The going rate of cardboard can vary considerably, and is influenced by a number of factors. Supply and demand constantly influence the current purchase price.
Generally cardboard is purchased in 53’ truckloads and a full truck sells at a premium.
Paper mills typically purchase cardboard from paper recycling companies as they can supply full truckloads reliably as well as offer decontamination and transport functions.
Selling your bales through a paper recycling company will give you a way to sell your carboard, but it means that they take a piece of the margin to cover their costs.
A little research can help you determine what you kind of profit you could make before making final decisions.