Year End Inventory problem

QB uses only the average-cost method.
Some other software uses some other methods, most often "FIFO". 

When inventory turns over frequently there is little or no difference in the results of any of the common inventory cost methods.

What you say you want sounds like "replacement cost" which is not a commonly accepted method, but FIFO may produce very similar results in most circumstances.  I suggest you discuss your requirements with your own professional accountant.  If this is important you may want to investigate a 3rd-party inventory addition to QB, or investigate other bookkeeping software.

QB  ***CAN***  track your most recent cost, but it will not use this amount for valuation of inventory or COGS.  If you open the profile of an inventory item you will notice a field labelled "Cost" in addition to the average cost.  You can manually enter a value in the Cost field, and there is an option to let QB update this value with each new purchase.  If QB does not currently update the Cost field or ask you whether to update it when you purchase inventory at a new price, it is because you have turned the option "off".  In that case you can turn it back on as follows:
Edit >> Preferences >> General >> My Preferences:
"Bring back all one time messages."
Then, next time you record an inventory purchase at a new price you should be asked whether to let QB "update the cost of this item" - select "Yes" and "Do not ask again", and QB should henceforth automatically update the Cost field.

Perhaps this will help solve your problem.  For example, you might be able to modify an Inventory report to include a column for the Cost field, then export the report to Excel to use this field in calculating new inventory values.