Question

"A company is considering two types of machines for a manufacturing process. Machine A has an immediate cost of $87,000, and its salvage value at the end of 8 years of service life is $29,000. The operating costs of this machine are estimated to be $5700 per year. Extra income taxes are estimated at $1500 per year. Machine B has an immediate cost of $44,000, and its salvage value at the end of 8 years' service is neglible. The annual operating costs for Machine B will be $5,000. There are no extra income taxes with Machine B. Compare these two mutually exclusive alternatives by the present-worth method at i = 14.2%. Enter the ""net present cost"" as a positive number for the machine that you would select. You must select one of the two machines."

Answer 1

Net present cost, Machine A = 87,000 + (5,700 + 1,500) x P/A(14.2%, 8) - 29,000 x P/F(14.2%, 8)

= 87,000 + 7,200 x P/A(14.2%, 8) - 29,000 x P/F(14.2%, 8)

= 87,000 + 7,200 x 4.6079** - 29,000 x 0.3457**

= 87,000 + 33,176.88 - 10,025.3

= 110,151.58

Net present cost, Machine B = 44,000 + 5,000 x P/A(14.2%, 8) - 0 x P/F(14.2%, 8)

= 44,000 + 5,000 x P/A(14.2%, 8)

= 44,000 + 5,000 x 4.6079**

= 44,000 + 23,039.5

= 67,039.5

Since Machine B has lower Net present cost of $67,039.5, Machine B is better option.

**P/A(14.2%, 8) = [1 - (1.142)-8] / 0.142 = (1 - 0.3457) / 0.142 = 0.6543 / 0.142 = 4.6079

**P/F(14.2%, 8) = (1.142)-8 = 0.3457