Cash/Free Debt Free vs. EV

Struggling with wrapping my head around a "cash-free, debt-free" acquisition. Assuming no NCI and no preferred stock, wouldn't a buyer be paying equity value in a transaction and not enterprise value. (Equity Value = EV + cash - debt). 

Also, I thought the buyer assumed/ refinanced the debt in an acquisition. In a cash-free debt-free acquisition such as the example above, the seller is paying off all the existing debt and thus buyer is never assuming any debt off of the balance sheet. Is this correct?  (I understand how the buyer may create new debt if they are financing the acquisition with a mix of debt and equity but I am confused about what happens to the existing debt on the balance sheet and how it relates to the price paid in an acquisition).