Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,800,000; the new one will cost, $2,183,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $540,000 after five years.

The old computer is being depreciated at a rate of $408,000 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 $612,000; in two years, it will probably be worth $180,000. The new machine will save us $359,000 per year in operating costs. The tax rate is 22 percent, and the discount rate is 9 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		-1800000
=Initial Investment outlay		-1800000
							100.00%
Sales			0	0	0	0
Profits	Sales-variable cost		0	0	0	0
-Depreciation	(Cost of equipment-salvage value)/no. of years		-492000	-492000	-492000	-492000	-168000	=Salvage Value
=Pretax cash flows			-492000	-492000	-492000	-492000
-taxes	=(Pretax cash flows)*(1-tax)		-383760	-383760	-383760	-383760
+Depreciation			492000	492000	492000	492000
=after tax operating cash flow			108240	108240	108240	108240
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)					140400
+Tax shield on salvage book value	=Salvage value * tax rate					-36960
=Terminal year after tax cash flows						103440.00
Total Cash flow for the period		-1800000	108240	108240	108240	211680
Discount factor=	(1+discount rate)^corresponding period	1	1.09	1.1881	1.295029	1.41158161
Discounted CF=	Cashflow/discount factor	-1800000	99302.75229	91103.44247	83581.13988	149959.4487
NPV=	Sum of discounted CF=	-1376053.22

Year or period		0	1	2	3	4
EAC			-424744.506	-424744.506	-424744.506	-424744.5064
Discount factor=	(1+discount rate)^corresponding period		1.09	1.1881	1.295029	1.41158161
Discounted CF=	Cashflow/discount factor		-389673.859	-357498.953	-327980.691	-300899.7166
NPV=	-1376053.22
EAC is equivalent yearly CF with same NPV =	-424744.51

new machine

Time line		0	1	2	3	4	5
Cost of new machine		-2183000
=Initial Investment outlay		-2183000
								100.00%
Savings			359000	359000	359000	359000	359000
-Depreciation	Cost of equipment/no. of years		-436600	-436600	-436600	-436600	-436600	0	=Salvage Value
=Pretax cash flows			-77600	-77600	-77600	-77600	-77600
-taxes	=(Pretax cash flows)*(1-tax)		-60528	-60528	-60528	-60528	-60528
+Depreciation			436600	436600	436600	436600	436600
=after tax operating cash flow			376072	376072	376072	376072	376072
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						421200
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							421200
Total Cash flow for the period		-2183000	376072	376072	376072	376072	797272
Discount factor=	(1+discount rate)^corresponding period	1	1.09	1.1881	1.295029	1.41158161	1.538624
Discounted CF=	Cashflow/discount factor	-2183000	345020.1835	316532.2784	290396.5857	266418.886	518172.1
NPV=	Sum of discounted CF=	-446459.97

Year or period		0	1	2	3	4	5
EAC			-114781.491	-114781.491	-114781.491	-114781.4906	-114781.5
Discount factor=	(1+discount rate)^corresponding period		1.09	1.1881	1.295029	1.41158161	1.538624
Discounted CF=	Cashflow/discount factor		-105304.12	-96609.2843	-88632.3709	-81314.10172	-74600.09
NPV=	-446459.97
EAC is equivalent yearly CF with same NPV =	-114781.49

a-2