15.5k views
2 votes
A semi-annual coupon bond has a face value of $1,000 and a coupon rate of 3.4%. Time to maturity is 23 years and the current yield to maturity is 2.5%. How much is this bond worth?

1 Answer

5 votes

Final answer:

The current value of a semi-annual coupon bond can be calculated by discounting each future semi-annual coupon payment and the bond's face value back to the present using the yield to maturity as the discount rate.

Step-by-step explanation:

To calculate the value of a semi-annual coupon bond with a face value of $1,000, a coupon rate of 3.4%, a time to maturity of 23 years, and a current yield to maturity of 2.5%, we need to determine the present value of the coupon payments and the face value. The coupon payment for each six-month period is (3.4% / 2) * $1,000 = $17. For a bond with 23 years to maturity, there would be 46 semi-annual coupon payments.

You discount each of these payments and the face value of the bond back to the present using the current yield to maturity. The yield to maturity is semi-annual, so you would use 2.5% / 2 = 1.25% as the discount rate for each period. Then, by summing the present values of all the coupon payments and the face value, we can find the current worth of the bond. This requires using the present value formula for an annuity (for the coupons) and the present value of a single sum (for the face value).\

User Ernestina Juan
by
7.6k points