My best advice is to ask for the wage rise. A lot of people think about asking for a raise but never actually get around to asking for it.
If the HR budget allocated to you is seen as a done thing then the money just goes somewhere else, nothing will happen unless you ask for it. Part of that is your attitude towards a raise and not necessarily whether one is available. No one is going to spend money unless they feel they need to. If someone seems perfectly happy with what they're being paid then the idea of offering a rise never enters the equation because it makes no financial sense to consider it.
It sounds simple but I really think many people's problems with being underpaid (and I come from a graduate background of not being paid at all, so I really worked my confidence up in this respect) are to do with ultimately never asking for what they want and holding their ground when they are lowballed, or not looking for better opportunities because of decisions based on fear.
The cost of rehiring and training is always higher than paying someone a few % more so the value based assessment is pretty basic. Like you say the worst you can get is a "no".
The only comparable situation for me at the moment is in sales pitches. This advice is sort of relevant, but somewhat reversed:
https://doubleyourfreelancing.com/never ... ance-rate/savvy clients managers, almost all of which were business owners, knew know that it can’t hurt to ask for a discount pay slightly less than they can afford to. And I totally get it. Let’s say you’re hiring someone to work on a 3-month project (480 hours) at $100 an hour. A $10 an hour discount saves $4,800 — not a bad return for taking a minute or so to ask a question expecting a candidate to never ask for more.
Almost everyone who asks for offers a lower salary will pay what you originally quoted actually wanted
Because I work — both directly and through osmosis — with literally thousands of freelancers, I can tell you it’s pretty rare to find a client who walks because they can’t score a last minute discount on a project.
If a is your salary and b is the budget (or portion of it), and c is the cost of hire
And if (b-a) <= c
The logical answer is probably yes to at least a % of the difference between a and b
Obviously this assumes you're objectively the best candidate so far, or have some other qualitative reason; this isn't going to work if someone is gooseberry fool at their job and just grinds through the day to day. It helps if time is a factor.
And expectations will be higher, so do a good job. And if you don't want to do a good job because you're not getting what you want or some other reason, be prepared to go down in flames - which is why if you ask for a raise, you should try to get as much as possible to make it worth your while. It's kind of an unwritten rule in all negotiation situations that you can't change the negotiation because you felt you got it wrong. That really pisses anyone with purchasing power off because it seems to take quite a lot of energy to make that original offer, regardless of what it is, and have to lock horns over it
again.