Question

  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 8​%.

	Machine A	Machine B	Machine C
Initial investment ​(CF 0CF0​)	​$84,500	​$59,600	​$130,200
Year​ (t)	Cash inflows ​(CF Subscript tCFt​)
1	​$18,400	​$11,900	​$50,200
2	​$18,400	​$14,400	​$30,100
3	​$18,400	​$15,800	​$20,100
4	​$18,400	​$18,100	​$19,900
5	​$18 comma 40018,400	​$20 comma 10020,100	​$20,300
6	​$18,400	​$25,000	​$30,200
7	​$18,400		​$39,500
8	​$18,400	l	​$49500

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

(a)-The net present value ​(NPV​) of each press.

The Net Present Value ​(NPV​) of MACHINE-A

Year	Annual cash flows ($)	Present Value Factor (PVF) at 8.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	18,400	0.925926	17,037.04
2	18,400	0.857339	15,775.03
3	18,400	0.793832	14,606.51
4	18,400	0.735030	13,524.55
5	18,400	0.680583	12,522.73
6	18,400	0.630170	11,595.12
7	18,400	0.583490	10,736.22
8	18,400	0.540269	9,940.95
TOTAL			1,05,738.16

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $1,05,738.16 - $84,500

= $21,238.16

The Net Present Value ​(NPV​) of MACHINE-B

Year	Annual cash flows ($)	Present Value Factor (PVF) at 8.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	11,900	0.925926	11,018.52
2	14,400	0.857339	12,345.68
3	15,800	0.793832	12,542.55
4	18,100	0.735030	13,304.04
5	20,100	0.680583	13,679.72
6	25,000	0.630170	15,754.24
TOTAL			78,644.75

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $78,644.75 - $59,600

= $19,044.75

The Net Present Value ​(NPV​) of MACHINE-C

Year	Annual cash flows ($)	Present Value Factor (PVF) at 8.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	50,200	0.925926	46,481.48
2	30,100	0.857339	25,805.90
3	20,100	0.793832	15,956.03
4	19,900	0.735030	14,627.09
5	20,300	0.680583	13,815.84
6	30,200	0.630170	19,031.12
7	39,500	0.583490	23,047.87
8	49,500	0.540269	26,743.31
TOTAL			1,85,508.64

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $1,85,508.64 - $130,200

= $55,308.64

(b)-The acceptability of each press.

The Machine-C should be accepted, since has the highest NPV of $55,308.64

(c)-The ranking of the presses from best to worst using NPV.

MACHINE-C = Rank 1

MACHINE-A = Rank 2

MACHINE-B = Rank 3

(d)-The profitability index​ (PI) for each press.

The Profitability Index (PI) for Machine-A = Present Value of annual cash inflows / Initial Investment

= $1,05,738.16 / $84,500

= 1.25

The Profitability Index (PI) for Machine-B = Present Value of annual cash inflows / Initial Investment

= $78,644.75 / $59,600

= 1.32

The Profitability Index (PI) for Machine-C = Present Value of annual cash inflows / Initial Investment

= $1,85,508.64 / $130,200

= 1.42

(e)-The ranking of the presses from best to worst using PI

MACHINE-C = Rank 1

MACHINE-B = Rank 2

MACHINE-C = Rank 3

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.