Question

An airline is considering two types of engine systems for use in its planes. Each has the same life and the same maintenance and repair record. System A costs ​$90,000 and uses 40,000 gallons per​ 1,000 hours of operation at the average load encountered in passenger service. System B costs ​$220,000 and uses 25,000 gallons per​ 1,000 hours of operation at the same level. Both engine systems have​ three-year lives before any major overhaul is required. On the basis of the initial​ investment, the systems have 10​% salvage values. If jet fuel costs ​$2.24 a gallon​ (year 1) and fuel consumption is expected to increase at the rate of 5​% per year because of degrading engine​ efficiency, which engine system should the firm​ install? Assume 5,000 hours of operation per year and a MARR of 9​%. Use the AE criterion. What is the equivalent operating cost per hour for each​ engine? Assume an​ end-of-year convention for the fuel cost.

The equivalent annual costs for system A are:

The equivalent annual costs for system B are:

Answer 1

Given

Slno	System A	Amount ($)	System B	Amount ($)
1	Initial cost	90000		220000
2	Estimated life	3 years	Estimated life	3 years
3	Salvage value	9000	Salvage value	22000
4	Fuel cost Year 01 (40000*5*2.24)	448000	Fuel cost Year 01 (25000*5*2.24)	280000
5	Fuel cost Year 02 (42000*5*2.24)	470400	Fuel cost Year 02 (26250*5*2.24)	294000
6	Fuel cost Year 02 (44000*5*2.24)	492800	Fuel cost Year 02 (27500*5*2.24)	308000

Solution

System A

Annual worth = 90000(A/P,9,3) - 9000(A/F,9,3) + 448000(P/F,9,1) (A/P,9,3) + 470400(P/F,9,2) (A/P,9,3) +492800(P/F,9,3) (A/P,9,3)

Using DCIF Tables

Annual worth = 90000(0.3951) - 9000(0.3051) + 448000(0.9174) (0.3951) + 470400(0.8417) (0.3951) +492800(0.7722) (0.3951)

The equivalent annual worth for system A are = $501982.9

System B

Annual worth = 220000(A/P,9,3) - 22000(A/F,9,3) + 280000(P/F,9,1) (A/P,9,3) + 294000(P/F,9,2) (A/P,9,3) +308000(P/F,9,3) (A/P,9,3)

Using DCIF Tables

Annual worth = 220000(0.3951) - 22000(0.3051) + 280000(0.9174) (0.3951) + 294000(0.8417) (0.3951) +308000(0.7722) (0.3951)

The equivalent annual worth for system B are = $373440.9