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One year ago your company purchased a machine for $110,000. You have learned that the new,...

One year ago your company purchased a machine for $110,000. You have learned that the new, much better machine is available for $150,000. In will be depreciated on a straight line basis and has no salvage value. You expect the machine to produce $60,000 per year in revenue and cost $20,000 per year to operate for the next ten years. The current machine is expected to produce $40,000 per year in revenue and also costs $20,000 per year to operate. The current machine’s depreciation expense is $10,000 per for the next 10 years, after which it will be discarded. It will have no salvage value. The market value of the current machine today is $50,000. Your company’s tax rate is 45% and the opportunity cost of capital is 10%. Should your company replace its year-old machine

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Expert Solution

Time line 0 1 2 3 4 5 6 7 8 9 10
Proceeds from sale of existing asset =selling price* ( 1 -tax rate) 27500
Tax shield on existing asset book value =Book value * tax rate 45000
Cost of new machine -150000
=Initial Investment outlay -77500
Incremental Profits 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000
-Depreciation Cost of equipment/no. of years -15000 -15000 -15000 -15000 -15000 -15000 -15000 -15000 -15000 -15000
=Pretax cash flows 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000
-taxes =(Pretax cash flows)*(1-tax) 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750
+Depreciation 15000 15000 15000 15000 15000 15000 15000 15000 15000 15000
=after tax operating cash flow 17750 17750 17750 17750 17750 17750 17750 17750 17750 17750
+Tax shield on salvage book value =Salvage value * tax rate 0
=Terminal year after tax cash flows 0
Total Cash flow for the period -77500 17750 17750 17750 17750 17750 17750 17750 17750 17750 17750
Discount factor= (1+discount rate)^corresponding period 1 1.1 1.21 1.331 1.4641 1.61051 1.771561 1.9487171 2.1435888 2.357948 2.593742
Discounted CF= Cashflow/discount factor -77500 16136.36364 14669.421 13335.838 12123.489 11021.353 10019.412 9108.556599 8280.506 7527.733 6843.393
NPV= Sum of discounted CF= 31566.06613

Buy new machine as incremental NPV is positive

jeff jeffy answered 9 months ago
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