Question

IRR AND NPV A company is analyzing two mutually exclusive projects, S and L, with the following cash flows: 1 2 Project S - $1,000 $902.08 $240 $5 $15 Project L - $1,000 $5 $260 $380 $838.13 The company's WACC is 9.5%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places.

Answer 1

NPV = PV of cash Inflows - PV of Cash Outflows

Project with higher NPV is better Project.

Project S:

Year	CF	PVF @9.5%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00
1	$     902.08	0.9132	$     823.82
2	$     240.00	0.8340	$     200.16
3	$          5.00	0.7617	$          3.81
4	$        15.00	0.6956	$        10.43
NPV			$        38.22

Project L:

Year	CF	PVF @9.5%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00
1	$          5.00	0.9132	$          4.57
2	$     260.00	0.8340	$     216.84
3	$     380.00	0.7617	$     289.43
4	$     838.13	0.6956	$     582.98
NPV			$        93.82

Hence Project L is Better.

IRR of Better Projetc:

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows.

Year	CF	PVF @12%	Disc CF	PVF @13%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00	1.0000	$ -1,000.00
1	$          5.00	0.8929	$          4.46	0.8850	$          4.42
2	$     260.00	0.7972	$     207.27	0.7831	$     203.62
3	$     380.00	0.7118	$     270.48	0.6931	$     263.36
4	$     838.13	0.6355	$     532.65	0.6133	$     514.04
NPV			$        14.86		$      -14.56

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1% inc in DIsc Rate ] * 1%

= 12% + [ 14.86 / 29.42 ] * 1%

= 12% + 0.51%

= 12.51%

IRR of better Project is 12.51%