Question

Lang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $268,000, has a four-year life, and requires $82,000 in pretax annual operating costs. System B costs $378,000, has a six-year life, and requires $76,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever project is chosen, it will not be replaced when it wears out. The tax rate is 35 percent and the discount rate is 10 percent.

Calculate the NPV for both conveyor belt systems.

Answer 1

System A

Time line		0	1	2	3	4
Cost of new machine		-268000
=Initial Investment outlay		-268000
Sales			0	0	0	0
Profits	Sales-variable cost		0	0	0	0
Operating cost			-82000	-82000	-82000	-82000
-Depreciation	Cost of equipment/no. of years		-67000	-67000	-67000	-67000
=Pretax cash flows			-149000	-149000	-149000	-149000
-taxes	=(Pretax cash flows)*(1-tax)		-96850	-96850	-96850	-96850
+Depreciation			67000	67000	67000	67000
=after tax operating cash flow			-29850	-29850	-29850	-29850
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						0
Total Cash flow for the period		-268000	-29850	-29850	-29850	-29850
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor	-268000	-27136.4	-24669.4	-22426.75	-20387.95
NPV=	Sum of discounted CF=	-362620.4836

System B

Time line		0	1	2	3	4	5	6
Cost of new machine		-378000
=Initial Investment outlay		-378000
Sales			0	0	0	0	0	0
Profits	Sales-variable cost		0	0	0	0	0	0
Operating cost			-76000	-76000	-76000	-76000	-76000	-76000
-Depreciation	Cost of equipment/no. of years		-63000	-63000	-63000	-63000	-63000	-63000
=Pretax cash flows			-139000	-139000	-139000	-139000	-139000	-139000
-taxes	=(Pretax cash flows)*(1-tax)		-90350	-90350	-90350	-90350	-90350	-90350
+Depreciation			63000	63000	63000	63000	63000	63000
=after tax operating cash flow			-27350	-27350	-27350	-27350	-27350	-27350
+Tax shield on salvage book value	=Salvage value * tax rate							0
=Terminal year after tax cash flows								0
Total Cash flow for the period		-378000	-27350	-27350	-27350	-27350	-27350	-27350
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051	1.771561
Discounted CF=	Cashflow/discount factor	-378000	-24863.6	-22603.3	-20548.46	-18680.42	-16982.2	-15438.36
NPV=	Sum of discounted CF=	-497116.3801