Question

A firm is considering an investment in a new machine with a price of $15.6 million to replace its existing machine. The current machine has a book value of $5.4 million and a market value of $4.1 million. The new machine is expected to have a 4-year life, and 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 $6.3 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it also will need an investment of $250,000 in net working capital. The required return on the investment is 10 percent and the tax rate is 21 percent. The company uses straight-line depreciation. What are the NPV and IRR of the decision to replace the old machine?

Answer 1

Time line		0	1	2	3	4
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	3239000
Tax shield on existing asset book value	=Book value * tax rate	1134000
Cost of new machine		-15600000
Initial working capital		-250000
=Initial Investment outlay		-11477000
Savings			6E+06	6300000	6300000	6300000
-Depreciation	Cost of equipment/no. of years		-4E+06	-3900000	-3900000	-3900000
=Pretax cash flows			2E+06	2400000	2400000	2400000
-taxes	=(Pretax cash flows)*(1-tax)		2E+06	1896000	1896000	1896000
+Depreciation			4E+06	3900000	3900000	3900000
=after tax operating cash flow			6E+06	5796000	5796000	5796000
reversal of working capital						250000
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						250000
Total Cash flow for the period		-11477000	6E+06	5796000	5796000	6046000
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor	-11477000	5E+06	4790083	4354620.6	4129499.4
NPV=	Sum of discounted CF=	7066293.491

Total Cash flow for the period		-11477000	6E+06	5796000	5796000	6046000
Discount factor=	(1+discount rate)^corresponding period	1	1.3594	1.848074	2.5123436	3.4153776
Discounted CF=	Cashflow/discount factor	-11477000	4E+06	3136238	2307009.2	1770228.9
NPV=	Sum of discounted CF=	0
IRR is discount rate at which NPV = 0 =	35.94%