Amulet of Cold Resistance
This amulet looks like a shining shard of ice. The wearer of this amulet gains cold resistance 10. Once the amulet has absorbed 100 points of cold damage, it loses its magic and becomes useless.
How to calculate the cost for such an item? Please help.
It's resist energy (CL3) without an action required to cast. As an item it's most similar to a lesser talisman. I'd price it like a lesser talisman of protection from flames, reduced for being based on resist energy rather than protection from energy i.e. (2x3 / 3x5) = 0.4 of the cost of that talisman which makes 500 gp. The potential difference in duration can be countered by the way this takes up the entire neck slot, unlike a lesser talisman which can share the neck slot with two others.
All IMO of course. Everyone has different opinions on what custom items should cost.