The brief
The 528i had crossed 120,000 km. The owner reads the workshop manual schedule and acts on it, so he booked the car in for fan belt service before any squeal or slip showed up.
The fan belt, the long ribbed accessory belt, drives the alternator, the air-con compressor and the other engine accessories off the crankshaft pulley. It runs every minute the engine is on, over the tensioner that keeps it tight and the idler pulleys it wraps around. At high mileage the belt glazes and starts to crack, and the tensioner and idler bearings wear, and the failure point on a lot of high-mileage cars is exactly this part.
The diagnosis
On inspection the existing belt was glazed along the rib face with fine surface cracks just starting to show, the tensioner had a touch of bearing roughness, and the idler pulleys were still smooth but on the same age and mileage clock as the rest.
None of it had failed yet, but it was all close, and the labour to do the belt is the same labour you would do to reach the tensioner and idlers. So the sensible scope was the whole set in one go, rather than replacing the belt now and being back for the tensioner in a few months.
The work
The tensioner was released, the old belt taken off, and the worn tensioner pulley out. New BMW-spec parts went in, including a fresh idler, then a new belt routed correctly through the accessory drive and re-tensioned to spec.
The engine was run warm with the air-con and other loads applied, and the belt drive checked for any squeal or slip before the car went back to the owner.
The outcome
No squeal under any combination of air-con and alternator load, and a silent belt drive right across the rev range.
The 528i went home with the front of the engine reset to like-new and the most common high-mileage failure point dealt with before it could leave the owner stranded with a dead alternator or a thrown belt. For someone who services on schedule, that is the whole point: the part gets renewed on a planned visit, not on the hard shoulder.