Question

A $1,000 par bond with a semi-annual coupon and 12 years to maturity is currently priced $880 and has a yield to maturity of 5.37%. What is the bonds coupon rate

Answer 1

Annual Coupon rate = 0.040005 or 4.0005% rounded off to 4.00%

Step-by-step explanation:

To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = C

Total periods (n) = 12 * 2 = 24

r or YTM = 0.0537 * 6/12 = 0.02685 or 2.685%%

The formula to calculate the price of the bonds today is attached.

We will first calculate the value of semi coupon payment made by the bond.

880 = C * [( 1 - (1+0.02685)^-24) / 0.02685] + 1000 / (1+0.02685)^24

880 = C * 17.52482779 + 529.4583737

880 - 529.4583737 = C * 17.52482779

350.5416263 / 17.52482779 = C

C = 20.0025718 rounded off to 20.00

The annual coupon payment will be = 20.0025718 * 2 = 40.00514361 rounded off to 40.01

Annual Coupon rate = 40.00514361 / 1000 = 0.040005 or 4.0005% rounded off to 4.00%