Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,620,000; the new one will cost, $1,949,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $405,000 after five years.

The old computer is being depreciated at a rate of $336,000 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 $531,000; in two years, it will probably be worth $153,000. The new machine will save us $363,000 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.) a-1. Old computer EAC = ? New computer EAC = -93,897.05 a-2. NPV = ?

OLD Comp EAC is NOT : -72,563.29
NPV is NOT: -230007.40

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J
2
3		a-1)
4		Calculation of EAC of Old Computer:
5		Equivalent uniform annual cost (EAC) can be calculated using following formula:
6		EAC	=NPV of the cash flows *(A/P,i,n)
7
8		Given the following data:
9		Initial Cost	1620000
10		Planning horizon	2	years
11		Salvage value at the End of 2 Year	153000
12		Remaining Life of Computer	=D10	years
13		Current Market Value	531000
14		Annual Operating Cost	0
15		MARR	0.1
16		Tax Rate	0.23
17		Depreciation per year	336000
18		Since with this depreciation rate, the computer will be written off in 3 years,
19		Book Value of old computer at present	=D17*3
20		Book Balue at the end of 2 year	=D19-2*D17
21		Calculation of opportunity cost:
22		Current market value of the old Computer will act as a opportunity cost.
23		Current market value	=D13
24		Book value at Present	=D19
25		Gain or loss on sale	=D23-D24
26		Tax Expense on gain or loss	=-D25*D16	=-D25*D16
27		Net Proceed from sale of Old Computer	=D23+D26	=D23+D26
28
29		NPV of Old Computer can be calculated by finding the present value of cash flows.
30		Current market value of Old Computer will be the opportunity cost to use the Computer further.
31
32		Cash flows for Old Computer can be represented as follows:
33		Year	0	1	2
34		Depreciation		=-$D$17	=E34
35		EBIT		=SUM(E34:E34)	=SUM(F34:F34)
36		Tax Expense		=-E35*$D$16	=-F35*$D$16
37		EBIT*(1-T)		=E35+E36	=F35+F36
38		Add Depreciation		=-E34	=-F34
39		Operating Cash Flow		=E37+E38	=F37+F38
40		Opportunity Cost	=-D27
41		After Tax Proceed from sale of Computer			=D11-((D11-D20)*D16)
42		Free cash flow	=D40	=SUM(E39:E41)	=SUM(F39:F41)
43
44		NPV calculation:
45		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
46		Given the following cash flow and WACC, NPV for the project can be calculated as follows:
47		Year	0	1	2
48		Free Cash Flow (FCF)	=D42	=E42	=F42
49		MARR (i)	=D15
50		(P/F,i,n) for each year		=1/((1+$D49)^E47)	=1/((1+$D49)^F47)
51		Present Value of cash flows = FCF*(P/F,i,n)		=E48*E50	=F48*F50
52		Present value if future cash flows	=SUM(E51:F51)	=SUM(E51:F51)
53
54		NPV of Cash Flows	=Present value fo future cash flows - Initial investment
55			=D52+D48
56
57		EAC Calculation
58		EAC	=NPV of the cash flows *(A/P,i,n)
59
60		NPV of cash flow	=D55
61		MARR	=D15
62		n	=D12
63
64		EAC	=NPV of the cash flows *(A/P,i,n)
65			=D55*(1/PV(D61,D62,-1,0))
66
67		Hence EAC for Old Computer is	=D65
68
69
70		Calculation of EAC of New Computer:
71		Equivalent uniform annual cost (EAC) can be calculated using following formula:
72		EAC	=NPV of the cash flows *(A/P,i,n)
73
74		Given the following data:
75		Investment in New Computer
76		Life of the Computer	5	years
77		Salvage value at the End of 5 Year	0
78		Market value at the End of 5 Year	405000
79		Price of New Computer	1949000
80		Annual Savings in Operating Cost	363000
81		MARR	=D15
82
83		Depreciation each year can be calculated as follows:
84		Capital cost (B)	=D79
85		Using Straight line method,
86		Depreciation per Year	=(Initial Cost - Salvage Value)/Life
87			=(D79-D77)/D76	=(D79-D77)/D76
88
89		Hence depreciation each year can be calculated as follows:
90				Year 1	Year 2	Year 3	Year 4	Year 5
91		Depreciation per Year		=$D$87	=$D$87	=$D$87	=$D$87	=$D$87
92		Book Value	=D84	=D92-E91	=E92-F91	=F92-G91	=G92-H91	=H92-I91
93
94		Net Proceed from sale of Computer calculation:
95
96		Proceed from sale of Computer at the end of 5th year	=D78
97		Book Value of Computer at the end of 5th year	=I92
98		Gain or Loss on sale	=Proceed From Sale - Book value at the end of sale
99			=D96-D97	=D96-D97
100
101		Gain or Loss on sale of Computer	=D99
102		Tax on Gain & Loss	=D101*D16	=D101*D16
103		Net Proceed from Sale	=Proceed from Sale - Tax Expense on gain or loss
104			=D96-D102	=D96-D102
105
106		NPV of New Computer can be calculated by finding the present value of cash flows.
107		Current market value of new Computer will be the opportunity cost to use the Computer further.
108		Cash flows for new Computer can be represented as follows:
109		Year	0	1	2	3	4	5
110		Annual Saving in O&M Cost		=$D$80	=$D$80	=$D$80	=$D$80	=$D$80
111		Depreciation		=-E91	=-F91	=-G91	=-H91	=-I91
112		EBIT		=SUM(E110:E111)	=SUM(F110:F111)	=SUM(G110:G111)	=SUM(H110:H111)	=SUM(I110:I111)
113		Tax Expense		=-E112*$D$16	=-F112*$D$16	=-G112*$D$16	=-H112*$D$16	=-I112*$D$16
114		EBIT*(1-T)		=E112+E113	=F112+F113	=G112+G113	=H112+H113	=I112+I113
115		Add Depreciation		=-E111	=-F111	=-G111	=-H111	=-I111
116		Operating Cash Flow		=E114+E115	=F114+F115	=G114+G115	=H114+H115	=I114+I115
117		Initial investment	=-D79
118		Net Proceed from Sale of Computer						=D104
119		Free cash flow	=D117	=SUM(E116:E118)	=SUM(F116:F118)	=SUM(G116:G118)	=SUM(H116:H118)	=SUM(I116:I118)
120
121		NPV calculation:
122		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
123		Given the following cash flow and WACC, NPV for the project can be calculated as follows:
124		Year	0	1	2	3	4	5
125		Free Cash Flow (FCF)	=D119	=E119	=F119	=G119	=H119	=I119
126		MARR (i)	=D81
127		(P/F,i,n) for each year		=1/((1+$D126)^E124)	=1/((1+$D126)^F124)	=1/((1+$D126)^G124)	=1/((1+$D126)^H124)	=1/((1+$D126)^I124)
128		Present Value of cash flows = FCF*(P/F,i,n)		=E125*E127	=F125*F127	=G125*G127	=H125*H127	=I125*I127
129		Present value if future cash flows	=SUM(E128:N128)
130
131		NPV of Cash Flows	=Present value fo future cash flows - Initial investment
132			=D129+D125
133
134		EAC Calculation
135		EAC	=NPV of the cash flows *(A/P,i,n)
136
137		NPV of cash flow	=D132
138		MARR	=D81
139		n	5
140
141		EAC	=NPV of the cash flows *(A/P,i,n)
142			=D132*(1/PV(D138,D139,-1,0))	=D132*(1/PV(D138,D139,-1,0))
143
144		Hence EAC for New Computer is	=D142
145
146		a-2)
147		Should Old Computer be replaced with new Computer?
148		Using the following data:
149		EAC of Old Computer	=D67
150		EAC of New Computer	=D144
151
152		Net Cash flow for decision to replace computer now can be calculated as follows:
153		Year	0	1	2	3	4	5
154		EAC of New Computer		=$D$150	=$D$150	=$D$150	=$D$150	=$D$150
155		EAC of Old Computer		=$D$149	=$D$149
156		Cash Flow of Decision to replace old computer		=E154-E155	=F154-F155	=G154-G155	=H154-H155	=I154-I155
157
158		NPV calculation:
159		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
160		Given the following cash flow and WACC, NPV for the project can be calculated as follows:
161		Year	0	1	2	3	4	5
162		Free Cash Flow (FCF)	=D156	=E156	=F156	=G156	=H156	=I156
163		MARR (i)	=D15
164		(P/F,i,n) for each year		=1/((1+$D163)^E161)	=1/((1+$D163)^F161)	=1/((1+$D163)^G161)	=1/((1+$D163)^H161)	=1/((1+$D163)^I161)
165		Present Value of cash flows = FCF*(P/F,i,n)		=E162*E164	=F162*F164	=G162*G164	=H162*H164	=I162*I164
166		Present value if future cash flows	=SUM(E165:N165)
167
168		Hence NPV to replace the old computer is	=D166
169