Question

Matta manufacturing is trying to decide between two different conveyor belt systems. System A costs $264,000, has a four year-life, and requires $81,000 in pretax annual operating costs. System B costs $372,000, has a six year life, and requires $75,000 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 system is chosen, it will not be replaced when it wears out. The tax rate is 34 percent and the discount rate is 8 percent.

A/ Calculate the NPV for both conveyor belt systems

B/ Which conveyor belt system should the firm choose?

Answer 1

System A

Time line		0	1	2	3	4
Cost of new machine		-264000
=Initial Investment outlay		-264000
							100.00%
Sales			0	0	0	0
Profits	Sales-variable cost		0	0	0	0
Operating cost			-81000	-81000	-81000	-81000
-Depreciation	Cost of equipment/no. of years		-66000	-66000	-66000	-66000	0	=Salvage Value
=Pretax cash flows			-147000	-147000	-147000	-147000
-taxes	=(Pretax cash flows)*(1-tax)		-97020	-97020	-97020	-97020
+Depreciation			66000	66000	66000	66000
=after tax operating cash flow			-31020	-31020	-31020	-31020
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						0
Total Cash flow for the period		-264000	-31020	-31020	-31020	-31020
Discount factor=	(1+discount rate)^corresponding period	1	1.08	1.1664	1.259712	1.360489
Discounted CF=	Cashflow/discount factor	-264000	-28722.22	-26594.65	-24624.68	-22800.63
NPV=	Sum of discounted CF=	-366742.17

System B

Time line		0	1	2	3	4	5	6
Cost of new machine		-372000
=Initial Investment outlay		-372000
									100.00%
Sales			0	0	0	0	0	0
Profits	Sales-variable cost		0	0	0	0	0	0
Operating cost			-75000	-75000	-75000	-75000	-75000	-75000
-Depreciation	Cost of equipment/no. of years		-62000	-62000	-62000	-62000	-62000	-62000	0	=Salvage Value
=Pretax cash flows			-137000	-137000	-137000	-137000	-137000	-137000
-taxes	=(Pretax cash flows)*(1-tax)		-90420	-90420	-90420	-90420	-90420	-90420
+Depreciation			62000	62000	62000	62000	62000	62000
=after tax operating cash flow			-28420	-28420	-28420	-28420	-28420	-28420
+Tax shield on salvage book value	=Salvage value * tax rate							0
=Terminal year after tax cash flows								0
Total Cash flow for the period		-372000	-28420	-28420	-28420	-28420	-28420	-28420
Discount factor=	(1+discount rate)^corresponding period	1	1.08	1.1664	1.259712	1.360489	1.4693281	1.5868743
Discounted CF=	Cashflow/discount factor	-372000	-26314.81	-24365.57	-22560.71	-20889.55	-19342.17	-17909.42
NPV=	Sum of discounted CF=	-503382.24

B

System A

Year or period		0	1	2	3	4
EAC			-110727.1	-110727.1	-110727.1	-110727.1
Discount factor=	(1+discount rate)^corresponding period		1.08	1.1664	1.259712	1.360489
Discounted CF=	Cashflow/discount factor		-102525.1	-94930.63	-87898.73	-81387.72
NPV=	-366742.17
EAC is equivalent yearly CF with same NPV =	-110727.091

System B

Year or period		0	1	2	3	4	5	6
EAC			-108889.3	-108889.3	-108889.3	-108889.3	-108889.3	-108889.3
Discount factor=	(1+discount rate)^corresponding period		1.08	1.1664	1.259712	1.360489	1.4693281	1.5868743
Discounted CF=	Cashflow/discount factor		-100823.4	-93355.04	-86439.86	-80036.9	-74108.24	-68618.74
NPV=	-503382.24
EAC is equivalent yearly CF with same NPV =	-108889.3237

Choose System B as it has higher EAC