A bond has a 6% coupon rate and is currently selling at a discount. Which of the following must be true?

Question

BlackTom AI · Accepted Answer

When a bond trades at a discount, its yield to maturity (market yield) must exceed its coupon rate. 1. Relevant knowledge points and concepts - Coupon rate = annual coupon payment divided by face (par) value. Here coupon = 6% of par. - Bond price relative to par: - If market yield (YTM) = coupon rate, price = par. - If market yield > coupon rate, price < par (discount). - If market yield < coupon rate, price > par (premium). - Intuition: the bond’s fixed coupon payments are less attractive when investors require a higher return, so the bond’s price must fall to deliver that higher yield. 2. Step-by-step reasoning - Coupon = 6% of par. If market yield were 6%, the present value of the coupon stream plus par repayment equals par (no discount/premium). - If the market yield rises above 6%, each coupon payment and the par repayment are discounted at a higher rate, producing a lower present value (price) than par. - Therefore, a bond selling below par (discount) implies the discounting rate (market yield) is greater than the coupon rate (6%). 3. Calculation (illustrative) - Take par = $1,000 so annual coupon = $1,000 × 6% = $60. - Perpetuity approximation: Price ≈ Coupon / yield = 60 / y. - If y = 0.06, Price = 60 / 0.06 = $1,000 (par). - If y = 0.08, Price = 60 / 0.08 = $750 (discount). - If y = 0.05, Price = 60 / 0.05 = $1,200 (premium). - This shows clearly that price < par when y > 6%. 4. Why the correct answer is correct - A discount price means investors require a yield higher than the bond’s fixed coupon; thus market yield > coupon rate = 6%. 5. Why other options are incorrect - "The bond must be close to maturity": Irrelevant—price relative to par depends on yields, not maturity length (though maturity affects sensitivity). - "The market yield is equal to 6%": If yield were 6%, the bond would trade at par, not at a discount. - "The market yield is less than 6%": That would cause the bond to sell at a premium, not a discount. Conclusion: The market yield is greater than 6%, which matches the provided correct answer.

A bond has a 6% coupon rate and is currently selling at a discount. Which of the following must be true?单项选择题

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