If you have the 2.0L, it looks like that engine is an interference engine. Meaning that the Intake/Exhaust valves can protrude far enough into the combustion chamber that they contact with the pistons.
When an interference motor jumps time, it almost always causes severe damage. You're looking at likely having to have head work done, replacing valves possibly springs etc OR swaping in different heads. Worst case scenario could extend to a complete rebuild of the engine OR replacing the entire engine. I'm going with around roughly $1800 for the engine and a minimum of 20 hours at $100/hr. It would be more rational for you to call your local Volvo dealership, or any mechanic(s) you have a rapport with, and ask them for a rough quote for the cost of replacing the entire engine.
If you are not to interested in keeping the vehicle, it might not be worth spending the diagnostic fees. That kind of work can take a long time, and cost a good amount. Prices are rather irrelevant because they vary so much from region to region.
If the mechanics initial diagnosis of the engine skipping timing is correct, it's likely to cost close to replacing the vehicle with a known-reliable quality used vehicle with a decent service history.
The diagnostic fee is not in anyway unfair, so if you are o.k. with that fee to be certain about the extent of the damage, I suggest you go ahead with it.
I hope this helps.