Question

Denton is considering purchasing a 7-year bond that is selling for $1,017. Which of the following is correct if this bond has a 2.5% coupon, paid semiannually? a. The YTM < coupon rate. b. The current yield > coupon rate c. The current yield < YTM. d. All the above.

Answer 1

The correct answer is (a) The YTM < Coupon Rate

Reasoning:

Formula for YTM -

F -P . YTM=C+ /F+P)/2

where, C is Coupon (assuming par value is $1000, coupon amount is $25); F is Face Value (Assumed $1000); P is Current Price ($1017); N is period (i.e. 14 since semi-annual compounding).

Hence, on solving the equation, YTM derived is 2.35 which is less than Coupon rate.

Formula for Current Yield -

CurrentYield = Coupon Price

Hence, CY is 2.46% (25/1017), which is less than Coupon rate and more than YTM. Hence, the answer is not b,c, or d.

Thank you.