The "down payment" on the car is what they have invested in the car. All the payments are pure profit.
This isn't true, although good rule of thumb is that they buy at the auction, triple the lot ready price and take whatever down they can (usually $500-$1K)
So, buy a Taurus for $2500 at auction + $500 to make it lot ready makes it a $8995 car.
Buy here/Pay here don't want to carry that note forever - they actually hope to get enough payment history to sell the note off to buyers.
Same scenario as above...down payment of $1K and then payments of $150/week for a few months get the Capital back and then sell the balance of the note off for 70% (That's the profit).
I know some owners so I have intimate knowledge of how these businesses work.