A company that manufactures clear PVC pipe is investigating the production options of batch and continuous processing. Estimated cash flows are:

Question

The chief operating officer (COO) has asked you to determine if the batch option would ever have a lower annual worth than the continuous flow sys­tem using an interest rate of 15% per year. The continuous flow process was previously deter­mined to have its lowest cost over a 5-year life cycle, but the batch process can be used from 3 to 10 years. If selecting the batch process is sensitive to its useful life, what is the minimum life that makes it more attractive? Solve (a) by hand, and (b) by spreadsheet.

Answer 1

(a) By hand:

AWcont = -140,000(A/P,15%,5) - 31,000 + 25,000(A/F,15%,5)

= -140,000(0.29832) - 31,000 + 25,000(0.14832)

= $-69,057



The lowest cost for batch will occur when its life is longest, 10 years

At n = 10: AWbatch = -80,000(A/P,15%,10) – 52,000 + 10,000(A/F,15%,10)

= -80,000(0.19925) – 52,000 + 10,000(0.04925)

= $-67,448 (< $-69,057; acceptable)



Try n = 9: AWbatch = -80,000(A/P,15%,9) – 52,000 + 10,000(A/F,15%,9)

= -80,000(0.20957) – 52,000 + 10,000(0.05957)

= $-68,170 (< $-69,057; acceptable)



Try n = 8: AWbatch = -80,000(A/P,15%,8) – 52,000 + 10,000(A/F,15%,8)

= -80,000(0.22285) – 52,000 + 10,000(0.07285)

= $-69,100 (> $-69,057; marginally not acceptable)



The batch system will be less expensive than continuous flow if it lasts at least 8 years



(b) Spreadsheet: An expected life of slightly over 8 years is required to select the batch

process.