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:

The​ firm's cost of capital is 13​%.

Initial investment   $84,800   $60,100   $130,300
Year          
1   $18,500   $12,300   $50,000
2   $18,500   $13,700   $29,500
3   $18,500   $16,100   $20,500
4   $18,500   $18,300   $20,500
5   $18,500   $20,400   $20,300
6   $18,500   $25,100   $30,000
7   $18,500   $0 $40,000
8   $18,500   $0 $49,900

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

Part A:

NPV = PV of Cash Inflows - PV of Cash Outflows

Machine A:

Year	CF	PVF @13%	Disc CF
0	$ -84,800.00	1.0000	$ -84,800.00
1	$ 18,500.00	0.8850	$ 16,371.68
2	$ 18,500.00	0.7831	$ 14,488.21
3	$ 18,500.00	0.6931	$ 12,821.43
4	$ 18,500.00	0.6133	$ 11,346.40
5	$ 18,500.00	0.5428	$ 10,041.06
6	$ 18,500.00	0.4803	$    8,885.89
7	$ 18,500.00	0.4251	$    7,863.62
8	$ 18,500.00	0.3762	$    6,958.96
NPV			$    3,977.25

Machine B:

Year	CF	PVF @13%	Disc CF
0	$ -60,100.00	1.0000	$ -60,100.00
1	$ 12,300.00	0.8850	$ 10,884.96
2	$ 13,700.00	0.7831	$ 10,729.11
3	$ 16,100.00	0.6931	$ 11,158.11
4	$ 18,300.00	0.6133	$ 11,223.73
5	$ 20,400.00	0.5428	$ 11,072.30
6	$ 25,100.00	0.4803	$ 12,056.00
7	$                 -	0.4251	$                 -
8	$                 -	0.3762	$                 -
NPV			$    7,024.20

Machine C:

Year	CF	PVF @13%	Disc CF
0	$ -1,30,300.00	1.0000	$ -1,30,300.00
1	$      50,000.00	0.8850	$      44,247.79
2	$      29,500.00	0.7831	$      23,102.83
3	$      20,500.00	0.6931	$      14,207.53
4	$      20,500.00	0.6133	$      12,573.03
5	$      20,300.00	0.5428	$      11,018.03
6	$      30,000.00	0.4803	$      14,409.56
7	$      40,000.00	0.4251	$      17,002.43
8	$      49,900.00	0.3762	$      18,770.38
NPV			$     25,031.56

Part B:

As Each Project has +ve NPV, We can select all projects.

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 @13%	Disc CF
1	$      18,500.00	0.8850	$      16,371.68
2	$      18,500.00	0.7831	$      14,488.21
3	$      18,500.00	0.6931	$      12,821.43
4	$      18,500.00	0.6133	$      11,346.40
5	$      18,500.00	0.5428	$      10,041.06
6	$      18,500.00	0.4803	$        8,885.89
7	$      18,500.00	0.4251	$        7,863.62
8	$      18,500.00	0.3762	$        6,958.96
PV of Cash Inflows			$      88,777.25
PV of Cash Out flows			$      84,800.00
PI			1.05

Machine B:

Year	CF	PVF @13%	Disc CF
1	$      12,300.00	0.8850	$      10,884.96
2	$      13,700.00	0.7831	$      10,729.11
3	$      16,100.00	0.6931	$      11,158.11
4	$      18,300.00	0.6133	$      11,223.73
5	$      20,400.00	0.5428	$      11,072.30
6	$      25,100.00	0.4803	$      12,056.00
7	$                    -	0.4251	$                    -
8	$                    -	0.3762	$                    -
PV of Cash Inflows			$      67,124.20
PV of Cash Out flows			$      60,100.00
PI			1.12

Machine C:

Year	CF	PVF @13%	Disc CF
1	$      50,000.00	0.8850	$      44,247.79
2	$      29,500.00	0.7831	$      23,102.83
3	$      20,500.00	0.6931	$      14,207.53
4	$      20,500.00	0.6133	$      12,573.03
5	$      20,300.00	0.5428	$      11,018.03
6	$      30,000.00	0.4803	$      14,409.56
7	$      40,000.00	0.4251	$      17,002.43
8	$      49,900.00	0.3762	$      18,770.38
PV of Cash Inflows			$ 1,55,331.56
PV of Cash Out flows			$ 1,30,300.00
PI			1.19

Part E:

Ranking :

Machine C

Machine B

Machine A