the first person to say a number losesThis is really just a myth. If you present a buyer with well-justified and thought-out reasons for your number, it's going to be hard for them to counter-offer with something ridiculous, unless they're just being an ass. Not to mention you should always have your base number in mind, at which point you just walk away. The OP also said the company has agreed with most of his initial estimations, so he's clearly in a better position with regards to the number he can ask.
In my deals, I usually take $Well-Justified-Price and then tack on $Extra to swing the deal far in my favor. Usually $Extra brings the price close to where I think the buyer would walk away. Then it's up to the buyer to do their due diligence and we can talk about the facts behind the number and do our negotiating there. Usually it comes down, but that's the point of inflating your own value first.
Regardless, I've done this for selling my Facebook apps, vehicles, negotiating job salary, etc. If a buyer is pulling lowball crap, you basically tell them to cut the BS, reiterate the facts behind the number and make a call-to-action (i.e. "Buyer, you know everything behind this number is legit, now let's come to agreement"). If not, you walk away, simple as that.
Sometimes the buyer does have legitimate sticking points though, and that's usually where you just have to listen and go into "understanding" mode to get to the root of their concerns. Once you hear them out, you cut them a little slack on the price and then again reiterate all the facts behind what you're giving them (ABC - Always Be Closing)... When you present someone with solid facts, they can't help but agree with you, so it helps to get that final "Yes" when you ask them to close with you.
For the OP, you really need to do your research and come up with a solid justification for a number you have in your head. Drew gave one example of revenue * X, which is what I used when I sold one of my Facebook apps. If you're adding $$$ to their bottom line, then use that to make your argument also. This is a flexible process and depends greatly on industry. For websites it can often just be Drew's formula. Regardless, make sure there's at least some "science" behind your wild-ass-guess, and that way it'll at least look like you put in the work to come up with a legitimate price.
To be honest though, that's the fun of deals... it's really a flexible process and there's a ton of learning involved, so have fun with it. Don't be afraid to ask for something inflated though, so long as it's well justified and not pulled from your rear. After that it's the buyer's responsibility to negotiate down.