Smiley Industrial Goods has $1,000 face value bonds on the market with semiannual interest payments, 13.5 years to maturity, and a market price of $1,023.At this price, the bonds yield 6.4 percent. What must be the coupon rate on these bonds?A) 3.75 percentB) 6.66 percentC) 7.50 percentD) 7.33 percentE) 3.33 percent

Annual Coupon rate =  66.56990711 / 1000 = 0.06656990711 or 6.656990711% rounded off to 6.66%

Option B is the correct answer

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) = 13.5 * 2 = 27

r or YTM = 0.064 * 6/12 = 0.032 or 3.2%

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.

1023 = C * [( 1 - (1+0.032)^-27) / 0.032]  + 1000 / (1+0.032)^27

1023 = C * 17.8994796  +  427.2166529

1023 -  427.2166529  =  C * 17.8994796

595.7833471 / 17.8994796  =  C

C = 33.28495355 rounded off to 33.28

The annual coupon payment will be = 33.28495355 * 2 = 66.56990711 rounded off to 66.57

Annual Coupon rate =  66.56990711 / 1000 = 0.06656990711 or 6.656990711% rounded off to 6.66%

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