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 10​%.

	Machine A	Machine B	Machine C
Initial investment ​(CF 0CF0​)	​$85,300	​$60,400	​$130,400
Year​ (t)	Cash inflows ​(CF Subscript tCFt​)
1	​$18,100	​$12,400	​$49,700
2	​$18,100	​$13,700	​$30,300
3	​$18,100	​$15,900	​$19,500
4	​$18,100	​$18,400	​$19,800
5	​$18,100	​$19,500	​$19,900
6	​$18,100	​$24,600	​$30,200
7	​$18,100	—	​$40,100
8	​$18,100	—	​$49,700

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) NPV of Machine A

=-85300+ 18100/1.1+ 18100/1.1^2+...+18100/1.1^8

=-85300+18100/0.1*(1-1/1.1^8)

=-85300+96562.16

=$11262.16

NPV of Machine B

=-60400+ 12400/1.1+ 13700/1.1^2+15900/1.1^3+18400/1.1^4+19500/1.1^5+24600/1.1^6

=-60400+73102.42

=$12702.42

NPV of Machine C

=-130400+ 49700/1.1+ 30300/1.1^2+19500/1.1^3+19800/1.1^4+19900/1.1^5+30200/1.1^6+ 40100/1.1^7+49700/1.1^8

=-130400+171563.95

=$41163.95

b) As the NPV of all the three presses are positive , all the three presses are acceptable

c) The better the NPV, better the ranking

As NPV(C)>NPV(B)>NPV(A)

C is the best followed by B and A is the worst

d) PI of machine A = PV of Benefit/Initial Cost = 96562.16/85300 = 1.13203

PI of machine B = PV of Benefit/Initial Cost = 73102.42/60400 = 1.2103

PI of machine C = PV of Benefit/Initial Cost = 171563.95/130400 = 1.315674

e)

The better the PI, better the ranking

As PI(C)>PI(B)>PI(A)

C is the best followed by B and A is the worst