Washington County’s Board of Representatives is considering the construction of

Question

Washington County’s Board of Representatives is considering the construction of a longer runway at the county airport. Currently, the airport can handle only private aircraft and small commuter jets. A new, long runway would enable the airport to handle the midsize jets used on many domestic flights. Data pertinent to the board’s decision appear below.

In addition to the preceding data, two other facts are relevant to the decision. First, a longer runway will require a new snowplow, which will cost $170,000. The old snowplow could be sold now for $17,000. The new, larger plow will cost $15,000 more in annual operating costs. Second, the County Board of Representatives believes that the proposed long runway, and the major jet service it will bring to the county, will increase economic activity in the community. The board projects that the increased economic activity will result in $76,000 per year in additional tax revenue for the county.

In analyzing the runway proposal, the board has decided to use a 10-year time horizon. The county’s hurdle rate for capital projects is 11 percent.

Use Appendix A for your reference. (Use appropriate factor(s) from the tables provided.)

Required:

1. Prepare a net-present-value analysis of the proposed long runway.

2. Should the County Board of Representatives approve the runway considering NPV?

3-a. Which of the data used in the analysis are likely to be most uncertain?

3-b. Which of the data used in the analysis are likely to be least uncertain?

Prepare a net-present-value analysis of the proposed long runway. (Round your "Annuity discount factor" to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Which of the data used in the analysis are likely to be most uncertain? (Select which of the following statements (is) are true by selecting an "X".)

Which of the data used in the analysis are likely to be least uncertain? (Select which of the following statements (is) are true by selecting an "X".)

Cost of acquiring additional land for runway $ 79,500 Cost of runway construction 270,000 Cost of extending perimeter fence 19,840 Cost of runway lights 43,000 Annual cost of maintaining new runway 21,500 Annual incremental revenue from landing fees 52,500 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

1) Additional tax revenue 76000 Incremental operating costs for new snow plow -15000 Incremental revenue from landing fees 52500 Runway maintenance -21500 Annual incremental benefit 92000 Annuity discount factor 5.889 Present value of annual benefits 541788 Initial costs: Cost of acquiring additional land for runway Cost of runway construction -270000 Cost of extending perimeter fence -19840 Cost of runway lights -43000 Cost of new snowplow -170000 Sale price of old snowplow 17000 Incremental initial costs -485840 Net present value 55948 NOTE: The Appendix for annuity discount factor does not give the factor for 11%; it gives factors for 10% and 12% only.Hence, the factor for 11% is worked out as (1.11^10-1)/(0.11*1.11^10) = 5.889. Alternatively the average of factors for 10% and 12% can be used, which is equal to (6.145+5.650)/2 = 5.898. The answer would then be as below: Additional tax revenue 76000 Incremental operating costs for new snow plow -15000 Incremental revenue from landing fees 52500 Runway maintenance -21500 Annual incremental benefit 92000 Annuity discount factor 5.898 Present value of annual benefits 542616 Initial costs: Cost of acquiring additional land for runway Cost of runway construction -270000 Cost of extending perimeter fence -19840 Cost of runway lights -43000 Cost of new snowplow -170000 Sale price of old snowplow 17000 Incremental initial costs -485840 Net present value 56776 2) Yes, the County Board of Representatives should approve the runway project as the NPV is positive. 3-a) Most uncertain data: Cost of acquiring land xxxxxxxxxxx Annual cost of maintaining new runway Annual incremental revenue from landing fees Cost of new snow plow Cost of runway lights Annual additional tax revenue Salvage value of old snow plow Cost of land is unassessable unless there is already a deal in place. All other items are less uncertain as they can be predicted with reasonable accuracy from the exisiting figures for costs and revenues. 3-b) Least Uncertain data: Annual additional tax revenue xxxxxxxxxxx Annual cost of maintaining new runway xxxxxxxxxxx Cost of acquiring land Annual incremental revenue from landing fees xxxxxxxxxxx Cost of runway lights xxxxxxxxxxx Salvage value of old snow plow Cost of new snow plow The items marked 'xxx' can be reasonably estimated from the existing operating data.

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