Question

Consider the following project:

                               Y0         Y1       Y2         Y3         Y4        Y5         Y6         Y7

CF                            $0    –$100   $50        $80     $30       $30       $30     –$60

a) What is the IRR?

b) What is the payback time?

Answer 1

a)	IRR	36%
Working:
IRR is the rate at which Net Present value is zero.
Net Present Value at 10%							Net Present Value at 40%
Year	CF	Discount factor		Present Value			Year	CF	Discount factor		Present Value
0	0	1.0000		0			0	0	1.0000		0
1	$       -100	0.9091		$         -91			1	$      -100	0.7143		$         -71
2	$           50	0.8264		$          41			2	$          50	0.5102		$          26
3	$           80	0.7513		$          60			3	$          80	0.3644		$          29
4	$           30	0.6830		$          20			4	$          30	0.2603		$             8
5	$           30	0.6209		$          19			5	$          30	0.1859		$             6
6	$           30	0.5645		$          17			6	$          30	0.1328		$             4
7	$         -60	0.5132		$         -31			7	$         -60	0.0949		$           -6
								34.17%
	Net Present Value			$          36				Net Present Value			$           -5
IRR	=	10%+(40%-10%)*(36/(36+5))
	=	36%
Note:Above method is approximate method for calculating IRR.So, calculated IRR is approximate . Actual IRR may be approx to 36%.
b)
Payback time		4 years
Working:
Payback time is the time period upto which cost of project is recovered back.
Total cost of project is $ 160 ($ 100 in Y1 and $ 60 in Y7).
Upto Year 4 total cash inflows are $ 160 ($ 50+$ 80+$ 30).It means project pays back in 4 years.