Question

You are considering two different systems for pollution control. System 1 costs $960,000 has an eight year life, and has a pre-tax operating cost of $7,150 per year. System Two costs $580,000, has a five year life and has a pre-tax operating cost of $35,000 per year. Fort both systems use straight line depreciation and assume neither system has any salvage value. If your tax rate is 39% and your discount rate is 13%, which do you prefer?

Answer 1

System 1

Time line		0	1	2	3	4	5	6	7	8
Cost of new machine		-960000
=Initial Investment outlay		-960000
Sales			0	0	0	0	0	0	0	0
Profits	Sales-variable cost		0	0	0	0	0	0	0	0
Operating cost			-7150	-7150	-7150	-7150	-7150	-7150	-7150	-7150
-Depreciation	Cost of equipment/no. of years		-120000	-120000	-120000	-120000	-120000	-120000	-120000	-120000
=Pretax cash flows			-127150	-127150	-127150	-127150	-127150	-127150	-127150	-127150
-taxes	=(Pretax cash flows)*(1-tax)		-77561.5	-77561.5	-77561.5	-77561.5	-77561.5	-77561.5	-77561.5	-77561.5
+Depreciation			120000	120000	120000	120000	120000	120000	120000	120000
=after tax operating cash flow			42438.50	42438.5	42438.5	42438.5	42438.5	42438.5	42438.5	42438.5
+Tax shield on salvage book value	=Salvage value * tax rate									0
=Terminal year after tax cash flows										0
Total Cash flow for the period		-960000	42438.5	42438.5	42438.5	42438.5	42438.5	42438.5	42438.5	42438.5
Discount factor=	(1+discount rate)^corresponding period	1	1.13	1.2769	1.442897	1.6304736	1.8424352	2.0819518	2.352605	2.6584442
Discounted CF=	Cashflow/discount factor	-960000	37556.19469	33235.57	29412.009	26028.327	23033.918	20383.998	18038.94	15963.66
NPV=	Sum of discounted CF=	-756347.39

System 2

Time line		0	1	2	3	4	5
Cost of new machine		-580000
=Initial Investment outlay		-580000
Sales			0	0	0	0	0
Profits	Sales-variable cost		0	0	0	0	0
Operating cost			-35000	-35000	-35000	-35000	-35000
-Depreciation	Cost of equipment/no. of years		-116000	-116000	-116000	-116000	-116000
=Pretax cash flows			-151000	-151000	-151000	-151000	-151000
-taxes	=(Pretax cash flows)*(1-tax)		-92110	-92110	-92110	-92110	-92110
+Depreciation			116000	116000	116000	116000	116000
=after tax operating cash flow			23890.00	23890	23890	23890	23890
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
Total Cash flow for the period		-580000	23890	23890	23890	23890	23890
Discount factor=	(1+discount rate)^corresponding period	1	1.13	1.2769	1.442897	1.6304736	1.8424352
Discounted CF=	Cashflow/discount factor	-580000	21141.59292	18709.37	16556.968	14652.184	12966.535
NPV=	Sum of discounted CF=	-495973.35

Choose system 2 as it has higher NPV