Hello,
There are some items in inventory which we received free of cost.
We want to set the cost price of these items as 1 only.
This price can not be calculated using CP, AP or LP Price. If we use SI Price for these items, for the time being, then the next time the cost is updated, the cost will be updated using CP, AP or LP (whatever is set in the master), for these items, and hence the inventory valuation will go up.
Is there any solution to avoid this?

In your actual calculation code you specify the priority of Si, Cp, Ap and Lp.
If Si has a higher priority and you have a Si value against the calc code it will always be used and not the other options. If you do not have Si against the calc. code the following priority will be used.