The supervisor of the county Department of Transportation (DOT) is considering the replacement of some machinery. This machinery has zero book value but its current market value is $890. One possible alternative is to invest in new machinery, which has a cost of $39,900. This new machinery would produce estimated annual operating cash savings of $12,950. The estimated useful life of the new machinery is four years. The DOT uses straight-line depreciation. The new machinery has an estimated salvage value of $2,090 at the end of four years. The investment in the new machinery would require an additional investment in working capital of $3,000, which would be recovered after four years. If the DOT accepts this investment proposal, disposal of the old machinery and investment in the new equipment will take place on December 31, 20x1. The cash flows from the investment will occur during the calendar years 20x2 through 20x5. Use Appendi A for your reference. (Use appropriate factor(s) from the tables provided.) Required: Prepare a net-present-value analysis of the county DOT's machinery replacement decision. The county has a 10 percent hurdle rate. (Round your "Discount factors" to 3 decimal places and final dollar amounts to whole dollars. Negative amounts should be indicated by a minus sign.) Time 1 Time 4 Time 0 Time 2 Time 3 Acquisition cost Investment in working capital Recovery of working capital Salvage value of old machinery Salvage value of new machinery Annual operating cash savings $ 0 $ $ $ 0 Total cash flow 0 0 Discount factor $ S Present value 0 0 Net present value Future Value and Present Value Tables Table I Future Value of $1.00(1+ Period 4% 6% 8% 10% 12% 14% 20% 1.040 1.060 1.080 1.100 1.120 1.140 1.200 1 2 1.082 1.254 1.300 1.124 1.166 1.210 1.440 3 1.125 1.191 1.260 1.331 1.405 1.482 1.728 4 1.170 1.263 1.361 1.464 1.574 1.689 2.074 5 1.217 1.338 1.469 1.611 1.762 1.925 2.488 6 1.265 1.419 1.587 1.772 1,974 2.195 2.986 7 1.316 1.504 1.714 1.949 2.211 2.502 3.583 1.851 2.853 4.300 1.369 1.594 2.144 2.476 1.423 1.690 1.999 2.359 2.773 3.252 5.160 2.159 3.707 10 1.480 1.791 2.594 3.106 6.192 11 1.540 1.898 2.332 2.853 3.479 4.226 7.430 12 1.601 2.012 2.518 3.139 3.896 4.818 8.916 13 1.665 2.133 2.720 3.452 4.364 5.492 10.699 2.937 14 1.732 2.261 3.798 4.887 6.261 12.839 15 1.801 2.397 3.172 4.177 5.474 7.138 15.407 20 2.191 3.207 4.661 6.728 9.646 13.743 38.338 30 17.450 3.243 5.744 10.063 29.960 50.950 237.380 40 4.801 10.286 21.725 45.260 93.051 188.880 1,469.800 Table II 20% Period 4% 6% 8% 10% 12% 14% Future Value of a Series of 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 $1.00 Cash Flows (Ordinary Annulty (1+n"-1 2.040 2.060 2.100 2.120 2.220 2 2.080 2.140 3 3.122 3.246 3.310 3.640 3.184 3.374 3.440 4 4.247 5.368 4.375 4.506 4.641 4.779 4.921 7.442 5 5.416 5.637 5.867 6.105 6.353 6.610 6 6.633 6.975 7.336 7.716 8.115 8.536 9.930 7 7.898 8.394 8.923 9.487 10.089 10.730 12.916 9.214 9.898 10.637 11.436 12.300 13.233 16.499 9 10.583 11.491 14.776 16.085 20.799 12.488 13.580 10 12.006 13.181 15.938 17.549 19.337 25.959 14.487 11 13.486 14.972 16.646 18.531 20.655 23.045 32.150 12 15.026 16.870 18.977 21.385 27.271 39.580 24.133 13 16.627 18.882 21.495 24.523 28.029 32.089 48.497 14 18.292 21.015 24.215 27.976 32.393 37.581 59.196 15 20.024 23.276 27.152 31.773 37.280 43.842 72.035 20 29.778 36.778 45.762 57.276 75.052 91.025 186.690 30 56.085 79.058 113.283 164.496 241.330 356.790 1,181.900 7,343.900 40 95.026 154.762 259.057 442.597 767.090 1,342.000 Table III Present Value of $1.00 1 (1n 8% 10% 12% 18% 30% 32% Period 4% 6% 14% 16% 20% 22% 24% 26% 28% 962 943 926 .909 893 .877 862 847 833 820 .806 794 781 769 758 1 2 925 .890 857 826 797 769 743 718 694 672 .650 630 610 592 574 889 794 751 712 675 609 579 551 524 455 435 3 840 641 500 477 855 792 735 683 636 552 516 482 423 397 350 329 4 592 451 373 5 822 747 681 621 567 519 476 437 402 370 341 315 291 269 250 370 335 303 6 790 705 630 564 507 456 410 275 250 227 207 189 7 760 665 583 513 452 400 354 314 279 249 222 198 178 .159 143 8 731 627 540 467 404 351 305 266 233 204 .179 157 139 .123 .108 9 703 592 500 424 308 263 225 .167 .144 125 094 361 .194 108 082 10 676 558 463 386 322 270 227 .191 .162 .137 .116 099 085 073 062 650 527 429 350 287 237 .195 .135 079 .066 056 047 11 162 .112 .094 397 319 257 036 12 625 497 208 .168 137 112 092 .076 062 .052 043 13 601 469 368 290 229 .182 145 .116 093 075 061 050 040 033 027 577 442 340 263 205 .125 099 078 062 049 039 .032 025 021 14 .160 15 555 315 417 239 .183 .140 .108 084 065 051 040 031 025 020 016 215 037 20 456 312 149 104 .073 051 026 019 .014 010 007 005 004 30 308 174 099 057 033 020 012 .007 004 003 .002 001 001 40 208 097 046 022 011 005 003 001 001 Table IV Present Value of Series of $1.00 Cash Flows 1 (1 r Period 4% 28% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 25% 26% 30% 0.820 0.943 0.806 1 0.962 0.877 0.847 0.833 0.926 0.909 0.893 0.862 0.800 0.794 0.781 0.769 2 1.886 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 1.492 1.457 1.440 1.424 1.392 1.361 2.775 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 2.042 1.981 1.952 1.923 1.868 1.816 4 3.630 3.465 3.037 3.312 3.170 2.914 2.798 2.690 2.589 2.494 2.404 2.362 2.320 2.241 2.166 2.864 2.745 5 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 2.689 2.635 2.532 2.436 4.917 3.020 5.242 4.623 4.355 4.111 3.889 3.685 3.498 3.326 3.167 2.951 2.885 2.759 2.643 7 6.002 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 3.416 3.242 3.161 3.083 2.937 2.802 5.335 3.619 6.210 3.837 6.733 5.747 4.078 3.241 3.076 2.925 4.968 4.639 4.344 3.421 3.329 9 7.435 6.802 6.247 4.303 4.031 3.019 5.759 5.328 4.946 4.607 3.786 3.566 3.463 3.366 3.184 10 8.111 7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.192 3.923 3.682 3.571 3.465 3.269 3.092 11 8.760 7.887 7.139 6.495 5.938 5.453 5.029 4.656 4.327 4.035 3.776 3.656 3.544 3.335 3.147 9.385 8.384 7.536 6.814 4.793 4.439 4.127 3.851 3.725 3.387 3.190 12 6.194 5.660 5.197 3.606 13 9.986 8.853 7.904 7.103 6.424 5.842 5.342 4.910 4.533 4.203 3.912 3.780 3.656 3.427 3.223 14 10.563 9.295 8.244 7.367 6.628 6.002 5,468 5.008 4.611 4.265 3.962 3.824 3.695 3.459 3.249 6.142 3.726 15 11.118 9.712 8.559 7.606 6.811 5.575 5.092 4.675 4.001 3.859 3.483 3.268 4.315 11.470 4.870 20 13,590 9.818 8.514 7.469 5.929 5,353 4.460 3.954 3.808 3.546 3.316 6.623 4.110 30 17.292 13.765 11.258 9.427 8.055 7.003 6.177 5.517 4.979 4.534 4.160 3.995 3.842 3.569 3.332 4.997 15.046 11.925 9.779 7.105 5.548 3.333 40 19.793 8.244 6.234 4.544 4,166 3.999 3.846 3.571