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.

Cost of acquiring additional land for runway $ 70,000

Cost of runway construction 200,000

Cost of extending perimeter fence 29,840

Cost of runway lights 39,600

Annual cost of maintaining new runway 28,000

Annual incremental revenue from landing fees 40,000

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 $100,000. The old snowplow could be sold now for $10,000. The new, larger plow will cost $12,000 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 $64,000 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 12 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.

Transcribed Image Text:Future Value and Present Value Tables Table I Future Value of $1.00(1+r)^ Period 4% 6% 8% 10% 12% 14% 20% 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 7 1.316 1.504 1.714 1.949 2.211 2.502 3.583 8 1.369 1.594 1.851 2.144 2.476 2.853 4.300 9 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 13 1.665 2.133 2.720 3.452 4.364 5.492 10.699 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 30 3.243 5.744 40 40 4.801 2.191 3.207 4.661 6.728 9.646 13.743 10.063 17.450 29.960 10.286 21.725 45.260 93.051 188.880 1,469.800 38.338 50.950 237.380 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity) (1 + r)n - 1 r Period 4% 6% 8% 10% 12% 14% 20% 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 2.040 2.060 2.080 2.100 2.120 2.140 2.220 3 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 8 9.214 9.898 10.637 11.436 12.300 13.233 16.499 9 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 11 13.486 14.972 16.646 18.531 20.655 23.045 32.150 12 15.026 16.870 18.977 21.385 24.133 27.271 39.580 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 57.276 75.052 30 40 56.085 79.058 95.026 154.762 45.762 91.025 113.283 164.496 241.330 356.790 1,181.900 259.057 442.597 767.090 1,342.000 7,343.900 186.690 Table III 1 Present Value of $1.00 (1 + r)" Period 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% 1 2 3 4 5 .822 .747 .681 .621 .567 .519 .476 .437 .962 .943 .926 .909 .893 .877 .862 .847 .833 .820 .806 .781 .769 .925 .890 .857 .826 .797 .769 .743 .718 .694 .672 .650 .630 .610 .592 .889 .840 .794 .751 .712 .675 .641 .609 .579 .551 .524 .500 .477 .455 .855 .792 .735 .683 .636 .592 .552 .516 .482 .451 .423 .397 .373 .350 .402 .370 .341 .315 .291 .269 .794 .758 .574 .435 .329 .250 671 o 8 .731 9 10 .676 .558 .463 .386 .322 .270 .227 .191 .162 .137 .116 .099 .085 .790 .705 .630 .564 .507 .456 .410 .370 .335 .303 .275 .760 .665 .583 .513 .452 .400 .354 .314 .279 .249 .222 .627 .540 .467 .404 .351 .305 .266 .233 .204 .179 .703 .592 .500 .424 .361 .308 .263 .225 .194 .167 .144 .125 .108 .094 .073 .250 .227 .207 .189 .198 .178 .159 .143 .157 .139 .123 .108 .082 .062 11 12 13 14 15 .145 .116 .577 .442 .340 .263 .205 .160 .125 .099 .555 .417 .315 .239 .183 .140 .108 .084 .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 .093 .075 .061 .050 .040 .033 .027 .078 .062 .049 .039 .032 .025 .021 .065 .051 .040 .031 .025 .020 .016 20 30 40 .456 .312 .215 .149 .104 .073 .051 .037 .026 .019 .308 .174 .099 .057 .033 .020 .012 .007 .004 .003 .208 .097 .046 .022 .011 .005 .003 .001 .001 .014 .010 .007 .002 .001 .001 .005 .004 Table IV Present Value of Series of $1.00 Cash Flows 1½ ( 1 (1 1 (1 pm) Period 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 25% 26% 28% 30% 1 2 3 4 5 3.630 3.465 4.452 4.212 0.962 0.943 0.926 0.909 0.893 0.877 1.886 1.833 1.783 1.736 1.690 1.647 2.775 2.673 2.577 2.487 2.402 2.322 3.312 3.170 3.037 3.993 3.791 3.605 0.862 0.847 0.833 0.820 0.806 0.800 0.794 0.781 3.433 3.274 3.127 2.991 0.769 1.605 1.566 1.528 1.492 1.457 1.440 1.424 1.392 1.361 2.246 2.174 2.106 2.042 1.981 1.952 1.923 1.868 1.816 2.914 2.798 2.690 2.589 2.494 2.404 2.362 2.320 2.241 2.166 2.864 2.745 2.689 2.635 2.532 2.436 6 5.242 4.917 4.623 7 8 6.733 6.210 5.747 5.335 4.968 4.639 9 10 8.111 4.344 4.078 3.837 3.619 7.435 6.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 3.786 7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.192 3.923 4.355 4.111 3.889 3.685 3.498 3.326 3.167 3.020 2.951 2.885 2.759 2.643 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 3.421 3.329 3.241 3.076 2.925 3.566 3.463 3.366 3.184 3.019 3.682 3.571 3.465 3.269 3.092 11 12 13 14 15 155 11.118 20 30 40 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 6.194 5.660 5.197 4.793 4.439 4.127 3.851 3.725 3.606 3.387 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 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 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 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 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 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 3.190 3.223
Transcribed Image Text:Incremental operating costs for new snow plow Incremental revenue from landing fees 40,000 Additional tax revenue 64,000 Runway maintenance (28,000) Annual incremental benefit Annuity discount factor Present value of annual benefits Initial costs: Add: Salvage value of old snow plow Less: New snow plow Less: Extension of perimeter fence $ 76,000 5.650 $ 429,400 10,000 Less: Land acquisition Less: Runway construction Less: Runway lights Net present value $ 439,400

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.


Cost of acquiring additional land for runway	$	70,000
Cost of runway construction		200,000
Cost of extending perimeter fence		29,840
Cost of runway lights		39,600
Annual cost of maintaining new runway		28,000
Annual incremental revenue from landing fees		40,000

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 $100,000. The old snowplow could be sold now for $10,000. The new, larger plow will cost $12,000 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 $64,000 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 12 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.

Future Value and Present Value Tables
Table I
Future Value of $1.00(1+r)^
Period
4%
6%
8%
10%
12%
14%
20%
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
7
1.316 1.504
1.714 1.949
2.211
2.502
3.583
8
1.369
1.594
1.851
2.144
2.476
2.853
4.300
9
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
13
1.665
2.133
2.720
3.452
4.364
5.492
10.699
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
30
3.243
5.744
40
40
4.801
2.191 3.207 4.661 6.728 9.646 13.743
10.063 17.450 29.960
10.286 21.725 45.260 93.051 188.880 1,469.800
38.338
50.950
237.380
Table II
Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity)
(1 + r)n - 1
r
Period 4%
6%
8%
10%
12%
14%
20%
1
1.000
1.000
1.000
1.000
1.000
1.000
1.000
2
2.040
2.060
2.080
2.100
2.120
2.140
2.220
3
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
8
9.214
9.898
10.637
11.436
12.300
13.233
16.499
9
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
11
13.486
14.972
16.646
18.531
20.655
23.045
32.150
12
15.026
16.870
18.977
21.385
24.133
27.271
39.580
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
57.276
75.052
30
40
56.085 79.058
95.026 154.762
45.762
91.025
113.283 164.496 241.330 356.790 1,181.900
259.057 442.597 767.090 1,342.000 7,343.900
186.690
Table III
1
Present Value of $1.00
(1 + r)"
Period 4% 6% 8% 10% 12% 14%
16% 18% 20% 22% 24%
26% 28% 30% 32%
1
2
3
4
5
.822 .747 .681 .621 .567 .519 .476 .437
.962 .943 .926 .909 .893 .877 .862 .847 .833 .820 .806
.781 .769
.925 .890 .857 .826 .797 .769 .743 .718 .694 .672 .650 .630 .610 .592
.889 .840 .794 .751 .712 .675 .641 .609 .579 .551 .524 .500 .477 .455
.855 .792 .735 .683 .636 .592 .552 .516 .482 .451 .423 .397 .373 .350
.402 .370 .341 .315 .291 .269
.794
.758
.574
.435
.329
.250
671 o
8
.731
9
10
.676 .558 .463 .386 .322 .270 .227 .191 .162 .137 .116 .099 .085
.790 .705 .630 .564 .507 .456 .410 .370 .335 .303 .275
.760 .665 .583 .513 .452 .400 .354 .314 .279 .249 .222
.627 .540 .467 .404 .351 .305 .266 .233 .204 .179
.703 .592 .500 .424 .361 .308 .263 .225 .194 .167 .144 .125 .108 .094
.073
.250 .227 .207 .189
.198 .178 .159 .143
.157 .139 .123 .108
.082
.062
11
12
13
14
15
.145 .116
.577 .442 .340 .263 .205 .160 .125 .099
.555 .417 .315 .239 .183 .140 .108 .084
.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
.093 .075 .061 .050 .040 .033 .027
.078 .062 .049 .039 .032 .025 .021
.065 .051 .040 .031 .025
.020 .016
20
30
40
.456 .312 .215 .149 .104 .073 .051 .037 .026 .019
.308 .174 .099 .057 .033 .020 .012 .007 .004 .003
.208 .097 .046 .022 .011 .005 .003 .001 .001
.014 .010 .007
.002 .001 .001
.005
.004
Table IV
Present Value of Series of $1.00 Cash Flows
1½ ( 1
(1
1
(1 pm)
Period 4%
6%
8%
10% 12% 14% 16% 18% 20% 22% 24% 25% 26% 28% 30%
1
2
3
4
5
3.630 3.465
4.452 4.212
0.962 0.943 0.926 0.909 0.893 0.877
1.886 1.833 1.783 1.736 1.690 1.647
2.775 2.673 2.577 2.487 2.402 2.322
3.312 3.170 3.037
3.993 3.791 3.605
0.862 0.847 0.833 0.820 0.806 0.800 0.794 0.781
3.433 3.274 3.127 2.991
0.769
1.605 1.566 1.528 1.492 1.457 1.440 1.424 1.392 1.361
2.246 2.174 2.106 2.042 1.981 1.952 1.923 1.868 1.816
2.914 2.798 2.690 2.589 2.494 2.404 2.362 2.320 2.241 2.166
2.864 2.745 2.689 2.635 2.532 2.436
6
5.242 4.917 4.623
7
8
6.733 6.210
5.747 5.335 4.968 4.639
9
10
8.111
4.344 4.078 3.837 3.619
7.435 6.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 3.786
7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.192 3.923
4.355 4.111 3.889 3.685 3.498 3.326 3.167 3.020 2.951 2.885 2.759 2.643
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
3.421 3.329 3.241 3.076 2.925
3.566 3.463 3.366 3.184 3.019
3.682 3.571 3.465 3.269 3.092
11
12
13
14
15
155
11.118
20
30
40
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 6.194 5.660 5.197 4.793 4.439 4.127 3.851 3.725 3.606 3.387
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
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
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
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
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
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
3.190
3.223

Incremental operating costs for new snow plow
Incremental revenue from landing fees
40,000
Additional tax revenue
64,000
Runway maintenance
(28,000)
Annual incremental benefit
Annuity discount factor
Present value of annual benefits
Initial costs:
Add: Salvage value of old snow plow
Less: New snow plow
Less: Extension of perimeter fence
$
76,000
5.650
$
429,400
10,000
Less: Land acquisition
Less: Runway construction
Less: Runway lights
Net present value
$
439,400

Accepted Answer

Net Present Value is referred to as NPV. By contrasting the present value of an investment's…