Well I’ll guess that’s a N43 engine and without extended BMW warranty you’ve not got a hope in hells chance of BMW doing anything but quoting you a similar amount for the same work; another garage might quote slightly cheaper. Timing chains can and do “stretch”.. more of a wear through use which all adds to slackness. This is normally attributed to long lengths of time between oil changes.

To answer your questions though:

A. Yes, if you like the car and intend on keeping it for a while. Big jobs do come round once in a while on all cars.
B. If the overall car is tidy and you get work done it might make your £3.5-4000 on a private sale, probably half that as trade in if you’re lucky.
C. Private sale declaring required work maybe £2-2500, or if you don’t declare price as above. But be beware of buyers rights and all that nonsense as it could come back to bite with a repair bill for selling faulty goods/with known fault and not fessing up.

Values quoted are a guess based on the upper scale of the cars value. Long story short here it’s a 10-11 year old vehicle.

 

What engine is it ?.
Petrol or diesel.

 

The car is not broken, it is an assessment determined on experience (you quoted the word Possibly!) on the garages appraisal.

Price Paid/Residual Value = Bad feeling.

 

Surely you can just trade it in & get rid. No come back as a decent dealer will just end up down the auctions as its too old. Recently traded my 330d as it had 2 problems but they didnt care didnt write down the faults (fuel pump cutting out & starter that didnt always start ) just said its auction fodder!! Buy a 6 cylinder BMW next as they dont or its very rare to have any of the 2.0 problems. I heard years ago that tensioners/chains are crap & a rumour of them being from Citroens parts bins !!