I am haveing a lot of trouble with the following question and need help on how t
ID: 2812706 • Letter: I
Question
I am haveing a lot of trouble with the following question and need help on how to solve it:
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 $120,000 and uses 36,000 gallons per 1,000 hours of operation at the average load encountered in passenger service. System B costs $330,000 and uses 30,000 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 19% salvage values. If jet fuel costs $2.27 a gallon (year 1) and fuel consumption is expected to increase at the rate of 9 % 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 14%. 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 $
Explanation / Answer
EVALUATION OF SYSTEM A Present Value (PV) of Cash Flow: (Cash Flow)/((1+i)^N) i=Discount Rate=MARR=14%=0.14 N=Year of Cash Flow Fuelconsumption in year 1 180000 (36000*(5000/1000) Fuelconsumption in year 2 196200 (180000*1.09) Fuelconsumption in year 3 213858 (196200*1.09) N Year 0 1 2 3 A Initial Cost $120,000 B Amount of fuel consumption(Gallons) 180000 196200 213858 C=B*$2.27 Cost of fuel $ 408,600 $ 445,374 $ 485,458 D=0.19*A Salvage value at end of year 3 $22,800 E=A+C-D Net annual cost $120,000 $ 408,600 $ 445,374 $ 462,658 SUM PV=E/(1.14^N) Present Value (PV) of Cost $ 120,000 $ 358,421 $ 342,701 $ 312,281 $ 1,133,403 Net Present Worth of Cost $ 1,133,403 F Equvalant AnnualCost $488,192 (Using PMT function of excelwith Rate=14%, Nper=3,PV=-1133403) G Annual operation hour 5000 H=F/G Equivalent Operating Cost per hour $97.64 EVALUATION OF SYSTEM B Fuelconsumption in year 1 150000 (30000*(5000/1000) Fuelconsumption in year 2 163500 (150000*1.09) Fuelconsumption in year 3 178215 (163500*1.09) N Year 0 1 2 3 A Initial Cost $330,000 B Amount of fuel consumption(Gallons) 150000 163500 178215 C=B*$2.27 Cost of fuel $ 340,500 $ 371,145 $ 404,548 D=0.19*A Salvage value at end of year 3 $62,700 E=A+C-D Net annual cost $330,000 $ 340,500 $ 371,145 $ 341,848 SUM PV=E/(1.14^N) Present Value (PV) of Cost $ 330,000 $ 298,684 $ 285,584 $ 230,738 $ 1,145,006 Net Present Worth of Cost $ 1,145,006 F Equvalant AnnualCost $493,190 (Using PMT function of excelwith Rate=14%, Nper=3,PV=-1145006) G Annual operation hour 5000 H=F/G Equivalent Operating Cost per hour $98.64 The equivalent annual costs for system A are $97.64 The equivalent annual costs for system B are $98.64
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