Hi Lamounia,
If you open the "on-hand stock" window available in the manage stock tab you can identify the current (so-called running cost) price of an item. I believe this is the best place checking an item's current cost price and requires only one mouse click more :-). That is because the price field you refer to can only hold one cost price and cannot deal with situations where you have different cost prices for different inventory dimensions such as sites, warehouses and alike. For that reason, the information you display there might even be misleading.
I suggest that you make one mouse click more and use the Standard AX functionality rather than trying to bring a value into this field that might possibly not help much.
All the best,
Ludwig