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 10%. 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.

Machine 1 2 3

Initial investment   85,000   60,100   129,700
Year          
1 18,400   11,600   50,300
2   18,400   14,100   29,900
3 18,400   16,400   20,100
4 18,400   18,200   20,000
5 18,400   20,300   19,900
6 18,400   25,000   29,800
7 18,400   0   39,800
8 18,400   0   49,500

Answer 1

a) NPV is calcualted as follows:

Machine 1:

Year	CF	Discount Factor	Discounted CF
0	$-85,000.00	1/(1+0.1)^0=	1	1*-85000=	-85,000.00
1	$ 18,400.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*18400=	16,727.27
2	$ 18,400.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*18400=	15,206.61
3	$ 18,400.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*18400=	13,824.19
4	$ 18,400.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*18400=	12,567.45
5	$ 18,400.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*18400=	11,424.95
6	$ 18,400.00	1/(1+0.1)^6=	0.56447393	0.564473930053777*18400=	10,386.32
7	$ 18,400.00	1/(1+0.1)^7=	0.513158118	0.513158118230706*18400=	9,442.11
8	$ 18,400.00	1/(1+0.1)^8=	0.46650738	0.466507380209733*18400=	8,583.74
				NPV = Sum of all Discounted CF	13,162.64

Machine 2:

Year	CF	Discount Factor	Discounted CF
0	$-60,100.00	1/(1+0.1)^0=	1	1*-60100=	-60,100.00
1	$ 11,600.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*11600=	10,545.45
2	$ 14,100.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*14100=	11,652.89
3	$ 16,400.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*16400=	12,321.56
4	$ 18,200.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*18200=	12,430.84
5	$ 20,300.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*20300=	12,604.70
6	$ 25,000.00	1/(1+0.1)^6=	0.56447393	0.564473930053777*25000=	14,111.85
				NPV = Sum of all Discounted CF	13,567.31

Machine 3:

Year	CF	Discount Factor	Discounted CF
0	$ -1,29,700.00	1/(1+0.1)^0=	1	1*-129700=	-1,29,700.00
1	$      50,300.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*50300=	45,727.27
2	$      29,900.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*29900=	24,710.74
3	$      20,100.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*20100=	15,101.43
4	$      20,000.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*20000=	13,660.27
5	$      19,900.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*19900=	12,356.33
6	$      29,800.00	1/(1+0.1)^6=	0.56447393	0.564473930053777*29800=	16,821.32
7	$      39,800.00	1/(1+0.1)^7=	0.513158118	0.513158118230706*39800=	20,423.69
8	$      49,500.00	1/(1+0.1)^8=	0.46650738	0.466507380209733*49500=	23,092.12
				NPV = Sum of all Discounted CF	42,193.18

b) As machine 3 has the highest NPV it should be invested in even though all the NPVs are positive because only one machine can replace the old one and therefore these projects are mutually exclusive

c)

Machine 3 is ranked 1st with highest NPV

Machine 2 is ranked 2nd with the second highest NPV

Machine 1 is ranked 3rd with lowest NPV

d) Pi is calculated by the following formula:

e) Again the same rankings are given as the highest PI is for machine 3 and lowest for machine 1