Question

A company is considering a new inventory system that will cost $120,000. The system is expected to generate positive cash flows over the next four years in the amounts of $35,000 in year 1, $55,000 in year 2, $65,000 in year 3, and $40,000 in year 4. The firm’s required rate of return is 9%. What is the payback period of this project?

1.95 years

2.46 years

2.99 years

3.10 years

--------- What is the net present value (NPV) of the project?

		$28,830.29
		$30,929.26
		$36,931.43
		$39,905.28

--------what is the internal rate of return (IRR) of this project?

		14.03%
		17.56%
		19.26%
		21.78%

--------what is the profitability index (PI) of this project?

		0.87
		1.11
		1.31
		1.83.

-------& should the company accept the project?

		Yes
		No

Answer 1

1) Payback Period
Cost = 120000
First 2 year, Cash flows are 90,000(35000+55000)
Payback Period = 2 + (120000-90000)/65000
Payback Period = 2.46 years
2) NPV
Required rate = 9%
NPV is calculated as per table below
Year	Cash flow	PV of Cash flow @ 9%(Cashflow/(1.09^year)
0	-$120,000	-$120,000
1	$35,000.00	32110
2	$55,000.00	46292
3	$65,000.00	50192
4	$40,000.00	28337
	NPV	$36,931
NPV is $36,931
3) We will use trial and error approach for IRR calculation
As the NPV is in positive(much higher than cost), let us try IRR of 21.78%
Year	Cash flow	PV of Cash flow @ 21.78%(Cashflow/(1.2178^year)
0	-$120,000	-$120,000
1	$35,000.00	$28,740
2	$55,000.00	$37,085
3	$65,000.00	$35,989
4	$40,000.00	$18,186
	NPV	$0
Hence, the IRR is 21.78%
4)
Profitability Index   = (NPV + Initial Investment) / Initial Investment
	=	(36931+120000)/120000
Profitability Index   = 1.31
5) Yes the Company should accept the project as the it has the positive NPV