Question

Present Value of Annuity of $1 Periods 1.0% 2.0% 3.0% 3.75% 4.0% 4.25% 5.0% 6.0% 7.0% 0.99010 1.97040 2.94099 3.90197 4.85343 5.79548 6.72819 7.65168 8.56602 9.47130 10.36763 11.25508 12.13374 13.00370 13.86505 14.71787 15.56225 16.39827 17.22601 18.04555 22.02316 25.80771 0.98039 1.94156 2.88388 3.80773 4.71346 5.60143 6.47199 7.32548 8.16224 8.98259 9.78685 10.57534 11.34837 12.10625 12.84926 13.57771 14.29187 14.99203 15.67846 16.35143 19.52346 22.39646 0.97087 1.91347 2.82861 3.71710 4.57971 5.41719 6.23028 7.01969 7.78611 8.53020 9.25262 9.95400 10.63496 11.29607 11.93794 12.56110 13.16612 13.75351 14.32380 14.87747 17.41315 19.60044 0.96386 1.89287 2.78831 3.65138 4.48326 5.28507 6.05790 6.80280 7.52077 8.21279 8.87979 9.52269 10.14236 10.73962 11.31530 11.87017 12.40498 12.92046 13.41731 13.89620 16.04320 17.82925 0.96154 1.88609 2.77509 3.62990 4.45182 5.24214 6.00205 6.73274 7.43533 8.11090 8.76048 9.38507 9.98565 10.56312 11.11839 11.65230 12.16567 12.65930 13.13394 13.59033 15.62208 17.29203 0.95923 1.87936 2.76198 3.60861 4.42073 5.19974 5.94699 6.66378 7.35135 8.01089 8.64354 9.25039 9.83251 10.39090 10.92652 11.44031 11.93315 12.40590 12.85938 13.29437 15.21734 16.77902 0.95238 1.85941 2.72325 3.54595 4.32948 5.07569 5.78637 6.46321 7.10782 7.72173 8.30641 8.86325 9.39357 9.89864 10.37966 10.83777 11.27407 11.68959 12.08532 12.46221 14.09394 15.37245 0.94340 1.83339 2.67301 3.46511 4.21236 4.91732 5.58238 6.20979 6.80169 7.36009 7.88687 8.38384 8.85268 9.29498 9.71225 10.10590 10.47726 10.82760 11.15812 11.46992 12.78336 13.76483 0.93458 1.80802 2.62432 3.38721 4.10020 4.76654 5.38929 5.97130 6.51523 7.02358 7.49867 7.94269 8.35765 8.74547 9.10791 9.44665 9.76322 10.05909 10.33560 10.59401 11.65358 12.40904 Periods 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 0.92593 1.78326 2.57710 3.31213 3.99271 4.62288 5.20637 5.74664 6.24689 6.71008 7.13896 7.53608 7.90378 8.24424 8.55948 8.85137 9.12164 9.37189 9.60360 9.81815 10.67478 11.25778 0.91743 1.75911 2.53129 3.23972 3.88965 4.48592 5.03295 5.53482 5.99525 6.41766 6.80519 7.16073 7.48690 7.78615 8.06069 8.31256 8.54363 8.75563 8.95011 9.12855 9.82258 10.27365 0.90909 1.73554 2.48685 3.16987 3.79079 4.35526 4.86842 5.33493 5.75902 6.14457 6.49506 6.81369 7.10336 7.36669 7.60608 7.82371 8.02155 8.20141 8.36492 8.51356 9.07704 9.42691 0.90090 1.71252 2.44371 3.10245 3.69590 4.23054 4.71220 5.14612 5.53705 5.88923 6.20652 6.49236 6.74987 6.98187 7.19087 7.37916 7.54879 7.70162 7.83929 7.96333 8.42174 8.69379 0.89286 1.69005 2.40183 3.03735 3.60478 4.11141 4.56376 4.96764 5.32825 5.65022 5.93770 6.19437 6.42355 6.62817 6.81086 6.97399 7.11963 7.24967 7.36578 7.46944 7.84314 8.05518 0.88496 1.66810 2.36115 2.97447 3.51723 3.99755 4.42261 4.79877 5.13166 5.42624 5.68694 5.91765 6.12181 6.30249 6.46238 6.60388 6.72909 6.83991 6.93797 7.02475 7.32998 7.49565 0.87719 1.64666 2.32163 2.91371 3.43308 3.88867 4.28830 4.63886 4.94637 5.21612 5.45273 5.66029 5.84236 6.00207 6.14217 6.26506 6.37286 6.46742 6.55037 6.62313 6.87293 7.00266 0.86957 1.62571 2.28323 2.85498 3.35216 3.78448 4.16042 4.48732 4.77158 5.01877 5.23371 5.42062 5.58315 5.72448 5.84737 5.95423 6.04716 6.12797 6.19823 6.25933 6.46415 6.56598 0.83333 1.52778 2.10648 2.58873 2.99061 3.32551 3.60459 3.83716 4.03097 4.19247 4.32706 4.43922 4.53268 4.61057 4.67547 4.72956 4.77463 4.81219 4.84350 4.86958 4.94759 4.97894 0.80000 1.44000 1.95200 2.36160 2.68928 2.95142 3.16114 3.32891 3.46313 3.57050 3.65640 3.72512 3.78010 3.82408 3.85926 3.88741 3.90993 3.92794 3.94235 3.95388 3.98489 3.99505

Answer 1

Solution:

a)

Case A – Issue Price – Market interest rate (annual): 4 percent

Face value of bonds = $508,500

Half yearly maturity period = 7 years * 2 = 14

Semiannual market interest = 4 /2 = 2%

Semiannual Cash Interest = Face value 508,500 * Coupon Rate 6% * ½ = $15,255

Issue Price = Cash Interest * Present value annuity factor at 2% for 14 period + Face value * Present value interest factor at 2% for 14 period

= ($15,255*12.10625) + (508,500*0.75788)

$184,680.84 + $385,382

= $570,063

Issue Price = $570,063

b)

Case B – Issue Price – Market interest rate (annual): 6 percent

Face value of bonds = $508,500

Half yearly maturity period = 7 years * 2 = 14

Semiannual market interest = 6 /2 = 3%

Semiannual Cash Interest = Face value 508,500 * Coupon Rate 6% * ½ = $15,255

Issue Price = Cash Interest * Present value annuity factor at 3% for 14 period + Face value * Present value interest factor at 3% for 14 period

= ($15,255*11.29607) + (508,500*0.66112)

= $172,321.55 + 336,179.52

= $508,501

Issue Price = $508,501

c)

Case C – Issue Price – Market interest rate (annual): 6 percent

Face value of bonds = $508,500

Half yearly maturity period = 7 years * 2 = 14

Semiannual market interest = 8.5 /2 = 4.25%

Semiannual Cash Interest = Face value 508,500 * Coupon Rate 6% * ½ = $15,255

Issue Price = Cash Interest * Present value annuity factor at 4.25% for 14 period + Face value * Present value interest factor at 4.25% for 14 period

= ($15,255*10.39090) + (508,500*0.55839)

= $158,513.18 + 283,941.32

= $442,454

Issue Price = $442,454

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