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