Is there a possible compatibility between immutability and God's mercy?

Objection: 1. If God exists, He is immutable. 2. If God exists, he is merciful. 3. An immutable being cannot be affected by any event (since God is not subject to change). 4. A merciful being must be affected by certain events (to be merciful one must feel pity). 5. Therefore, it is impossible for an immutable being to feel mercy. 6. Therefore, God does not exist. Is this really contradictory? How can this objection be refuted?