Question

You are evaluating the following mutually exclusive projects for your firm, whose cost of capital is 14%, and all dollar amounts are in millions.

1. Verify the NPV and IRR of each project.

2. What is your recommendation?

Show how to calculate NPV and IRR

Project	Required Return	Life	IO	NCF1-n	NPV	IRR
Alpha	12%	10 years	$50	$20
Beta	8%	5	$50	$25

Answer 1

NPV = PV of Cash Inflows - PV of Cash Outflows

Project Alpha:

Year	CF	PVF @12%	Disc CF
0	$ -50.00	1.0000	$ -50.00
1	$   20.00	0.8929	$   17.86
2	$   20.00	0.7972	$   15.94
3	$   20.00	0.7118	$   14.24
4	$   20.00	0.6355	$   12.71
5	$   20.00	0.5674	$   11.35
6	$   20.00	0.5066	$   10.13
7	$   20.00	0.4523	$      9.05
8	$   20.00	0.4039	$      8.08
9	$   20.00	0.3606	$      7.21
10	$   20.00	0.3220	$      6.44
NPV			$   63.00

Project Beta:

Year	CF	PVF @8%	Disc CF
0	$ -50.00	1.0000	$ -50.00
1	$   25.00	0.9259	$   23.15
2	$   25.00	0.8573	$   21.43
3	$   25.00	0.7938	$   19.85
4	$   25.00	0.7350	$   18.38
5	$   25.00	0.6806	$   17.01
NPV			$   49.82

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

Project Alpha:

Year	CF	PVF @38%	Disc CF	PVF @39%	Disc CF
0	$ -50.00	1.0000	$ -50.00	1.0000	$ -50.00
1	$   20.00	0.7246	$   14.49	0.7194	$   14.39
2	$   20.00	0.5251	$   10.50	0.5176	$   10.35
3	$   20.00	0.3805	$      7.61	0.3724	$      7.45
4	$   20.00	0.2757	$      5.51	0.2679	$      5.36
5	$   20.00	0.1998	$      4.00	0.1927	$      3.85
6	$   20.00	0.1448	$      2.90	0.1386	$      2.77
7	$   20.00	0.1049	$      2.10	0.0997	$      1.99
8	$   20.00	0.0760	$      1.52	0.0718	$      1.44
9	$   20.00	0.0551	$      1.10	0.0516	$      1.03
10	$   20.00	0.0399	$      0.80	0.0371	$      0.74
NPV			$      0.53		$    -0.62

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

= 38% + [ 0.53 / 1.15 ] * 1%

= 38% + 0.46%

= 38.46%

Project Beta:

Year	CF	PVF @41%	Disc CF	PVF @42%	Disc CF
0	$ -50.00	1.0000	$ -50.00	1.0000	$ -50.00
1	$   25.00	0.7092	$   17.73	0.7042	$   17.61
2	$   25.00	0.5030	$   12.57	0.4959	$   12.40
3	$   25.00	0.3567	$      8.92	0.3492	$      8.73
4	$   25.00	0.2530	$      6.33	0.2459	$      6.15
5	$   25.00	0.1794	$      4.49	0.1732	$      4.33
NPV			$      0.03		$    -0.79

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

= 41% + [ 0.03 / 0.82 ] * 1%

= 41% + 0.04%%

= 41.04%

Incase of Mutually exclsuive Projects, Seletc the Project with Higher NPV. Hence select Alpha Project.