A Fractional company pilot reported they initiated a go around from short final approach when ATC issued a takeoff clearance to an aircraft on the same runway.

Narrative

Our flight from ZZZ to ZZZ1 went smoothly until we were on short final to land. We were fully configured; stabilized and flying visually by hand. We were cleared to land. At 500 feet we booth said stabilized. However; Tower gave a take off clearance to a aircraft holding short our landing runway (runway XX). We were short final below 500 ft. We recognized this as a critical threat to the flight and executed a go-around. I am confident that if we continued to land that we would have collided with the aircraft taxing into position and taking off.After we did our stabilized calls at 500 feet I heard tower give a takeoff clearance to a aircraft holding short our landing runway. I also visually seen the aircraft slowly cross the hold short bars as we were still on short final below 500 ft.Cause: ATC giving a takeoff clearance to an aircraft holding short our landing runway when we were short final below 500 feet. I was the PF and immediately recognized this as a runway incursion issue. I reached up and annunciated 'going around' and we executed a go around. I believed it to be time critical to transmit our intentions so the aircraft does not takeoff under us. Tower heard our call and immediate canceled the takeoff clearance for the other aircraft. We made left traffic and landed after a second approach.I think tower could have noticed the traffic conflict prior to US. Secondly; the aircraft on the ground likely did not look to make sure they were clear of traffic before they took the runway. I believe looking out the window would have made us a very apparent traffic conflict to them. I believe that I always have room for improvement. This was a very unexpected go around and it will help us be more on guard in the future.