Lower payment and price of a car are two different things

Understand that a lower payment does not mean the same as lowering the price of the car. It is pretty easy to get to almost any payment by reducing the interest rate and extending the terms of the loan. If you can qualify for a reduced interest rate at one price, you can certainly qualify at a lower overall price for the car. Extending your payment terms just obligates you to pay longer, and it does nothing to reduce how much you will actually end up paying out of pocket.