The chief ranger of the state’s Department of Natural Resources is considering a

Question

The chief ranger of the state’s Department of Natural Resources is considering a new plan for fighting forest fires in the state’s forest lands. The current plan uses eight fire-control stations, which are scattered throughout the interior of the state forest. Each station has a four-person staff, whose annual compensation totals $370,000. Other costs of operating each base amount to $270,000 per year. The equipment at each base has a current salvage value of $290,000. The buildings at these interior stations have no other use. To demolish them would cost $27,000 each.

The chief ranger is considering an alternative plan, which involves four fire-control stations located on the perimeter of the state forest. Each station would require a six-person staff, with annual compensation costs of $470,000. Other operating costs would be $280,000 per base. Building each perimeter station would cost $370,000. The perimeter bases would need helicopters and other equipment costing $670,000 per station. Half of the equipment from the interior stations could be used at the perimeter stations. Therefore, only half of the equipment at the interior stations would be sold if the perimeter stations were built.

The state uses a 10 percent hurdle rate for all capital projects. The chief ranger has decided to use a 10-year time period for the analysis.

Use the incremental-cost approach to prepare a net-present-value analysis of the chief ranger’s decision between the interior fire-control plan and the perimeter fire-control plan. (Round your "Discount factors" to 3 decimal places. Negative amounts should be indicated by a minus sign.)

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Future Value and Present Value Tables Period 8% Future Value of $1.00(1 + ) 1.210 1.254 1.263 1.762 3.583 2.476 3.252 2.159 4.226 2.012 2.518 8.916 15.407 38.338 237.380 1,469.800 5.474 13.743 50.950 188.880 20 3.207 29.960 10.286 21.725 45.260 93.051 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity) 2.060 3.246 3.374 4.779 4.247 5.368 6.610 8.115 10.089 12.300 14.776 6.975 8.394 8.536 7.898 9.214 10.583 12.006 12.916 16.499 10.637 13.233 13.181 19.337 23.045 27.271 32.089 37.581 43.842 25.959 32.150 39.580 14.487 20.655 12 15.026 16.627 18.292 20.024 29.778 56.085 95.026 21.385 16.870 18.882 21.015 23.276 36.778 79.058 113.283 164.496 241.330 24.215 27.976 32.393 37.280 75.052 72.035 20 45.762 57.276 186.690 356.790 154.762 259.057 442.597 767.090 1,342.000 7,343.900 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 .604 .672 .650 .630 .610 .592 .574 889 840 794 751 712 675 641 .609 579 551 524 .500 477455435 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 .513 452 400 354 314 279 249 222 198 178 159 143 8 .731 627 .540 467 404 351 305 266 233 204 179 57 139 123 108 .703 .592 .500 424 361 308 263 .225 194 167 144 125 108 094 082 676 .558 463.386 322 .270 227 191 162 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 .239 183 140 108 084 065 05040 031 .025 020 .016 456 312 215 149 104 .073 051 037 026 019 014 .010 .007 005 004 6 12 20 .308 174 099 057 033 .020 012 .007 004 003 002 001 .001 208 097 046 .022 . 011 .005 003 .001 001 Table IV Present Value of Series of $1.00 Cash Flows Period 4% 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 0.794 0.781 0.769 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 2402 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 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 1118 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

Explanation / Answer

Incremental cost approach Year Particulars Cashflow Present value @ 10% Present value of cashflow 0 Savings in demolition cost 27000 1 27000 Building each perimeter station -370000 1 -370000 helicopters and other equipment -670000 1 -670000 Half of the equipment from the interior stations sold (290000*1/2) 145000 1 145000 1 to 10 Incremental annual compensation (470000-370000) -100000 6.145 -614500 (Table IV) Incremental other operating cost (280000-270000) 10000 6.145 61450 (Table IV) 10 Salvage value of equipment lost -290000 0.386 -111940 (Table III) Net present value (Sum of above figures) -1532990

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