Question

Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $1,850,000 and will last for 4 years. Variable costs are 39 percent of sales, and fixed costs are $123,000 per year. Machine B costs $4,420,000 and will last for 7 years. Variable costs for this machine are 29 percent of sales and fixed costs are $124,000 per year. The sales for each machine will be $8.84 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis.

(a)	If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine A?(Do not round your intermediate calculations.)

(b)	If the company plans to replace the machine when it wears out on a perpetual basis, what is the EAC for machine B? (Do not round your intermediate calculations.)

Answer 1

a)

Time line		0	1	2	3	4
Cost of new machine		-1850000
=Initial Investment outlay		-1850000
Sales			8840000	8840000	8840000	8840000
Profits	Sales-variable cost		5392400	5392400	5392400	5392400
Fixed cost			-123000	-123000	-123000	-123000
-Depreciation	Cost of equipment/no. of years		-462500	-462500	-462500	-462500
=Pretax cash flows			4806900	4806900	4806900	4806900
-taxes	=(Pretax cash flows)*(1-tax)		3124485	3124485	3124485	3124485
+Depreciation			462500	462500	462500	462500
=after tax operating cash flow			3586985	3586985	3586985	3586985
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						0
Total Cash flow for the period		-1850000	3586985	3586985	3586985	3586985
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor	-1850000	3260895.5	2964450.41	2694954.9	2449959
NPV=	Sum of discounted CF=	9520259.81
					IRR False False Center Center 0
EAC	3003364.013
Year or period		0	1	2	3	4
EAC			3003364	3003364.01	3003364	3003364
Discount factor=	(1+discount rate)^corresponding period		1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor		2730330.9	2482119.02	2256471.8	2051338
NPV=	9520259.808
EAC is equivalent yearly CF with same NPV =	3003364.013

b)

Time line		0	1	2	3	4	5	6	7
Cost of new machine		-4420000
=Initial Investment outlay		-4420000
Sales			8840000	8840000	8840000	8840000	8840000	8840000	8840000
Profits	Sales-variable cost		6276400	6276400	6276400	6276400	6276400	6276400	6276400
Fixed cost			-124000	-124000	-124000	-124000	-124000	-124000	-124000
-Depreciation	Cost of equipment/no. of years		-631428.6	-631428.57	-631428.6	-631428.6	-631429	-631428.6	-631429
=Pretax cash flows			5520971.4	5520971.43	5520971.4	5520971.4	5520971	5520971.4	5520971
-taxes	=(Pretax cash flows)*(1-tax)		3588631.4	3588631.43	3588631.4	3588631.4	3588631	3588631.4	3588631
+Depreciation			631428.57	631428.571	631428.57	631428.57	631428.6	631428.57	631428.6
=after tax operating cash flow			4220060	4220060	4220060	4220060	4220060	4220060	4220060
+Tax shield on salvage book value	=Salvage value * tax rate								0
=Terminal year after tax cash flows									0
Total Cash flow for the period		-4420000	4220060	4220060	4220060	4220060	4220060	4220060	4220060
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051	1.771561	1.948717
Discounted CF=	Cashflow/discount factor	-4420000	3836418.2	3487652.89	3170593.5	2882357.8	2620325	2382113.9	2165558
NPV=	Sum of discounted CF=	16125019.5
					IRR False False Center Center 0
EAC	3312167.691
Year or period		0	1	2	3	4	5	6	7
EAC			3312167.7	3312167.69	3312167.7	3312167.7	3312168	3312167.7	3312168
Discount factor=	(1+discount rate)^corresponding period		1.1	1.21	1.331	1.4641	1.61051	1.771561	1.948717
Discounted CF=	Cashflow/discount factor		3011061.5	2737328.67	2488480.6	2262255.1	2056596	1869632.3	1699666
NPV=	16125019.52
EAC is equivalent yearly CF with same NPV =	3312167.691