Two types of machine tools are available for performing a particular job in a ce
ID: 1122089 • 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. 20. Machine A Machine B First cost O&M; costs/year Service life Salvage value Depreciation method $30,000 $3,000 6 vears $6,000 MACRS (GDS) $40,000 $%2,500 8 years $4,000 MACRS (GDS) (Straight-line method) 5 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
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
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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