Air carrier Captain reported executing a go-around at SAN when Tower cleared an aircraft for take-off with insufficient spacing.

Narrative

On short final for Runway 27 on the RNP-M in SAN. Shortly after my FO (First Officer) called 500 [ft.]; we heard ATC clear an aircraft for immediate takeoff off Runway 27. I instantly conferred whether there was an aircraft on the runway with my First Officer as I could not see anything. We had a very brief conversation about it; questioning if we had a wrong frequency in Comms 2; that had come in for a different airport as we could not see another aircraft on the runway; and it seemed unlikely that such clearance was being issued given how close to touchdown we were. I suddenly noticed the center lights of the runway disappearing and reappearing; subsequently realizing there was in fact an aircraft taking off. Within a second or two; ATC issued a go-around; which I was anticipating at that point and executed instantly. ATC told us to start a left turn almost immediately; which I did as I was concerned about climbing over the departing aircraft.There was a bit of confusion on the heading ATC wanted us to fly on our part; so I continued the turn over the bay where I knew I would have the best visibility due to the lack of city lights. The go-around was uneventful; and ATC gave us further climb and heading instructions putting [us] on the downwind for Runway 27. We ran through our procedures to get the aircraft set up for landing on Runway 27; and landed uneventfully.