Of course your answer is: Preferably as little as possible;. But you don't help anyone with that. If you spend a budget on a supplier, you soon have the feeling that you are in danger of losing all control. Why should they handle this budget critically? And don't waste it? What guarantees do I get that my budget is well spent?
HOW DO YOU DETERMINE YOUR BUDGET?
How you determine your budget is very personal. You can use different starting points.
Percentage of the (expected) turnover.
Many companies use a certain percentage of their turnover for their marketing budget, which often includes branding. The exact percentage differs per company and per sector, but 5 to 15% is a good measure.
Percentage of the (expected) profit.
Turnover does not guarantee profit. That is why there are companies that fix the budget based on the expected profit. The percentage can vary enormously here, from 25 to 100%, and depends on how much you want to invest in your company in the long term.
Fixed amount.
Of course there are also companies that assume a fixed amount based on what they consider necessary. You don't need a new branding or website every year. Many companies start planning for the following year from October and calculate the costs thereof. Choices are made based on necessity. For the development of your branding this means that you ask your agency to draw up a cost. However, this process is very time-consuming and requires extra energy from your desk.
GUARANTEES THAT YOUR BUDGET IS WELL USED
No agency has all the answers, so don't expect solid guarantees. No one is going to tell you in January what is at the bottom of December. But you can express a certain realistic expectation based on the budget and see how an agency can respond to this. How they can present an objective within that expectation.