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/1.089⁶ + X/1.089¹² + X/1.089¹⁸

PW = - $ 41313.66

Machine Y:

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

PW = Y + Y/1.089¹²

PW = - $ 30176.13

Machine Z:

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

PW = Z + Z/1.089⁸ + Z/1.089¹⁶

PW = - $ 37180.03

(Lowest cost option = Machine Y)