If an “American Water Company” bond (with face value= $1,000) has a coupon rate of 9.0% and is selling for $1,020, then the yield to maturity must be:

Question

BlackTom AI · Accepted Answer

A bond priced above par is a premium bond, so its yield to maturity (YTM) must be below the coupon rate. Relevant concepts: - Coupon rate = annual coupon / face value. Here coupon = 9.0% of $1,000 = $90 per year. - Current price = $1,020 (greater than face $1,000) means the bond sells at a premium. - For fixed-coupon bonds, when price > face value, the YTM < coupon rate; when price < face, YTM > coupon rate; when price = face, YTM = coupon rate. Step-by-step reasoning and calculations: 1. Compute the annual coupon: 0.09 × $1,000 = $90. 2. Compute the current yield (a simple indicator, not exact YTM): current yield = annual coupon / price = $90 / $1,020. - $90 / $1,020 = 0.088235 ≈ 8.8235%, which is already below 9%. 3. Consider extreme cases to confirm the inequality holds regardless of maturity: - If the bond had one year to maturity, price = (face + coupon) / (1 + y). Solve 1 + y = (1,000 + 90) / 1,020 = 1,090 / 1,020 = 1.068627 → y ≈ 6.8627% (<9%). - If the bond were a perpetuity, price = coupon / y → y = coupon / price = 8.8235% (<9%). 4. Because price > par, the investor pays a premium and receives coupon payments whose rate (9%) is higher than the yield they earn when accounting for the price paid and eventual redemption at $1,000; this reduces the effective return below the coupon rate. Why the correct answer is correct: - Premium price implies YTM < coupon rate; the calculated current yield (8.8235%) and the one-year example (6.8627%) both demonstrate yields below 9%. Why other options are incorrect: - "Zero" is impossible because coupons and redemption produce positive cash flows. - "Greater than 9%" contradicts the premium-bond logic (price > par implies YTM < coupon). - "Equal to 9%" would require price = par ($1,000), which is not the case. Conclusion: The yield to maturity must be lower than 9% (correct answer: lower than 9%).

If an “American Water Company” bond (with face value= $1,000) has a coupon rate of 9.0% and is selling for $1,020, then the yield to maturity must be:单项选择题

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