Ashes Divide Corporation has bonds on the market with 16 years to maturity, a YT

Question

Ashes Divide Corporation has bonds on the market with 16 years to maturity, a YTM of 8.2 percent, and a current price of $1,286.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

11.55%

22.96%

8.90%

11.45%

17.84%

Ashes Divide Corporation has bonds on the market with 16 years to maturity, a YTM of 8.2 percent, and a current price of $1,286.50. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round your intermediate calculations.)

Explanation / Answer

Price of bond is the present value of cash flow from bond. Step-1:Calculation of present value of Par Value Present value of Par Value = Par Value x Present value of 1 = $ 1,000.00 x       0.27642 = $     276.42 Working: Present value of 1 = (1+i)^-n Where, = (1+0.041)^-32 i 4.10% =       0.27642 n 32 Step-2:Calculation of present value of semi annual coupon Current Price of bond $ 1,286.50 Less:Present value of Par Value of bond $     276.42 Present value of semi annual coupon interest $ 1,010.08 Step-3:Calculation of semi annual coupon interest Semi annual coupon interest = Present value of semi annual coupon interest/Present value of annuity of 1 = $ 1,010.08 / 17.648181 = $       57.23 Working: Present value of annuity of 1 = (1-(1+i)^-n)/i = (1-(1+0.041)^-32)/0.041 = 17.648181 Step-4:Calculation of coupon rate Coupon rate = Annual coupon amount/Par Value = $     114.47 / $ 1,000.00 = 11.45% Working: Annual coupon amount = $       57.23 x 2 = $     114.47

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