Question

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?

Answer 1

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