If you target a creature with ward, you may still pay the ward cost, but Abrupt Decay won't be countered even if you don't.

A spell or ability that counters spells can still target Abrupt Decay. When that spell or ability resolves, Abrupt Decay won't be countered, but any additional effects of the countering spell or ability will still happen.

The mana value of a token that isn't a copy of another object is 0. A token that is a copy of another object has the same mana cost as that object.

If a permanent has {X} in its mana cost, X is considered to be 0.