Question

A new machine will cost $150,000 to place into operation. It is expected to have yearly cash flows of $50,000 for the first five years. The company required rate of return is 9%.

1. Compute the Project's NPV.

2. Compute the Project's IRR.

3. How long is the project's payback period?

4. How long is the project's discounted payback period?

Answer 1

		Answer =1
		Years	Cash Flows	PVF @ 9%	Present Value
		0	-$1,50,000	1	-$1,50,000.00
		1	$50,000	0.9174	$45,871.56
		2	$50,000	0.8417	$42,084.00
		3	$50,000	0.7722	$38,609.17
		4	$50,000	0.7084	$35,421.26
		5	$50,000	0.6499	$32,496.57
		Total	$1,00,000		$44,483
		Answer =3)
		CALCULATION OF THE PAYBACK PERIOD OF THE PROJECT
		Years	Cash Flows	Cumulative Cash Flow
		0	-$1,50,000	-$1,50,000.00
		1	$50,000	-$1,00,000.00
		2	$50,000	-$50,000.00
		3	$50,000	$0.00
		4	$50,000	$50,000.00
		5	$50,000	$1,00,000.00
		Total	$1,00,000
		All the money invested is came full in the 3rd year so payback period is 3 years
		Answer = 4 years
		Years	Cash Flows	PVF @ 9%	Present Value	Cumulative Value
		0	-$1,50,000	1	-$1,50,000.00		-$1,50,000.00
		1	$50,000	0.9174	$45,871.56		-$1,04,128.44
		2	$50,000	0.8417	$42,084.00		-$62,044.44
		3	$50,000	0.7722	$38,609.17		-$23,435.27
		4	$50,000	0.7084	$35,421.26		$11,985.99
		5	$50,000	0.6499	$32,496.57		$44,482.56
		Total	$1,00,000		$44,483
		In the 4th year all the money is recovered , but not full year is required,
		So Payback period = 3 Years + $ 23,435.27 / $ 35,421.26
		So Payback period = 3 Years + 0.66 Years
		So Payback period = 3.66 Years
		Answer = 1
		IRR : IRR Means with a particular Percentage rate , At that point the present value become the zero
		CALCULATION OF THE IRR OF THE PROJECT
		First we calculate randomly present value with @ 19% discounting rate
		Years	Cash Flows	PVF @19%	Present Value
		0	-$1,50,000	1	-$1,50,000.00
		1	$50,000	0.8403	$42,016.81
		2	$50,000	0.7062	$35,308.24
		3	$50,000	0.5934	$29,670.79
		4	$50,000	0.4987	$24,933.44
		5	$50,000	0.4190	$20,952.47
			Net Present Value =		$2,881.74
		With PVF of 19% we are getting positive =			$2,881.74
		Secondly we calculate randomly present value @ 20 % discounting rate
		Years	Cash Flows	PVF @ 20%	Present Value
		0	-$1,50,000	1	-$1,50,000.00
		1	$50,000	0.8333	$41,666.67
		2	$50,000	0.6944	$34,722.22
		3	$50,000	0.5787	$28,935.19
		4	$50,000	0.4823	$24,112.65
		5	$50,000	0.4019	$20,093.88
			Net Present Value =		-$469.39
		With PVF of 20 % we are getting negative =			-469.39
		In the given case the pv with 19% is coming to postive means the present value is more
		then 19 % but with 20 % Present value cash flow become negative so the present value
		is between 19% and 20 %
		So the differecne in both % net present value is =			$2,881.74	-	-$469.39
		Total is become =			$3,351.14
		So , the difference % =			$2,881.74	"/"By	$3,351.14
		So , the difference % =			0.86
		So, the IRR =			19.86%
		Answer = IRR =		19.86%