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Which of the following bonds would you prefer to be buying?A) a $10,000 face-value security with a 10 percent coupon selling for $9,000B) a $10,000 face-value security with a 7 percent coupon selling for $10,000C) a $10,000 face-value security with a 9 percent coupon selling for $10,000D) a $10,000 face-value security with a 10 percent coupon selling for $10,000

Question

Which of the following bonds would you prefer to be buying?A) a 10,000face−valuesecuritywitha10percentcouponsellingfor10,000 face-value security with a 10 percent coupon selling for 9,000B) a 10,000face−valuesecuritywitha7percentcouponsellingfor10,000 face-value security with a 7 percent coupon selling for 10,000C) a 10,000face−valuesecuritywitha9percentcouponsellingfor10,000 face-value security with a 9 percent coupon selling for 10,000D) a 10,000face−valuesecuritywitha10percentcouponsellingfor10,000 face-value security with a 10 percent coupon selling for 10,000

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Solution

To determine which bond is the best to buy, we need to calculate the yield to maturity (YTM) for each bond. The YTM is the total return anticipated on a bond if it is held until it matures.

A) The bond is selling at a discount (9,000insteadof9,000 instead of 10,000). The coupon payment per year is 10% of the face value, which is 1,000.TheYTMisthecouponpaymentdividedbytheprice,sotheYTMis1,000. The YTM is the coupon payment divided by the price, so the YTM is 1,000 / $9,000 = 11.11%.

B) The bond is selling at face value (10,000).Thecouponpaymentperyearis710,000). The coupon payment per year is 7% of the face value, which is 700. The YTM is the coupon payment divided by the price, so the YTM is 700/700 / 10,000 = 7%.

C) The bond is selling at face value (10,000).Thecouponpaymentperyearis910,000). The coupon payment per year is 9% of the face value, which is 900. The YTM is the coupon payment divided by the price, so the YTM is 900/900 / 10,000 = 9%.

D) The bond is selling at face value (10,000).Thecouponpaymentperyearis1010,000). The coupon payment per year is 10% of the face value, which is 1,000. The YTM is the coupon payment divided by the price, so the YTM is 1,000/1,000 / 10,000 = 10%.

Based on the YTM, bond A would be the best to buy because it has the highest yield to maturity at 11.11%.

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