Question

8. NPVARR. A new computer system will require an initial outlay of $20,000 but it will in- crease the firm's cash flows by $4,000 a year for each ofthe next 8 years. Is the system worth installing if the required rate of returm is 9 percent? What if it is 14 percent How high can the discount rate be be fore you would reject the project?

Answer 1

	CALCULATION OF THE NET PRESENT VALUE OF THE PROJECT WITH 9% INTEREST
	Answer =A)
	Years	Cash Flows	PVF of $ 1 @ 9%	Present Value
	0	-$20,000	1.00000	-$20,000.00
	1	$4,000	0.90171	$3,606.85
	2	$4,000	0.81309	$3,252.35
	3	$4,000	0.73317	$2,932.68
	4	$4,000	0.66111	$2,644.44
	5	$4,000	0.59613	$2,384.53
	6	$4,000	0.53754	$2,150.16
	7	$4,000	0.48471	$1,938.83
	8	$4,000	0.43707	$1,748.27
	Total	$12,000		$658
		Net present Value is positive it means it is worth to invest.
	Answer =b)
	Years	Cash Flows	PVF of $ 1 @ 14%	Present Value
	0	-$20,000	1.00000	-$20,000.00
	1	$4,000	0.87719	$3,508.77
	2	$4,000	0.76947	$3,077.87
	3	$4,000	0.67497	$2,699.89
	4	$4,000	0.59208	$2,368.32
	5	$4,000	0.51937	$2,077.47
	6	$4,000	0.45559	$1,822.35
	7	$4,000	0.39964	$1,598.55
	8	$4,000	0.35056	$1,402.24
	Total	$12,000		-$1,445
		Net present Value is Negative so no meaning to invest
	Answer = c
	First we calculate randomly present value with @ 11% discounting rate
	Years	Cash Flows	PVF @11%	Present Value
	0	-$20,000	1.0000	-$20,000.00
	1	$4,000	0.9009	$3,603.60
	2	$4,000	0.8116	$3,246.49
	3	$4,000	0.7312	$2,924.77
	4	$4,000	0.6587	$2,634.92
	5	$4,000	0.5935	$2,373.81
	6	$4,000	0.5346	$2,138.56
	7	$4,000	0.4817	$1,926.63
	8	$4,000	0.4339	$1,735.71
		Net Present Value =		$584.49
	With PVF of 12% we are getting positive =			$584.49
	Secondly we calculate randomly present value @ 12 % discounting rate
	Years	Cash Flows	PVF @ 12%	Present Value
	0	-$20,000	1.0000	-$20,000.00
	1	$4,000	0.8929	$3,571.43
	2	$4,000	0.7972	$3,188.78
	3	$4,000	0.7118	$2,847.12
	4	$4,000	0.6355	$2,542.07
	5	$4,000	0.5674	$2,269.71
	6	$4,000	0.5066	$2,026.52
	7	$4,000	0.4523	$1,809.40
	8	$4,000	0.4039	$1,615.53
		Net Present Value =		-$129.44
	With PVF of 12 % we are getting negative =			-129.44
	So the differecne in both % net present value is =			$584.49	"-"	-$129.44
	Total is become =			$713.93
	So , the difference % =			$584.49	"/"By	$713.93
	So , the difference % =			0.82
	So, the IRR =			11.82%
	Answer = We can accept the discount upto 11.82 % after this we can reject the project