The VAT you paid out privately could appear as VAT paid out by the company which could reduce the companies' apparent VAT liability or even trigger an actual cash refund from the tax authority.
Curious, how does that work, exactly?
Well you privately would pay VAT to the supplier (company Y), for which you don't have to account to anyone. Also you'd be handing over company X's VAT number to company Y, who would record in their books that they received <whatever> VAT from company X (because that's who you've presented yourself as).
One of two things then happen unless you down the full "
you purchase + VAT from X, who then purchase + VAT from Y" route.
Company X have to account for their VAT transactions to the tax authorities, to kept their records straight they say that they had to hand out <whatever> VAT to company Y, this amount comes off the bill they owe to the VATman (i.e. amount due to VAT man = VAT on sales - VAT on purchases, hence
value added tax) but they didn't actually pay it out - so fraud.
Alternative scenario, company X don't account for the VAT, an audit of X or Y reveals the accounting discrepancy, a charge of failing to properly keep accounts for VAT follows. Under the EU way of doing things, you don't pay VAT for cross border transactions but you do record the value, VAT number and country - the governments then settle up the balance between themselves and it's the audit trail during this reconciliation that is most likely to cause you to come a cropper if there's anything irregular going on.
The only way you can keep it straight is to actually buy the service/part from X and hand over money to X for it, who then actually buy the service/part from Y, and properly account for both the sales and purchase monies and VAT.
My personal company is idling at the moment, which means I have no sales. Thus every quarter I get a VAT refund for all the things the company still has to buy while it's idling, which basically amounts to the VAT on my accountant's fees.