Value Added Tax on Nothing

I asked this question on Twitter and got a lot of guesses, so I'll try it here for the blog crowd.

In February we're about to start another coffee cup giveaway with our McMenüs (Value Meals). Even though the cup is free, we have to adjust our Value Added Tax (similar to sales tax) programming in the registers. Why do you think we have to pay VAT on an item that is free?

So you don't get distracted... yes, Germany has different VAT rates for restaurant food eaten in or taken out. A porcelain cup is not food, so is taxed the same regardless. The answer has nothing to do with eat-in vs take-out.

Update: The answer is below in the comments, for everyone curious about German VAT regulations!