Question

Suppose a machine (defender) was purchased 2 years ago with an initial cost of $30,000. The CCA rate for the machine is 30%. The tax rate is 40%, and the company’s MARR is 15%. The operating cost of the machine is $4,000 per year. The current market value of the machine is $8,000, and this value decreases by $2,000 per year until it reaches zero. (a) What is the current net market value of the machine? (b) What will be the Annual Equivalent Cost if we decide to keep the machine for another 3 years? (Use the opportunity cost approach)

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Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J
2
3		Input Data
4			Old Machine
5		Purchase Cost	30000
6
7		Number of years ago machine bought	2
8		Salvage Value	0
9		Remaining Useful life	3
10		Depreciation	CCA 30%
11		Current Market Value	8000
12		Tax Rate	0.4
13		MARR	0.15
14
15		a)
16		Calculation of Net market value of the machine:
17
18		Equipment Cost	=D5
19		Life of Machine	=D7+D9	years
20		Salvage value	0
21
22		CCA Rate	0.3
23		Year	-2	-1	0	1	2	3
24		Depreciation Expense		=D25*$D$22	=E25*$D$22	=F25*$D$22	=G25*$D$22	=H25*$D$22
25		Book Value	=D18	=D25-E24	=E25-F24	=F25-G24	=G25-H24	=H25-I24
26
27		Before Tax market value	=D11
28		Book value of old Machine	=F25
29		Gain or loss on sale	=D27-D28	=D27-D28
30		Tax Expense on gain or loss	=-D29*D12	=-D29*D12
31		Net Proceed from sale of old Machine	=D27+D30	=D27+D30
32
33		Hence net market value of the machine is	=D31
34
35		b)
36		Equivalent uniform annual cost (EUAC) can be calculated using following formula:
37		EUAC	=-NPV of the cash flows *(A/P,i,n)
38
39		Cash flow for old Machine:
40		Operating cash flow needs to be calculated using the following formula:
41		Operating Cash Flow = EBIT*(1-T)+Depreciation
42		Free cash flow can be calculated using following equation:
43		Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital
44
45		Year	0	=D45+1	=E45+1	=F45+1
46		Opportunity cost	=-D31
47		Depreciation Expense		=-G24	=-H24	=-I24
48		EBIT		=SUM(E47:E47)	=SUM(F47:F47)	=SUM(G47:G47)
49		Tax expense		=-E48*$D$12	=-F48*$D$12	=-G48*$D$12
50		EBIT*(1-T)		=SUM(E48:E49)	=SUM(F48:F49)	=SUM(G48:G49)
51		Add Depreciation		=-E47	=-F47	=-G47
52		Operating Cash Flow		=E50+E51	=F50+F51	=G50+G51
53		Market Value at the end f year 3				0
54		Tax expense on gain from sale				=-(G53-I25)*D12
55		Net Proceed from sale of machine				=G53+G54
56		Free Cash flow for old Machine	=D46	=E52	=F52	=G52+G55
57
58		NPV calculation:
59		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
60		Given the following cash flow and MARR, NPV for the project can be calculated as follows:
61		Year	0	=D61+1	=E61+1	=F61+1
62		Free Cash Flow (FCF)	=D56	=E56	=F56	=G56
63		MARR (i)	=D13
64		(P/F,i,n) for each year		=1/((1+$D63)^E61)	=1/((1+$D63)^F61)	=1/((1+$D63)^G61)
65		Present Value of cash flows = FCF*(P/F,i,n)		=E62*E64	=F62*F64	=G62*G64
66		Present value if future cash flows	=SUM(E65:G65)	=SUM(E62:G62)
67
68		NPV for Project	=Present value fo future cash flows - Initial investment
69			=D66+D62	=D66+D62
70
71		Hence NPV of the Project is	=D69
72
73		EUAC Calculation
74		EUAC	=-NPV of the cash flows *(A/P,i,n)
75
76		NPV of cash flow	=D71
77		MARR	=D13
78		n	=D9
79
80		EUAC	=-NPV of the cash flows *(A/P,i,n)
81			=-D71*(1/PV(D77,D78,-1,0))	=-D71*(1/PV(D77,D78,-1,0))
82
83		Hence EUAC for Old Machine is	=D81
84