Question

Your firm is contemplating the purchase of a new $1,478,400 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $132,000 at the end of that time. You will save $580,800 before taxes per year in order processing costs and you will be able to reduce working capital by $130,139 (this is a one-time reduction). Required : If the tax rate is 33 percent, what is the IRR for this project?

Answer 1

IRR of the project is 27.22%

Working:

IRR is the rate at which Net Present Value (NPV) is zero.
Calculate NPV at 13%
Step-1:Calculation of annual cash flow
	Saving				$    5,80,800
	Depreciation				-2,95,680
	Profit before tax				2,85,120
	Tax				-94,090
	Net Income				1,91,030
	Depreciation				2,95,680
	Annual cash flow				4,86,710
	Working:
	Straight Line depreciation			=	(Cost-Salvage Value)/Useful Life
				=	(1478400-0)/5
				=	2,95,680
Step-2:Calculation of NPV
	Year	1	2	3	4	5	6	7	8		Total
	Operating cash flow	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710
	Release of net working caital								1,30,139
	After tax sale of asset								88,440
	Cash flow	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	7,05,289
	Discount factor	0.8850	0.7831	0.6931	0.6133	0.5428	0.4803	0.4251	0.3762
	Present Value	4,30,717.17	3,81,165.64	3,37,314.72	2,98,508.60	2,64,166.91	2,33,776.02	2,06,881.44	2,65,301.56		24,17,832.06
	Less: Initial Investment
	Cost of fixed assets									14,78,400
	Cost of Net Woring Capital									1,30,139	16,08,539.00
	NPV										8,09,293.06
	Working:
	After tax sale of asset	=	132000*(1-0.33)
		=	88,440
Now Calculate NPV at 30%
Step-1:Calculation of annual cash flow
	Saving				$    5,80,800
	Depreciation				-2,95,680
	Profit before tax				2,85,120
	Tax				-94,090
	Net Income				1,91,030
	Depreciation				2,95,680
	Annual cash flow				4,86,710
Step-2:Calculation of NPV
	Year	1	2	3	4	5	6	7	8		Total
	Operating cash flow	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710
	Release of net working caital								1,30,139
	After tax sale of asset								88,440
	Cash flow	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	4,86,710	7,05,289
	Discount factor	0.7692	0.5917	0.4552	0.3501	0.2693	0.2072	0.1594	0.1226
	Present Value	3,74,392.62	2,87,994.32	2,21,534.09	1,70,410.84	1,31,085.26	1,00,834.82	77,565.24	86,461.06		14,50,278.24
	Less: Initial Investment
	Cost of fixed assets									14,78,400
	Cost of Net Woring Capital									1,30,139	16,08,539.00
	NPV										-1,58,260.76
Now , Calculation of IRR is made as follows:
	Discount rate		13%	30%
	NPV		8,09,293.06	-1,58,260.76
	IRR	=	L+(H-L)*(A/(A-B))			Where,
		=	13%+(30%-13%)*(809293.06/967553.81)			L	13%
		=	27.22%			H	20%
						A	8,09,293.06
						B	-1,58,260.76
						A-B	9,67,553.81