Question

a: coupon rate = 2.5%, ytm = 3%

• b: coupon rate = 3%, ytm = 2.75%
• c: coupon rate = 3.5%, ytm = 3.5%
• d: coupon rate = 4%, ytm = 3.5%

which of the bonds is selling at a discount?
o d
o a
o b
o c

Explanation:

Step1: Recall Bond Pricing Rule

A bond sells at a discount when its coupon rate (\(C\)) is less than its yield - to - maturity (\(YTM\)). Mathematically, if \(CYTM\), the bond is at a premium.

Step2: Analyze Option A

For option A: Coupon rate (\(C\)) = 2.5% and \(YTM=3\%\). Since \(2.5\%<3\%\), according to the bond pricing rule, this bond will sell at a discount.

Step3: Analyze Option B

For option B: Coupon rate (\(C\)) = 3% and \(YTM = 2.75\%\). Since \(3\%>2.75\%\), this bond will sell at a premium.

Step4: Analyze Option C

For option C: Coupon rate (\(C\)) = 3.5% and \(YTM=3.5\%\). Since \(C = YTM\), this bond will sell at par.

Step5: Analyze Option D

For option D: Coupon rate (\(C\)) = 4% and \(YTM = 3.5\%\). Since \(4\%>3.5\%\), this bond will sell at a premium.

Answer:

A. Coupon rate = 2.5%, YTM = 3%