Question

Your firm is contemplating the purchase of a new $570,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $58,000 at the end of that time. You will save $270,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $73,000 (this is a one-time reduction). If the tax rate is 35 percent, what is the IRR for this project?

Answer 1

Tax rate		35%
Calculation of annual depreciation
Depreciation		Year-1	Year-2	Year-3	Year-4	Year-5	Total
Cost (270000+54000)		$       570,000	$      570,000	$       570,000	$       570,000	$      570,000
Dep Rate		20.00%	20.00%	20.00%	20.00%	20.00%
Depreciation	Cost * Dep rate	$       114,000	$      114,000	$       114,000	$       114,000	$      114,000	$       570,000
Calculation of after-tax salvage value
Cost of machine			$      570,000
Depreciation			$      570,000
WDV	Cost less accumulated depreciation	$                -
Sale price			$        58,000
Profit/(Loss)	Sale price less WDV	$        58,000
Tax	Profit/(Loss)*tax rate	$        20,300
Sale price after-tax	Sale price less tax		$        37,700
Calculation of annual operating cash flow
		Year-1	Year-2	Year-3	Year-4	Year-5
Cost saving		$       270,000	$      270,000	$       270,000	$       270,000	$      270,000
Less: Depreciation		$       114,000	$      114,000	$       114,000	$       114,000	$      114,000
Profit before tax (PBT)		$       156,000	$      156,000	$       156,000	$       156,000	$      156,000
Tax@35%	PBT*Tax rate	$         54,600	$        54,600	$         54,600	$         54,600	$        54,600
Profit After Tax (PAT)	PBT - Tax	$       101,400	$      101,400	$       101,400	$       101,400	$      101,400
Add Depreciation	PAT + Dep	$       114,000	$      114,000	$       114,000	$       114,000	$      114,000
Cash Profit after-tax		$       215,400	$      215,400	$       215,400	$       215,400	$      215,400
Calculation of annual cash flow
Year		Capital	Working capital	Operating cash	Annual Cash flow
0		$     (570,000)	$        73,000		$     (497,000)
1				$       215,400	$       215,400
2				$       215,400	$       215,400
3				$       215,400	$       215,400
4				$       215,400	$       215,400
5		$         37,700	$       (73,000)	$       215,400	$       180,100
Calculation of IRR
			31.00%		32.00%
Year		Total cash flow	PV factor @ 31%	Present values	PV factor @ 32%	Present values
0		$     (497,000)	1.000	$     (497,000)	1.000	$     (497,000)
1		$       215,400	0.763	$       164,427	0.758	$      163,182
2		$       215,400	0.583	$       125,517	0.574	$      123,623
3		$       215,400	0.445	$         95,815	0.435	$        93,653
4		$       215,400	0.340	$         73,141	0.329	$        70,950
5		$       180,100	0.259	$         46,683	0.250	$        44,941
				$           8,583		$            (651)
		IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
		IRR	'=31%+ (32%-31%)*(8583.04/(8583.04-(-651.37)
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