Question

A company is evaluating the replacement of an old machine with a new one. Last year, the company hired a consultant to conduct a feasibility study about this replacement project, which cost them $500,000 at that time. The consulting fees were expensed last year.
The old machine was purchased 2 years ago for $3 million and was being depreciated using MACRS 5-year class (20%, 32%, 19.2%, 11.52%, 11.52% and 5.76%). The old machine can be sold for $1 million at this time. If the old machine is not replaced, it can be sold for $400,000 four years from now.
The replacement machine has a cost of $2 million, an estimated useful life of 4 years. This machine will be depreciated using straight-line method to 0 salvage value. The replacement machine would permit an output expansion, so sales would rise by $1 million per year; even so, the new machine’s much greater efficiency would cause operating expenses to decline by $250,000 per year. The new machine would require that inventories be increased by $1 million, but accounts payable and accrued expenses would simultaneously increase by $500,000 and 200,000 respectively. The interest expense on the debt component of the capital required for this project will be $250,000 annually. The new machine can be sold for $50,000 at the end of 4 years to another company.
The company’s marginal federal-plus-state tax rate is 40%, and its WACC is 12%.
What is the CF1 (The cash flow to be used in NPV calculation)?
What is the CF4 (The cash flow to be used in NPV calculation)?
What is the NPV of the project?

Answer 1

A1	B	C	D	E	F	G	H	I	J	K
2
3
4		Free cash flow can be calculated as follows:
5		Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital
6		Operating Cash Flow = EBIT*(1-Tax Rate)+Depreciation
7		Tax Rate	40%
8
9		Cost of new machine	$2,000,000
10
11		Increase in inventory	$1,000,000
12		Increase in accounts payable	$500,000
13		Increase in accrued expenses	$200,000
14		Initial investment in working capital	$300,000
15		Total initial investment	$2,300,000
16
17		Depreciation each year for new machine can be calculated as follows:
18		Machine Cost	$2,000,000
19		Life of Machine	4	years
20		Salvage value	0
21		Depreciation per year	=(Investment - Salvage Value)/Expected life of equipment
22			$500,000	=(D14-D16)/D15
23
24		Depreciation each year for old machine can be calculated as follows:
25
26		Capital cost (B)	$3,000,000
27		Depreciation follows MACRS 5 year-half year convention.
28
29		Hence depreciation each year can be calculated as follows:
30				Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
31		MACRS 5 Year depreciation rate (rt)		20.0%	32.0%	19.2%	11.5%	11.5%	5.8%
32		Depreciation (B*rt)		$600,000	$960,000	$576,000	$345,600	$345,600	$172,800
33		Book Value	$3,000,000	$2,400,000	$1,440,000	$864,000	$518,400	$172,800	$0
34
35
36		Calculation of Net Proceed from sale of old machine:
37		Market Value of old machine	$1,000,000
38		Book Value of old machine	$1,440,000	=F33
39		Gain or Loss on sale of Machine	=Proceed From Sale - Book value at the end of sale
40			($440,000)
41
42		Gain or Loss on sale of Machine	($440,000)
43		Tax on Gain & Loss	($176,000.00)
44		Net Proceed from Sale of old machine	=Proceed from Sale - Tax Expense on gain or loss
45			$1,176,000	=D37-D43
46
47		Calculation of Net Proceed from sale of new machine:
48		Market Value of new machine	$50,000
49		Book Value of new machine	$0
50		Gain or Loss on sale of Machine	=Proceed From Sale - Book value at the end of sale
51			$50,000
52
53		Gain or Loss on sale of Machine	$50,000
54		Tax on Gain & Loss	$20,000.00	=D53*D7
55		Net Proceed from Sale of new machine	=Proceed from Sale - Tax Expense on gain or loss
56			$30,000	=D48-D54
57