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 $320,000. Other costs of operating each base amount to $220,000 per year. The equipment at each base has a current salvage value of $240,000. The buildings at these interior stations have no other use. To demolish them would cost $22,000 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 $420,000. Other operating costs would be $230,000 per base. Building each perimeter station would cost $320,000. The perimeter bases would need helicopters and other equipment costing $620,000 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.) Required: 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.)

Answer 1

Assumptions:-

1. It is assumed that the calculations are done on the basis of 1 plant only and later it is multiplied by the number of plants.
2. the answer is presented in both ways i.e. on incremental approach and on an individual basis.

As per the calculation, the ranger has to continue with current interior plants

Incremental Plan Approach per station
Particulars	0	1	2	3	4	5	6	7	8	9	10
Annual Compensation of staff		$     100,000	$     100,000	$     100,000	$     100,000	$     100,000	$     100,000	$     100,000	$     100,000	$     100,000	$     100,000
Other operating costs		$        10,000	$        10,000	$        10,000	$        10,000	$        10,000	$        10,000	$        10,000	$        10,000	$        10,000	$        10,000
Helicoptors and other costs		$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000
Building costs one time	$        211,000
Total Costs	$        211,000	$     730,000	$     730,000	$     730,000	$     730,000	$     730,000	$     730,000	$     730,000	$     730,000	$     730,000	$     730,000
Discounting Factor @ 10 %	1	0.909	0.826	0.751	0.683	0.621	0.564	0.513	0.467	0.424	0.386
Present Value	$        211,000	$     663,636	$     603,306	$     548,460	$     498,600	$     453,273	$     412,066	$     374,605	$     340,550	$     309,591	$     281,447
Total Costs over a period of 10 years per station	$    4,274,534
Total number of stations	5
Hence total costs	$ 21,372,670

Interior Plan Approach per station
Particulars	0	1	2	3	4	5	6	7	8	9	10
Annual Compensation of staff		$     320,000	$     320,000	$     320,000	$     320,000	$     320,000	$     320,000	$     320,000	$     320,000	$     320,000	$     320,000
Other operating costs		$     220,000	$     220,000	$     220,000	$     220,000	$     220,000	$     220,000	$     220,000	$     220,000	$     220,000	$     220,000
Salvage value of equipment at each station
Total Costs		$     540,000	$     540,000	$     540,000	$     540,000	$     540,000	$     540,000	$     540,000	$     540,000	$     540,000	$     540,000
Discounting Factor @ 10 %	1	0.909	0.826	0.751	0.683	0.621	0.564	0.513	0.467	0.424	0.386
Present Value		$     490,909	$     446,281	$     405,710	$     368,827	$     335,298	$     304,816	$     277,105	$     251,914	$     229,013	$     208,193
Total Costs over a period of 10 years per station	$    3,318,066
Total number of stations	8
Hence total costs	$ 26,544,530
Perimeter Plan Approach per station
Particulars	0	1	2	3	4	5	6	7	8	9	10
Annual Compensation of staff		$     420,000	$     420,000	$     420,000	$     420,000	$     420,000	$     420,000	$     420,000	$     420,000	$     420,000	$     420,000
Other operating costs		$     230,000	$     230,000	$     230,000	$     230,000	$     230,000	$     230,000	$     230,000	$     230,000	$     230,000	$     230,000
Helicoptors and other costs		$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000	$     620,000
Building costs one time	$        211,000
Total Costs	$        211,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000	$ 1,270,000
Discounting Factor @ 10 %	1	0.909	0.826	0.751	0.683	0.621	0.564	0.513	0.467	0.424	0.386
Present Value	$        211,000	$ 1,154,545	$ 1,049,587	$     954,170	$     867,427	$     788,570	$     716,882	$     651,711	$     592,464	$     538,604	$     489,640
Total Costs over a period of 10 years per station	$    7,592,600
Total number of stations	5
Hence total costs	$ 37,963,001