Question

NPV—Mutually

exclusive projects   Hook Industries is considering the replacement of one of its old metal stamping machines. Three alternative replacement machines are under consideration. The relevant cash flows associated with each are shown in the following​ table:

	Machine A	Machine B	Machine C
Initial investment	$85,500	$59,700	$129,600
Year
1	$18,300	$11,600	$49,900
2	$18,300	$14,400	$30,500
3	$18,300	$16,000	$20,000
4	$18,300	$17,900	$20,400
5	$18,300	$19,600	$19,700
6	$18,300	$24,500	$29,600
7	$18,300	$0	$39,800
8	$18,300	$0	$49,600

. The​ firm's cost of capital is 12​%.

a.  Calculate the net present value ​(NPV​) of each press.

b.  Using​ NPV, evaluate the acceptability of each press.

c.  Rank the presses from best to worst using NPV.

d.  Calculate the profitability index​ (PI) for each press.

e.  Rank the presses from best to worst using PI.

Answer 1

NPV = PV of cash Inflows - PV of cash Outflows

Part A:

Machine A:

Year	CF	PVF @12%	Disc CF
0	$ -85,500.00	1.0000	$ -85,500.00
1	$ 18,300.00	0.8929	$ 16,339.29
2	$ 18,300.00	0.7972	$ 14,588.65
3	$ 18,300.00	0.7118	$ 13,025.58
4	$ 18,300.00	0.6355	$ 11,629.98
5	$ 18,300.00	0.5674	$ 10,383.91
6	$ 18,300.00	0.5066	$    9,271.35
7	$ 18,300.00	0.4523	$    8,277.99
8	$ 18,300.00	0.4039	$    7,391.06
NPV			$    5,407.81

Machine B:

Year	CF	PVF @12%	Disc CF
0	$ -59,700.00	1.0000	$ -59,700.00
1	$ 11,600.00	0.8929	$ 10,357.14
2	$ 14,400.00	0.7972	$ 11,479.59
3	$ 16,000.00	0.7118	$ 11,388.48
4	$ 17,900.00	0.6355	$ 11,375.77
5	$ 19,600.00	0.5674	$ 11,121.57
6	$ 24,500.00	0.5066	$ 12,412.46
7	$                 -	0.4523	$                 -
8	$                 -	0.4039	$                 -
NPV			$    8,435.02

Machine C:

Year	CF	PVF @12%	Disc CF
0	$ -1,29,600.00	1.0000	$ -1,29,600.00
1	$      49,900.00	0.8929	$      44,553.57
2	$      30,500.00	0.7972	$      24,314.41
3	$      20,000.00	0.7118	$      14,235.60
4	$      20,400.00	0.6355	$      12,964.57
5	$      19,700.00	0.5674	$      11,178.31
6	$      29,600.00	0.5066	$      14,996.28
7	$      39,800.00	0.4523	$      18,003.50
8	$      49,600.00	0.4039	$      20,032.61
NPV			$     30,678.86

Part B:

Project can be accepted, if it has +ve NPV. Thus all three Projects can be accpted.

Part C:

Ranking:

Machine C, Machine B, Machine A

part D:

PI = PV of cash Inflows / PV of Cash Outflows

Machine A:

Year	CF	PVF @12%	Disc CF
1	$ 18,300.00	0.8929	$ 16,339.29
2	$ 18,300.00	0.7972	$ 14,588.65
3	$ 18,300.00	0.7118	$ 13,025.58
4	$ 18,300.00	0.6355	$ 11,629.98
5	$ 18,300.00	0.5674	$ 10,383.91
6	$ 18,300.00	0.5066	$    9,271.35
7	$ 18,300.00	0.4523	$    8,277.99
8	$ 18,300.00	0.4039	$    7,391.06
PV of Cash Inflows			$ 90,907.81
PV of Cash Out flows			$ 85,500.00
PI			1.06

Machine B:

Year	CF	PVF @12%	Disc CF
1	$ 11,600.00	0.8929	$ 10,357.14
2	$ 14,400.00	0.7972	$ 11,479.59
3	$ 16,000.00	0.7118	$ 11,388.48
4	$ 17,900.00	0.6355	$ 11,375.77
5	$ 19,600.00	0.5674	$ 11,121.57
6	$ 24,500.00	0.5066	$ 12,412.46
7	$                 -	0.4523	$                 -
8	$                 -	0.4039	$                 -
PV of Cash Inflows			$ 68,135.02
PV of Cash Out flows			$ 59,700.00
PI			1.14

Machine C:

Year	CF	PVF @12%	Disc CF
1	$      49,900.00	0.8929	$      44,553.57
2	$      30,500.00	0.7972	$      24,314.41
3	$      20,000.00	0.7118	$      14,235.60
4	$      20,400.00	0.6355	$      12,964.57
5	$      19,700.00	0.5674	$      11,178.31
6	$      29,600.00	0.5066	$      14,996.28
7	$      39,800.00	0.4523	$      18,003.50
8	$      49,600.00	0.4039	$      20,032.61
PV of Cash Inflows			$ 1,60,278.86
PV of Cash Out flows			$ 1,29,600.00
PI			1.24

Part E:

Machine C, Machine B, Machine A respectively.