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One year​ ago, your company purchased a machine used in manufacturing for $95,000. You have learned...

One year​ ago, your company purchased a machine used in manufacturing for $95,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $165,000 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 $40,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $22,000 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 $8,636 per year. The market value today of the current machine is $50,000. 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?

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Expert Solution

book value of old equipment

Book value = (purchase price)*remaining life/total life
= (95000)*10/11
= 86363.64
Time line 0 1 2 3 4 5 6 7 8 9 10
Proceeds from sale of existing asset =selling price* ( 1 -tax rate) 29000
Tax shield on existing asset book value =Book value * tax rate 36272.7288
Cost of new machine -165000
=Initial Investment outlay -99727.2712
Profits 18000 18000 18000 18000 18000 18000 18000 18000 18000 18000
-Depreciation Cost of equipment/no. of years -16500 -16500 -16500 -16500 -16500 -16500 -16500 -16500 -16500 -16500
=Pretax cash flows 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500
-taxes =(Pretax cash flows)*(1-tax) 870 870 870 870 870 870 870 870 870 870
+Depreciation 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500
=after tax operating cash flow 17370 17370 17370 17370 17370 17370 17370 17370 17370 17370
+Tax shield on salvage book value =Salvage value * tax rate 0
=Terminal year after tax cash flows 0
Total Cash flow for the period -99727.2712 17370.00 17370.0000 17370.00 17370 17370 17370 17370 17370 17370 17370
Discount factor= (1+discount rate)^corresponding period 1 1.11 1.2321 1.367631 1.5180704 1.6850582 1.8704146 2.07616 2.3045378 2.558037 2.839421
Discounted CF= Cashflow/discount factor -99727.2712 15648.64865 14097.88167 12700.79429 11442.157 10308.25 9286.7113 8366.407 7537.3032 6790.363 6117.444
NPV= Sum of discounted CF= 2568.688834

Buy new machine as NPV is positive

jeff jeffy answered 1 year ago
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