**UPDATE**: I tested the payout timer for the game, and I was able to narrow it down to somewhere between an hour, and an hour and 15 minutes. So I believe that you will receive caps about every 1 hour, 10 minutes. As for how much the stores payout, my settlement that has 3 large shops receives 50 caps every payout. So I divided that by 3 which came to 16.66 repeating. So I believe that the large shops pay out 16 caps and the medium shops payout about 11. I will keep testing these ideas to get the best information to you!
This video details where to collect the income from your settlements shops in Fallout 4, as well as some tips for collecting them.