Question

"The Norcross Fiber Company is considering automating its piece-goods screen-printing system at a cost of $22,000. The firm expects to phase out the new printing system at the end of 5 years due to changes in style. At that time, the firm could scrap the system for $6,000 in today's dollars. The expected net savings (revenue - expenses) due to automation also are in today's (constant) dollars: Year 1 $17,000; Year 2 $13,000; Years 3-5 $12,000. The system qualifies as a 5-year MACRS property and will be depreciated accordingly. The general inflation rate over the next 5 years is 2% per year. Asume the net savings and the scrap value are subject to this inflation rate. The firm's inflation-free MARR is 10%. The firm's tax rate is 31%. What is the net present worth of this automation system? "

Answer 1

		Inflation Rate	2%
		Inflation free MARR	10%
		Nominal MARR	12%	(10+2)
		Scrap value at actual dollar	$        6,624	(6000*(1.02^5)
		Present Value of cash flow=(Cash Flow)/(1+i)^N
		i=Discount rate
		N=Year of cash flow
		Cash flow in actual dollar=(Cash flow in todays dollar)*(1+f)^N
		f=inflation rate=2%=0.02
		N=Year of cash flow
	N	Year	0	1	2	3	4	5
	A	Initial Cash flow	($22,000)
	B	Net savings in todays dollar		$17,000	$13,000	$12,000	$12,000	$12,000
	C=B*(1.02^N)	Net Savings in actual dollar(Before tax)		$        17,340	$        13,525	$        12,734	$        12,989	$        13,249
Tax Rate=31%	D=C*(1-0.31)	Net after tax Savings in actual dollar		$        11,965	$          9,332	$          8,787	$          8,963	$          9,142
		Depreciation Tax shield:
	E	MACRS Recovery Rate		0.2000	0.3200	0.1920	0.1152	0.1152	SUM
	F=22000*E	Depreciation expense		$          4,400	$          7,040	$          4,224	$          2,534	$          2,534	20733
	G=F*0.31	Depreciation Tax shield:		$          1,364	$          2,182	$          1,309	$              786	$              786
	H	Beforev tax salvage value in actual dollar						$6,624
	I=22000-20733	Book Value of equipment at end of 5 years						1267
	J=H-I	Gain on salvage						$5,357
	K=J*0.31	Tax on salvage						$1,661
	L=H-K	After tax salvage value						$4,963
	M=A+D+G+L	Net after tax Cash flow in actual dollar	($22,000)	$        13,329	$        11,515	$        10,096	$          9,748	$        14,891	SUM
	N=M/(1.12^N)	Present Value of Cash Flow	($22,000)	$        11,901	$          9,180	$          7,186	$          6,195	$          8,449	$20,911
		NET PRESENT WORTH OF THE SYSTEM	$20,911