Question

The manager of a canned food processing plant is trying to decide between two labeling. machines. Determine which machine should be selected on the basis of rate of return with a MARR of 20 % per year.

Answer 1

Net present value calculations are used to determine which project is the most efficient to choose from several alternatives by performing a comparative analysis among multiple projects. The project with the highest net present value is then chosen as the best investment option. Or similarly, we can reformulate selection criteria as a project which incurs the minimum cost (assuming the same level of profit from both machines after acquiring it) is chosen.

For a future value FV due after n years at a discount rate of r%, the present value is calculated as:

PV = \frac{FV}{(1+r)^n}

Common notation to express this calculation is P = (P/F, i%, n).

In the case of multiple equal size and space payments (Uniform series payments) like annual costs or benefits, notation is P = (P/A, i%, n)

For Machine A:

To do equivalent analysis since the life of machine B is 4 years, we have to assume that if machine A is purchased at t=0, it needs to be purchased again at t=2 for equivalency.

For Machine B:

Machine B provides a greater net present value or in another way we can say that Machine A incurs a larger cost when purchased twice in 4 years as compared to the one-time purchase of machine B.

Hence Machine B should be chosen.

FV PV = 1+r"

-15000 15000(P/F, 20%, 2)- 1600(P/A, 20%, 4)+ Net present value 3000(P/F, 20%, 2) 3000(P/F, 20%, 4) 15000 1600 1600 1600 1600 3000 3000 NPV -15000 1.22 1.21 1.22 1.23 1.24 1.22 1.24 925.93 771.612083.33+ -15000 10416.67 1333.33 1111.11 1446.76 -26028.56

Net present value 25000 400(P/A, 20%, 4) + 4000(P/F, 20%, 2)

400 400 400 400 4000 NPV =-25000 1.24 -24106.48 1.22 1.23 1.24 1.21

Answer 2