P9-12 (Algo) Comparing Options Using Present Value Concepts LO9-7 After hearing a knock at your front door, you are surprised to see the Prize Patrol from your state's online lottery agency. Upon opening your door, you learn you have won the lottery of $24.0 million. You discover that you have three options: (1) you can receive $2.40 million per year for the next 13 years, (2) you can have $22.0 million today, or (3) you can have $5.5 million today and receive $1.75 million for each of the next 11 years. Your lawyer tells you that it is reasonable to expect to earn an annual return of 10% on investments. Required: 1. What is the present value of the above options? (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided. Enter your answers in whole dollar not in millions (i.e., 1,000,000 not 1.0).) X Answer is not complete. Present Value Option 1 Option 2 Option 3 $ 22,000,000 Future Value of $1 Periods 1.0% 2.0% 3.0% 3.75% 4.0% 4.25% 5.0% 6.0% 7.0% 1 1.04000 2 3 4 5 5 6 7 1.01000 1.02010 1.03030 1.04060 1.05101 1.06152 1.07214 1.08286 1.09369 1.10462 1.02000 1.04040 1.06121 1.08243 1.10408 1.12616 1.14869 1.17166 1.19509 1.21899 1.03000 1.06090 1.09273 1.12551 1.15927 1.19405 1.22987 1.26677 1.30477 1.34392 1.03750 1.07641 1.11677 1.15865 1.20210 1.24718 1.29395 1.34247 1.39281 1.44504 1.08160 1.12486 1.16986 1.21665 1.26532 1.31593 1.36857 1.42331 1.48024 1.04250 1.08681 1.13300 1.18115 1.23135 1.28368 1.33824 1.39511 1.45440 1.51621 1.05000 1.10250 1.15763 1.21551 1.27628 1.34010 1.40710 1.47746 1.55133 1.62889 1.06000 1.12360 1.19102 1.26248 1.33823 1.41852 1.50363 1.59385 1.68948 1.79085 1.07000 1.14490 1.22504 1.31080 1.40255 1.50073 1.60578 1.71819 8 9 10 1.83846 1.96715 Future Value of $1 Periods 1.0% 2.0% 3.0% 3.75% 4.0% 4.25% 5.0% 7.0% 11 12 13 14 15 1.11567 1.12683 1.13809 1.14947 1.16097 1.17258 1.18430 1.19615 1.20811 1.22019 1.28243 1.34785 1.24337 1.26824 1.29361 1.31948 1.34587 1.37279 1.40024 1.42825 1.45681 1.48595 16 1.38423 1.42576 1.46853 1.51259 1.55797 1.60471 1.65285 1.70243 1.75351 1.80611 2.09378 2.42726 1.49923 1.55545 1.61378 1.67430 1.73709 1.80223 1.86981 1.93993 2.01268 2.08815 2.51017 3.01747 1.53945 1.60103 1.66507 1.73168 1.80094 1.87298 1.94790 2.02582 2.10685 2.19112 2.66584 3.24340 1.58065 1.64783 1.71786 1.79087 1.86699 1.94633 2.02905 2.11529 2.20519 2.29891 2.83075 3.48564 1.71034 1.79586 1.88565 1.97993 2.07893 2.18287 2.29202 2.40662 2.52695 6.0% 1.89830 2.01220 2.13293 2.26090 2.39656 2.54035 2.69277 2.85434 3.02560 3.20714 4.29187 5.74349 2.10485 2.25219 2.40985 2.57853 2.75903 2.95216 3.15882 3.37993 3.61653 3.86968 5.42743 7.61226 17 18 19 20 25 1.64061 1.81136 2.65330 3.38635 4.32194 30 Future Value of $1 Periods 8.0% 9.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 1 2 3 4 5 6 1.08000 1.16640 1.25971 1.36049 1.46933 1.58687 1.71382 1.85093 1.99900 2.15892 1.09000 1.18810 1.29503 1.41158 1.53862 1.67710 1.82804 1.99256 2.17189 2.36736 10.0% 1.10000 1.21000 1.33100 1.46410 1.61051 1.77156 1.94872 2.14359 2.35795 2.59374 1.11000 1.23210 1.36763 1.51807 1.68506 1.87041 2.07616 2.30454 2.55804 2.83942 1.12000 1.25440 1.40493 1.57352 1.76234 1.97382 2.21068 2.47596 2.77308 3.10585 1.13000 1.27690 1.44290 1.63047 1.84244 2.08195 2.35261 2.65844 3.00404 3.39457 1.14000 1.29960 1.48154 1.68896 1.92541 2.19497 2.50227 2.85259 3.25195 3.70722 1.15000 1.32250 1.52088 1.74901 2.01136 2.31306 2.66002 3.05902 3.51788 4.04556 1.20000 1.44000 1.72800 2.07360 2.48832 2.98598 3.58318 4.29982 5.15978 6.19174 1.25000 1.56250 1.95313 2.44141 3.05176 3.81470 4.76837 5.96046 7.45058 9.31323 7 8 9 9 10 Future Value of $1 Periods 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 11 12 13 14 15 16 17 18 19 20 25 30 2.33164 2.51817 2.71962 2.93719 3.17217 3.42594 3.70002 3.99602 4.31570 4.66096 6.84848 10.06266 2.58043 2.81266 3.06580 3.34173 3.64248 3.97031 4.32763 4.71712 5.14166 5.60441 8.62308 13.26768 2.85312 3.13843 3.45227 3.79750 4.17725 4.59497 5.05447 5.55992 6.11591 6.72750 10.83471 17.44940 3.15176 3.49845 3.88328 4.31044 4.78459 5.31089 5.89509 6.54355 7.26334 8.06231 13.58546 22.89230 3.47855 3.89598 4.36349 4.88711 5.47357 6.13039 6.86604 7.68997 8.61276 9.64629 17.00006 29.95992 3.83586 4.33452 4.89801 5.53475 6.25427 7.06733 7.98608 9.02427 10.19742 11.52309 21.23054 39.11590 4.22623 4.81790 5.49241 6.26135 7.13794 8.13725 9.27646 10.57517 12.05569 13.74349 26.46192 50.95016 4.65239 5.35025 6.15279 7.07571 8.13706 9.35762 10.76126 12.37545 14.23177 16.36654 32.91895 66.21177 7.43008 8.91610 10.69932 12.83918 15.40702 18.48843 22.18611 26.62333 31.94800 38.33760 95.39622 237.37631 11.64153 14.55192 18.18989 22.73737 28.42171 35.52714 44.40892 55.51115 69.38894 86.73617 264.69780 807.79357 Present Value of $1 Periods 1.0% 2.0% 3.0% 3.75% 4.0% 4.25% 5.0% 6.0% 7.0% 0.96386 0.92902 0.89544 0.86307 0.83188 1 0.99010 2 0.98030 3 0.97059 4. 0.96098 5 0.95147 6 6 0.94205 7 0.93272 8 0.92348 9 0.91434 10 0.90529 Present Value of $1 1 Periods 1.0% 0.98039 0.96117 0.94232 0.92385 0.90573 0.88797 0.87056 0.85349 0.83676 0.82035 0.97087 0.94260 0.91514 0.88849 0.86261 0.83748 0.81309 0.78941 0.76642 0.74409 0.96154 0.92456 0.88900 0.85480 0.82193 0.79031 0.75992 0.73069 0.70259 0.67556 0.95923 0.92013 0.88262 0.84663 0.81212 0.77901 0.74725 0.71679 0.68757 0.65954 0.95238 0.90703 0.86384 0.82270 0.78353 0.74622 0.71068 0.67684 0.64461 0.61391 0.94340 0.89000 0.83962 0.79209 0.74726 0.70496 0.66506 0.62741 0.59190 0.55839 0.93458 0.87344 0.81630 0.76290 0.71299 0.66634 0.62275 0.58201 0.54393 0.50835 0.80181 0.77283 0.74490 0.71797 0.69202 2.0% 3.0% 3.75% 4.0% 6.25% 5.0% % 6.0% 7.0% 11 12 13 14 15 16 17 18 19 20 25 30 0.89632 0.88745 0.87866 0.86996 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.77977 0.74192 0.80426 0.78849 0.77303 0.75788 0.74301 0.72845 0.71416 0.70016 0.68643 0.67297 0.60953 0.55207 0.72242 0.70138 0.68095 0.66112 0.64186 0.62317 0.60502 0.58739 0.57029 0.55368 0.47761 0.41199 0.66701 0.64290 0.61966 0.59726 0.57568 0.55487 0.53481 0.51548 0.49685 0.47889 0.39838 0.33140 0.64958 0.62460 0.60057 0.57748 0.55526 0.53391 0.51337 0.49363 0.47464 0.45639 0.37512 0.30832 0.63265 0.60686 0.58212 0.55839 0.53562 0.51379 0.49284 0.47275 0.45348 0.43499 0.35326 0.28689 0.58468 0.55684 0.53032 0.50507 0.48102 0.45811 0.43630 0.41552 0.39573 0.37689 0.29530 0.23138 0.52679 0.49697 0.46884 0.44230 0.41727 0.39365 0.37136 0.35034 0.33051 0.31180 0.23300 0.17411 0.47509 0.44401 0.41496 0.38782 0.36245 0.33873 0.31657 0.29586 0.27651 0.25842 0.18425 0.13137 Present Value of $1 Periods 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 1 1 2 3 4 5 6 7 7 8 9 9 10 0.92593 0.85734 0.79383 0.73503 0.68058 0.63017 0.58349 0.54027 0.50025 0.46319 0.91743 0.84168 0.77218 0.70843 0.64993 0.59627 0.54703 0.50187 0.46043 0.42241 0.90909 0.82645 0.75131 0.68301 0.62092 0.56447 0.51316 0.46651 0.42410 0.38554 0.90090 0.81162 0.73119 0.65873 0.59345 0.53464 0.48166 0.43393 0.39092 0.35218 0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197 0.88496 0.78315 0.69305 0.61332 0.54276 0.48032 0.42506 0.37616 0.33288 0.29459 0.87719 0.76947 0.67497 0.59208 0.51937 0.45559 0.39964 0.35056 0.30751 0.26974 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718 0.83333 0.69444 0.57870 0.48225 0.40188 0.33490 0.27908 0.23257 0.19381 0.16151 0.80000 0.64000 0.51200 0.40960 0.32768 0.26214 0.20972 0.16777 0.13422 0.10737 Present Value of $1 Periods 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 11 12 13 14 15 16 17 18 19 20 25 30 0.42888 0.39711 0.36770 0.34046 0.31524 0.29189 0.27027 0.25025 0.23171 0.21455 0.14602 0.09938 0.38753 0.35553 0.32618 0.29925 0.27454 0.25187 0.23107 0.21199 0.19449 0.17843 0.11597 0.07537 0.35049 0.31863 0.28966 0.26333 0.23939 0.21763 0.19784 0.17986 0.16351 0.14864 0.09230 0.05731 0.31728 0.28584 0.25751 0.23199 0.20900 0.18829 0.16963 0.15282 0.13768 0.12403 0.07361 0.04368 0.28748 0.25668 0.22917 0.20462 0.18270 0.16312 0.14564 0.13004 0.11611 0.10367 0.05882 0.03338 0.26070 0.23071 0.20416 0.18068 0.15989 0.14150 0.12522 0.11081 0.09806 0.08678 0.04710 0.02557 0.23662 0.20756 0.18207 0.15971 0.14010 0.12289 0.10780 0.09456 0.08295 0.07276 0.03779 0.01963 0.21494 0.18691 0.16253 0.14133 0.12289 0.10686 0.09293 0.08081 0.07027 0.06110 0.03038 0.01510 0.13459 0.11216 0.09346 0.07789 0.06491 0.05409 0.04507 0.03756 0.03130 0.02608 0.01048 0.00421 0.08590 0.06872 0.05498 0.04398 0.03518 0.02815 0.02252 0.01801 0.01441 0.01153 0.00378 0.00124 Future Value of Annuity of $1 Periods 1.0% 2.0% 3.0% 3.75% 4.0% 4.25% 5.0% 6.0% 7.0% 1.00000 1.00000 2.04250 2.07000 1 1.00000 2 2.01000 3 3.03010 4 4.06040 5 5.10101 6 6.15202 7 7 7.21354 8 8.28567 9 9.36853 10 10.46221 Future Value of Annuity of $1 Periods 1.0% 1.00000 2.02000 3.06040 4.12161 5.20404 6.30812 7.43428 8.58297 1.00000 2.03000 3.09090 4.18363 5.30914 6.46841 7.66246 8.89234 10.15911 11.46388 1.00000 2.03750 3.11391 4.23068 5.38933 6.59143 7.83861 9.13255 10.47503 11.86784 1.00000 2.04000 3.12160 4.24646 5.41632 6.63298 7.89829 3.12931 4.26230 5.44345 6.67480 7.95848 9.29671 10.69182 12.14622 1.00000 2.05000 3.15250 4.31013 5.52563 6.80191 8.14201 9.54911 11.02656 12.57789 1.00000 2.06000 3.18360 4.37462 5.63709 6.97532 8.39384 9.89747 3.21490 4.43994 5.75074 7.15329 8.65402 10.25980 11.97799 13.81645 9.21423 9.75463 10.94972 10.58280 12.00611 11.49132 13.18079 2.0% 3.0% 3.75% 4.0% 4.25% 5.0% 6.0% 7.0% 11 12 13 14 15 16 17 18 19 20 25 11.56683 12.68250 13.80933 14.94742 16.09690 17.25786 18.43044 19.61475 20.81090 22.01900 28.24320 34.78489 12.16872 13.41209 14.68033 15.97394 17.29342 18.63929 20.01207 21.41231 22.84056 24.29737 32.03030 12.80780 14.19203 15.61779 17.08632 18.59891 20.15688 21.76159 23.41444 25.11687 26.87037 36.45926 47.57542 13.31288 14.81212 16.36757 17.98135 19.65565 21.39274 23.19497 25.06478 27.00471 29.01739 40.27112 53.79924 13.48635 15.02581 16.62684 18.29191 20.02359 21.82453 23.69751 25.64541 27.67123 29.77808 41.64591 56.08494 13.66244 15.24309 16.89092 18.60879 20.39966 22.26665 24.21298 26.24203 28.35732 30.56250 43.07648 58.48553 14.20679 15.91713 17.71298 19.59863 21.57856 23.65749 25.84037 28.13238 30.53900 33.06595 47.72710 66.43885 14.97164 16.86994 18.88214 21.01507 23.27597 25.67253 28.21288 30.90565 33.75999 36.78559 54.86451 79.05819 15.78360 17.88845 20.14064 22.55049 25.12902 27.88805 30.84022 33.99903 37.37896 40.99549 63.24904 94.46079 30 40.56808 Future Value of Annuity of $1 Periods 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 1.00000 2.09000 3.27810 4.57313 5.98471 7.52333 9.20043 11.02847 13.02104 15.19293 1.00000 2.10000 3.31000 4.64100 6.10510 7.71561 1 1 1.00000 2 2.08000 3 3 3.24640 4 4.50611 5 5.86660 6 7.33593 7 8.92280 8 10.63663 9 12.48756 10 14.48656 Future Value of Annuity of $1 Periods 8.0% 1.00000 2.11000 3.34210 4.70973 6.22780 7.91286 9.78327 11.85943 14.16397 16.72201 1.00000 2.12000 3.37440 4.77933 6.35285 8.11519 10.08901 12.29969 14.77566 17.54874 1.00000 2.13000 3.40690 4.84980 6.48027 8.32271 10.40466 12.75726 15.41571 18.41975 1.00000 2.14000 3.43960 4.92114 6.61010 8.53552 10.73049 13.23276 16.08535 19.33730 1.00000 2.15000 3.47250 4.99337 6.74238 8.75374 1.00000 2.20000 3.64000 5.36800 7.44160 9.92992 12.91590 16.49908 20.79890 25.95868 1.00000 2.25000 3.81250 5.76563 8.20703 11.25879 15.07349 19.84186 25.80232 33.25290 9.48717 11.43589 11.06680 13.72682 16.78584 20.30372 13.57948 15.93742 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 11 12 13 14 15 16 17 18 19 20 25 16.64549 18.97713 21.49530 24.21492 27.15211 30.32428 33.75023 37.45024 41.44626 45.76196 73.10594 113.28321 17.56029 20.14072 22.95338 26.01919 29.36092 33.00340 36.97370 41.30134 46.01846 51.16012 84.70090 136.30754 18.53117 21.38428 24.52271 27.97498 31.77248 35.94973 40.54470 45.59917 51.15909 57.27500 98.34706 164.49402 19.56143 22.71319 26.21164 30.09492 34.40536 39.18995 44.50084 50.39594 56.93949 64.20283 114.41331 199.02088 20.65458 24.13313 28.02911 32.39260 37.27971 42.75328 48.88367 55.74971 63.43968 72.05244 133.33387 241.33268 21.81432 25.65018 29.98470 34.88271 40.41746 46.67173 53.73906 61.72514 70.74941 80.94683 155.61956 293.19922 23.04452 27.27075 32.08865 37.58107 43.84241 50.98035 59.11760 68.39407 78.96923 91.02493 181.87083 356.78685 24.34928 29.00167 34.35192 40.50471 47.58041 55.71747 65.07509 75.83636 88.21181 102.44358 212.79302 434.74515 32.15042 39.58050 48.49660 59.19592 72.03511 87.44213 105.93056 128.11667 154.74000 186.68800 471.98108 1181.88157 42.56613 54.20766 68.75958 86.94947 109.68684 138.10855 173.63568 218.04460 273.55576 342.94470 1054.79118 3227.17427 30 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% 0.94340 1.83339 2.67301 3.46511 4.21236 1 2 2 3 3 4 5 6 7 7 8 9 10 0.99010 1.97040 2.94099 3.90197 4.85343 5.79548 6.72819 7.65168 8.56602 9.47130 0.98039 1.94156 2.88388 3.80773 4.71346 5.60143 6.47199 7.32548 8.16224 8.98259 0.97087 1.91347 2.82861 3.71710 4.57971 5.41719 6.23028 7.01969 7.78611 8.53020 0.96386 1.89287 2.78831 3.65138 4.48326 5.28507 6.05790 6.80280 7.52077 8.21279 0.96154 1.88609 2.77509 3.62990 4.45182 5.24214 6.00205 6.73274 7.43533 8.11090 0.95923 1.87936 2.76198 3.60861 4.42073 5.19974 5.94699 6.66378 7.35135 8.01089 0.95238 1.85941 2.72325 3.54595 4.32948 5.07569 5.78637 6.46321 7.10782 7.72173 0.93458 1.80802 2.62432 3.38721 4.10020 4.76654 5.38929 5.97130 6.51523 7.02358 4.91732 5.58238 6.20979 6.80169 7.36009 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% 11 12 13 8.76048 9.38507 9.98565 8.30641 8.86325 9.39357 14 15 16 17 18 19 20 10.36763 11.25508 12.13374 13.00370 13.86505 14.71787 15.56225 16.39827 17.22601 18.04555 22.02316 25.80771 9.78685 10.57534 11.34837 12.10625 12.84926 13.57771 14.29187 14.99203 15.67846 16.35143 19.52346 22.39646 9.25262 9.95400 10.63496 11.29607 11.93794 12.56110 13.16612 13.75351 14.32380 14.87747 17.41315 19.60044 8.87979 9.52269 10.14236 10.73962 11.31530 11.87017 12.40498 12.92046 13.41731 13.89620 16.04320 17.82925 10.56312 11.11839 11.65230 12.16567 12.65930 13.13394 13.59033 15.62208 17.29203 8.64354 9.25039 9.83251 10.39090 10.92652 11.44031 11.93315 12.40590 12.85938 13.29437 15.21734 16.77902 9.89864 10.37966 10.83777 11.27407 11.68959 12.08532 12.46221 14.09394 15.37245 7.88687 8.38384 8.85268 9.29498 9.71225 10.10590 10.47726 10.82760 11.15812 11.46992 12.78336 13.76483 7.49867 7.94269 8.35765 8.74547 9.10791 9.44665 9.76322 10.05909 10.33560 10.59401 11.65358 12.40904 25 30 Present Value of Annuity of $1 Periods 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 20.0% 25.0% 1 2 3 4 5 6 7 0.92593 1.78326 2.57710 3.31213 3.99271 4.62288 5.20637 5.74664 6.24689 6.71008 0.91743 1.75911 2.53129 3.23972 3.88965 4.48592 5.03295 5.53482 5.99525 6.41766 0.90909 1.73554 2.48685 3.16987 3.79079 4.35526 4.86842 5.33493 5.75902 6.14457 0.90090 1.71252 2.44371 3.10245 3.69590 4.23054 4.71220 5.14612 5.53705 5.88923 0.89286 1.69005 2.40183 3.03735 3.60478 4.11141 4.56376 4.96764 5.32825 5.65022 0.88496 1.66810 2.36115 2.97447 3.51723 3.99755 4.42261 4.79877 5.13166 5.42624 0.87719 1.64666 2.32163 2.91371 3.43308 3.88867 4.28830 4.63886 4.94637 5.21612 0.86957 1.62571 2.28323 2.85498 3.35216 3.78448 4.16042 4.48732 4.77158 5.01877 0.83333 1.52778 2.10648 2.58873 2.99061 3.32551 3.60459 3.83716 4.03097 4.19247 0.80000 1.44000 1.95200 2.36160 2.68928 2.95142 3.16114 3.32891 3.46313 3.57050 8 9 10 Present Value of Annuity of $1 Periods 8.0% % 9.0% 10.0% 11.0% 12.0% % 13.0% 14.0% 15.0% 20.0% 25.0% 11 12 13 14 15 16 17 18 19 20 25 30 7.13896 7.53608 7.90378 8.24424 8.55948 8.85137 9.12164 9.37189 9.60360 9.81815 10.67478 11.25778 6.80519 7.16073 7.48690 7.78615 8.06069 8.31256 8.54363 8.75563 8.95011 9.12855 9.82258 10.27365 6.49506 6.81369 7.10336 7.36669 7.60608 7.82371 8.02155 8.20141 8.36492 8.51356 9.07704 9.42691 6.20652 6.49236 6.74987 6.98187 7.19087 7.37916 7.54879 7.70162 7.83929 7.96333 8.42174 8.69379 5.93770 6.19437 6.42355 6.62817 6.81086 6.97399 7.11963 7.24967 7.36578 7.46944 7.84314 8.05518 5.68694 5.91765 6.12181 6.30249 6.46238 6.60388 6.72909 6.83991 6.93797 7.02475 7.32998 7.49565 5.45273 5.66029 5.84236 6.00207 6.14217 6.26506 6.37286 6.46742 6.55037 6.62313 6.87293 7.00266 5.23371 5.42062 5.58315 5.72448 5.84737 5.95423 6.04716 6.12797 6.19823 6.25933 6.46415 6.56598 4.32706 4.43922 4.53268 4.61057 4.67547 4.72956 4.77463 4.81219 4.84350 4.86958 4.94759 4.97894 3.65640 3.72512 3.78010 3.82408 3.85926 3.88741 3.90993 3.92794 3.94235 3.95388 3.98489 3.99505