This is a great question. It is probably best to start with a definition of what a cash conversion cycle (CCC) is. CCC is the time that a company would be out of money if it seeks to expand their business. In this case, the hot dog cart owner buys whatever he or she needs with a credit card and then gets the money in cash every day.
In this scenario, the cash conversion cycle is on a daily basis. By 2 o'clock in the afternoon everyday, the seller has his or her money back hopefully with a profit. In light of this, there will not be a negative cash cycle. Moreover, when we consider the fact that hot dogs and the other material needed for a hot dog stand does not cost very much, it is highly unlikely that there will be a negative cash flow. Of course, if the hot dog stand owner wanted to buy a few more stands, this could cause some financial hardships, but with the one stand, all should be well.