Question

# A firm is considering an investment into a new machine with a price of \$18 million...

A firm is considering an investment into a new machine with a price of \$18 million to replace its existing machine. The current machine has a book value of \$6 million and a market value of \$4.5 million. The new machine is expected to have a four-year life, and also the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save \$6.5 million in cash operating costs each year over the next four years. Both machines will have no book value (e.g. they are fully depreciated) and no salvage value in four years (you may assume linear depreciation). If the firm purchases the new machine, it will also need an additional investment of \$600,000 in net working capital during the project lifetime. The required return on the investment is 10 percent, and the tax rate is 40 percent. Should the company replace the old machine based on NPV?

 Time line 0 1 2 3 4 Proceeds from sale of existing asset =selling price* ( 1 -tax rate) 2700000 Tax shield on existing asset book value =Book value * tax rate 2400000 Cost of new machine 18000000 Initial working capital -600000 =Initial Investment outlay 22500000 100.00% Savings 6500000 6500000 6500000 6500000 -Depreciation Cost of equipment/no. of years 4500000 4500000 4500000 4500000 0 =Salvage Value =Pretax cash flows 11000000 11000000 11000000 11000000 -taxes =(Pretax cash flows)*(1-tax) 6600000 6600000 6600000 6600000 +Depreciation -4500000 -4500000 -4500000 -4500000 =after tax operating cash flow 2100000 2100000 2100000 2100000 reversal of working capital 600000 +Tax shield on salvage book value =Salvage value * tax rate 0 =Terminal year after tax cash flows 600000 Total Cash flow for the period 22500000 2100000 2100000 2100000 2700000 Discount factor= (1+discount rate)^corresponding period 1 1.1 1.21 1.331 1.4641 Discounted CF= Cashflow/discount factor 22500000 1909090.909 1735537.19 1577761.082 1844136.3 NPV= Sum of discounted CF= 29566525.51

Replace as NPV is positive

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