Question

MPC CONSTRUCTORS HAS JUST ISSUED A 15 YEAR. R1250 PER VALUE BOND THAT PAYS INTEREST ANNUALLY. THE REQUIRED RETURN IS CURRENTLY 14% AND THE COMPANY IS CERTAIN THAT THE REQUIRED RETURN WILL REMAIN THE SAME UNTIL THE BOND'S MATURITY THE VALUE OF THE BOND PURCHASED TODAY IS R1096..45 WHAT IS THE BOND'S COUPON RATE?

Answer 1

Formula for bond price can be used to compute coupon payment and then coupon rate.

Bond price = C x [1 – (1+r)-n/r] + F/(1+r) n

F = Face value = R 1,250

C = Periodic coupon payment = Face value x Coupon rate/Annual coupon frequency

                                                = R 1,250 x Coupon Rate

r = Rate of return = 0.14

n = Number of periods to maturity = 15

Bond price = C x [1 – (1+0.014)-15]/0.033 + R 1,250/ (1+0.14) 15

                  R 1,096 = C x [1 – (1.14)-15]/0.014 + R 1,250 x (1.14) -15

                  R 1,096 = C x [(1 – 0.140096482069159)/0.14] + R 1,250 x 0.140096482069159

                  R 1,096 = C x (0.859903517930841/0.14) + R 175.120602586448

                  R 1,096 = C x 6.14216798522029 + R 175.120602586448

                  C x 6.14216798522029 = R 1,096 - R 175.120602586448                                           

                                                        = R 920.879397413552

                   C = R 920.879397413552/6.14216798522029

                      = R 149.927419704156

           R 1,250 x Coupon rate = R 149.927419704156

           Coupon rate = R 149.927419704156/ R 1,250

                                = 0.1199419357633 or 12 %

Bond’s coupon rate is 12 %.