Question
Exercise 9-90 (Algorithmic) (Appendix 9A) Calculating Bond Issue Price On January 1, 2020, University Theatres issued...
Exercise 9-90 (Algorithmic) (Appendix 9A) Calculating Bond Issue Price On January 1, 2020, University Theatres issued $461,000 face value of bonds. The stated rate is 8%, and interest is paid semiannually on June 30 and December 31. The bonds mature in 15 years. Do not round interim calculations. If required, round your answers to the nearest whole dollar. Follow the format shown in present value tables as you complete the requirements below. Required: a. Assuming the market rate of interest is 6%, calculate at what price the bonds are issued. b. Assuming the market rate of interest is 10%, calculate at what price the bonds are issued.
Exhibit A3.7 Future Value of a Single Amount FV=1(1+i)" ni 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 16% 18% 20% 25% 30% 1 101000 102000 103000 104000 105000 106000 107000 108000 109000 1.10000 112000 1.14000 1.16000 1 .18000 2102010 1040401060901081601.10250112360114090 1.16640 115010121000125440 1299601.34560 139240 3 103030106121109273112486 1.15763 1.19102122504125971 129503133100 140493 148154 1.56090 164303 4 104060 108243 1.12551 1.16986 1.21551 1.26248 131080136049 1.41158 146410 1.57352168996 181064 1.93878 5 105101 1104081.15927121665 127628 1.33023140255 146933 153862 161051 1.76234 1.82541 210034 225776 6 106152 1.126161.19605126532 1.34010 141052150073 1.58687 167710 177156 1.92382 2.19.497 243640 269955 7 107214 1.148691.229871315931.40710150363 60578 1.71382 1.82804 1.94872 221068 250727 282622 3. 18547 8 108286 1.17166 1.26677136857 147746 15935171819 185093199256 2.14359247596 285259327841 3.75886 1.00349 1.19509 1.30477142301 1.551331689880346 1.99900 2.17189 2.35795277308 3.25195330296 443545 10 5.10462 1.21899343921430241.62889 1.790851.96715 2.15092236736259374310585 3.70722441144 5.23334 11 1.11567 1.24337 1.38423153945 1.71034189830 2.10485 233164 258043 2.85312 3.47855 4.22623 5.11726 6.17593 12 1.126831.26824 142576160103 1.79586 201220 225219 2.51817 281266 313643389598 481290 5.93603 7 28759 131 .13809 1.293611468531665078565 2.13293 2409352.71962 306580 3.4522736349 5.49241 6.35579 8.59936 14 1.14947 131948 1.51259 1.73168 1.97993 2.26090 257853 2.93719 3.34173 3.797504.88711 6.261357.98752 10.14724 15 1.160971.34587 1.55797180094 2.07893 2.39656 2.75903 3.17217364248 4.17725 5.473577.13794926552 11.97375 16 1.17258 .37279160471 187298218287 254035 2.95216 3.42594397031 4.59097 6.13039 8.13725 10.74800 17 1.75430140024165205 1.94790 2.29202 269277 3.15882 3.700024327635054476.36604 927646 1246768 96,67225 18 1,19615 142825 1.70243 2.00582 2.40662 285434 3.379933.99602471712 555992768997 10 57517 14.46251 9.67325 19 1.20811 1.45681 1.75351 2.10685252095302560 361653 4.31570 5.141666.11591 8.61276 12.05569 16.77652 23 2164 20 1.22019143595 1806112191122653303.207143.36968 4.66096560641 6.72750 964629 13.74349 19.46076 27 39300 21 1.23239 1.51567 186029 2.27877 278596 3.39956 4.14056 5.03383 6.10381 740025 10.803851566758 22.57448 32 32378 221.24472 154598191610236992 2.92526 3.60354 4.43040 5.43654 65860 8.140271210031 17 8610426 1864038 14206 23 1.257161576901.97359 246472 3.071523.31975 4.740535.87146 7257873.95430 13.55235 20.36158 30.3762245.00763 24 1.26973 160844 203279 2.56330 3.22510 404893 5.07237 8.34118 791108 984973 15 17863 23.2122135 23642 53.10901 251.28243164061 2.09378 266584 3.38635 4.291875.42743 6.84848 62308 10.83471 17.00006 26.46192 40.87424 62.66863 26 129526167342 2.15650 2.77247 3.55567 454938 5.807357.39635 939916 11.91818 19.0400730.16658 47.41412 73.9488 27 130821 1.70689222129 2.68307 3.73346 4.32235 621387 7.90006 10 24508 13.10999 213243343099155.00033 87 25930 28 132129174102 2.28793 2.99870 3.92013 5.111696.64894 8.62711 11.16714 14.42099 23.88387 39 20449 63 80044 102.96656 29 133450177584 235657 3.11865 4.11614 541839 7.11426 931727 12.172181556309 26.74993 44.69312 7400851 121.50054 301.34785 1.81136 2.42726 3.26340 4321945.74340 761226 10.06.266 1326768 17 44900 29.95992 50.9501685.349581037064 1.20000 25000 30000 144000156250 169000 1.72800 1.95313 2.19700 2.07360 2.44141 285610 2.48832 305176 2.98598331470 432681 3.58318 4.76837 6.27435 4.29982 5.96046 8.15731 5.19078 74505 10.60450 6.19174 931323 13.78585 7.43008 1164153 17.92160 8.91610 14 55192 23.29509 10.69932 18.18989 30 28751 1283918 22.73737 39 37376 15.40702 28.42171 51.18599 18.4884335 52714 66 54166 22.18611 44.40892 36 50416 26 62333 55 51115 112.45541 31.94800 6938894 46.19203 33.33760 36.73617 19004946 46.00512 108.42022 247 06453 55 20614 135 52527 321 18389 66.24737 169.40659 417 53905 79.49685 21175824 542.80077 9 5 39622 264 69780 705 64100 11447546 330 87225 91733330 13737055413590311192.53329 164 84466 516 98788 1550 29328 197.81359 646 23485201538126 23737631 30279352 2619.99564
Exhibit A3.8 Present Value of a Single Amount PV= 7 (1+) Mi 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 16% 18% 20% 25% 30% + 0.99010 0.98039 0.97087 0.96154 0.95238 0.94340 093458 0.92593 0.91743 0.909090.89286 0.87719 0.86207 0.84746 0.83333 0.80000 0.76923 098030 0.96117 0.94260092456 0.90703069000087344 085734 084168 0.82645 0.79719 076947074316 0.71818069444 0.64000059172 0.97059 0.94232 0.91514 059900 0.36354 0.8.3962 0.316.30 0.79383 0.77218 0.75131 0.71178 067497 0.64066 0.60863 0.57870051200045517 096098 0.92385 085849085430 012270079209 076290 0735030 70543 068301063552 059208 055229 0.51579 0.48225 0.409600.35013 0.95147 0.90573 0.86261 082193 0.78353 074726 071299 0.68058 0.64993062092 0.56743 051937 0.47611 0.437110.40188 0.32768 0.26933 094205 0.88797 0.83749 0.79031 0.74622 0.70496066634 0.63017 0.59627 0.56447 050663 0.45559 0.41044 0.37043033490 0.26214 0.20718 093272 0.87056 0.81309 0.75992 0.71068 066506062275058349 054703051316 0.45235 0.39964 35333 031393027908 0.20972 0.15937 092348035349 0.789610.73069 0.67604 062741 58201 0.54027 050187 0.45651 0.40338 035056 0.30503026604 021257 016777 0.12259 091434 083676 076642070259 064461 059190054393 050025 0.46043 042410036061 030751 0.26295 0.225460.19381 0.13422 0.09430 090529 0.82035 0.744090.67556 0.61391 0.55839 050835 0.46319 0.42241 038554032197 026974 022668 0.19106 0.16151 0.10737 0.07254 0.89632 0.80426 072242 064958058468 0.52679 0.47509 0.42888 038753 035049 0.28743 023662 0.19542 016192 0.13459 0.08590 0.05580 038745 0.78849 0.70138 062460 055684 0.499704401039711 0.35553 031063 025668 0 20756 0.16846 0.13722011216 0.06872 004292 087866 0.77303068095 060057 053032 0464 041096 0.36770 0.32618 0.28956 022917 018207 0.145230.11629009346 0.05498 0.03302 0236996 0.75788 0.66112 0.57748 050507 0.44230 0.38782 0.34046 0.299250.26333 0.20462 0.15971 012520 0.09855 0.07799 0.04398002540 0.86135 0.74301 0.64186055526 0.481020.41727 036245 0.31524 0.27454 0.23939 018270014010 0.10793 0.083520.06491 0.03518 0.01954 0.85282 0.72845062317 053391 0.45811 039365 033873029189 025187 021763 0.16312012289009304 0.07078 0.05409 0.02515 0.01503 OM 0.71 016 052 051227 010 037 031437 022097 023107 01974 014401OPRO 00021 0105993 0.0002 012220011 083602 070016 058739 0.09363041552035034029586 025025 021199 0.17986 0.13004009456 006916 0.05083 0.00756 0.01801000339 082774 0.68643057029 047464 0.39573 0.33051 0.27651023171019449 016351 0.11611 008295 0.059610.04308 0.03130 0.01441 000684 081954 067297 055366045639 037689 31180 0.25842 021455017843014864 010367007276 0051.39 0.03651002608 0.01153 0.00526 081143 065978 0.53755 0433830.35894029416026151 019856 016370013513 0.09256 006330004430 0.030 0 02174 0.00022 0.00405 0.30340 0.4684052189 0.42196 0.34185 0.27751 22571 0.18.394 015018012255 0.00264 005599 0.038190.02622 0.01811 0.00738 0.00311 0.79544 063416 050569 060573032557026130021095 017032 0.13778 0.11168 0.07379 004911003292 0.02222 009509 0.00590 0.00239 078757 0.62172 0.49193039012 031007 0.24698019715 0.15270 0.12640 0.10153 0.06588 004308002838 0.01883001258 0.00472 0.00184 077977 0609530.47761 0.37512 0.29530 023300018425 0146020.11597 0.09230 0.0332003779002447 0.0156 001048 0.00378 000142 077205 059758 0.46309 0 9 028124021981 017220013520 0.10639 000391 0.0525200315 002109 0.01352000874 0.00302 0.00109 0.76440 0.58586 0.45019 0.34662 0.26785 020737 0.16093 0.12519009761 0.07628 0.04689002908 0.01818 0.011460.00728 0.00242 0.00004 0.75684 0.57437 0.43708 033348 0255090.19563 0.15040 0.11591 008955 0.06934 0.04187 002551 0.01567 0.00971 0.00607 0.00193 0.00065 074934 056311 0.42435032065 024295 0.18456 0.14056 0.10733 008215 005304 0.00738 002237 0.01351 0.00823 000506 0.00155 0.00050 074192 0.55207 0.41199 030802 023138 0.17411 0.13137 0.0938 007537 0.05731 0.033800196 0.01165 0.00697000421 0.00124 0.00033 28
Exhibit A3.9 Future Value of an Al 2 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 16% 18% 20% 25% 30% 1 00000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 2 2.01000202000 203000204000 2.05000 206000 2070002.08000 209000 210000 2.12000 2.14000 2.16000 2.18000220000 2.25000 230000 3 3.03010 30604 3.09090 312160 3.15250 2.18360 321490324640327810 3.31000 3.37403.43950 3505603.57240 3.64000 3.81250 3.99000 4 DO 12161 2 11013 50511 457313 0 72937 492116 SOOS 2153 S 10 SA 1700 551010520104530914 5:41632 5.52563563709575074 5 .96471 6105106352356 .61010 6.87714 7154217461608.207039 .0010 6 15202630812 646841643298 30191 697532 7.15329335937.52333 771561 8.11519 3.53552897748 9441079.9292 11.25879 1275603 7 21.354 428 786 7.898.29 14201 839384 88562 892280920043248217 10 0901 10 73049 11 41387 1214152 12.91590 15.07349 17.58254 8 828567 8.58297 8.89234921423 9.54911 9.8974710259801063663 11.02847 11.435899229969 13 23276 14.2400915 32700 16.49908 19.84186 2385769 93685397546) 10.159111058280 11.026569149132 11.97799 12.48756 13.02104 13.57948947756616 0853S 1751851 19 0858520.79890 2580232 32 01500 10 10.46221 10 94972146388 12.00611125778912.78079 13.81645443656 15.19293 15.93742 17.5474 1933730 2132147 2352131 25.95868 33.25290 261950 11 11.56663121687212.80780 13.48635 14.20579 1497164 15.7050 16.64549 17.56029 18:53117 20 65458 23.0445225732902875514 32.15042 42.5661356.40535 121268250 13.41209 14.1920315.02501 1591713 16 17 1845 18.97713 2014072 2135420 2413011 27 27075 30105017 3493107 39 SBOSO 54 20746 743295 13 13.80933 468033 15 617791662654 17.71293188214 201406421.495.30 2295338 2452271 20.02911 32068653678620 22186644966068.759589762506 14 14.4742 15.97394 17086321829191 19.5986321015022255049 2421492 26.01919 27.97498 32392603758102361995061802 59.1952 36.94947 127.91255 15 16.09690 17.2934118.591 2002359 21.5785623 27592 25.12902 27.15211 29.36092 31.77248 37.279713 34241 51 65951 60.96527 72.0851110968654 167 28631 16 17 257861863929 20.15688 2182453 23.65749 256725327 88805 30 32428 33.00340 35.9497342.75328 50.98035609250372.939013744213 138. 10855 218.47220 17 406 20 01 207 2076159 20 69251 25 32 28 2029 2034022 33 75033 35 973700 0 37 59 1760 7673038706204 10593056 173 63568 285 01386 18 19.6147521.41231 23.416442564541 28.13239 30.9056533.99903 37.45024 41.3013445.59917 55 74971683900 844072 1037402812811667 218. 0 0 37151802 19 20 31090 22 34056 25.11687 27 67123 30.53900 3375999373789641 44626 460184651.15909636796373969239360323 12341353 154.74000 273.55576 48397343 20 22019002429737 26.87037 2977000 33065953678559 10.9954957619651.16012 57 27500 72052449102093 115.37975 146827978 0800342.4470 630.16546 21 23 23919 25.783322867649 31.9692035.719253999273446518 5042292 56.764536400250 816954 10474842 13434051 17402100 22500560429808782021510 22 24 471592219 053678342479738 50521 43 5229 49 00574 55.45676 6287334 71402759250250 120.43600 1574161 20634479 2710307253810109 06727963 23 25 71630 2834496 32.45288 36.617894143043 46 99583 53.4361460 89330 6953194 79.54302 10460289 13829704 183.60138 244.4868532623656 673626.36 1388.46351 24 26.97346 30 42186 34 42647 3908260 44.50200 90 81558 58 17667 66 76476 76 7895188.49733 118.15534 15865862 213.97761 289.49448392.45424 343 03295 1806 00257 25 28 24320 32.03030 36.4592641 64591 47.72710 S436451 63 24904 73.10594 84.70090 98 34706 133.33387 18187083 24921402 34260349471.98108 105479118 2343 80334 26 29 52563 33.67091 38 55304643117651.11345 59.15638 68.67647 79.9544293.32398 109 18177 150 33393 20831274 290.06827 405 27211 567 37730 131945898 305441434 27 30 935 140 0 3 70805491) 1705774 87 3507 102.2013 12109904 169.37401 2349933 337 50239 47922109 015276 165036123 39717776 20 3212910 37 05121 42.9309209.9675858.40258685281180697609530883 11290122 13420994 19069309 272 1923 19250277 566.48009819 22331 2063 95153 516431093 29 334503938.79223521885 52.9629622271 7369808734653903.96594 124.13536 14863093 21458275 312.09373 456-30222 669.4414598406797 2580.93941 6714 60421 30 347848940.56808 4757542 56.08496 66.438857905619 446079 11328321 136 30754 164 9402 2413328 35678 53031173 790.94799 118188157 3227.17427 8729.99548
Exhibit A3.10 (1+i)" Present Value of an Annuity PVA = – m 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 18% 18% 20% 25% 30% 1 0.99010 0.93039 0.97087 0961540.95238 0.94340 0.93458 0.92593 0.91743 0909090.89286 0.877190.86207 0.54746 0.83333 0 30000 0.76923 1.92040 194156 1.91347 130918594118309 1 1 7826 1.759111735546900S164666160523 1.56564 1.52778 1.44000 1.36095 2.94009288388 282861 2.77500 2.72325 267301 2.62432 257710 2.53129248685240183 232163 2.245892.17427 210648 1.95.200 1.31611 4 3.90197 3307733.717103629903.54595346511 38721 3312133239722169873.00735291371 2.79818 269006258873236160 216624 435343 71348 457971 445182 43298 421236 410020 399271 3 95 3.79079 3.60478 343308 3.274293.12717 2.99061 268928 243557 5.79548 5.60143 5.41719 5.24214 07569 4.91732476654 462288 4.48592435526 4.11141 3.BBBS7 368474 3.49760332551 295142 264275 6.72819 6.47199 623028600205 5.78637 558238 5.38929 5.20637 5.03295 436842456376 428830403857 3.811533.60459 3.16114 280211 7.65168732548 701969 .73274 6.463216201795.97130 5.74664 5.53482 5.33493 4.96764 4.63586434059407757383716332891 2.92470 8.56602816224778611 7.43533710782 6.801696 .51523624619 5.99525 5.75902532825 494632400654 4300024030973.46313301900 9.47130 899259 53020110907 72173734009702358 6 71009 6.41766614497 565092 52161223323449409 419247 357050309154 10.36763 9.786859.25262 8.76048 830641788687 7.49867 7.13896 680519 6.49506 5.93770 5.45273 502864 4.65601 432706 3.65640 3.14734 12 11.25508 1057534 9.95400938507 8.86325838334 7.94269753608 7.160736813696.19437 5.66029 5.19711 4.793224.43922 3.72512 2.19026 13 12:13374 11 34837 1063495 9.955 19357 35268 35745 790078 748690710036 6.42355 584236 5 34230 4.90951 4.5328 378010322323 14 13.00370 12.10625 11 29607 10.56312 9.89864 9.294988.74547 2424 7.73615 736669 6.62817 6.00207 5.46753 .00806 461057 3.82403 3.24367 15 13.865051284926 11.93794 11.11539037966 9.71225 9.10791 855948 8.060697.60608 6.81086 6.14217 5.57546 5.09158 4.67547 3.85926 3.26821 16 14.7787 13.57771 12.56110 11.652301083777 10.105909.44665 885137 8.31256 782371 697399626506 566850 5.16235 4.72956 3.88741 3.28324 17 15.542251429187 13.1661212.16567 11.27407 10.47726 9.76322 9.12164 354363 02155 7,51963 6.37256 5.748705.22233 4.77463 3.90993329480 16.39527 1499203 13.75351 1265930 11.60959 10.12760 10.05909937189 3755638 20141 724967 6.45742 581785 5.273164.81219 3.927943.30369 19 17.22601 15.678461432380 13.133941208532 11.15812 10.33560 9.60360 8.95011 8.364927365786.55037 5.87746 5.31624 4.84350 3.94235331053 2018.04555 1635143 14.87747 13.5903392.46221 11.46992 10.59401 981815 9.12855 8.51356 746944662313 5.92884 5.35275 4.86958 3.95388 3.31579 18.65698 17.01121 15.41502 14.02916 12.82115 11.76408 10.30553 10.01680 9.29224864869756200 6.68696 597314 5.38368 4.89132 3.96311 3.31984 19.660381765805 15.936921445112 13.16300 12041501106124 10.20074 9.44243 77154 764465674294 6011335.409904909433.97049332296 20.45582 18.29220 16.4436114,85684 13.45357 12.30338 11.27219 10.37106 9.58021 8.88322 7.718436.79206 604425 5.432124.92453 3.97639 3.32535 24 21.2433918.9139316.93554 15.24696 13.79864 12.55036 11.46933 10.52876 9.70661 8.934747.78432 6.835146.07263 5.45095 4.93710 3.98111 3.32719 22.02316 19 52346 17 413151562208 140939412.78336 11.65358 1067478 9.32258907704 734314 6.872936097095.46691 494759 3.93489332861 22.79520 20.121041787684 15.98277 14.37519 13.00317 11.82578 10.80998 9.92097 916095739566 6.90608 6.11818 5.480434956323.98791332970 23.55961 207060183270316.329591464300 13.21053 11.98671 10.93516 10.02658923722 7.96255 693515 6.13636 5.491894.95.360 3.990333.33054 28 24.31644 2128127 18.764111666306 14.89813 13.40616 12.13711 11.05108 10.11613 9.30657 798442696066 6.15204 5.50160 4.96967 3.99226 3.33118 25.06579 21 84438 19.18845 16.98371 15.14107 13.5907212.2776711.15841 10.19828 9.369618.02181 698304 6.165555509834.974723.99381 3.33168 30 25.80771 2239646 19 600417.29203 1537245 13.76483 12.409041125778 10.273659.42691 8.05518 7002666.17720 5.51681 49789 3.99505 3.33206 TO
Answers
Bond face value = $461,000
Stated rate = 8%
Interest paid semi annually = $461,000 * 8% *6/12 = $18,440
tenure of bond (in years) = 15
tenure of bond (in periods) = 30
a) Market rate of interest = 6%
Market rate of interest = 6%/ 2 = 3% per period
Bond issue price = Face value* PV + Interest amount * PVA
Bond issue price = 461,000 * PV(3%,30) + 18,440 * PVA(3%,30)
Bond issue price = (461,000 * 0.41199) + (18,440 * 19.60044)
Bond issue price = $551,359.50
Bond issue price = $551,360
a) Market rate of interest = 10%
Market rate of interest = 10%/ 2 = 5% per period
Bond issue price = Face value* PV + Interest amount * PVA
Bond issue price = 461,000 * PV(5%,30) + 18,440 * PVA(5%,30)
Bond issue price = (461,000 * 0.23138) + (18,440 * 15.37245)
Bond issue price = $390,134.158
Bond issue price = $390,134
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