Question

In: Finance

One year​ ago, your company purchased a machine used in manufacturing for $105,000. You have learned...

One year​ ago, your company purchased a machine used in manufacturing for $105,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $140,000 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 $35,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $20,000 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 $9,545 per year. The market value today of the current machine is $65,000. Your​ company's tax rate is 45%​, and the opportunity cost of capital for this type of equipment is 11%. Should your company replace its​ year-old machine?

Solutions

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) 35750
Tax shield on existing asset book value =Book value * tax rate = (105000-9545)*0.45 42954.75
Cost of new machine -140000
=Initial Investment outlay -61295.25
Incremental Profits =35000-20000 15000 15000 15000 15000 15000 15000 15000 15000 15000 15000
-Depreciation Cost of equipment/no. of years -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000
=Pretax cash flows 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
-taxes =(Pretax cash flows)*(1-tax) 550 550 550 550 550 550 550 550 550 550
+Depreciation 14000 14000 14000 14000 14000 14000 14000 14000 14000 14000
=after tax operating cash flow 14550 14550 14550 14550 14550 14550 14550 14550 14550 14550
+Tax shield on salvage book value =Salvage value * tax rate 0
=Terminal year after tax cash flows 0
Total Cash flow for the period -61295.25 14550 14550 14550 14550 14550 14550 14550 14550 14550 14550
Discount factor= (1+discount rate)^corresponding period 1 1.11 1.2321 1.367631 1.5180704 1.6850582 1.8704146 2.07616 2.30454 2.558037 2.839421
Discounted CF= Cashflow/discount factor -61295.25 13108.108 11809.1064 10638.835 9584.5357 8634.7168 7779.0242 7008.13 6313.63 5687.955 5124.284
NPV= Sum of discounted CF= 24393.07576

Replace project as NPV is positive


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