Asked by Aaron Morris on Jul 22, 2024
Verified
The Goodie Barn has a 7% coupon bond outstanding that matures in 13.5 years. The bond pays interest semiannually. What is the market price per bond if the face value is $1,000 and the yield to maturity is 14.78%?
A) $255.27
B) $550.40
C) $674.66
D) $954.92
E) $967.38
Coupon Bond
A debt security that pays the holder a fixed interest payment (coupon) at regular intervals until the maturity date, when the principal amount is repaid.
Yield To Maturity
The total return anticipated on a bond if it is held until the date it matures, including both interest payments and the gain or loss realized on the principal amount.
Market Price
The current exchange rate for a service or asset in the open market.
- Calculate the selling price of bonds by analyzing their coupon rates, stated values, yields at maturity, and final due dates.
Verified Answer
MR
Monse RamirezJul 25, 2024
Final Answer :
B
Explanation :
The market price of a bond can be calculated using the present value of its future cash flows, which include the semiannual interest payments and the principal amount at maturity. The formula for the present value of an annuity (for the interest payments) and the present value of a lump sum (for the principal repayment) can be used. Given a 7% annual coupon rate on a $1,000 face value bond, the semiannual coupon payment is $35 ($1,000 * 7% / 2). With a yield to maturity of 14.78% annually or 7.39% per period (14.78% / 2), and 27 periods (13.5 years * 2), the present value of the bond can be calculated. The correct answer, $550.40, reflects the present value of these cash flows discounted at the given yield to maturity.
Learning Objectives
- Calculate the selling price of bonds by analyzing their coupon rates, stated values, yields at maturity, and final due dates.