Homework SourseYour firm is contemplating the purchase of a new 1478400 com
Your firm is contemplating the purchase of a new $1,478,400 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $132,000 at the end of that time. You will save $580,800 before taxes per year in order processing costs and you will be able to reduce working capital by $130,139 (this is a one-time reduction). Required : If the tax rate is 33 percent, what is the IRR for this project?
Solution
IRR of the project is 27.22%
Working:
| IRR is the rate at which Net Present Value (NPV) is zero. | ||||||||||||
| Calculate NPV at 13% | ||||||||||||
| Step-1:Calculation of annual cash flow | ||||||||||||
| Saving | $ 5,80,800 | |||||||||||
| Depreciation | -2,95,680 | |||||||||||
| Profit before tax | 2,85,120 | |||||||||||
| Tax | -94,090 | |||||||||||
| Net Income | 1,91,030 | |||||||||||
| Depreciation | 2,95,680 | |||||||||||
| Annual cash flow | 4,86,710 | |||||||||||
| Working: | ||||||||||||
| Straight Line depreciation | = | (Cost-Salvage Value)/Useful Life | ||||||||||
| = | (1478400-0)/5 | |||||||||||
| = | 2,95,680 | |||||||||||
| Step-2:Calculation of NPV | ||||||||||||
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Total | |||
| Operating cash flow | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | ||||
| Release of net working caital | 1,30,139 | |||||||||||
| After tax sale of asset | 88,440 | |||||||||||
| Cash flow | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 7,05,289 | ||||
| Discount factor | 0.8850 | 0.7831 | 0.6931 | 0.6133 | 0.5428 | 0.4803 | 0.4251 | 0.3762 | ||||
| Present Value | 4,30,717.17 | 3,81,165.64 | 3,37,314.72 | 2,98,508.60 | 2,64,166.91 | 2,33,776.02 | 2,06,881.44 | 2,65,301.56 | 24,17,832.06 | |||
| Less: Initial Investment | ||||||||||||
| Cost of fixed assets | 14,78,400 | |||||||||||
| Cost of Net Woring Capital | 1,30,139 | 16,08,539.00 | ||||||||||
| NPV | 8,09,293.06 | |||||||||||
| Working: | ||||||||||||
| After tax sale of asset | = | 132000*(1-0.33) | ||||||||||
| = | 88,440 | |||||||||||
| Now Calculate NPV at 30% | ||||||||||||
| Step-1:Calculation of annual cash flow | ||||||||||||
| Saving | $ 5,80,800 | |||||||||||
| Depreciation | -2,95,680 | |||||||||||
| Profit before tax | 2,85,120 | |||||||||||
| Tax | -94,090 | |||||||||||
| Net Income | 1,91,030 | |||||||||||
| Depreciation | 2,95,680 | |||||||||||
| Annual cash flow | 4,86,710 | |||||||||||
| Step-2:Calculation of NPV | ||||||||||||
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Total | |||
| Operating cash flow | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | ||||
| Release of net working caital | 1,30,139 | |||||||||||
| After tax sale of asset | 88,440 | |||||||||||
| Cash flow | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 4,86,710 | 7,05,289 | ||||
| Discount factor | 0.7692 | 0.5917 | 0.4552 | 0.3501 | 0.2693 | 0.2072 | 0.1594 | 0.1226 | ||||
| Present Value | 3,74,392.62 | 2,87,994.32 | 2,21,534.09 | 1,70,410.84 | 1,31,085.26 | 1,00,834.82 | 77,565.24 | 86,461.06 | 14,50,278.24 | |||
| Less: Initial Investment | ||||||||||||
| Cost of fixed assets | 14,78,400 | |||||||||||
| Cost of Net Woring Capital | 1,30,139 | 16,08,539.00 | ||||||||||
| NPV | -1,58,260.76 | |||||||||||
| Now , Calculation of IRR is made as follows: | ||||||||||||
| Discount rate | 13% | 30% | ||||||||||
| NPV | 8,09,293.06 | -1,58,260.76 | ||||||||||
| IRR | = | L+(H-L)*(A/(A-B)) | Where, | |||||||||
| = | 13%+(30%-13%)*(809293.06/967553.81) | L | 13% | |||||||||
| = | 27.22% | H | 20% | |||||||||
| A | 8,09,293.06 | |||||||||||
| B | -1,58,260.76 | |||||||||||
| A-B | 9,67,553.81 | |||||||||||
