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 $920. One possible alternative is to invest in new machinery, which has a cost of $40,200. This new machinery would produce estimated annual operating cash savings of $13,100. 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 $2,120 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 Appendix 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 0 Time 1 Time 2 Time 3 Time 4 Acquisition cost Investment in working capital Recovery of working capital Salvage value of old machinery Salvage value of new machinery Annual operating cash savings Total cash flow Discount factor Present value Net present value Table I 8% Perlod 4% 6% 10% 12% 14% 20% Future Value of $1.00(1 1 1.040 1.060 1.080 1.100 1.120 1.140 1.200 2 1.082 1.124 1,166 1.210 1.254 1.300 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 3.583 7 1.316 1.504 1.714 1,949 2.211 2.502 8 1,369 1.594 1.851 2,144 2.476 2,853 4.300 1.423 1.690 1.999 2.359 2.773 3.252 5.160 10 1.480 1.791 2.159 2.594 3.106 3.707 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 10.699 13 1.665 2.133 2.720 3.452 4.364 5.492 14 1.732 2.261 2.937 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 38.338 237,380 30 3.243 5.744 10.063 17.450 29.960 50.950 40 4,801 10.286 21.725 45.260 93.051 188.880 1,469.800 Table II Period 4% 6% 8% 10% 12% 14% 20% Future Value of a Serles of 1 1,000 1.000 1.000 1.000 1.000 1,000 1.000 $1.00 Cash Flows (Ordinary Annuity) (1 1 2.080 2 2.040 2.060 2,100 2.120 2.140 2.220 3,122 3.184 3.246 3,310 3.374 3.440 3,640 4 4.247 4,375 4.506 4.641 4.779 4.921 5.368 5 5.416 5,637 5.867 6.105 6.353 6.610 7.442 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 12.300 13.233 9.214 9.898 10.637 11.436 16,499 10.583 11.491 12.488 13.580 14.776 16,085 20.799 10 12.006 13.181 14.487 15.938 17.549 19.337 25.959 23.045 11 13.486 14,972 16.646 18,531 20,655 32.150 12 15.026 16.870 18.977 21.385 24.133 27.271 39.580 18.882 13 16.627 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 29.778 186.690 20 36.778 45.762 57.276 75.052 91.025 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 1,342.000 976 st LC CC Table III Present Value of $1.00 1 (1 + 6% Period 4% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% .962 .943 926 .909 893 877 .862 .847 833 820 806 .794 781 .769 758 2 .925 .890 857 826 797 769 743 718 .694 672 650 .630 610 592 574 .609 524 3 889 840 794 751 712 .675 641 579 551 500 .477 455 435 4 .855 792 735 .683 .636 .592 552 516 482 451 423 397 373 350 329 5 822 747 .681 621 .567 .519 .476 .437 402 370 341 315 .291 269 250 790 705 .630 564 507 456 410 370 335 303 275 250 .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 .500 424 361 308 263 225 194 167 144 125 108 .094 .082 10 676 .558 463 386 322 270 227 191 162 137 116 .099 085 .073 062 11 .650 527 429 350 .287 237 .195 .162 .135 .112 .094 079 ,066 .056 .047 12 625 497 397 319 257 .208 168 137 .112 .092 076 .062 .052 043 .036 13 .601 469 368 290 229 .182 145 .116 093 .075 ,061 .050 .040 .033 .027 14 .577 442 340 .263 205 .160 .125 ,099 078 .062 .049 039 .032 025 .021 15 555 417 315 239 .183 140 108 084 065 .051 ,040 031 .025 020 .016 20 456 312 215 149 .104 ,073 051 .037 .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 (1r) 4% 6% 8% 25% 28% Period 10% 12% 14% 16% 18% 20% 22% 24% 26% 30% 1 0.962 0.943 0.926 0.909 0,893 0,877 0,862 0.847 0.833 0.820 0.806 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 3 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 3,312 3.170 3,037 2.914 2.798 2,690 2,589 2,494 2,404 2.362 2,320 2.241 2.166 4.452 4.212 3.993 3.791 3,605 3.433 3.274 3.127 2.991 2.864 2.745 2.689 2.635 2.532 2.436 2.951 2.759 6 5,242 4,917 4,623 4.355 4.111 3,889 3.685 3.498 3.326 3.167 3.020 2,885 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 6.733 6.210 5.747 5.335 4.968 4,639 4,344 4.078 3.837 3.619 3.421 3.329 3,241 3.076 2.925 9 7.435 6.802 6.247 5.759 5.328 4,946 4.607 4.303 4,031 3.786 3.566 3.463 3.366 3.184 3.019 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 12 9.385 8.384 7.536 6,814 6.194 5.660 5.197 4,793 4.439 4.127 3.851 3.725 3,606 3.387 3.190 5,842 4,533 13 9.986 8.853 7.904 7.103 6,424 5.342 4,910 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 15 11.118 9.712 8.559 7.606 6.811 6.142 5,575 5.092 4,675 4.315 4.001 3.859 3.726 3.483 3.268 20 13,590 11.470 9.818 8,514 7.469 6.623 5.929 5.353 4.870 4.460 4.110 3.954 3.808 3.546 3.316 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 40 19.793 15,046 11.925 9.779 8.244 7.105 6.234 5,548 4,997 4.544 4.166 3.999 3,846 3.571 3.333