Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows: 2 3 Project S - $1,000 $890.56 $250 $10 $10 Project L - $1,000 $0 $250 $400 $799.39 The company's WACC is 8.0%. 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

In case of nutually exclsuive Projects, Better Project is the Project with higher NPV.

NPV = PV of Cash Inflows - PV of Cash Outflows.

NPV of Project S:

Year	CF	PVF@8%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00
1	$     890.56	0.9259	$     824.59
2	$     250.00	0.8573	$     214.33
3	$        10.00	0.7938	$          7.94
4	$        10.00	0.7350	$          7.35
NPV			$        54.22

NPV of Project L:

Year	CF	PVF@8%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00
1	$              -	0.9259	$              -
2	$     250.00	0.8573	$     214.33
3	$     400.00	0.7938	$     317.53
4	$     799.39	0.7350	$     587.58
NPV			$     119.44

Project L is better Project as it has higher NPV.

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

Year	CF	PVF@11%	Disc CF	PVF@12%	Disc CF
0	$ -1,000.00	1.0000	$ -1,000.00	1.0000	$ -1,000.00
1	$              -	0.9009	$              -	0.8929	$              -
2	$     250.00	0.8116	$     202.91	0.7972	$     199.30
3	$     400.00	0.7312	$     292.48	0.7118	$     284.71
4	$     799.39	0.6587	$     526.58	0.6355	$     508.03
NPV			$        21.97		$        -7.96

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

= 11% + [ 21.97 / 29.93 ] * 1%

= 11% + 0.73%

= 11.73%