QB Issue Resolution:
Pay the expense using a current asset account you create called something like wip
then open the original bill that stocked the item purchased
add a portion of the expense to each items total cost
change the expense part of the purchase, list the wip account, enter the amount of the expense as a negative number
the bill should now be the same amount as it started out, save and click through any warnings about payments being applied
QB will redo the purchase average cost for the item as of the bill date, and any sales of that item since that date will also be adjusted for the new item cost – you will see “Bill” in the COGS detail report
Resolution for Issue 'How do I enter an additional expense for a stock item after the purchase has been entered to increase the cost of the item but not add another one to the inventory?' available: Yes (Solved).
Source: Intuit Community forum.
How do I enter an additional expense for a stock item after the purchase has been entered to increase the cost of the item but not add another one to the inventory?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.Support for COGS detail
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