One year ago, your company purchased a machine used in manufacturing for $ 105 comma 000....
One year ago, your company purchased a machine used in manufacturing for $ 105 comma 000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 150 comma 000 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 $ 45 comma 000 per year for the next 10 years. The current machine is expected to produce a gross margin of $ 23 comma 000 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 $ 9 comma 545 per year. The market value today of the current machine is $ 60 comma 000. Your company's tax rate is 38 %, and the opportunity cost of capital for this type of equipment is 10 %. Should your company replace its year-old machine? The NPV of replacing the year-old machine is
Homework Answers
Answer:
Current Machine:
Book value now = Purchase cost - Depreciation for 1 year = 105000 - $9545 =$95455
Market value now = $60,000
Loss on sale = 95455 - 60000 = $35455
Tax benefit on loss = 35455 * 38% = $13472.90
Sales proceeds including tax benefit = 60000 + 13472.90 = $73,472.90
Year 0 cash out flow:
Initial investment = New machine cost - Sales proceeds of current machine including tax benefit
= 150000 - 73472.90
= $76,527.10
Annual cash flow:
Gross margin new machine = $45,000
Gross margin current machine = $23,000
Incremental margin net of tax =(45000 - 23000) * (1 - 38%) = $13,640
Annual depreciation new machine = 150000 / 10 = $15,000
Incremental depreciation = 15000 - 9545 = $5455
Depreciation tax shield = 5455 * 38% = $2072.90
Annual cash flow = 13640 + 2072.90 = $15,712.90
NPV = Annual cash flow * PV of $1 annuity for 10 years at 10% rate - Initial investment
= 15712.90 * (1 - 1 /(1 +10%) 10) / 10% - 76527.10
= $20021.87
NPV = $20,022
[Note: The depreciation of current machine is taken as $9545 as given in the question. However of we take exact depreciation (105000/ 11=) $9545.45, then NPV will work out at $20,020.64 or $20,021.]
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One year ago, your company purchased a machine used in
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