The chief ranger of the states Department of Natural Resources is considering a new plan for fighting forest fires in the states 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 $300,000. Other costs of operating each base amount to $200,000 per year. The equipment at each base has a current salvage value of $220,000. The buildings at these interior stations have no other use. To demolish them would cost $20,000 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 $400,000. Other operating costs would be $210,000 per base. Building each perimeter station would cost $300,000. The perimeter bases would need helicopters and other equipment costing $600,000 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 Appendix A for your reference. (Use appropriate factor(s) from the tables provided.)

APPENDIX A TO CHAPTER 16

Future Value and Present Value Tables

Table I Future Value of $1.00(1 + r)ⁿ

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	2.191	3.207	4.661	6.728	9.646	13.743	38.338
30	3.243	5.744	10.063	17.450	29.960	50.950	237.380
40	4.801	10.286	21.725	45.260	93.051	188.880	1,469.800

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	45.762	57.276	75.052	91.025	186.690
30	56.085	79.058	113.283	164.496	241.330	356.790	1,181.900
40	95.026	154.762	259.057	442.597	767.090	1,342.000	7,343.900

Page 723

Table III Present Value of $1.00 1 ( 1 + r ) n

Period		4%		6%		8%		10%		12%		14%		16%		18%		20%		22%		24%		26%		28%		30%		32%
1		.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
3		.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		.451		.423		.397		.373		.350		.329
5		.822		.747		.681		.621		.567		.519		.476		.437		.402		.370		.341		.315		.291		.269		.250
6		.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 1 r 1 1 ( 1 + r n )

Period		4%		6%		8%		10%		12%		14%		16%		18%		20%		22%		24%		25%		26%		28%		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
5		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
6		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
8		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
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		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

Required:

1. Use the incremental-cost approach to prepare a net-present-value analysis of the chief rangers 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.)