value calculation of each cash flow, weighted by the time until the cash flow occurs, and then summing these values.