Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,920,000; the new one will cost, $2,339,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $630,000 after five years.

The old computer is being depreciated at a rate of $456,000 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 $666,000; in two years, it will probably be worth $198,000. The new machine will save us $401,000 per year in operating costs. The tax rate is 23 percent, and the discount rate is 10 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

Calculation for life of old machine

Old machine accounting life = integer value of(purchase price/yearly depr)

= integer value of (1920000/456000)

= integer value of (4.21)

=4

Salvage value = Purchase price-annual depr*life

Salvage value = 1920000-456000*4

Salvage value = 96000

Current BV of old machine = annual depr*(total life -remaining life)+salvage value

Current BV of old machine = 456000*(4 -2+96000)

Current BV of old machine = 1008000

a-1

old machine

Time line		0	1	2	3	4
Cost of new machine		-1920000
=Initial Investment outlay		-1920000
							100.00%
Sales			0	0	0	0
Profits	Sales-variable cost		0	0	0	0
-Depreciation	(Cost of equipment-salvage value)/no. of years		-504000	-504000	-504000	-504000	-96000	=Salvage Value
=Pretax cash flows			-504000	-504000	-504000	-504000
-taxes	=(Pretax cash flows)*(1-tax)		-388080	-388080	-388080	-388080
+Depreciation			504000	504000	504000	504000
=after tax operating cash flow			115920	115920	115920	115920
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)					152460
+Tax shield on salvage book value	=Salvage value * tax rate					-22080
=Terminal year after tax cash flows						130380
Total Cash flow for the period		-1920000	115920	115920	115920	246300
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor	-1920000	105381.8182	95801.65289	87092.41172	168226.21
NPV=	Sum of discounted CF=	-1463497.90

Year or period		0	1	2	3	4
EAC			-461690.859	-461690.859	-461690.859	-461690.9
Discount factor=	(1+discount rate)^corresponding period		1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor		-419718.962	-381562.693	-346875.176	-315341.1
NPV=	-1463497.9
EAC is equivalent yearly CF with same NPV =	-461690.86

New machine

Time line		0	1	2	3	4	5
Cost of new machine		-2339000
=Initial Investment outlay		-2339000
								100.00%
Savings			401000	401000	401000	401000	401000
-Depreciation	Cost of equipment/no. of years		-467800	-467800	-467800	-467800	-467800	0	=Salvage Value
=Pretax cash flows			-66800	-66800	-66800	-66800	-66800
-taxes	=(Pretax cash flows)*(1-tax)		-51436	-51436	-51436	-51436	-51436
+Depreciation			467800	467800	467800	467800	467800
=after tax operating cash flow			416364	416364	416364	416364	416364
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						485100
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							485100
Total Cash flow for the period		-2339000	416364	416364	416364	416364	901464
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051
Discounted CF=	Cashflow/discount factor	-2339000	378512.7273	344102.4793	312820.4358	284382.21	559738.22
NPV=	Sum of discounted CF=	-459443.92

Year or period		0	1	2	3	4	5
EAC			-121200.149	-121200.149	-121200.149	-121200.1	-121200.1
Discount factor=	(1+discount rate)^corresponding period		1.1	1.21	1.331	1.4641	1.61051
Discounted CF=	Cashflow/discount factor		-110181.953	-100165.412	-91059.4656	-82781.33	-75255.76
NPV=	-459443.92
EAC is equivalent yearly CF with same NPV =	-121200.15

a-2