Like Arnie said, for a club of Liverpool's size, especially with CL money and huge TV revenue... why not? £10m or £20m -- it's kind of irrelevant. If a player can improve you significantly, the price isn't really that much to concern yourself with unless it's some astronomical £50m+ figure. Even though he didn't play particularly well yesterday, Fernandinho has probably been the signing of the season and he was £30m despite being 28. I'd do that again in a heartbeat if we could sign another player that age who ended up playing such a huge role in our next season.
It's all relative really.