Question

NPV and IRR for Mutually Exclusive Projects 10. A company is considering two mutually exclusive projects, A and B. Project A requires an initial investment of $200, followed by cash flows of $185, $40, and $15. Project B requires an initial investment of $200, followed by cash flows of S0, $50, and $230. What is the NPV and IRR for each of the projects? Which project should the company choose? The firm's cost of capital is 10 percent.
Please use Excel to solve.

Answer 1

NPV = PV of Cash Inflows - PV of Cash Outflows

Project A:

Year	CF	PVF @10%	Disc CF
0	$ -200.00	1.0000	$ -200.00
1	$ 185.00	0.9091	$    168.18
2	$    40.00	0.8264	$      33.06
3	$    15.00	0.7513	$      11.27
NPV			$      12.51

Project B:

Year	CF	PVF @10%	Disc CF
0	$ -200.00	1.0000	$ -200.00
1	$           -	0.9091	$             -
2	$    50.00	0.8264	$      41.32
3	$ 230.00	0.7513	$    172.80
NPV			$      14.12

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

Project A:

Year	CF	PVF @15%	Disc CF	PVF @16%	Disc CF
0	$ -200.00	1.0000	$ -200.00	1.0000	$ -200.00
1	$ 185.00	0.8696	$    160.87	0.8621	$ 159.48
2	$    40.00	0.7561	$      30.25	0.7432	$    29.73
3	$    15.00	0.6575	$        9.86	0.6407	$       9.61
NPV			$        0.98		$     -1.18

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

= 15% + [ 0.98 / 2.16 ] * 1%

= 15% + 0.45%

= 15.45%

Project B:

Year	CF	PVF @12%	Disc CF	PVF @13%	Disc CF
0	$ -200.00	1.0000	$ -200.00	1.0000	$ -200.00
1	$           -	0.8929	$             -	0.8850	$           -
2	$    50.00	0.7972	$      39.86	0.7831	$    39.16
3	$ 230.00	0.7118	$    163.71	0.6931	$ 159.40
NPV			$        3.57		$     -1.44

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

= 12% + [ 3.57 / 5.01 ] * 1%

= 12% + 0.71%

= 12.71%

Project B is selected as it has higher NPV @discount Rate 10%