Question

HopHeart Brewery is considering 3 different bottling machines.
It is expected that each machine will be replaceable at the same
cost when their useful life ends. The details of the machines are
as follows:

Machine X has a useful life of 6 years. It costs $10,000 to
purchase and $2,000 per year to maintain.

Machine Y has a useful life of 12 years. It costs $15,000 to
purchase, and $1,000 per year to maintain.

Machine Z has a useful life of 8 years. It costs $20,000 to
purchase, and $200 per year to maintain.

a) What is the appropriate planning horizon for analyzing these
choices? years

b) Using the planning horizon from part a, analyze the present
worth of the cost of each alternative if HopHeart has a MARR of
8.9%/year.

Answer #1

a) Appropriate planning horizon = LCM (6,12,8) = 24 years

b)

Machine X:

X = -10000 - 2000/(1 + 8.9%) - .... - 2000/(1 +
8.9%)^{6} = - $ 18998.65

PW = X + X/1.089^{6} + X/1.089^{12} +
X/1.089^{18}

PW = - $ 41313.66

Machine Y:

Y = -15000 - 1000/(1 + 8.9%) - .... - 1000/(1 +
8.9%)^{12} = - $ 22196.94

PW = Y + Y/1.089^{12}

PW = - $ 30176.13

Machine Z:

Z = -20000 - 200/(1 + 8.9%) - .... - 200/(1 + 8.9%)^{8}
= - $ 21111.09

PW = Z + Z/1.089^{8} + Z/1.089^{16}

PW = - $ 37180.03

(Lowest cost option = Machine Y)

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It is expected that each machine will be replaceable at the same
cost when their useful life ends. The details of the machines are
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purchase and $2,000 per year to maintain.
Machine Y has a useful life of 12 years. It costs $15,000 to
purchase, and $1,000 per year to maintain.
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