A 30-year, $1,000 Sunoco bond is trading at a $397 premium. The bond carries a coupon rate of 11% and it was issued 12 years ago. Determine the yield to maturity.

Question

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The yield to maturity (YTM) on a bond is the interest rate that equates the present value of all future cash flows from the bond (coupon payments and the repayment of the principal) with its current price. Given that the bond was issued at $1,000 and is now trading at a $397 premium, its current price is $1,397. The bond has an annual coupon rate of 11%, which means it pays $110 in interest each year ($1,000 * 11%). Since the bond was issued 12 years ago and it's a 30-year bond, it has 18 years left until maturity. The YTM calculation involves solving for the interest rate in the present value formula, which is not straightforward and typically requires financial calculators or software. Among the given options, 7.068% compounded semiannually is the most plausible estimate for the YTM, considering the bond's premium price, the time to maturity, and the coupon rate. Higher coupon rates and premiums generally lead to a lower YTM compared to the coupon rate, and the compounding frequency affects the effective annual rate.

A 30-Year, $1,000 Sunoco Bond Is Trading at a $397