Question

"A company is considering two types of machines for a
manufacturing process. Machine A has an immediate cost of $61,000,
and its salvage value at the end of 4 years of service life is
$14,000. The operating costs of this machine are estimated to be
$3900 per year. Extra income taxes are estimated at $1800 per
year.

Machine B has an immediate cost of $45,000, and its salvage value
at the end of 4 years' service is neglible. The annual operating
costs for Machine B will be $17,000. There are no extra income
taxes with Machine B.

Compare these two mutually exclusive alternatives by the
present-worth method at i = 17.6%. 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

PW of cost, Machine A ($) = 61,000 + (3,900 + 1,800) x P/A(17.6%, 4) - 14,000 x P/F(17.6%, 4)

= 61,000 + 5,700 x 2.7111** - 14,000 x 0.5228^{#} =
61,000 + 15,453.27 - 7,319.2

= 69,134.07

PW of cost, Machine B ($) = 45,000 + 17,000 x P/A(17.6%, 4)

= 45,000 + 17,000 x 2.7111** = 45,000 + 46,088.7

= 91,088.7

Since Machine A has a lower PW of costs, **Machine A is
selected (with PW = $69,134.07).**

**P/A(r%, N) = [1 - (1 + r)^{-N}] / r

P/A(17.6%, 4) = [1 - (1.176)^{-4}] / 0.176 = (1 -
0.5228) / 0.176 = 0.4772 / 0.176 = 2.7111

#P/F(r%, N) = (1 + r)^{-N}

P/A(17.6%, 4) =(1.176)^{-4} = 0.5228

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