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?

b) Using the planning horizon from part a, analyze the present worth of the cost of each alternative if HopHeart has a MARR of 9.8%/year.

Machine X _____________

Machine Y _____________

Machine Z _____________

Answer 1

Since, each machine is replaceable at the same cost when their useful life ends, appropriate planning horizon will be lowest possible multiple of useful life of all three machines i.e. lowest common multiple of 6, 12 & 8 years.

Hence, appropriate planning horizon is 24 years.

Cash flow for Machine X

• Capital expenditure of $10000 at time 0, 6, 12 & 18
• Maintenance expenditure of $2000 from time 1 to 24

PW (Machine X) = -10000 – 10000/(1+9.8%)^6 – 10000/(1+9.8%)^12 – 10000/(1+9.8%)^18 – 2000*PVIFA(9.8%,24)

Cash flow for Machine Y

• Capital expenditure of $15000 at time 0 & 12
• Maintenance expenditure of $1000 from time 1 to 24

PW (Machine Y) = -15000 – 15000/(1+9.8%)^12 – 1000*PVIFA(9.8%,24)

Cash flow for Machine Z

• Capital expenditure of $20000 at time 0, 8 & 16
• Maintenance expenditure of $200 from time 1 to 24

PW (Machine X) = -20000 – 20000/(1+9.8%)^8 – 20000/(1+9.8%)^16 – 200*PVIFA(9.8%,24)

PVIFA(9.8%,24) = (1-(1+9.8%)^(-24))/9.8% = 9.121856

Calculating NPV from above equations, using the value of PVIFA(9.8%,24)

PW (Machine X) = -10000 – 5706.71 – 3256.66 – 1858.48 – 18243.7 = -$39065.56

PW (Machine Y) = -15000 – 4884.98 – 9121.86 = -$29006.84

PW (Machine Z) = -20000 – 9466.98 – 4481.18 – 1824.37 = -$35772.53