Question

A company is considering a project that has the following cash flows: Co 3,000, C, +500, = +1,500, and C3 = +5,000, with a risk-adjusted discount rate of 15%.

Calculate the Net Present Value (NPV), Internal Rate of Return (IRR), Profitability Index, and the Payback of this project.

If you were the manager of the firm, will you accept or reject the project based on the calculation results above?

Answer 1

1)	Net Present Value				$       1,857
Working:
Year	Cash flow		Discount factor		Present Value
1	$           500		0.869565		$           435
2	$       1,500		0.756144		$       1,134
3	$       5,000		0.657516		$       3,288
	Total				$       4,857
	Less:Cost in Year 0				$       3,000
	Net Present value				$       1,857
2)	IRR				34.82%
Working:
IRR is the rate at which net present value becomes zero.
IRR	=	L+(H-L)*(A/(A-B))			Where,
	=	15%+(25%-15%)*(1857/937)			L	Lower discount rate			15%
	=	34.82%			H	Higher discount rate			25%
					A	NPv at lower discount rate			$    1,857
					B	NPV at higher discount rate			$        920
					A-B	$    1,857	-920	=	$        937
Net Present Value (NPV) at 25%
Year	Cash flow		Discount factor		Present Value
1	$           500		0.8000		$           400
2	$       1,500		0.6400		$           960
3	$       5,000		0.5120		$       2,560
	Total				$       3,920
	Less:Cost in Year 0				$       3,000
	Net Present value				$           920
3)	profitability Index			1.62
Working:
	profitability Index		=	Present Value of Cash inflows/Cost in Year 0
			=	$    4,857	/	$    3,000
			=	1.62
4)	Payback	2.20 Years
Working:
Year	Cash flow	Cumulative cash flow
1	$           500	$        500
2	$       1,500	$    2,000
3	$       5,000	$    7,000
Payback is the time upto which initial cash cost is recovered back.
Payback	=	2+((3000-2000)/5000)
	=	2.20
5)
	Net Present Value (NPV)			$    1,857
	Internal rate of return (IRR)			34.82%
	profitability Index			1.62
	Payback			2.20 Years
	Net Present Value is positive, Internal rate of return is more than cost of project, profitability index is more than 1 and payback period is before the end of project.
	Based on above , all measures are favorable.So, it is advisable to accept the project.