Re-mapped chip = The magic beans sold to Jack (and the bean stalk), they have magical powers.....
A re-mapped ECU chip DOES work (i have one) and does have a noticeable effect on a 2.0lt,
but it is mild to say the least and i bet my House you can not get a extra 20bhp (170bhp on the rollers) out of that engine from a chip, even with exhaust and induction kit, its impossible, its a dream! Anyone that claims other wise has no clue what a re-map actually does (apart from make fire come out the back and you enter warp-speed like out of Star Trek lol). When people say a "NEW EXHAUST they normally mean just 30 -50% at the back, it will still have the CAT's (this is where most of the restriction in a exhaust is) and standard manifold and down pipe.
Induction kits do let more air in and make a great noise, but with out frequent cleaning they let more crud in your throttle & engine and long term this reduces performance.
If you can justify the cost GO FOR IT, but short of a slightly more vigorous pick up in the mid range 2 & 3rd gears if you puss the car past 4000rpm you would never notice the difference.
Face facts, the BMW 2.0lt engine is 150bhp out of the box, its possibly the least exciting and tunable of Any 2.0lt engines out there (apart from Hyundai) Honda do 1 with 25% (a quarter more) thats 50bhp more power, and that can be tuned up a lot further.
Its a mediocre engine dropped into a awesome roadster chassis. The 2.0lt Z4 is a great car because its amazing looks and classic Front engined rear wheel drive set up. I love mine.
To summarize:
It'll make 2nd and 3rd gear more fun, and might save you a few pennies fuel on the motorway (not much) but it wont make your car faster top end and you wont be as fast as a Golf or a Civic