Two types of machine tools are available for performing a particular job in a ce
ID: 2588928 • Letter: T
Question
Two types of machine tools are available for performing a particular job in a certain manufacturing firm. The estimated costs and salvage values are sum marized in the following table. Machine A Machine B First cost O&M; costs/year Service life Salvage value Depreciation method $30,000 $3,000 6 years $6,000 MACRS (GDS) $40,000 $2,500 8 vears $4,000 MACRS (GDS) (Straight-line method) vears Recovery period 5 years The effective state and federal tax rate is 50%, and the capital-gains rate is 35%. Make your comparison after income taxes, using a MARR of 10% and in dicate the study periodExplanation / Answer
ANALYSIS OF MACHINE A Initial cash flow $30,000 Annual cash flow for O&M $3,000 Calculation of Depreciation Tax shield N A B=30000*A C=B*0.5 Year MACRS Depreciation Depreciation Recovery rate Amount Tax shield 1 20% $ 6,000 $ 3,000 2 32% $ 9,600 $ 4,800 3 19.20% $ 5,760 $ 2,880 4 11.52% $ 3,456 $ 1,728 5 11.52% $ 3,456 $ 1,728 6 5.76% $ 1,728 $ 864 Terminal Cash flow: Salvage value(Before tax) $6,000 Tax(6000*0.5) $3,000 After tax salvage value $3,000 Service life 6 Years Present Value (PV)of cash flow=(Cash flow)/((1+i)^N) i=discount rate=MARR=10%= 0.10 N=Year of cash flow Year wise cash flow and PV of cash flow given below N A B C D E=A+B+C+D F=E/(1.1^N) Year Initial Annual Depreciation Terminal Net PV of net Cash outflow Cash outflow Tax shield Cashoutflow Cash outflow Cash outflow 0 $30,000 $0 $0 $0 $30,000 30000 1 $0 $3,000 $ (3,000) $0 $0 0 2 $0 $3,000 $ (4,800) $0 ($1,800) -1487.60331 3 $0 $3,000 $ (2,880) $0 $120 90.15777611 4 $0 $3,000 $ (1,728) $0 $1,272 868.7931152 5 $0 $3,000 $ (1,728) $0 $1,272 789.8119229 6 $0 $3,000 $ (864) ($3,000) ($864) -487.705476 TOTAL 29773.45403 PRESENT VALUE OF NET COST $ 29,773.45 ANALYSIS OF MACHINE B Initial cash flow $40,000 Annual cash flow forO&M $2,500 Calculation of Depreciation Tax shield N A B=40000*A C=B*0.5 Year MACRS Depreciation Depreciation Recovery rate Amount Tax shield 1 20% $ 8,000 $ 4,000 2 32% $ 12,800 $ 6,400 3 19.20% $ 7,680 $ 3,840 4 11.52% $ 4,608 $ 2,304 5 11.52% $ 4,608 $ 2,304 6 5.76% $ 2,304 $ 1,152 Terminal Cash flow: Salvage value(Before tax) $4,000 Tax(4000*0.5) $2,000 After tax salvage value $2,000 Sevice life 8 Years Present Value (PV)of cash flow=(Cash flow)/((1+i)^N) i=discount rate=MARR=10%= 0.10 N=Year of cash flow Year wise cash flow and PV of cash flow given below N A B C D E=A+B+C+D F=E/(1.1^N) Year Initial Annual Depreciation Terminal Net PV of net Cash outflow Cash outflow Tax shield Cashoutflow Cash outflow Cash outflow 0 $40,000 $0 $0 $0 $40,000 40000 1 $0 $2,500 $ (4,000) $0 ($1,500) -1363.63636 2 $0 $2,500 $ (6,400) $0 ($3,900) -3223.1405 3 $0 $2,500 $ (3,840) $0 ($1,340) -1006.76183 4 $0 $2,500 $ (2,304) $0 $196 133.8706373 5 $0 $2,500 $ (2,304) $0 $196 121.7005793 6 $0 $2,500 $ (1,152) $0 $1,348 760.9108577 7 $0 $2,500 $0 $0 $2,500 1282.895296 8 $0 $2,500 $0 ($2,000) $500 233.2536901 TOTAL 36939.09237 PRESENT VALUE OF NET COST $ 36,939.09 PRESENT WORTH OF COST OF MACHINE A $ 29,773.45 PRESENT WORTH OF COST OF MACHINE B $ 36,939.09 Machine A should be preferred
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