A client is asking us for cost breakdown on a job and wants us to include how much profit we will be making on the job. Are they allowed to ask?

They're allowed to ask, but unless your contract requires you to reveal this information, they must pay the contract price without having such information disclosed to them. In other words, if they have not contracted for revelation of your profit, it is a breach of their contract for them to attempt to condition their payment on provision of the requested information. Of course, if they don't pay you, you'll end up having to sue them, and the amount of your profit will come out during the course of discovery. Moreover, whatever profit you have (or don't have) will be reduced by the cost of litigation. So, ultimately you will want to think about what is the best and quickest course to getting paid. It may simply be that revealing your profit is the best business judgment, even if you have no duty to do so.