Question
In: Economics
A firm is considering investing $42,000 in equipment that is expected to have a useful life...
A firm is considering investing $42,000 in equipment that is expected to have a useful life of four years and is expected to reduce (save) the firm’s labor costs by $8,900 per year. The equipment can be sold for $18,000 at the end of the period. Assume the firm pays a 40% income tax rate on its taxable income and uses the declining balance (200%) depreciation method. The firm’s after tax MARR is 5% per year.
What are the after-tax cash flow amounts for years 1 through 4? Is this investment profitable or not?
Solutions
Expert Solution
depreciation rate = 2 / 4 = 0.5
Depreciation in any year m = P *(1-d)^(m-1) * d
Depreciation in year 1 = 42000 *(1-0.5)^(1-1) * 0.5 = 21000
Depreciation in year 2 = 42000 *(1-0.5)^(2-1) * 0.5 = 10500
Depreciation in year 3 = 42000 *(1-0.5)^(3-1) * 0.5 = 5250
Depreciation in year 4 = 42000 *(1-0.5)^(4-1) * 0.5 = 2625
Tax rate = 40%
Taxable income = Net cash flow - Depreciation
Tax = Tax rate * Taxable income
ATCF = Taxable income - Tax + Depreciation
| Year | Untaxed BTCF | Taxed BTCF | DDB Dep | Recaptured Dep | Tax income | Tax | ATCF |
| 0 | -42000 | -42000 | |||||
| 1 | 8900 | 21000.00 | -12100.00 | -4840.00 | 13740.00 | ||
| 2 | 8900 | 10500.00 | -1600.00 | -640.00 | 9540.00 | ||
| 3 | 8900 | 5250.00 | 3650.00 | 1460.00 | 7440.00 | ||
| 4 | 18000 | 8900 | 2625.00 | 15375.00 | 21650.00 | 8660.00 | 18240.00 |
| NPW | 1,171.82 |
NPW = 1171.82 ~ 1172
As NPW is positive, project should be selected
Showing formula in excel
| Year | Untaxed BTCF | Taxed BTCF | DDB Dep | Recaptured Dep | Tax income | Tax | ATCF |
| 0 | -42000 | =B12 | |||||
| 1 | 8900 | 21000 | =C13-D13 | =F13*0.4 | =C13-G13 | ||
| 2 | 8900 | 10500 | =C14-D14 | =F14*0.4 | =C14-G14 | ||
| 3 | 8900 | 5250 | =C15-D15 | =F15*0.4 | =C15-G15 | ||
| 4 | 18000 | 8900 | 2625 | =B16-(42000-SUM(D13:D16)) | =C16-D16+E16 | =F16*0.4 | =B16+C16-G16 |
| NPW | =NPV(5%,H13:H16)+H12 |
Rahul Sunny answered 2 years agoRelated Solutions
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