General Matter’s outstanding bond issue has a coupon rate of 9.4%, and it sells

Question

General Matter’s outstanding bond issue has a coupon rate of 9.4%, and it sells at a yield to maturity of 7.80%. The firm wishes to issue additional bonds to the public at face value. What coupon rate must the new bonds offer in order to sell at face value? (Round your answer to 2 decimal places.)

General Matter’s outstanding bond issue has a coupon rate of 9.4%, and it sells at a yield to maturity of 7.80%. The firm wishes to issue additional bonds to the public at face value. What coupon rate must the new bonds offer in order to sell at face value? (Round your answer to 2 decimal places.)

Explanation / Answer

Solution: Coupon rate = 9.4%, Yield to Maturity (YTM) = 7.8%, Let the face value of bond (F)= $100

Now,                                           YTM = (C + (F-P)/n ) / ((F+P)/2)

where C = Coupon payments, P = Issue price of bond

Now, the firm wishes to issue additional bonds at face value , therefore P = F

Putting the same in the above equation, we get

                                        YTM = C/F
                                     C = YTM * F
                                         = 7.8% * 100
                                         = $ 7.8
Hence coupon payments = $7.8, Therefore coupon rate = 7.80%

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