A SINGLE ENG ACFT UNDER PRC'S ATC CONTROL NEARLY COLLIDED WITH A HIGH PERFORMANCE SINGLE ENG ACFT ON FINAL WITHOUT RADIO CONTACT.

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WE TURNED L DOWNWIND FOR RWY 30 AND WERE INSTRUCTED BY PRESCOTT ATCT THAT THEY WOULD ADVISE THE BASE LEG. WE SLOWLY CLBED TO 6500 FT TO CLEAR GLASSFORD HILL. OVER GLASSFORD HILL WE WERE TOLD TO FOLLOW CESSNA TFC ON A 3 MI FINAL. WE RPTED THE TFC IN SIGHT AND WERE TOLD TO FOLLOW. WE TURNED AN APPROX 4 MI FINAL. ON ABOUT A 1 MI FINAL; TWR ASKED US TO VERIFY OUR POS. WE RPTED A 1 MI FINAL; AND RECEIVED OUR LNDG CLRNC. AFTER APPROX 30 SECONDS TO 1 MIN; WE HEARD AN ENG NOISE AND SAW A HIGH PERFORMANCE SINGLE ENG ACFT JUST ABOVE (50 FT) AND TO OUR R (50 FT). THE ACFT WAS DSNDING ON FINAL DIRECTLY IN FRONT OF US. 2-5 SECONDS AFTER VISUAL CONTACT WITH ACFT; TWR ASKED IF WE HAD THE TFC IN SIGHT. I THOUGHT THAT THE STUDENT CALLED TWR SAYING; 'KINDA HARD TO MISS;' BUT THIS CALL IS NOT VERIFIED BY THE PRC STREAMING RADIO RECORDING ON THE FLT WEBSITE. TWR ASKED THE OTHER ACFT IF THEY WERE ON FINAL; TO WHICH THEY RESPONDED THAT THEY WERE AND HAD CALLED TWR 3 TIMES PREVIOUSLY. OBVIOUSLY THE OTHER ACFT CONTINUED INBOUND WITHOUT ACTUALLY HAVING BEEN ACKNOWLEDGED BY TWR. TWR CLRED THE HIGH PERFORMANCE SINGLE ENG ACFT TO LAND AND INSTRUCTED US TO GO AROUND; WHICH WE DID.