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12 Required information [The following information applies to the questions displayed below.) Part 1 of 2 Following is information on an investment in a manufacturing machine. The machine has zero salvage value. The company requires a 6% return from its investments. $ (400,000) 01:40:11 Initial investment Net cash flows: Year 1 Year 2 Year 3 125,000 92,000 95,000 Compute this machine's net present value. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (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 7% Periods 1% 2% 3% 4% 5% 6% 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 0.8696 1 0.8929 0.7972 olol I 2 0.9612 0.9070 0.8900 0.8734 0.8417 0.8264 2. 0.9803 0.9706 3 0.9423 3 0.9426 0.9151 0.8885 0.8626 0.8573 0.7938 0.7350 0.8396 0.7921 0.8163 0.7629 IT 0.8638 0.8227 0.7835 0.7722 0.7084 0.7513 0.6830 0.7118 0.6355 4 0.9610 0.7561 0.6575 0.5718 0.4972 0.9238 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 4 5 0.9057 0.7473 0.7130 I. 0.6806 0.6499 0.6209 0.5674 5 0.9515 0.9420 6 0.8880 0.8375 0.7462 0.6663 0.5645 0.5066 6 0.7050 0.6651 0.6302 0.5835 0.5963 0.5470 7 0.7107 0.5132 I. 0.8706 0.8535 7 0.9327 0.9235 0.9143 0.8131 0.7894 0.4323 0.3759 0.3269 0.4523 0.4039 8 0.7307 0.6227 0.5820 0.5439 0.6768 0.6274 0.5403 0.5019 0.4665 8 9 0.8368 0.7664 0.7026 0.5919 0.5002 0.4604 0.4241 0.3606 0.2843 9 0.6446 0.6139 10 0.9053 0.8203 0.7441 0.5584 0.2472 10 0.6756 0.6496 0.5083 0.4751 0.4224 0.3875 11 0.3220 0.2875 0.8963 0.8043 0.7224 0.4632 0.4289 0.3971 0.5847 0.3855 0.3505 0.3186 0.5268 0.4970 0.2149 11 12 0.8874 0.7885 0.7014 0.6246 0.4440 0.3555 0.2567 0.1869 12 13 0.6006 0.4688 0.4150 0.3677 13 0.8787 0.8700 0.8613 0.7730 0.7579 0.6810 0.6611 0.3262 0.2992 0.2897 0.2633 0.2292 0.2046 0.1625 0.1413 14 0.5775 0.3878 0.3405 14 0.4423 0.4173 15 0.6419 0.5553 0.3624 0.3152 0.2745 0.2394 0.1229 15 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.1827 0.1631 16 0.6232 0.5339 0.3387 0.2519 0.1069 16 0.7430 0.7284 0.7142 0.7002 0.8528 0.8444 17 0.5134 0.3936 0.3714 0.3503 0.2919 0.2703 0.2502 0.0929 0.2176 0.1978 0.1799 17 0.2311 0.2120 18 0.3166 0.2959 0.2765 0.8360 0.4936 0.1456 0.1300 0.1161 0.0808 18 19 0.6050 0.5874 0.5703 0.5537 0.4776 0.8277 0.6864 0.4746 0.3305 0.2317 0.1945 0.0703 19 | | 20 0.8195 0.6730 0.4564 0.3769 0.0611 20 0.2584 0.1842 0.2145 0.1460 0.1784 0.1160 0.1635 0.1486 0.0923 0.0573 0.1037 0.0588 25 0.0304 25 0.7798 0.7419 0.6095 0.5521 0.3751 0.3083 0.2953 0.2314 30 0.3118 0.2330 0.1741 0.1301 0.0972 0.4120 0.1314 0.0994 0.0754 0.0334 0.0151 30 35 0.7059 0.2534 0.1813 0.0937 0.0676 0.0490 0.0356 0.0189 0.0075 35 0.5000 0.4529 0.3554 0.3066 40 0.6717 0.2083 0.1420 0.0668 0.0460 0.0318 0.0221 0.0107 0.0037 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.21 Future Value of 1 f= (1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 10% 15% Periods 9% 1.0000 0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0 1.0000 1.0100 1 1.0200 1.0300 1.0400 1.0600 1.0700 1.0800 1.1500 1 1.0900 1.1881 1.1000 1.2100 12% 1.0000 1.1200 1.2544 1.4049 1.5735 2 1.0201 1.0404 1.0609 1.0816 1.1236 1.1449 1.1664 1.3225 2 3 1.0303 1.0927 1.1910 1.5209 3 1.0612 1.0824 1.1249 1.1699 1.2250 1.3108 1.2950 1.4116 4 1.0406 1.2625 1.2597 1.3605 1.4693 1.3310 1.4641 1.6105 1.7490 4. 5 1.0510 1.2167 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.3382 1.4026 1.5386 2.0114 1.1041 1.1262 5 1.1255 1.1593 1.1941 1.2299 1.2668 1.7623 1.9738 6 1.0615 1.2653 1.5869 1.6771 1.7716 2.3131 6 1.5007 1.6058 7 1.1487 1.3159 1.4185 1.5036 1.5938 1.7138 1.8280 2.6600 1.0721 1.0829 7 8 1.1717 1.3686 1.7182 1.8509 1.9926 8 3.0590 3.5179 9 1.0937 1.1951 1.3048 1.4233 1.6895 1.8385 1.9990 2.1719 9 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 10 1.1046 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 4.0456 10 2.3674 2.5804 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 11 1.1157 1.3842 1.5395 4.6524 1.2190 1.2434 1.2682 1.2936 1.3195 1.7103 1.7959 2.1049 2.2522 2.3316 2.5182 11 12 1.4258 12 13 2.8127 1.1268 1.1381 1.1495 1.4685 1.5126 13 1.6010 1.6651 1.7317 1.8009 1.8983 2.0122 2.1329 2.2609 2.3966 1.8856 1.9799 2.4098 2.5785 2.7196 2.9372 3.1722 3.0658 3.3417 14 4.3635 4.8871 5.4736 14 15 1.1610 1.3459 1.5580 2.7590 3.6425 15 2.0789 2.1829 4.1772 4.5950 16 1.6047 2.5404 2.9522 3.4259 6.1304 1.1726 1.1843 16 1.3728 1.4002 1.4282 17 5.3503 6.1528 7.0757 8.1371 9.3576 10.7613 12.3755 14.2318 16.3665 2.6928 5.0545 6.8660 17 1.8730 1.9479 2.0258 2.1068 1.6528 1.7024 2.2920 2.4066 3.1588 3.3799 3.9703 4.3276 4.7171 5.1417 3.7000 3.9960 18 1.1961 5.5599 7.6900 18 2.8543 3.0256 19 1.7535 2.5270 4.3157 8.6128 19 1.2081 1.2202 1.4568 1.4859 6.1159 6.7275 20 2.1911 3.2071 4.6610 5.6044 9.6463 20 2.6533 3.3864 3.6165 3.8697 5.4274 7.6123 25 1.8061 2.0938 2.4273 1.2824 32.9190 1.6406 1.8114 25 2.6658 3.2434 4.2919 5.7435 6.8485 10.0627 8.6231 13.2677 30 1.3478 4.3219 66.2118 30 10.8347 17.4494 28.1024 45.2593 17.0001 29.9599 52.7996 93.0510 35 1.4166 1.9999 3.9461 5.5160 7.6861 10.6766 14.7853 133.1755 35 2.8139 3.2620 20.4140 31.4094 40 1.4889 2.2080 4.8010 7.0400 10.2857 14.9745 21.7245 267.8635 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 x 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 0.9434 0.9346 0.9259 0.9174 1 0.8929 0.8696 1 0.9524 1.8594 le 0.9091 1.7355 2 1.9416 1.9135 2 1.9704 2.9410 3.9020 3 2.8286 1.8861 2.7751 3.6299 2.7232 1.8334 2.6730 3.4651 2.8839 3.8077 1.8080 2.6243 3.3872 1.6257 2.2832 1.7833 2.5771 3.3121 1.7591 2.5313 3.2397 1.6901 2.4018 3.0373 3 2.4869 3.1699 4 3.7171 2.8550 4 3.5460 4.3295 5 4.8534 4.5797 4.4518 4.1002 3.9927 3.8897 3.7908 3.6048 3.3522 5 4.2124 4.9173 6 4.7135 5.6014 6.4720 5.2421 4.6229 4.4859 4.3553 4.1114 3.7845 6 5.7955 6.7282 7.6517 5.4172 6.2303 5.0757 5.7864 7 6.0021 4.7665 5.3893 5.9713 4.5638 4.1604 5.5824 6.2098 7 5.0330 5.5348 4.8684 5.3349 8 7.3255 7.0197 5.2064 5.7466 6.2469 6.7327 6.4632 4.9676 4.4873 8 9 8.5660 8.1622 7.7861 7.4353 6.8017 6.5152 5.9952 5.7590 5.3282 4.7716 9 10 8.9826 8.5302 8.1109 7.1078 7.7217 8.3064 5.0188 10 9.4713 10.3676 7.3601 7.8869 6.7101 7.1390 11 9.7868 9.2526 7.0236 7.4987 7.9427 8.7605 11 5.6502 5.9377 6.1944 12 5.2337 5.4206 11.2551 10.5753 9.9540 9.3851 8.8633 6.4177 6.8052 7.1607 7.4869 7.7862 8.3838 6.1446 6.4951 6.8137 7.1034 7.3667 7.5361 12 13 12.1337 11.3484 10.6350 9.9856 9.3936 8.8527 8.3577 7.9038 6.4235 5.5831 13 14 11.2961 631 9.2950 8.2442 6.6282 14 9.8986 10.3797 8.7455 9.1079 15 13.8651 12.8493 11.9379 11.1184 9.7122 8.5595 8.0607 6.8109 5.8474 15 16 13.5777 10.1059 8.8514 6.9740 5.9542 12.5611 13.1661 16 7.6061 7.8237 8.0216 10.8378 11.2741 11.6523 12.1657 12.6593 9.4466 9.7632 17 14.2919 10.4773 9.1216 6.0472 17 8.3126 8.5436 8.7556 8.9501 7.1196 7.2497 18 14.9920 13.7535 10.8276 10.0591 9.3719 8.2014 6.1280 18 19 15.6785 14.3238 11.6896 12.0853 12.4622 10.3356 9.6036 7.3658 6.1982 14.7179 15.5623 16.3983 17.2260 18.0456 22.0232 25.8077 29.4086 19 20 16.3514 9.8181 11.1581 11.4699 12.7834 7.4694 6.2593 13.1339 13.5903 15.6221 17.2920 20 8.3649 8.5136 9.0770 14.8775 17.4131 19.6004 10.5940 11.6536 9.1285 9.8226 14.0939 25 30 6.4641 19.5235 22.3965 24.9986 25 30 13.7648 10.2737 9.4269 6.5660 15.3725 16.3742 12.4090 12.9477 10.6748 11.2578 11.6546 11.9246 7.8431 8.0552 8.1755 8.2438 35 14.4982 10.5668 6.6166 35 21.4872 23.1148 18.6646 19.7928 9.6442 9.7791 40 32.8347 27.3555 17.1591 15.0463 13.3317 10.7574 6.6418 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 ($2,000 6.4177). Table B.4$Future 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 1.0000 2.0600 2 1.0000 2.1200 2.0200 2.0300 2.0400 1.0000 2.0700 3.2149 2.0800 2.0900 1.0000 2.1000 3.3100 2.0100 3.0301 2 2.1500 3.4725 3 3.0909 3.1216 3.1836 3.2464 3.2781 3 3.0604 4.1216 3.3744 4.7793 4 4.0604 1.0000 2.0500 3.1525 4.3101 5.5256 6.8019 8.1420 4.3746 4.4399 4.5061 4.6410 4.9934 4.1836 5.3091 4 4.2465 5.4163 4.5731 5.9847 5 5.1010 5.6371 6.1051 6.3528 5 5.7507 7.1533 5.2040 6.3081 7.4343 5.8666 7.3359 6.7424 8.7537 6 6.1520 6.4684 6.6330 7.5233 7.7156 8.1152 6 6.9753 8.3938 7 7.2135 7.6625 7.8983 8.6540 8.9228 9.2004 9.4872 10.0890 11.0668 7 8 8.2857 8.5830 8.8923 12.2997 8 9.5491 11.0266 10.2598 11.9780 10.6366 12.4876 9.2142 10.5828 12.0061 11.0285 13.0210 11.4359 13.5795 9 9.3685 9.7546 10.1591 9 9.8975 11.4913 13.1808 14.9716 10 10.4622 10.9497 11.4639 13.8164 14.4866 15.1929 10 12.5779 14.2068 15.9374 18.5312 11 11.5668 12.1687 12.8078 13.4864 16.6455 17.5603 14.7757 17.5487 20.6546 24.1331 28.0291 11 12 13.4121 14.1920 15.0258 16.8699 15.7836 17.8885 20.1406 22.5505 20.1407 22.9534 21.3843 24.5227 12 13 13 16.6268 12.6825 13.8093 14.9474 16.0969 17.2579 14 14.6803 15.9739 17.2934 14 15.6178 17.0863 18.5989 20.1569 21.7616 18.2919 20.0236 21.8245 18.9771 21.4953 24.2149 27.1521 30.3243 33.7502 26.0192 29.3609 27.9750 31.7725 32.3926 37.2797 15 13.7268 16.7858 20.3037 24.3493 29.0017 34.3519 40.5047 47.5804 55.7175 65.0751 75.8364 88.2118 102.4436 15.9171 17.7130 19.5986 21.5786 23.6575 25.8404 28.1324 30.5390 15 25.1290 27.8881 16 33.0034 35.9497 42.7533 16 17 18.4304 18.6393 20.0121 21.4123 36.9737 48.8837 17 18 19.6147 23.4144 18.8821 21.0151 23.2760 25.6725 28.2129 30.9057 33.7600 36.7856 54.8645 79.0582 111.4348 154.7620 18 30.8402 33.9990 37.3790 37.4502 41.4463 23.6975 25.6454 27.6712 29.7781 41.6459 41.3013 46.0185 19 55.7497 63.4397 20.8109 22.8406 25.1169 40.5447 45.5992 51.1591 57.2750 98.3471 19 20 22.0190 24.2974 26.8704 33.0660 40.9955 45.7620 51.1601 20 72.0524 133.3339 25 28.2432 36.4593 73.1059 84.7009 212.7930 25 47.7271 66.4388 32.0303 40.5681 49.9945 63.2490 94.4608 30 56.0849 164.4940 34.7849 41.6603 30 47.5754 60.4621 136.3075 215.7108 241.3327 431.6635 35 113.2832 172.3168 259.0565 271.0244 73.6522 95.0255 90.3203 120.7998 35 138.2369 199.6351 434.7451 881.1702 1,779.0903 40 48.8864 60.4020 75.4013 337.8824 442.5926 767.0914 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 x 7.3359)