The Cost Price can be changed in Dimensions in the following location:
Navigate to Stock Control, Stock
Locate the Stock Item
Select Cost Price
Click Edit
Update the cost price and select save
It should be noted that there are other methods of changing stock prices, such as import utility and Access Office Integration (AOI). Note that changing a cost price only changes the cost price for stock movements going forward - there will be no change on existing movements.
If you see stock movements where a cost price changes for a period of time before changing back to the previous value it is likely that the cost price was updated and then changed back to the original value