2 GA ACFT EXPERIENCED AN NMAC WHILE ON THE ILS AT PRC.

Narrative

I WAS ON AN IFR FLT PLAN INTO PRC. THE WX WAS EXCELLENT WITH A FEW CLOUDS AND UNLIMITED VISIBILITY. I HAD A NON PLT IN THE R SEAT WHO WAS INSTRUCTED TO WATCH FOR OTHER ACFT. ZAB CANCELED MY FLT PLAN AND TURNED ME OVER TO PRC TWR. I REQUESTED THE ILS APCH AND WAS VECTORED S WITH A TURN TO GO DIRECT TO DRK VOR AND PROCEED OUTBOUND TO HUMTY INTXN AND FLY THE FULL ILS APCH. I HEARD ANOTHER ACFT ALSO ASKING FOR THE ILS APCH. PRC TWR ASKED THE OTHER ACFT IS HE HAD SUFFICIENT SPACING FROM ME AND IF HE WAS IN FRONT OF OR BEHIND ME. THE OTHER ACFT ANSWERED THAT THERE WAS PLENTY OF SPACING. FROM THIS I ASSUMED THAT THE ACFT WAS BEHIND ME AND NOT A FACTOR. BAD ASSUMPTION ON MY PART. AT THIS TIME I HAD DSNDED TO 8500 FT. SINCE THE FINAL APCH FIX CALLED FOR 8300 FT; I GAVE MYSELF A 200 FT CUSHION TO AVOID ANY OTHER ACFT THAT MIGHT BE APCHING THE FAF. AS I APCHED HUMTY; I NOTICED ANOTHER ACFT AHEAD ABOUT 1/2 MI AND A LITTLE TO MY L AND AT MY ALT. AT WHAT APPEARED TO ME TO BE HUMTY INTXN; THE OTHER ACFT TURNED L AT WHAT APPEARED TO BE A 90 DEG TURN. I LOST SIGHT OF THE OTHER ACFT AND REACHED HUMTY. I ASSUMED THAT THE OTHER ACFT WAS NOT SHOOTING THE ILS SINCE HE APPEARED TO LEAVE THE PATTERN. BAD ASSUMPTION. I TURNED APPROX 30 DEGS L ONTO THE OUTBOUND ILS HDG. I STARTED MY CLOCK AND TIMED OUTBOUND FOR 1 MIN. I THEN TURNED L INTO THE PROC TURN AND AGAIN STARTED MY CLOCK FOR 1 MIN. AT THE END OF THIS TIME; I STARTED A STANDARD RATE TURN TO THE R AND ROLLED OUT ONTO THE RECIPROCAL HDG. I STARTED THE CLOCK AGAIN AND APPROX 1 MIN LATER THE ILS NEEDLE STARTED TO CTR AND I TURNED INBOUND. AT THIS TIME; MY FRONT SEAT PAX SHOUTED OUT A WARNING FOR ME TO LOOK R. IMAGINE MY SURPRISE WHEN I SAW A BLUE AND WHITE CESSNA 172 APCHING FROM R; LESS THAN 500 FT AWAY. FORTUNATELY; WE WERE NOT ON A COLLISION COURSE. GOOD THING; TOO; BECAUSE THERE WAS NO TIME TO REACT. THE OTHER ACFT PASSED BEHIND ME. I THEN HEARD A RADIO CALL; PRESUMABLY FROM THE OTHER ACFT; THAT STATED THAT THE ACFT BEHIND THAT WAS HIM WAS NOW IN FRONT AND THAT HE WOULD TAKE SPACING. I CONTINUED WITH MY APCH AND LANDED WITHOUT INCIDENT. AS I HAVE SINCE BEEN TOLD BY A TWR SUPVR; THE OTHER ACFT HAD AN INSTRUCTOR AND STUDENT THAT WERE GOING TO TRY TO SHOOT THE ILS. SEEMS THE STUDENT OVERSHOT THE FINAL APCH HDG AND THEY WENT AROUND FOR A SECOND TRY.