I've got news for you. Every time I've bought a new business, I've had a few suprises on how much money I would need. Whatever the projections were, I needed more. Whether it is from opportunities which I believe the previous owner wasn't interested in, or the performance of the previous owner wasn't as easy as it looked, I've found at least a few situations that cried out for more spending. My justification was that by spending early on, I would reap benefits later. It is really only obvious once you start actually taking control.
I believe the exact amount is relative to the revenues and it has to be money you can afford to not touch for a long time. To begin with, the first month may be worse than you expected, because all the receivables stayed with the old owner. You have to plan for that. You also need working capital to make payroll, pay for supplies, rent, wait for people to pay you, etc. Your bills will come due, believe me. I think you need about two months revenue minus profit. That is the only way to prepare for the contigencies.
If you agree with me that you will need that much, I'm sad to say that it has to be subtracted from the purchase price you can pay, thereby reducing then size of business you can acquire. So, if you have an amount (x) available to buy a place (presumably in the form of a down payment, don't buy anything that someone, preferably a bank but if no one else at least the seller, won't finance a decent portion of) ( how do I say that without ending the sentence with a preposition?)
For the entire purchase price, including the working capital, make sure you can live without it if you fail! Many a (now) famous business owner has gone bust in a business proposition before the success he became famous for later.
You must leave your families living expenses, at a minimum, out of the business no matter what!!!