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A&Y Inc. considers a 7-year project that requires $500,000 of investment in new machinery and $40,000...
A&Y Inc. considers a 7-year project that requires $500,000 of investment in new machinery and $40,000 in NWC (that will stay constant for the entire life of the project). At the end of the project the equipment will be sold for a salvage value of $70,000. The cost of capital is 10%, the equipment belongs to a CCA class with d=40%, and the corporate tax rate is 30%
Problem 20: Prof Reynolds was able to use his industry connections to get a 3% discount on the equipment (i.e., it can be purchased for $485,000 instead of $500,000). By how much will this increase the project’s NPV?
Solutions
Expert Solution
| Tax rate | 30% | ||||||||
| Calculation of annual depreciation | |||||||||
| Depreciation | Year-1 | Year-2 | Year-3 | Year-4 | Year-5 | Year-6 | Year-7 | Total | |
| Cost | $ 500,000 | $ 300,000 | $ 180,000 | $ 108,000 | $ 64,800 | $ 38,880 | $ 23,328 | ||
| Dep Rate | 40.00% | 40.00% | 40.00% | 40.00% | 40.00% | 40.00% | 40.00% | ||
| Depreciation | Cost * Dep rate | $ 200,000 | $ 120,000 | $ 72,000 | $ 43,200 | $ 25,920 | $ 15,552 | $ 9,331 | $ 486,003 |
| Closing WDV | $ 300,000 | $ 180,000 | $ 108,000 | $ 64,800 | $ 38,880 | $ 23,328 | $ 13,997 | ||
| Calculation of annual depreciation after discount | |||||||||
| Depreciation | Year-1 | Year-2 | Year-3 | Year-4 | Year-5 | Year-6 | Year-7 | Total | |
| Cost | $ 485,000 | $ 291,000 | $ 174,600 | $ 104,760 | $ 62,856 | $ 37,714 | $ 22,628 | ||
| Dep Rate | 40.00% | 40.00% | 40.00% | 40.00% | 40.00% | 40.00% | 40.00% | ||
| Depreciation | Cost * Dep rate | $ 194,000 | $ 116,400 | $ 69,840 | $ 41,904 | $ 25,142 | $ 15,085 | $ 9,051 | $ 471,423 |
| Closing WDV | $ 291,000 | $ 174,600 | $ 104,760 | $ 62,856 | $ 37,714 | $ 22,628 | $ 13,577 | ||
| Differential depreciation | $ 6,000 | $ 3,600 | $ 2,160 | $ 1,296 | $ 778 | $ 467 | $ 280 | ||
| Tax benefit | $ 1,800 | $ 1,080 | $ 648 | $ 389 | $ 233 | $ 140 | $ 84 | ||
| Calculation of after-tax salvage value | Without discount | With discount | |||||||
| Cost of machine | $ 500,000 | $ 485,000 | |||||||
| Depreciation | $ 486,003 | $ 471,423 | |||||||
| WDV | Cost less accumulated depreciation | $ 13,997 | $ 13,577 | ||||||
| Sale price | $ 70,000 | $ 70,000 | |||||||
| Profit/(Loss) | Sale price less WDV | $ 56,003 | $ 56,423 | ||||||
| Tax | Profit/(Loss)*tax rate | $ 16,801 | $ 16,927 | ||||||
| Sale price after-tax | Sale price less tax | $ 53,199 | $ 53,073 | ||||||
| Differential salvage value | $ 126 | ||||||||
| Calculation of differential NPV | |||||||||
| (1) | 10.00% | ||||||||
| Year | Capital | Operating cash | Annual Cash flow | PV factor, 1/(1+r)^time | Present values | ||||
| 0 | $ 15,000 | $ 15,000 | 1.0000 | $ 15,000.00 | |||||
| 1 | $ (1,800.00) | $ (1,800) | 0.9091 | $ (1,636.36) | |||||
| 2 | $ (1,080.00) | $ (1,080) | 0.8264 | $ (892.56) | |||||
| 3 | $ (648.00) | $ (648) | 0.7513 |
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