The problem refers to the bonds of The Apollo Corporation, all of which have a c
ID: 2761481 • Letter: T
Question
The problem refers to the bonds of The Apollo Corporation, all of which have a call feature. The call feature allows Apollo to pay off bonds anytime after the first 15 years, but requires that bondholders be compensated with an extra year's interest at the coupon rate if such a payoff is exercised. Apollo's Alpha bond was issued 10 years ago for 30 years with a face value of $1,000. Interest rates were very high at the time, and the bond's coupon rate is 20%. The interest rate is now 14.5%. Assume bond coupons are paid semiannually. At what price should an Alpha bond sell? Round the answer to the nearest cent. $ At what price would it sell without the call feature? Round the answer to the nearest cent. $Explanation / Answer
semiannuals interest present value @7.25% present value of cash flow 1 100 0.932400932 93.24009324 2 100 0.869371499 86.93714987 3 100 0.810602796 81.0602796 4 100 0.755806803 75.58068028 5 100 0.704714968 70.47149677 6 100 0.657076893 65.70768929 7 100 0.612659108 61.26591076 8 100 0.571243923 57.12439232 9 100 0.532628367 53.26283666 10 100 0.496623186 49.66231857 11 100 0.463051921 46.30519214 12 100 0.431750043 43.17500432 13 100 0.402564143 40.25641429 14 100 0.375351182 37.53511822 15 100 0.349977792 34.99777922 16 100 0.32631962 32.63196198 17 100 0.304260718 30.42607178 18 100 0.283692977 28.36929769 19 100 0.264515596 26.45155962 20 100 0.246634589 24.66345885 21 100 0.22996232 22.99623203 22 100 0.214417082 21.44170819 23 100 0.199922687 19.99226871 24 100 0.1864081 18.64080998 25 100 0.173807086 17.38070861 26 100 0.162057889 16.20578891 27 100 0.151102927 15.11029269 28 100 0.14088851 14.08885099 29 100 0.131364578 13.1364578 30 100 0.122484455 12.2484455 31 100 0.11420462 11.42046201 32 100 0.106484494 10.64844943 33 100 0.099286242 9.928624173 34 100 0.092574584 9.257458437 35 100 0.086316629 8.631662878 36 100 0.080481705 8.048170516 37 100 0.075041217 7.504121693 38 100 0.069968501 6.996850063 39 100 0.065238695 6.523869523 40 100 0.06082862 6.082862026 1000 0.06082862 60.82862026 present value of the bond if held till Maturity 1356.23742 Answer to A At present this bond should be sold at 1356.23 value of the bond if held till minimum time for call option i.e.15 years cash inflow Present value annuity factors@7.25% per semiannual present value of cash flow Interest 100 4.072896998 407.2896998 call value 200 0.496623186 99.32463713 face value 1000 0.496623186 496.6231857 Value of the bond with call option if held till 15 Years 1003.237523 Value of bond without call option at the date of 15 Years cash inflow Present value annuity factors@7.25% per semiannual present value of cash flow 100 4.072896998 407.2896998 1000 0.496623186 496.6231857 Value of bond without call option if held till minimum time of call option 15 years 903.9128854
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