Calculating depreciation
Initial cost = $6500
Depreciation for a year under MACRS = Rate of depreciation for a year x initial cost
For year 1, Rate of depreciation = 33.33% , Depreciation = 33.33% x 6500 =2166.45
Similarly we can find the depreciation for other years, we get the following values
Depreciation under 3 year MACRS class | |||||
Year | 1 | 2 | 3 | 4 | |
Depreciation rate | 33.33% | 44.45% | 14.81% | 7.41% | |
Depreciation | 2166.45 | 2889.25 | 962.65 | 481.65 |
For year 5 depreciation = 0
Calculating after tax operating cash flow
After tax operating cash flow = EBIT(1-tax rate) + depreciation
After tax operating cash flow = (Annual operating benefits - Annual operating costs - depreciation)(1-tax rate) + depreciation
For year1, After tax operating cash flow = (3500 - 1200 - 2166.45)(1-34%) + 2166.45 = 133.55 x 66% + 2166.45 = 88.1430 + 2166.45 = 2254.5930
Similarly after tax operating cash flows can be calculated for other years, we get the following values
Calculating After tax Operating Cash flow | |||||
Year | 1 | 2 | 3 | 4 | 5 |
Annual operating benefits | 3500 | 3500 | 3500 | 3500 | 3500 |
Annual operating costs | 1200 | 1200 | 1200 | 1200 | 1200 |
Depreciation | 2166.4500 | 2889.2500 | 962.6500 | 481.6500 | 0.0000 |
EBIT | 133.5500 | -589.2500 | 1337.3500 | 1818.3500 | 2300.0000 |
EBIT(1-tax rate) | 88.1430 | -388.9050 | 882.6510 | 1200.1110 | 1518.0000 |
Plus: Depreciation | 2166.4500 | 2889.2500 | 962.6500 | 481.6500 | 0.0000 |
After tax operating Cash Flow | 2254.5930 | 2500.3450 | 1845.3010 | 1681.7610 | 1518.0000 |
Calculating after tax terminal cash flow
Book value at end of 5 years = Initial cost - (Sum of depreciation for 5 years) = 6500 - (2166.45 +2889.45 + 962.65 + 481.65 + 0) = 6500 - 6500 = 0
After tax Terminal cash flow at end of year 5 = Salvage value at end of 5 years - tax from sale of equipment at end of 5 years
After tax Terminal cash flow at end of year 5 = Salvage value at end of 5 years - tax rate (Salvage value at end of 5 years - Book valueat end of 5 years)
After tax Terminal cash flow at end of year 5 = 800 - 34%(800 - 0) = 800 - 272 = 528
Calculating present worth at MARR = 10%
After tax Present Worth = - Inital cost + Sum of present values of after tax operating cash flows discounted at MARR of 10% + Present value of After tax Terminal cash flow at MARR of 10%
After tax Present worth = -6500 + 2254.5930 / (1 + 10%) + 2500.3450 / (1 + 10%)2 + 1845.3010 / (1 + 10%)3 + 1681.7610 / (1 + 10%)4 + 1518 / (1 + 10%)5 + 528 / (1 + 10%)5
After tax Present worth = -6500 + 2049.6300 + 2066.4008 + 1386.4019 + 1148.6653 + 942.5585 + + 327.8464 = 1421.5029 = 1421.50 (rounded to two decimal places)
Hence after tax present worth = $1421.50
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