Question

(NPV, PV, and IRR calculations) You are considering two independent projects, project A and project B. The initial cash outlay associated with project Als $55,000 and the initial cash outlay associated with project is $75,000. The required role of return on both projects is 12 percent. The expected arvual free cash inflows from each project are in the popup window. Calculate the NPV, Pt, and IRR for each project and indicate if the project should be accepted. a. What is the NPV of project A? S (Round to the nearest cent.) Data Table PROJECT B - $75,000 17 000 Initial Outlay Inew year 1 Infow year 2 Inow year 3 new year now years inflow Year 6 PROJECT A - $55.000 16.000 16,000 16,000 16.000 16.000 16,000 17,000 17,000 17.000 17 000 17 000 Print Done

Answer 1

NPV = PV of cash Inflows - PV of Cash outflows

Project A:

Year	CF	PVF @12%	Disc CF
0	$ -55,000.00	1.0000	$ -55,000.00
1	$ 16,000.00	0.8929	$ 14,285.71
2	$ 16,000.00	0.7972	$ 12,755.10
3	$ 16,000.00	0.7118	$ 11,388.48
4	$ 16,000.00	0.6355	$ 10,168.29
5	$ 16,000.00	0.5674	$    9,078.83
6	$ 16,000.00	0.5066	$    8,106.10
NPV			$ 10,782.52

Project B:

Year	CF	PVF @12%	Disc CF
0	$ -75,000.00	1.0000	$ -75,000.00
1	$ 17,000.00	0.8929	$ 15,178.57
2	$ 17,000.00	0.7972	$ 13,552.30
3	$ 17,000.00	0.7118	$ 12,100.26
4	$ 17,000.00	0.6355	$ 10,803.81
5	$ 17,000.00	0.5674	$    9,646.26
6	$ 17,000.00	0.5066	$    8,612.73
NPV			$   -5,106.08

PI = PV of Cash Inflows / PV of Cash Outflows

Project A:

Year	CF	PVF @12%	Disc CF
1	$ 16,000.00	0.8929	$ 14,285.71
2	$ 16,000.00	0.7972	$ 12,755.10
3	$ 16,000.00	0.7118	$ 11,388.48
4	$ 16,000.00	0.6355	$ 10,168.29
5	$ 16,000.00	0.5674	$    9,078.83
6	$ 16,000.00	0.5066	$    8,106.10
PV of Cash Inflows			$ 65,782.52
PV of Cash Outflows			$ 55,000.00
PI			1.20

Project B:

Year	CF	PVF @12%	Disc CF
1	$ 17,000.00	0.8929	$ 15,178.57
2	$ 17,000.00	0.7972	$ 13,552.30
3	$ 17,000.00	0.7118	$ 12,100.26
4	$ 17,000.00	0.6355	$ 10,803.81
5	$ 17,000.00	0.5674	$    9,646.26
6	$ 17,000.00	0.5066	$    8,612.73
PV of Cash Inflows			$ 69,893.92
PV of Cash Outflows			$ 75,000.00
PI			0.93

IRR is the rate at which PV of cash inflows are equal to PV of Cash Outflows.

Project A:

Year	CF	PVF @18%	Disc CF	PVF @19%	Disc CF
0	$ -55,000.00	1.0000	$ -55,000.00	1.0000	$ -55,000.00
1	$ 16,000.00	0.8475	$ 13,559.32	0.8403	$ 13,445.38
2	$ 16,000.00	0.7182	$ 11,490.95	0.7062	$ 11,298.64
3	$ 16,000.00	0.6086	$    9,738.09	0.5934	$    9,494.65
4	$ 16,000.00	0.5158	$    8,252.62	0.4987	$    7,978.70
5	$ 16,000.00	0.4371	$    6,993.75	0.4190	$    6,704.79
6	$ 16,000.00	0.3704	$    5,926.90	0.3521	$    5,634.28
NPV			$        961.64		$      -443.56

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

= 19% + [ 961.64 / 1405.21 ] *1%

= 19% + 0.68%

= 19.68%

Project B:

Year	CF	PVF @9%	Disc CF	PVF @10%	Disc CF
0	$ -75,000.00	1.0000	$ -75,000.00	1.0000	$ -75,000.00
1	$ 17,000.00	0.9174	$ 15,596.33	0.9091	$ 15,454.55
2	$ 17,000.00	0.8417	$ 14,308.56	0.8264	$ 14,049.59
3	$ 17,000.00	0.7722	$ 13,127.12	0.7513	$ 12,772.35
4	$ 17,000.00	0.7084	$ 12,043.23	0.6830	$ 11,611.23
5	$ 17,000.00	0.6499	$ 11,048.83	0.6209	$ 10,555.66
6	$ 17,000.00	0.5963	$ 10,136.54	0.5645	$    9,596.06
NPV			$    1,260.62		$      -960.57

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

= 9% + [ 1260.62 / 2221.18 ] *1%

= 9% + 0.57%

= 9.57%

Project A is selected as it has higher NPV, PI & IRR.