The Ford Motor Company is considering three mutually exclusive electronic stabil
ID: 2483111 • Letter: T
Question
The Ford Motor Company is considering three mutually exclusive electronic stability control systems for protection against rollover of its automobiles. The investment period is four years (equal lives), and the MARR is 15% per year. Data for fixturing costs of the systems are given on the right. The alternatives all have a MACRS (GDS) property class of three years. If the effective income tax rate is 37% and the aftertaxMARR (1 0.37)(15%) 9.45% per year, calculate PW of each alternative. IRR A) 10.7% B) 21.7% C) 22.6% Capital Investment A) $12,600 B) $15,900 C) $8,100 Annual Receipts Less Expenses A) $3,500 B) $5,600 C) $3,000 Salvage Value A) $2,500 B) $4,100 C) $1,600
Explanation / Answer
Calculation of Present Worth (PW):
Case A:
Year 0
Year 1
Year 2
Year 3
Year 4
Capital Investment
$ (12,600.00)
Annual Receipts Less Expenses (Net of Tax) = 3500* (1-37%)
$ 2,205.00
$ 2,205.00
$ 2,205.00
$ 2,205.00
Tax Saving on Depreciation (See Note Below)
$ 1,553.84
$ 2,072.26
$ 690.44
$ 345.45
Salvage Value (Net of Tax) = 2500* (1-37%) =
$ 1,575.00
Net cash Flows (CF)
$ (12,600.00)
$ 3,758.84
$ 4,277.26
$ 2,895.44
$ 4,125.45
PVF (9.45%)
1.00000
0.91366
0.83477
0.76270
0.69685
1/(1+9.45%)^0
1/(1+9.45%)^1
1/(1+9.45%)^2
1/(1+9.45%)^3
1/(1+9.45%)^4
PV = CF*PVF =
$ (12,600.00)
$ 3,434.30
$ 3,570.54
$ 2,208.35
$ 2,874.81
PW = Sum of PVs =
$ (512.00)
Note: Calculation of Tax Saving on Depreciation:
Cost = 12600
MACRS 3 Years Depreciation rate
33.33%
44.45%
14.81%
7.41%
Depreciation = Cost * Depreciation Rate =
$ 4,199.58
$ 5,600.70
$ 1,866.06
$ 933.66
Tax Saving on Depreciation = Depreciation * 37% =
$ 1,553.84
$ 2,072.26
$ 690.44
$ 345.45
Case B:
Year 0
Year 1
Year 2
Year 3
Year 4
Capital Investment
$ (15,900.00)
Annual Receipts Less Expenses (Net of Tax) = 5600* (1-37%)
$ 3,528.00
$ 3,528.00
$ 3,528.00
$ 3,528.00
Tax Saving on Depreciation (See Note Below)
$ 1,960.80
$ 2,614.99
$ 871.27
$ 435.93
Salvage Value (Net of Tax) = 4100* (1-37%) =
$ 2,583.00
Net cash Flows (CF)
$ (15,900.00)
$ 5,488.80
$ 6,142.99
$ 4,399.27
$ 6,546.93
PVF (9.45%)
1.00000
0.91366
0.83477
0.76270
0.69685
1/(1+9.45%)^0
1/(1+9.45%)^1
1/(1+9.45%)^2
1/(1+9.45%)^3
1/(1+9.45%)^4
PV = CF*PVF =
$ (15,900.00)
$ 5,014.90
$ 5,128.01
$ 3,355.32
$ 4,562.20
PW = Sum of PVs =
$ 2,160.42
Note: Calculation of Tax Saving on Depreciation:
Cost = 15900
MACRS 3 Years Depreciation rate
33.33%
44.45%
14.81%
7.41%
Depreciation = Cost * Depreciation Rate =
$ 5,299.47
$ 7,067.55
$ 2,354.79
$ 1,178.19
Tax Saving on Depreciation = Depreciation * 37% =
$ 1,960.80
$ 2,614.99
$ 871.27
$ 435.93
Case C:
Year 0
Year 1
Year 2
Year 3
Year 4
Capital Investment
$ (8,100.00)
Annual Receipts Less Expenses (Net of Tax) = 3000* (1-37%)
$ 1,890.00
$ 1,890.00
$ 1,890.00
$ 1,890.00
Tax Saving on Depreciation (See Note Below)
$ 998.90
$ 1,332.17
$ 443.86
$ 222.08
Salvage Value (Net of Tax) = 1600* (1-37%) =
$ 1,008.00
Net cash Flows (CF)
$ (8,100.00)
$ 2,888.90
$ 3,222.17
$ 2,333.86
$ 3,120.08
PVF (9.45%)
1.00000
0.91366
0.83477
0.76270
0.69685
1/(1+9.45%)^0
1/(1+9.45%)^1
1/(1+9.45%)^2
1/(1+9.45%)^3
1/(1+9.45%)^4
PV = CF*PVF =
$ (8,100.00)
$ 2,639.47
$ 2,689.78
$ 1,780.03
$ 2,174.21
PW = Sum of PVs =
$ 1,183.49
Note: Calculation of Tax Saving on Depreciation:
Cost = 8100
MACRS 3 Years Depreciation rate
33.33%
44.45%
14.81%
7.41%
Depreciation = Cost * Depreciation Rate =
$ 2,699.73
$ 3,600.45
$ 1,199.61
$ 600.21
Tax Saving on Depreciation = Depreciation * 37% =
$ 998.90
$ 1,332.17
$ 443.86
$ 222.08
Calculation of Present Worth (PW):
Case A:
Year 0
Year 1
Year 2
Year 3
Year 4
Capital Investment
$ (12,600.00)
Annual Receipts Less Expenses (Net of Tax) = 3500* (1-37%)
$ 2,205.00
$ 2,205.00
$ 2,205.00
$ 2,205.00
Tax Saving on Depreciation (See Note Below)
$ 1,553.84
$ 2,072.26
$ 690.44
$ 345.45
Salvage Value (Net of Tax) = 2500* (1-37%) =
$ 1,575.00
Net cash Flows (CF)
$ (12,600.00)
$ 3,758.84
$ 4,277.26
$ 2,895.44
$ 4,125.45
PVF (9.45%)
1.00000
0.91366
0.83477
0.76270
0.69685
1/(1+9.45%)^0
1/(1+9.45%)^1
1/(1+9.45%)^2
1/(1+9.45%)^3
1/(1+9.45%)^4
PV = CF*PVF =
$ (12,600.00)
$ 3,434.30
$ 3,570.54
$ 2,208.35
$ 2,874.81
PW = Sum of PVs =
$ (512.00)
Note: Calculation of Tax Saving on Depreciation:
Cost = 12600
MACRS 3 Years Depreciation rate
33.33%
44.45%
14.81%
7.41%
Depreciation = Cost * Depreciation Rate =
$ 4,199.58
$ 5,600.70
$ 1,866.06
$ 933.66
Tax Saving on Depreciation = Depreciation * 37% =
$ 1,553.84
$ 2,072.26
$ 690.44
$ 345.45
Case B:
Year 0
Year 1
Year 2
Year 3
Year 4
Capital Investment
$ (15,900.00)
Annual Receipts Less Expenses (Net of Tax) = 5600* (1-37%)
$ 3,528.00
$ 3,528.00
$ 3,528.00
$ 3,528.00
Tax Saving on Depreciation (See Note Below)
$ 1,960.80
$ 2,614.99
$ 871.27
$ 435.93
Salvage Value (Net of Tax) = 4100* (1-37%) =
$ 2,583.00
Net cash Flows (CF)
$ (15,900.00)
$ 5,488.80
$ 6,142.99
$ 4,399.27
$ 6,546.93
PVF (9.45%)
1.00000
0.91366
0.83477
0.76270
0.69685
1/(1+9.45%)^0
1/(1+9.45%)^1
1/(1+9.45%)^2
1/(1+9.45%)^3
1/(1+9.45%)^4
PV = CF*PVF =
$ (15,900.00)
$ 5,014.90
$ 5,128.01
$ 3,355.32
$ 4,562.20
PW = Sum of PVs =
$ 2,160.42
Note: Calculation of Tax Saving on Depreciation:
Cost = 15900
MACRS 3 Years Depreciation rate
33.33%
44.45%
14.81%
7.41%
Depreciation = Cost * Depreciation Rate =
$ 5,299.47
$ 7,067.55
$ 2,354.79
$ 1,178.19
Tax Saving on Depreciation = Depreciation * 37% =
$ 1,960.80
$ 2,614.99
$ 871.27
$ 435.93
Case C:
Year 0
Year 1
Year 2
Year 3
Year 4
Capital Investment
$ (8,100.00)
Annual Receipts Less Expenses (Net of Tax) = 3000* (1-37%)
$ 1,890.00
$ 1,890.00
$ 1,890.00
$ 1,890.00
Tax Saving on Depreciation (See Note Below)
$ 998.90
$ 1,332.17
$ 443.86
$ 222.08
Salvage Value (Net of Tax) = 1600* (1-37%) =
$ 1,008.00
Net cash Flows (CF)
$ (8,100.00)
$ 2,888.90
$ 3,222.17
$ 2,333.86
$ 3,120.08
PVF (9.45%)
1.00000
0.91366
0.83477
0.76270
0.69685
1/(1+9.45%)^0
1/(1+9.45%)^1
1/(1+9.45%)^2
1/(1+9.45%)^3
1/(1+9.45%)^4
PV = CF*PVF =
$ (8,100.00)
$ 2,639.47
$ 2,689.78
$ 1,780.03
$ 2,174.21
PW = Sum of PVs =
$ 1,183.49
Note: Calculation of Tax Saving on Depreciation:
Cost = 8100
MACRS 3 Years Depreciation rate
33.33%
44.45%
14.81%
7.41%
Depreciation = Cost * Depreciation Rate =
$ 2,699.73
$ 3,600.45
$ 1,199.61
$ 600.21
Tax Saving on Depreciation = Depreciation * 37% =
$ 998.90
$ 1,332.17
$ 443.86
$ 222.08
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