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 $950. One possible alternative is to invest in new machinery, which has a cost of $40,500. This new machinery would produce estimated annual operating cash savings of $13,250. 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 $2,150 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.)

PROBLEM:

Prepare a net-present-value analysis of the county DOTs 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.)

APPENDIX A:

Time O 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 0 0 0 Future Value and Present Value Tables Period 8% 10% 20% Future Value of $1.001 + n 1.200 1.254 1.260 1.170 1.574 1.762 1.974 2.211 2.074 2.488 1.925 1.316 1.714 3.583 4.300 2.773 3.106 3.479 3.896 3.252 3.707 4.226 2.159 2.332 8.916 10.699 12.839 15.407 38.338 237.380 1,469.800 12 2.012 5.492 6.261 1.732 2.937 5.474 20 3.207 17.450 45.260 29.960 93.051 13.743 50.950 188.880 3.243 10.063 10.286 21.725 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity) 8% 10% 20% 3.310 3.374 4.779 6.353 8.115 10.089 12.300 14.776 17.549 20.655 24.133 28.029 32.393 37.280 75.052 79.058 113.283 164.496 241.330 767.090 3.246 3.440 3.640 5.368 4.247 4.375 5.637 6.975 8.394 9.898 6.633 7.898 9.214 10.583 12.006 13.486 15.026 16.627 18.292 20.024 29.778 56.085 95.026 6.610 8.536 10.730 13.233 16.085 19.337 23.045 27.271 32.089 37.581 43.842 91.025 356.790 9.930 12.916 16.499 20.799 25.959 32.150 39.580 48.497 59.196 72.035 186.690 1,181.900 7,343.900 10.637 12.488 14.487 16.646 11.436 13.580 15.938 13.181 12 16.870 18.882 21.385 24.215 27.976 23.276 20 30 36.778 45.762 57.276 154.762 259.057 442.597 1,342.000 Table III Present Value of $1.00 Table III Present Value of $1.00 Period 4% 6% 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 .889 840 794 751 712 675 .641 609 579 .551 .524 .500 477 455 435 4 855 792 735 683 636 .592 .552 .516 482 423 397 373 350 329 822 747 681 .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 .760 .665 .583 .513 452 400 354 314 279 249 222 198 178 59 143 8 731 .627 .540 467 404 351 305 266 233 204 79 157 139 123 108 .703 .592 .500 424 361 308 263 .225 194 167 144 125 108 094 082 .676 .558 463386 322 .270 27 191 162 137116 099 085 .073 062 650 527 429 350 287 .237 195 162 135 112 .094 079 066 056 047 .625 497 397 319 257 208 168 137 112 092 076 062 .052 043 036 .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 .555 417 .315 .239 183 140108 084 065 05 040 031 .025 020 .016 456 312 215 149 104 .073 051 .037 026 019 .014 010 007 005 004 2 2 .308 174 099 057 033 020 012 .007 004 003 002 001 .001 208 097 046 .022 .011 Present Value of Series of $1.00 Cash Flows Period 4% 8% 10% 12% 14% 16% 18% 20% 22% 24% 25% 26% 28% 30% 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.806 0.800 0.74 0.781 0.769 1.886 1833 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 2402 2.322 2.246 2.174 2.106 2.042 1.981 1.952 1.923 1.868 1.816 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 2689 2.635 2.532 2.436 5.242 4.917 4.623 4.355 4.111 3.889 3.685 3.498 3.326 3.167 3.020 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 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 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 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 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 15 1.118 9.712 8.559 7.606 6.811 6.142 5.575 5.092 4675 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