Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,660,000; the new one will cost, $2,001,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $435,000 after five years.

The old computer is being depreciated at a rate of $352,000 per year. It will be completely written off in three years. If we don’t replace it now, we will have to replace it in two years. We can sell it now for $549,000; in two years, it will probably be worth $159,000. The new machine will save us $373,000 per year in operating costs. The tax rate is 25 percent, and the discount rate is 12 percent.

a-1.  
Calculate the EAC for the the old computer and the new computer. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

a-2.   What is the NPV of the decision to replace the computer now? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a-1

old machine

Time line		0	1	2	3	4
Cost of new machine		-1660000
=Initial Investment outlay		-1660000
							100.00%
Sales			0	0	0	0
Profits	Sales-variable cost		0	0	0	0
-Depreciation	(Cost of equipment-salvage value)/no. of years		-478000	-478000	-478000	-478000	-252000	=Salvage Value
=Pretax cash flows			-478000	-478000	-478000	-478000
-taxes	=(Pretax cash flows)*(1-tax)		-358500	-358500	-358500	-358500
+Depreciation			478000	478000	478000	478000
=after tax operating cash flow			119500	119500	119500	119500
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)					119250
+Tax shield on salvage book value	=Salvage value * tax rate					-63000
=Terminal year after tax cash flows						56250
Total Cash flow for the period		-1660000	119500	119500	119500	175750
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928	1.5735194
Discounted CF=	Cashflow/discount factor	-1660000	106696.4286	95264.66837	85057.73961	111692.3
NPV=	Sum of discounted CF=	-1261288.86

Year or period		0	1	2	3	4
EAC			-415259.727	-415259.727	-415259.727	-415259.7
Discount factor=	(1+discount rate)^corresponding period		1.12	1.2544	1.404928	1.5735194
Discounted CF=	Cashflow/discount factor		-370767.613	-331042.512	-295573.671	-263905.1
NPV=	-1261288.86
EAC is equivalent yearly CF with same NPV =	-415259.73

new machine

Time line		0	1	2	3	4	5
Cost of new machine		-2001000
=Initial Investment outlay		-2001000
								100.00%
Savings			373000	373000	373000	373000	373000
-Depreciation	Cost of equipment/no. of years		-400200	-400200	-400200	-400200	-400200	0	=Salvage Value
=Pretax cash flows			-27200	-27200	-27200	-27200	-27200
-taxes	=(Pretax cash flows)*(1-tax)		-20400	-20400	-20400	-20400	-20400
+Depreciation			400200	400200	400200	400200	400200
=after tax operating cash flow			379800	379800	379800	379800	379800
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						326250
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							326250
Total Cash flow for the period		-2001000	379800	379800	379800	379800	706050
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928	1.5735194	1.7623417
Discounted CF=	Cashflow/discount factor	-2001000	339107.1429	302774.2347	270334.1381	241369.77	400631.73
NPV=	Sum of discounted CF=	-446782.99

Year or period		0	1	2	3	4	5
EAC			-123941.949	-123941.949	-123941.949	-123941.9	-123941.9
Discount factor=	(1+discount rate)^corresponding period		1.12	1.2544	1.404928	1.5735194	1.7623417
Discounted CF=	Cashflow/discount factor		-110662.455	-98805.7633	-88219.4315	-78767.35	-70327.99
NPV=	-446782.99
EAC is equivalent yearly CF with same NPV =	-123941.95

a-2