Required Information [The following Information applies to the questions displayed below.] Following is Information on an Investment In a manufacturing machine. The machine has zero salvage value. The company requires a 3% return from its Investments. Initial investment Net cash flows: Year 1 Year 2 Year 3 $ (200,000) 100,000 128,000 79,000 Compute this machine's net present value. (PV of $3 FV of $1, PVA of $1. and FVA of $1) Note: Use appropriate factor(s) from the tables provided. Round all present value factors to 4 decimal places. Round present value amounts to the nearest dollar. Net Cash Flow Present Value Factor Present Value of Net Cash Flows Year 1 Year 2 Year 3 Totals Initial investment Net present value 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% Periods 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.8929 0.8696 1 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.7972 0.7561 2 3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118 0.6575 3 4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355 0.5718 4 5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6499 0.6302 0.5963 0.6209 0.5674 0.4972 5 0.5645 0.5066 0.4323 6 7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523 0.3759 7 8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039 0.3269 8 9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606 0.2843 9 10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220 0.2472 10 11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.2875 0.2149 11 12 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2567 0.1869 12 13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2292 0.1625 13 14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2046 0.1413 14 15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.1827 0.1229 15 16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1631 0.1069 16 17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1456 0.0929 17 18 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1300 0.0808 18 19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1161 0.0703 19 20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1037 0.0611 20 25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923 0.0588 0.0304 25 30 0.7419 0.5521 0.4120 0.3083 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573 0.0334 0.0151 30 35 0.7059 0.5000 0.3554 0.2534 40 0.6717 0.4529 0.3066 0.2083 0.1813 0.1420 0.1301 0.0972 0.0937 0.0668 0.0676 0.0460 0.0490 0.0318 0.0356 0.0221 0.0189 0.0107 0.0075 0.0037 35 40 *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 n = 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 ($5,000 0.5568). Table B.2 Future Value of 1 f = (1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% Periods 0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0 1 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 1.1200 1.1500 1 2 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 1.2544 1.3225 2 3 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049 1.5209 3 4 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 1.7490 4 5 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623 2.0114 5 6 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738 2.3131 6 7 1.0721 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107 2.6600 7 8 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760 3.0590 8 9 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731 3.5179 9 10 1.1046 1.2190 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058 4.0456 10 11 1.1157 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.4785 4.6524 11 12 1.1268 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.8960 5.3503 12 13 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 4.3635 6.1528 13 14 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.8871 7.0757 14 15 1.1610 1.3459 1.5580 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 5.4736 8.1371 15 16 1.1726 1.3728 1.6047 1.8730 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950 6.1304 9.3576 16 17 1.1843 1.4002 1.6528 1.9479 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545 6.8660 10.7613 17 18 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599 7.6900 12.3755 18 19 1.2081 1.4568 1.7535 2.1068 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159 8.6128 14.2318 19 20 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 9.6463 16.3665 20 25 1.2824 1.6406 2.0938 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 30 1.3478 1.8114 2.4273 3.2434 4.3219 5.7435 35 1.4166 1.9999 2.8139 3.9461 5.5160 40 1.4889 2.2080 3.2620 4.8010 7.6123 10.0627 7.6861 10.6766 14.7853 7.0400 10.2857 14.9745 21.7245 13.2677 10.8347 17.4494 17.0001 29.9599 32.9190 25 20.4140 28.1024 52.7996 31.4094 45.2593 93.0510 267.8635 66.2118 133.1755 30 35 40 *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 1.4859). Table B.3 Present Value of an Annuity of 1 p = [1 - 1/(1 + i)"]/i Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% Periods 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.8929 0.8696 1 2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.6901 1.6257 2 3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 2.2832 3 4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373 2.8550 4 5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 3.6048 4.1114 3.7845 3.3522 5 6 7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 4.1604 7 8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 4.4873 8 9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.3282 4.7716 9 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502 5.0188 10 11 10.3676 9.7868 9.2526 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 5.9377 5.2337 11 12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.1944 5.4206 12 13 12.1337 11.3484 10.6350 14 13.0037 15 16 13.8651 12.8493 11.9379 14.7179 13.5777 12.5611 17 18 19 20 15.5623 14.2919 13.1661 16.3983 14.9920 13.7535 17.2260 15.6785 14.3238 18.0456 16.3514 14.8775 25 22.0232 19.5235 17.4131 30 35 40 15.6221 14.0939 25.8077 22.3965 19.6004 17.2920 15.3725 29.4086 24.9986 21.4872 18.6646 16.3742 32.8347 27.3555 23.1148 19.7928 9.9856 12.1062 11.2961 10.5631 9.8986 11.1184 10.3797 11.6523 10.8378 12.1657 11.2741 12.6593 11.6896 10.8276 13.1339 12.0853 11.1581 10.3356 13.5903 12.4622 11.4699 10.5940 12.7834 11.6536 13.7648 12.4090 14.4982 12.9477 15.0463 13.3317 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.4235 5.5831 13 9.2950 8.7455 8.2442 7.7862 7.3667 6.6282 5.7245 14 9.7122 9.1079 8.5595 8.0607 7.6061 6.8109 5.8474 15 10.1059 9.4466 8.8514 8.3126 7.8237 6.9740 5.9542 16 10.4773 9.7632 9.1216 8.5436 8.0216 7.1196 6.0472 17 10.0591 9.3719 8.7556 8.2014 7.2497 6.1280 18 9.6036 8.9501 8.3649 7.3658 6.1982 19 17.1591 9.8181 10.6748 9.8226 11.2578 10.2737 9.4269 11.6546 10.5668 9.6442 11.9246 10.7574 9.7791 9.1285 8.5136 7.4694 6.2593 20 9.0770 7.8431 6.4641 25 8.0552 6.5660 8.1755 6.6166 8.2438 6.6418 30 35 40 *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 = 9%), the PV factor is 6.4177. $2,000 per year for 10 years is the equivalent of $12,835 today ($2,000 6.4177). Table B.4Future Value of an Annuity of 1 f= [(1+ i)* - 1]/i Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% Periods 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1 2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1200 2.1500 2 3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 3.4725 3 4 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 4.9934 4 5 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 6 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8 8.2857 8.5830 9 9.3685 8.8923 9.7546 10.1591 9.2142 10.5828 9.5491 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 48.8864 22.0190 24.2974 26.8704 29.7781 33.0660 28.2432 32.0303 36.4593 41.6459 47.7271 34.7849 40.5681 47.5754 56.0849 66.4388 41.6603 49.9945 60.4621 73.6522 90.3203 60.4020 75.4013 95.0255 120.7998 6.1051 6.3528 7.5233 7.7156 8.1152 8.6540 8.9228 9.2004 9.4872 10.0890 9.8975 10.2598 10.6366 11.0285 11.4359 12.2997 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.7757 10.4622 10.9497 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 11.5668 12.1687 12.8078 13.4864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 20.6546 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843 24.1331 13.8093 14.6803 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 28.0291 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 32.3926 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725 37.2797 47.5804 17.2579 18.6393 20.1569 21.8245 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497 42.7533 55.7175 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 30.8402 33.7502 36.9737 40.5447 48.8837 65.0751 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 55.7497 75.8364 20.8109 22.8406 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 63.4397 36.7856 40.9955 45.7620 51.1601 57.2750 72.0524 54.8645 63.2490 73.1059 84.7009 98.3471 133.3339 212.7930 79.0582 94.4608 113.2832 136.3075 164.4940 241.3327 434.7451 111.4348 138.2369 172.3168 215.7108 271.0244 431.6635 881.1702 154.7620 199.6351 259.0565 337.8824 442.5926 767.0914 1,779.0903 5.7507 5.8666 5.9847 6.7424 5 7.1533 7.3359 8.7537 6 11.0668 7 13.7268 8 16.7858 9 20.3037 10 24.3493 11 29.0017 12 34.3519 13 40.5047 14 15 16 17 18 88.2118 102.4436 19 20 25 30 35 40 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 7.3359).