Earth Lab plans to purchase a new centrifuge machine for its Virginia facility. The machine costs $333,000 and is expected to have a useful life of 5 years, with a terminal disposal value of $33,000. Savings in cash operating costs are expected to be $100,000 per year. However, additional working capital is needed to keep the machine running efficiently. The working capital must continually be replaced, so an investment of $16,000 needs to be maintained at all times, but this investment is fully recoverable (will be "cashed in") at the end of the useful life. Earth Lab's required rate of return is 14%. Ignore income taxes in your analysis. Assume all cash flows occur at year-end except for initial investment amounts. Earth Lab uses straight-line depreciation for its machines.

1. Calculate net present value.

2. Calculate internal rate of return.

3. Calculate accrual accounting rate of return based on net initial investment.

4. Calculate accrual accounting rate of return based on average investment.

5. You have the authority to make the purchase decision. Why might you be reluctant to base you decision on the DCF methods?

Reference 6.362 Compound Amount of Annuity of $1.00 in Arrears* (Future Value of Annuity) Periods 2% 4% 4% 6% 6% 8% 10% 12% % 14% 16% 18% 20% 22% 24% 26% 28% Period 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Perlod 22.020 2.040 2.060 2.080 2.100 2.120 2.140 2.160 2.180 2.200 2.220 2.240 2.260 2.280 Period 3 3.080 3.122 3.134 3.246 3.310 3.374 3.440 3.506 3.572 3.610 3.708 3.778 3.845 3.913 Period 4 4.122 4.246 4.375 4.506 4.641 4.770 4.92 5.066 5.215 5.368 5.524 5.684 5.848 6.016 Perlod 5 5.204 5.416 5.637 5 5.867 5.105 6.353 6.610 6.877 7.154 7.442 7.740 8.048 8.368 8.700 Period 6 8.308 6.633 8.975 6 7.336 7.716 3.115 8.536 8.977 9.112 9.930 10.112 10.980 11.5111 12.136 Period 7 7.434 7.898 8.394 8.923 9.487 10.089 10.730 11,414 12.142 12.916 13.740 14.615 15.546 16.534 Period 8 8.583 9.214 9.897 10.637 11.436 12.300 13.233 14.240 15,327 16.499 17.762 19.123 20.588 22.163 Period 9 9.755 10.583 11.491 12.483 13.579 14.776 16.005 17.519 19.000 20.799 22.870 24.712 26.940 29.369 Period 10 10.950 12.006 13.181 14.487 15.937 17.549 19.337 21.321 23.521 25.959 28.657 31.643 34.945 38.593 Period 11 12.169 13.486 14.972 16.645 18.531 20.655 23.045 25.733 28.755 32.150 35.962 40.238 45.031 50.398 Period 12 13.412 15.026 18.870 18.977 21.384 24.133 27.271 30.050 34.931 39.581 44.074 50.895 57.739 65.510 Period 13 14.680 16.627 18.882 21.495 24.523 28.029 32.089 36.786 42.219 48.497 55.746 64.110 73,761 84.853 Period 14 15.974 18.292 21.015 24.215 27.975 32.393 37.581 43.672 50.818 59.196 69.010 80.496 93.926 109.612 Period 15 17.293 20.024 23.276 27.152 31.772 37.280 43.842 51.660 43.842 51.660 60.965 72.035 85. 192 100.815 119.347 141.303 Period 16 18.639 21.825 25.673 30.324 35.950 42.753 50.980 60.925 72.939 87.442 104.935 126.011 151.377 181.868 Period 17 20.012 23.698 28.213 33.750 40.545 48.884 59.118 71.673 87.068 105.931 129.020 157.253 191.735 233.791 Period 18 21.412 25.645 30.906 37.450 45.599 55.750 68.394 84.141 103.740 128.117 158.405 195.994 242.585 300.252 Period 19 22.841 27.671 33.760 41.448 51.159 83.440 78.989 98.603 123.414 154.740 194.254 244.033 306.658 385.323 Period 20 24.297 29.778 36.786 45.762 57.275 72.052 91.025 115.380 146.628 186.688 237.989 303.601 387.389 494 213 Period 21 25.783 31.969 39.993 50.423 64.002 01.699 104.768 134.841 174.021 225.026 291.347 377.465 489. 110 633.593 Period 22 27.299 34.248 43.392 55.457 71.403 92.503 120.436 157.415 206.345 271.031 356.443 489.056 617.278 811.999 Period 23 28.845 36.618 46.996 60.893 79.543 104.603 138.297 183.601 244 487 326.237 435.861 582.630 778.771 1040.358 Period 24 30.422 39.083 50.816 66.765 88.497 118.155 155.659 213.978 289.494 392.484 532.750 723.161 982.251 1332.659 Period 25 32.030 41.646 54.865 73.106 98.347 133.334 181.871 249.214 342.603 471.981 650.955 898.092 1238.636 1706.803 Period 26 33.671 44,312 59.156 79.954 109.182 150,334 208.333 290.088 405.272 567 377 795,165 1114.634 1561.682 2185.708 Period 27 35.344 17.041 63.706 87.351 121.100 169.374 236.499 337.502 179.221 681.553 971.102 1383.146 1960.719 2793.706 Period 28 37.051 49.968 68.528 95.339 134.210 190.699 272.889 392.503 566.481 819.223 1185.744 1716.101 2481.586 3583.344 Period 29 38.792 52.966 73.640 103.966 148.631 214,583 312.094 456,303 669.447 984.068 1447.608 2128.965 3127.798 4587.680 Period 30 40 568 56 085 79 058 113283 164 494 241 333 356 787 530 312 790 948 1181 8821767 081 2641 916 1942 1/26 5873 231 % 30% 1.000 2.300 3.990 6.187 9.043 12.756 17.583 23.858 32.015 42.619 56.405 74.327 97.628 127.913 167.286 218.473 285.014 371.518 483.973 630.165 320.215 1067.280 1388.464 1806.003 2348.803 3054.444 3971.778 5164.311 6714.604 8729 985 32% 40% 1.000 1.000 2.320 2.400 4.062 4.380 7.104 9.398 10.946 13.106 18.324 18.696 23.853 25.678 34.395 34.895 49.153 47.062 69.814 63.122 98.739 84.320 139.235 112.303 195.929 149 240 275.300 197.997 386.420 262.356 541.988 347 309 759,784 459.449 1064.697 807.472 1491.576 802.863 2089.206 1060.779 2925.889 140 1.229 4097.245 1850.622 5737.142 2443.821 8032.999 3226.844 11247.199 4260.434 15747.079 5624.772 22018.910 7425.699 30866.674 9802.923 43214 343 12940 859 60501 081 Periods Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 Period 16 Period 17 Period 18 Period 19 Period 20 Period 21 Period 22 Period 23 Period 24 Period 25 Period 26 Period 27 Period 28 Period 29 Period 30 Reference Compound Amount of $1.00 (The Future Value of $1.00) Periods 2% 4% 6% 8% 10% 12% 14% Period 1 1.020 1.040 1.080 1.080 1.100 1.120 1.140 Period 2 1.040 1.082 1.124 1.166 1.210 1.254 1.300 Period 3 1.061 1.125 1.191 1.260 1.331 1.405 1.482 Period 4 1.082 1.170 1.262 1.360 1.464 1.574 1.689 Period 5 1.104 1.217 1.338 1.469 1.611 1.762 1.925 Period 6 1.126 1.265 1.419 1.587 1.772 1.974 2.195 Period 7 1.149 1.316 1.504 1.714 1.949 2.211 2.502 Period 8 1.172 1.369 1.594 1.851 2.144 2.476 2.853 Period 9 1.195 1.423 1.689 1.999 2.358 2.773 3.252 Period 10 1.219 1.480 1.791 2.159 2.594 3.106 3.707 Period 11 1.243 1.539 1.898 2.332 2.853 3.479 4.226 Period 12 1.268 1.601 2.012 2.518 3.138 3.896 4.818 Period 13 1.294 1.665 2.133 2.720 3.452 4.363 5.492 Period 14 1.319 1.732 2.261 2.937 3.797 4.887 6.261 Period 15 1.346 1.801 2.397 3.172 4.177 5.474 7.138 Perlod 16 1.373 1.873 2.540 3.426 4.595 6.130 8.137 Period 17 1.400 1.948 2.693 3.700 5.054 6.866 9.276 Period 18 1,429 2.026 2.854 3.996 5.560 7.690 10.575 Period 19 1.457 2.107 3.026 4.316 6.116 8.613 12.056 Period 20 1.486 2.191 3.207 4.661 6.727 9.646 13.743 Period 21 1.516 2.279 3.400 5.034 7.400 10.804 15.668 Period 22 1.546 2.370 3.604 5.437 8.140 12.100 17.861 Period 23 1.577 2.465 3.820 5.871 8.954 13.552 20.362 Period 24 1.608 2.563 4.049 6.341 9.850 15.179 23.212 Period 25 1.641 2.666 4.292 6.848 10.835 17.000 26.462 Period 26 1.673 2.772 4.549 7.396 11.918 19.040 30.167 Period 27 1.707 2.883 4.822 7.988 13.110 21.325 21.325 34.390 Period 28 1.741 2.999 5.112 8.627 14.421 23,884 39 204 Period 29 1.776 3.119 5.418 9.317 . 15.863 26.750 44.693 16% 1.160 1.346 1.561 1.811 2.100 2.436 2.826 3.278 3.803 4.411 5.117 5.936 6.886 7.988 9.266 10.748 12.468 14.463 16.777 19.461 22.574 26.186 30.376 35.236 40.874 47.414 55.000 63.800 74.009 18% 1.180 1.392 1.643 1.939 2.288 2.700 3.185 3.759 4.435 5.234 6.176 7.288 8.599 10.147 11.974 14.129 16.672 19.673 23.214 27.393 32.324 38.142 45.008 53.109 62.669 73.949 20% 1.200 1.440 1.728 2.074 2.488 2.986 3.583 4.300 5.180 6.192 7.430 8.916 10.699 12.839 15.407 18.488 22.186 26.623 31.948 38.338 46.005 55.206 66.247 79.497 95.396 114.475 137.371 164.845 197.814 22% 1.220 1.488 1.816 2.215 2.703 3.297 4.023 4.908 5.987 7.305 8.912 10.872 13.264 16.182 19.742 24.086 29.384 35.849 43.736 53.358 65.096 79.418 96.889 118.205 144.210 175.936 214.642 261.864 319.474 24% 1.240 1.538 1.907 2.364 2.932 3.635 4.508 5.590 6.931 8.594 10.657 13.215 16.386 20.319 25.196 31.243 38.741 48.039 59.568 73.864 91.592 113.574 140.831 174.631 216.542 268.512 332.955 412.864 511.952 26% 1.260 1.588 2.000 2.520 3.176 4.002 5.042 6.353 8.005 10.086 12.708 16.012 20.175 25.421 32.030 40.358 50.851 64.072 80.731 101.721 128.169 161.492 203.480 256.385 323.045 407,037 512.867 646.212 814.228 28% 1.280 1.638 2.097 2.684 3.438 4.398 5.629 7.206 9.223 11.806 15.112 19.343 24.759 31.691 40.565 51.923 66.481 85.071 108.890 139.380 178.406 228.360 292.300 374.144 478.905 612.998 784.638 1004.336 1285.550 30% 1.300 1.690 2.197 2.856 3.713 4.827 6.275 8.157 10.604 13.786 17.922 23.298 30.288 39.374 51.186 66.542 86.504 112.455 146.192 190.050 247.065 321.184 417.539 542.801 705.641 917.333 1192.533 1550.293 2015.381 32% 1.320 1.742 2.300 3.036 4.007 5.290 6.983 9.217 12.166 16.060 21.199 27.983 38.937 48.757 64.359 84.954 112.139 148.024 195.391 257.916 340.449 449.393 593.199 783,023 1033.590 1364.339 1800.927 2377.224 3137.935 40% Periods 1.400 Period 1 1.960 Period 2 2.744 Period 3 3.842 Period 4 5.378 Period 5 7.530 Period 6 10.541 Period 7 14.758 Period 8 20.661 Period 9 28.925 Period 10 40.496 Period 11 56.694 Period 12 79.371 Period 13 111.120 Period 14 155.568 Period 15 217.795 Period 16 304.913 Period 17 426.879 Period 18 597.630 Period 19 836.683 Period 20 1171.356 Period 21 1639.898 Period 22 2295.857 Period 23 3214.200 Period 24 4499.880 Period 25 6299.831 Period 26 8819.764 Period 27 12347.670 Period 28 17286.737 Period 29 87 260 102.967 121.501 Reference 16% 0.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 Present Value of Annuity of $1.00 in Arrears* Periods 2% 4% 6% 8% 10% Period 1 0.980 0.962 0.943 0.926 0.909 Period 2 1.942 1.886 1.833 1.783 1.736 Period 3 2.884 2.775 2.673 2.577 2.487 Period 4 3.808 3.630 3.465 3.312 3.170 Period 5 4.713 4.452 4.212 3.993 3.791 Period 6 5.601 5.242 4.917 4.623 4.355 Period 7 6.472 6.002 5.582 5.206 4.868 Period 8 7.325 8 6.733 6.210 5.747 5.335 Period 9 8.162 7.435 6.802 6.247 5.759 Period 10 8.983 8.111 7.360 6.710 6.145 Period 11 9.787 8.760 7.887 7.139 6.495 Period 12 10.575 9.385 8.384 7.536 6.814 Period 13 11.348 9.986 8.853 7.904 7.103 Period 14 12.106 10.563 9.295 8.244 7.367 Period 15 12.849 11.118 9.712 8.559 7.606 Period 16 13.578 11.652 10.106 8.851 7.824 Period 17 14.292 12. 166 10.477 9.122 8.022 Period 18 14.992 12.659 10.828 9.372 8.201 Period 19 15.678 13.134 11.158 9.604 8.365 Period 20 16.351 13.590 11.470 9.818 8.514 Period 21 17.011 14.029 11.764 10.017 8.649 Period 22 17.658 14.451 12.042 10.201 8.772 Period 23 18.292 14.857 12.303 10.371 8.883 Period 24 18.914 15.247 12.550 10.529 8.985 Period 25 19.523 15.622 12.783 10.675 9.077 Period 26 20.121 15.983 13.003 10.810 9.161 Period 27 20.707 16.330 13.211 10.935 9.237 Period 28 21.281 16.663 13.406 11.051 9.307 Period 29 21.844 16.984 13.591 11.158 9.370 Period 30 22 396 17 292 13 765 11 258 9427 12% 0.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5,650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 7.469 7.562 7.645 7.718 7.784 7.843 7.896 7.943 7.984 8.022 8055 14% 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 6.550 6.623 6,687 6.743 6.792 6.835 6.873 6.906 6.935 6.961 6.983 7 002 4.833 5.029 5.197 5.342 5.468 5.575 5.668 5.749 5.818 5.877 5.929 5.973 6.011 6.044 6.073 6.097 6.118 6.136 6.152 6.166 6 177 18% 0.847 1.566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 4.793 4.910 5.008 5.092 5.162 5.222 5.273 5.316 5.353 5.384 5.410 5.432 5.451 5.467 5.480 5.492 5.502 5.510 5.517 20% 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.730 4.775 4.812 4.843 4.870 4.891 4.909 4.925 4.937 4.948 4.956 4.964 4.970 4.975 4 979 22% 0.820 1.492 2.042 2.494 2.864 3.167 3.416 3.619 3.786 3.923 4.035 4.127 4.203 4.265 4.315 4.357 4.391 4.419 4.442 4.460 4.476 4.488 4.499 4.507 4.514 4.520 4.524 4.528 4.531 4 534 24% 0.806 1.457 1.981 2.404 2.745 3.020 3.242 3.421 3.566 3.682 3.776 3.851 3.912 3.962 4.001 4.033 4.059 4.080 4.097 4.110 4.121 4.130 4.137 4.143 4.147 4.151 4.154 4.157 4.159 4 160 26% 0.794 1.424 1.923 2.320 2.635 2.885 3.083 3.241 3.36 3.465 3.543 3.606 3.656 3.695 3.726 3.751 3.771 3.786 3.799 3.808 3.816 3.822 3.827 3.831 3.834 3.837 3.839 3.840 3.841 2842 28% 30% 0.781 0.769 1.392 1.361 1.868 1.816 2.241 2.166 2.532 2.436 2.759 2.643 2.937 2.802 3.076 2.925 3.184 3.019 3.269 3.092 3.335 3.147 3.387 3.190 3.427 3.223 3.459 3.249 3.483 3.268 3.503 3.283 3.518 3.295 3.529 3.304 3.539 3.311 3.546 3.316 3.551 3.320 3.556 3.323 3.559 3.325 3.562 3.327 3.564 3.329 3.566 3.330 3.567 3.331 3.568 3.331 3.569 3.332 3.569 3232 32% 0.758 1.331 1.766 2.096 2.345 2.534 2.677 2.786 2.868 2.930 2.978 3.013 3.040 3.061 3.076 3.088 3.097 3.104 3.109 3.113 3.116 3.118 3.120 3.121 3.122 3.123 3.123 3.124 3.124 3 124 40% Periods 0.714 Period 1 1.224 Period 2 1.589 Period 3 1.849 Period 4 2.035 Period 5 2.168 Period 6 2.263 Period 7 2.331 Period 8 8 2.379 Period 9 2.414 Period 10 2.438 Period 11 2.456 Period 12 2.469 Period 13 2.478 Period 14 2.484 Period 15 2.489 Period 16 2.492 Period 17 2.494 Period 18 2.496 Period 19 2.497 Period 20 2.498 Period 21 2.498 Period 22 2.499 Period 23 2.499 Period 24 2.499 Period 25 2.500 Period 26 2.500 Period 27 2.500 Period 28 2.500 Period 29 2 500 Period 30 6% 0.943 0.890 0.840 0.792 0.747 0.705 14% 0.877 0.769 0.675 0.592 0.519 0.456 0.665 0.400 0.249 0.198 Present value of $1 Periods 2% 4% Period 1 0.980 0.962 Period 2 0.961 0.925 Period 3 0.942 0.889 Period 4 0.924 0.855 Period 5 0.906 0.822 Period 6 0.888 0.790 6 Period 7 0.871 0.760 Period 8 0.853 0.731 Period 9 0.837 0.703 Period 10 0.820 0.676 Period 11 0.804 0.650 Period 12 0.788 0.625 Period 13 0.773 0.601 Period 14 0.758 0.577 Period 15 0.743 0.555 Period 16 0.728 0.534 Period 17 0.714 0.513 Period 18 0.700 0.494 Period 19 0.686 0.475 Period 20 0.673 0.456 Period 21 0.660 0.439 Period 22 0.647 0.422 Period 23 0.634 0.406 Period 24 0.622 0.390 Period 25 0.610 0.375 Period 26 0.598 0.361 Period 27 0.586 0.347 Period 28 0.574 0.333 Period 29 0.563 0.321 Period 30 0.552 0.308 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.312 0.294 0.278 0.262 8% 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215 0.199 0.184 0.170 0.158 0.146 0.135 0.125 0.116 0.107 0.099 10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 0.135 0.123 0.112 0.102 0.092 0.084 0.076 0.069 0.063 0.057 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104 0.093 0.083 0.074 0.066 0.059 0.053 0.047 0.042 0.037 0.033 16% 0.862 0.743 0.641 0.552 0.476 0.410 0.354 0.305 0.263 0.227 0.195 0.168 0.145 0.125 0.108 0.093 0.080 0.069 0.060 0.051 0.044 0.038 0.033 0.028 0.024 0.021 0.018 0.016 0.014 0.012 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 0.064 0.056 0.049 0.043 0.038 0.033 0.029 0.026 0.022 0.020 18% 0.847 0.718 0.609 0.516 0.437 0.370 0.314 0.266 0.225 0.191 0.162 0.137 0.116 0.099 0.084 0.071 0.060 0.051 0.043 0.037 0.031 0.026 0.022 0.019 0.016 0.014 0.011 0.010 0.008 0.007 20% 22% 0.833 0.820 0.694 0.672 0.579 0.551 0.482 0.451 0.402 0.370 0.335 0.303 0.279 0.233 0.204 0.194 0.167 0.162 0.137 0.135 0.112 0.112 0.092 0.093 0.075 0.078 0.062 0.065 0.051 0.054 0.042 0.034 0.038 0.028 0.031 0.023 0.026 0.019 0.022 0.015 0.018 0.013 0.015 0.010 0.013 0.008 0.010 0.007 0.009 0.006 0.007 0.005 0.006 0.004 0.005 0.003 0.003 24% 0.806 0.650 0.524 0.423 0.341 0.275 0.222 0.179 0.144 0.116 0.094 0.076 0.061 0.049 0.040 0.032 0.026 0.021 0.017 0.014 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.002 0.002 26% 28% 30% 0.794 0.781 0.769 0.630 0.610 0.592 0.500 0.477 0.455 0.397 0.373 0.350 0.315 0.291 0.269 0.250 0.227 0.207 0.178 0.159 0.157 0.139 0.123 0.125 0.108 0.094 0.099 0.085 0.073 0.079 0.066 0.056 0.062 0.052 0.043 0.050 0.040 0.033 0.039 0.032 0.025 0.031 0.025 0.020 0.025 0.019 0.015 0.020 0.015 0.012 0.016 0.012 0.009 0.012 0.009 0.007 0.010 0.007 0.005 0.008 0.006 0.004 0.006 0.004 0.003 0.005 0.003 0.002 0.004 0.003 0.002 0.003 0.002 0.001 0.002 0.002 0.001 0.002 0.001 0.001 0.002 0.001 0.001 0.001 0.001 0.000 0.001 0.001 0.000 32% 0.758 0.574 0.435 0.329 0.250 0.189 0.143 0.108 0.082 0.062 0.047 0.036 0.027 0.02 0.016 0.012 0.009 0.007 0.005 0.004 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.000 0.000 0.000 40% Periods 0.714 Period 1 0.510 Period 2 0.364 Period 3 0.260 Period 4 0.186 Period 5 5 0.133 Period 6 6 0.095 Period 7 0.068 Period 8 0.048 Period 9 9 0.035 Period 10 0.025 Period 11 0.018 Period 12 0.013 Period 13 0.009 Period 14 0.006 Period 15 0.005 Period 16 0.003 Period 17 0.002 Period 18 0.002 Period 19 0.001 Period 20 0.001 Period 21 0.001 Period 22 0.000 Period 23 0.000 Period 24 0.000 Period 25 0.000 Period 26 0.000 Period 27 0.000 Period 28 0.000 Period 29 0.000 Period 30 0.045 0.247 0.233 0.220 0.207 0.196 0.185 0.174 0.004