Question

Evans Industries wishes to select the best of three possible​ machines, each of which is expected to satisfy the​ firm's ongoing need for additional​ aluminum-extrusion capacity. The three machines -A, B, and C -are equally risky. The firm plans to use a cost of capital of 11.9 % to evaluate each of them. The initial investment and annual cash inflows over the life of each machine are shown in the following table.

	Machine A	Machine B	Machine C
Initial investment	92700	65600	100000
Year		Cash inflows
1	11200	10100	29500
2	11200	20200	29500
3	11200	30000	29500
4	11200	39200	29500
5	11200	-	29500
6	11200	-	-

a. Calculate the NPV for each machine over its life. Rank the machines in descending order on the basis of NPV.

b. Use the annualized net present value​ (ANPV) approach to evaluate and rank the machines in descending order on the basis of ANPV.

c. Compare and contrast your findings in parts​(a​) and ​(b​).Which machine would you recommend that the firm​ acquire?

Answer 1

a) NPV

For Machine A

Statement showing NPV

Year	Cash Inflow	PVIF @ 11.9%	PV
	A	B	C = A x B
1	11200	0.8937	10009
2	11200	0.7986	8945
3	11200	0.7137	7993
4	11200	0.6378	7143
5	11200	0.5700	6384
6	11200	0.5094	5705
PV of cash Inflow			46178
Less : Initial Investment			92700
NPV			-46522

Thus NPV = -46522 $

For Machine B

Statement showing NPV

Year	Cash Inflow	PVIF @ 11.9%	PV
	A	B	C = A x B
1	10100	0.8937	9026
2	20200	0.7986	16132
3	30000	0.7137	21411
4	39200	0.6378	25001
PV of cash Inflow			71570
Less : Initial Investment			65600
NPV			5970

Thus NPV = $5970

For Machine C

Statement showing NPV

Year	Cash Inflow	PVIF @ 11.9%	PV
	A	B	C = A x B
1	29500	0.8937	26363
2	29500	0.7986	23559
3	29500	0.7137	21054
4	29500	0.6378	18815
5	29500	0.5700	16814
PV of cash Inflow			106605
Less : Initial Investment			100000
NPV			6605

Thus NPV = $6605

Statement showing rank of machine according to NPV

Rank	Machine	NPV
1	C	6605
2	B	5970
3	A	-46522

b)  annualized net present value​ (ANPV)

For Machine A

Statement showing ANPV

Particulars	Amount
NPV	-46522
PVIFA(11.9%,6)	4.1231
ANPV (-46522/4.1231)	-11283

For Machine B

Statement showing ANPV

Particulars	Amount
NPV	5970
PVIFA(11.9%,4)	3.0438
ANPV (-46522/3.0438)	1961

For Machine C

Statement showing ANPV

Particulars	Amount
NPV	6605
PVIFA(11.9%,5)	3.6137
ANPV (-46522/3.6137)	1828

Statement showing rank of machine according to ANPV

Rank	Machine	ANPV
1	B	1961
2	C	1826
3	A	-11283

c) As per NPV appraoch machine C should be selected and as per ANPV approach Machine B should be selected. sometimes it may happen that due to life of machine NPV of one projects is higher than other project having less life. In such cases it is prudent to compare them on equal standings. Thus Benefits are seen on annual basis and than selection shall be made. ANPV does the same. Hence Machine B should be selected