Question

Y 5 Transit (Bus) work 0 Saved Happy Valley Corporation has bonds on the market with 14.5 years to maturity, a YTM of 6.1%, and a current price of $1.038. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Round the final answer to 2 decimal places.) Coupon rate 3 249 %

Answer 1

Below is the discounted cash flow schedule of the bond which shows how the current price is arrived at

.||| | | B]"|"| | | | | | | નાનાસાનો મIિR AARIRIRIR/Aી*મિક/ Year CF Discount Factor Discounted CF | 1 $ 32.49|1/(10.061/20*1= | 0.970403|0.970403*32.49= | 31.53 2 $ 32.49|1/(1+0.061/25*2= | 0.941681|o.9416817*32.49= | $ 30.60 3| $ 32.49|1/(1+0.061/2)^3 | 0.91381|0.91381*32.49= | $ 29.69 4| $ 32.49|1/(1+0.061/2)^45 | 0.886764|0.886764*32.49= 28.81| 5| $ 32.49|1/(1+0.061/25*5= | 0.860518|0.860518*32.49= | $ 27.96 | 6] $ 32.49|1/(1+0.061/25*6= | 0.8350490.835049*32.49= | $ 27.13 7| $ 32.49|1/(1+0.061/25*7= | 0.8103340.810334*32.49= $ 26.33| 8| $ 32.49|1/(1+0.061/2)^8= | 0.78635|0.78635*32.49- $ 25.55. 9| $ 32.49 | (1+0.061/25*9= | 0.763076oિ.763076*32.49= | $ 24.79 | 10| $ 32.49|1/(1+0.061/2)-10=| 0.740491|0.740491*32.49= $ 24.06 11| $ 32.49|1/10.061/25-11= | 0.718575|0.718575*32.49= 3 23.35. 12| $ 32.49|1/(1+0.061/25*12= | 0.697307|0.697307*32.49= | $ 22.66 13| $ 32.49/1/10.061/25*13 | 0.676669|o.67666932.49= | $ 21.99 14 $ 32.49|1/(1+0.061/2)^14=| 0.6566410.656641*32.49= | $ 21.34 15[ $ 32.49|1/(1+0.061/2)^15= | 0.637205|0.637206*32.49= | $ 20.70 16| $ 32.49|1/(1+0.061/25*16=| 0.618347|0.618347*32.49= $ 20.09 17| $ 32.49|1/(1+0.061/2)^17=| 0.600045|0.600045*32.49= | $ 19.50 18| $ 32.49|1/(1+0.061/2)^18=[ 0.582286|0.582286*32.49= | $ 18.92 | 19| $ 32.49|1/(1+0.061/2)-19=| 0.565052/0.565052*32.49= 3 18.36 20 $ 32.49|1/(1+0.061/2)^20= | 0.548328|0.548328*32.49= | $ 17.82 21| $ 32.49 | (1+0.061/25*21= | 0.53209970.53209932.49= | $ 17.29 22| $ 32.49|1/(1+0.061/2)-22=| 0.51635|0.51635*32.49= | $ 16.78 23| $ 32.49|1/(1+0.061/20^23=| 0.501067|0.501067*32.49= | $ 16.28 24 $ 32.49|1/(1+0.061/2)^?4=| 0.4862370.486237*32.49= | $ 15.80 25| $ 32.49|1/(1+0.061/25*25=| 0.471846|o.471846*32.49= | $ 15.33 26| $ 32.49|1/(1+0.061/2)^26 | 0.45788|0.45788*32.49= | $ 14.88 27| $ 32.49||(1+0.061/2)-27= | 0.4443280.444328*32.49= | $ 14.44 28 $ 32.49|1/(1+0.061/2)^28=[ 0.431178|0.431178*32.49= | $ 14.01 29| $1,032.49|1/(1+0.061/2)^29=| 0.4184160.418416*1032.49= 432.01 Price=sum of all Discounted cF | 1,038.00 |

This can be expressed in the form of an equation as follows:

FV 1-(1+ Free )-nx frequency PV = Coupon x — frequency (1+ Freatene)nx frequency 1- (1 + 0.061) -14.5x2 1038 = Coupon x - 1000 (1 + 0.061 ) 14.5x2 0.061 Coupon = 32.49

Now when the coupon is calculated to 32.49 over a par value of 1000 and it being a semi annual coupon, the coupon rate is calculates as follows:

Coupon x frequency Coupon rate = 60 par value 100 Coupon rate = 32.49 x 2 1000 100 x 100 Coupon rate = 6.5%

So the coupon rate is 6.5%