TABLE B.1 Present Value of 1 p=1/(1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0 OWN 8686cown 0.9901 0.9803 0.9706 0.9610 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787 0.8700 0.8613 0.8528 0.8444 0.8360 0.8277 0.8195 0.7798 0.7419 0.7059 0.6717 0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730 0.7579 0.7430 0.7284 0.7142 0.7002 0.6864 0.6730 0.6095 0.5521 0.5000 0.4529 0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6810 0.6611 0.6419 0.6232 0.6050 0.5874 0.5703 0.5537 0.4776 0.4120 0.3554 0.3066 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006 0.5775 0.5553 0.5339 0.5134 0.4936 0.4746 0.4564 0.3751 0.3083 0.2534 0.2083 0.9524 0.9434 0.9346 0.9070 0.8900 0.8734 0.8638 0.8396 0.8163 0.8227 0.7921 0 .7629 0.7835 0.7473 0.7130 0.7462 0.7050 0.6663 0.7107 0.6651 0.6227 0.6768 0.6274 0.5820 0.6446 0.5919 0.5439 0.6139 0.5584 0.5083 0.5847 0.5268 0.4751 0.5568 0.4970 0.4440 0.5303 0.4688 0.4150 0.5051 0.4423 0.3878 0.4810 0.4173 0.3624 0.45810.39360.3387 0.4363 0.3714 0.3166 0.4155 0.3503 0.2959 0.3957 0.3305 0.2765 0.3769 0.3118 0.2584 0.2953 0.2330 0.1842 0.2314 0.1741 0.1314 0.1813 0.1301 0.0937 0.1420 0.0972 0.0668 0.9259 0.8573 0.7938 .7350 0.6806 0.6302 0.5835 0.5403 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 0.3152 0.2919 0.2703 0.2502 0.2317 0.2145 0.1460 0.0994 0.0676 0.0460 0.9174 0.9091 0.8417 0.8264 0.7722 0.7513 0.7084 0.6830 0.6499 0.6209 0.5963 0.5645 0.5470 0.5132 0.50190.4665 0.4604 0.4241 0.4224 0.3855 0.3875 0.3505 0.3555 0.3186 0.3262 0.2897 0.2992 0.2633 0.2745 0.2394 0.2519 0.2176 0.2311 0.1978 0.2120 0.1799 0.1945 0.1635 0.1784 0.1486 0.1160 0.0923 0.0754 0.0573 0.0490 0.0356 0.0318 0.0221 0.8929 0.8696 0.7972 0.7561 0.7118 0.6575 0.6355 0.5718 0.5674 0.4972 0.5066 0.4323 0.3759 0.40390.3269 0.3606 0.2843 0.3220 0.2472 0.2875 0.2149 0.2567 0.1869 0.2292 0.1625 0.2046 0.1413 0.1827 0.1229 0.1631 0.1069 0.1456 0.0929 0.13000.0808 0.1161 0.0703 0.1037 0.0611 0.0588 0.0304 0.0334 0.0151 0.0189 0.0075 0.0107 0.0037 *Used to compute the present value of a known future amount. For example: How much would you need to invest today at 10% compounded semiannually to accumulate $5,000 in 6 years from today? Using the factors of r= 12 and i = 5% (12 semiannual periods and a semiannual rate of 5%), the factor is 0.5568. You would need to invest $2,784 today (55.000 x 0.5568). TABLE B.2+ Future Value of 1 f=(1 + i)" Rate 7% Periods 18. 2% 3% 4% 5% 6% 8% 9% 10% 12% 15% 1.0000 1.0600 1.1236 1.1910 1.2625 1.3382 1.0000 1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2824 1.3478 1.4166 1.4889 1.0000 1.0000 1.0200 1.0300 1.0404 1.0609 1.0612 1.0927 1.0824 1.1255 1.1041 1.1593 1.1262 1.1941 1.1487 1.2299 1.1717 1.2668 1.1951 1.3048 1.21901.3439 1.2434 1.3842 1.2682 1.4258 1.2936 1.4685 1.3195 1.5126 1.3459 1.5580 1.3728 1.6047 1.4002 1.6528 1.4282 1.7024 1.4568 1.7535 1.4859 1.8061 1.6406 2.0938 1.8114 2.4273 1.99992.8139 2.2080 3.2620 1.0000 1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.0000 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 3.3864 4.3219 5.5160 7.0400 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 4.2919 5.7435 7.6861 10.2857 1.0000 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 5.4274 7.6123 10.6766 14.9745 1.0000 1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4 .3157 4.6610 6.8485 10.0627 14.7853 21.7245 1.0000 1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 8.6231 13.2677 20.4140 31.4094 1.0000 1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 10.8347 17.4494 28.1024 45.2593 1.0000 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8 .6128 9.6463 17.0001 29.9599 52.7996 93.0510 1.0000 1.1500 1.3225 1.5209 1.7490 2.0114 2.3131 2.6600 3.0590 3.5179 4.0456 4.6524 5.3503 6.1528 7.0757 8.1371 9.3576 10.7613 12.3755 14.2318 16.3665 32.9190 66.2118 133.1755 267.8635 1.9479 2.0258 2.1068 2.1911 2.6658 3.2434 3.9461 4.8010 *Used to compute the future value of a known present amount. For example: What is the accumulated value of $3,000 invested today at 8% compounded quarterly for 5 years? Using the factors of n= 20 and i = 2% (20 quarterly periods and a quarterly interest rate of 2%), the factor is 1.4859. The accumulated value is $4.457.70 ($3.000 x 1.4859). p=fi-atoni TABLE B.3 Present Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0 0.9901 0.9804 0.9709 1.9704 1.9416 1.9135 2.9410 2.88392.8286 3.9020 3.8077 3.7171 4.8534 4.7135 4.5797 5.7955 5.6014 5.4172 6.7282 6.4720 6.2303 7.6517 7.3255 7.0197 8.5660 8.1622 7.7861 9.4713 8.9826 8.5302 10.3676 9.7868 9.2526 11.2551 10.5753 9.9540 12.1337 11.3484 10.6350 13.0037 12.1062 11.2961 13.8651 12.8493 11.9379 14.7179 13.5777 12.5611 15.5623 14.291913.1661 16.3983 14.9920 13.7535 17.2260 15.6785 14.3238 18.0456 16.3514 14.8775 22.0232 19.5235 17.4131 25.8077 22.3965 19.6004 29.4086 24.9986 21.4872 32.834727.3555 23.1148 .9615 0.9524 0.9434 0.9346 1.8861 1.8594 1.8334 1.8080 2.7751 2.7232 2.6730 2.6243 3.6299 3.5460 3.4651 3.3872 4.4518 4.3295 4.2124 4.1002 5.2421 5.0757 4.9173 4.7665 6.0021 5.7864 5.5824 5.3893 6.7327 6.4632 6.2098 5.9713 7.4353 7.1078 6.8017 6.5152 8.1109 7.7217 7.3601 7.0236 8.7605 8.3064 7.8869 7.4987 9.3851 8.8633 8.3838 7.9427 9.98569 .3936 8.8527 8 3577 10.5631 9.8986 9.2950 8.7455 11.1184 10.3797 9.7122 9.1079 11.6523 10.8378 10.1059 9.4466 12.1657 11.274110.4773 9 .7632 12.6593 11.6896 10.8276 10.0591 13.1339 12.0853 11.1581 10.3356 13.5903 12.4622 11.4699 10.5940 15.6221 14.0939 12.7834 11.6536 17.2920 15.3725 13.764812.4090 18.6646 16.3742 14.498212.9477 19.7928 17.1591 15.0463 13.3317 0.9259 0.9174 0.9091 0.8929 1.7833 1.7591 1.73551.6901 2.5771 2.5313 2.4869 2.4018 3.3121 3.2397 3.1699 3.0373 3.9927 3.8897 3.7908 3.6048 4.6229 4.4859 4.3553 4.1114 5.2064 5.0330 4.8684 4.5638 5.7466 5.5348 5.3349 4.9676 6.2469 5.9952 5.7590 5.3282 6.71016.4177 6.1446 5.6502 7.1390 6.8052 6.4951 6.4951 5.9377 7.5361 7.1607 6.8137 6.1944 7.90387.48697.1034 6.4235 8.2442 7.7862 7.3667 6.6282 8.5595 8.0607 7.6061 6.8109 8.8514 8.3126 7.8237 6.9740 9.1216 8.5436 8.0216 7.1196 9.3719 8.7556 8.2014 7.2497 9.6036 8.9501 8.36497.3658 9.8181 9.1285 8.5136 7.4694 10.6748 9.8226 9.0770 7.8431 11.2578 10.2737 9.42698.0552 11.6546 10.5668 9.6442 8.1755 11.9246 10.7574 9.77918.2438 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.4641 6.5660 6.6166 6.6418 *Used to calculate the present value of a series of equal payments made at the end of each period. For example: What is the present value of $2,000 per year for 10 years assuming an annual interest rate of 9%? For (n= 10. i=956), the PV factor is 6.4177. $2,000 per year for 10 years is the equivalent of $12,835 today (52,000 X 6.4177). a. A new operating system for an existing machine is expected to cost $590,000 and have a useful life of six years. The system yields an incremental after-tax income of $285,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $24,400. b. A machine costs $400,000, has a $29,300 salvage value, is expected to last eight years, and will generate an after-tax income of $88,000 per year after straight-line depreciation. Assume the company requires a 12% rate of return on its investments. Compute the net present value of each potential investment (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) Complete this question by entering your answers in the tabs below. Required A Required B A new operating system for an existing machine is expected to cost $590,000 and have a useful life of six years. The system yields an incremental after-tax income of $285,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $24,400. (Round your answers to the nearest whole dollar.) Select Chart Amount x PV Factor Cash Flow Annual cash flow Residual value = Present Value = $ Net present value Required A. Required B > a. A new operating system for an existing machine is expected to cost $590,000 and have a useful life of six years. The system yields an incremental after-tax income of $285,000 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $24,400. b. A machine costs $400,000, has a $29,300 salvage value, is expected to last eight years, and will generate an after-tax income of $88,000 per year after straight-line depreciation. Assume the company requires a 12% rate of return on its investments. Compute the net present value of each potential investment. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) Complete this question by entering your answers in the tabs below. Required A Required B A machine costs $400,000, has a $29,300 salvage value, is expected to last eight years, and will generate an after-tax income of $88,000 per year after straight-line depreciation. (Round your answers to the nearest whole dollar.) Select Chart Amount x PV Factor = Cash Flow Annual cash flow Residual value Present Value $ 0 Net present value f=[(1 + i)" - 1]/i TABLE B.48 Future Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% GwOWN 1.0000 1.0000 2.0100 2.0200 3.03013.0604 4.0604 4.1216 5.1010 5.2040 6.1520 6.3081 7.2135 7.4343 8.2857 8.5830 9.3685 9.7546 10.4622 10.9497 11.5668 12.1687 12.6825 13.4121 13.8093 14.6803 14.9474 15.9739 16.0969 17.2934 17.2579 18.6393 18.4304 20.0121 19.6147 21.4123 20.8109 22.8406 22.0190 24.2974 28.2432 32.0303 34.7849 40.5681 41.6603 49.9945 48.8864 60.4020 1.0000 1.000 1.0000 1.0000 1.0000 1.0000 10000 10000 10000 1.0000 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1200 2.1500 3.0909 3.1216 3.15253.1836 3.21493 .2464 3.2781 3.3100 3.3744 3.4725 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 4.9934 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6.7424 6.4684 6.63306.80196.9753 7.1533 7.3359 7.5233 7.7156 8.1152 8.7537 7.6625 7.89838.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 11.0668 8.8923 9 .2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.435912.2997 13.7268 10.1591 10.5828 11.0266 1.4913 11.9780 12.4876 13.0210 13.5795 14.7757 16.7858 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 20.3037 12.8078 13.4864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 20.6546 24.3493 14.1920 15.025815.9171 16.8699 17.8885 18.9771 20.1407 21.3843 24.1331 29.0017 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 28.0291 34.3519 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 32.3926 40.5047 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.360931.7725 37.2797 47.5804 20.1569 21.8245 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497 42.7533 55.7175 21.7616 23.6975 25.8404 28.2129 30.8402 33.7502 36.9737 40.5447 48.8837 65.0751 23.4144 25.6454 28.1324 30.9057 33.999037.450241.3013 45.5992 55.7497 75.8364 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 63.4397 88.2118 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 72.0524 102.4436 36.4593 41.6459 47.7271 54.864563.2490 73.1059 84.700998.3471 133.3339 212.7930 47.5754 56.084966.4388 79.0582 94.4608 113.2832 136.3075 164.4940 241.3327 434.7451 60.4621 73.652290.3203 111.4348 138.2369172.3168 215.7108 271.0244 431.6635881.1702 75.401395.0255 120.7998 154.7620 199.6351 259.0565 337.8824 442.5926 767.0914 1.779.0903 Used to calculate the future value of a series of equal payments made at the end of each period. For example: What is the future value of $4.000 per year for 6 years assuming an annual interest rate of 8%? For (n=6,i=8%), the FV factor is 7.3359. $4,000 per year for 6 years accumulates to $29,343.60 ($4,000 x 7.3359)