Question
In: Finance
One year ago, your company purchased a machine used in manufacturing for $115000. You have learned...
One year ago, your company purchased a machine used in manufacturing for $115000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 165000 today. It will be depreciated on a straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin (revenues minus operating expenses other than depreciation) of $45000 per year for the next 10 years. The current machine is expected to produce a gross margin of $ 22000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, and has no salvage value, so depreciation expense for the current machine is $ 10455 per year. The market value today of the current machine is $60000. Your company's tax rate is 42%, and the opportunity cost of capital for this type of equipment is 11%. Should your company replace its year-old machine?
The NPV of replacing the year-old machine is $____. (Round to the nearest dollar.)
Solutions
Expert Solution
| Calculation of after tax amount received if old machine is replaced | |||||||||||
| Proceeds from sale | $60,000.00 | ||||||||||
| Less: Book value | $104,545.00 | (115000-10455) | |||||||||
| Loss on sale | -$44,545.00 | ||||||||||
| Tax benefit @ 42% | $18,708.90 | ||||||||||
| After tax amount | $78,708.90 | ||||||||||
| Cash outflow today | New machine - After tax amount on old machine | ||||||||||
| Cash outflow today | 165000-78708.90 | ||||||||||
| Cash outflow today | $86,291.10 | ||||||||||
| Incremental gross margin if old machine is replaced | |||||||||||
| Incremental gross margin | 45000-22000 | ||||||||||
| Incremental gross margin | $23,000 | ||||||||||
| Depreciation on new machine | (165000/10) | ||||||||||
| Depreciation on new machine | $16,500 | ||||||||||
| Incremental depreciation if old machine is replaced | |||||||||||
| Incremental depreciation | 16500-10455 | ||||||||||
| Incremental depreciation | $6,045 | ||||||||||
| Calculation of NPV of replacing the old machine | |||||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Incremental gross margin | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | $23,000.00 | |
| Less: Incremental depreciation | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | |
| Profit before taxes | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | $16,955.00 | |
| Less: Taxes @ 42% | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | $7,121.10 | |
| Net income | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | $9,833.90 | |
| Add: Depreciation | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | $6,045.00 | |
| Net operating cash flow | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | |
| Initial cash outflow | -$86,291.10 | ||||||||||
| Net cash flow | -$86,291.10 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 | $15,878.90 |
| Discount factor @ 11% | $1.00000 | $0.90090 | $0.81162 | $0.73119 | $0.65873 | $0.59345 | $0.53464 | $0.48166 | $0.43393 | $0.39092 | $0.35218 |
| Present value | -$86,291.10 | $14,305.32 | $12,887.67 | $11,610.51 | $10,459.92 | $9,423.35 | $8,489.51 | $7,648.21 | $6,890.28 | $6,207.46 | $5,592.30 |
| Net present value | $7,223.43 | ||||||||||
| Thus, NPV of replacing the year old machine is $7223. | |||||||||||
| Since NPV is positive the year old machine should be replaced | |||||||||||
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