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After the second upgrade in either path, there is a split-off point.
In the context of production, a split-off point is the point at which joint products appear in the production process.
Further processing cost is the cost incurred to make joint products ready for further use or sale after the production process' split-off point.
When sawing timber, both lumber and scrap wood appear, thus the activity of sawing is the split-off point in this production process.
Joint cost is the collection of the common operation costs incurred before a point called, split-off point, where joint products are identified as individual products.