Question

Unequal

liveslong dash—ANPV

approach   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

machineslong dash—​A,

​B, and

Clong dash—are

equally risky. The firm plans to use a cost of capital of

12.3 %

to evaluate each of them. The initial investment and annual cash inflows over the life of each machine are shown in the following table.  ​(Click on the icon located on the​ top-right corner of the data table below in order to copy its contents into a​ spreadsheet.)

	Machine A	Machine B	Machine C
Initial investment ​(CF 0CF0​)	​$92 comma 60092,600	​$64 comma 40064,400	​$101 comma 200101,200
Year ​(tt ​)	Cash inflows ​(CF Subscript tCFt​)
1	​$12 comma 20012,200	​$9 comma 0009,000	​$29 comma 70029,700
2	12 comma 20012,200	19 comma 30019,300	29 comma 70029,700
3	12 comma 20012,200	29 comma 70029,700	29 comma 70029,700
4	12 comma 20012,200	40 comma 80040,800	29 comma 70029,700
5	12 comma 20012,200	long dash—	29 comma 70029,700
6	12 comma 20012,200	long dash—	long dash—

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 each machine

MACHINE-A

Year	Annual Cash Flow	Present Value factor at 12.30%	Present Value of Cash Flow
1	12,200	0.890472	10,863.76
2	12,200	0.792940	9,673.87
3	12,200	0.706091	8,614.31
4	12,200	0.628754	7,670.80
5	12,200	0.559888	6,830.63
6	12,200	0.498565	6,082.49
TOTAL		4.076710	49,735.87

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

= $49,735.87 - $92,600

= -$42,964.13 (Negative NPV)

MACHINE-B

Year	Annual Cash Flow	Present Value factor at 12.30%	Present Value of Cash Flow
1	9,000	0.89047	8,014.25
2	19,300	0.79294	15,303.75
3	29,700	0.70609	20,970.91
4	40,800	0.62875	25,653.18
TOTAL		3.01826	69,942.08

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

= $69,942.08 - $64,400

= $5,542.08

MACHINE-C

Year	Annual Cash Flow	Present Value factor at 12.30%	Present Value of Cash Flow
1	29,700	0.890472	26,447.02
2	29,700	0.792940	23,550.33
3	29,700	0.706091	20,970.91
4	29,700	0.628754	18,674.00
5	29,700	0.559888	16,628.68
TOTAL		3.578146	1,06,270.93

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

= $1,06,270.93 - $101,200

= $5,070.93

Ranking of Machine Based on NPV on Descending Order

MACHINE – A = Rank 1

MACHINE – B = Rank 3

MACHINE – C = Rank 2

(b)-Annualized Net Present Value (ANPV)

MACHINE-A

Annualized Net Present Value (ANPV) = Net Present Value / [PVIFA 12.30%, 6 Years]

= -$42,864.13 / 4.076710

= -$10,514.39

MACHINE-B

Annualized Net Present Value (ANPV) = Net Present Value / [PVIFA 12.30%, 4 Years]

= $5,542.08 / 3.01826

= $1,836.18

MACHINE-C

Annualized Net Present Value (ANPV) = Net Present Value / [PVIFA 12.30%, 5 Years]

= $5,070.93 / 3.578146

= $1,417.19

Ranking of Machine Based on Annualized Net Present Value (ANPV) on Descending Order

MACHINE – A = Rank 1

MACHINE – B = Rank 3

MACHINE – C = Rank 2

(c)-DECISION

“Machine – B” Should be acquired since it offers the highest ANPV of $1,836.18

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.