Throughout my career I was asked this question at least once a week. I would always answer it in a non-direct way by saying something like "cash is good" or "we accept cash". The truth is paying cash may help you get a "better deal", but it probably is not going to affect the price of the vehicle in a positive way for you.
A huge part of the auto industry is what the call "back end money". You may have heard that term thrown around if you have ever wandered around a dealership. There are two parts of money a dealer makes on a car deal, the first one is "front end money", that is the money that is made on the markup of the car itself. Back end money is the money that is made in the finance office. Sometimes the back end can be the most profitable part of the deal for a dealer. Dealers most generally be paid "2 percent reserve" on the interest rate. This means that if a dealer signs you up at an 8 percent rate, the dealer is getting paid 2 percent from the bank. Does this mean the dealer could sign you up at a rate 2 percent lower? Yes! Exceptions to this would be "special interest rates" somtimes thrown out by the manufactuer. In these deals the dealer is usually paid a small flat fee from the manufactuers inhouse finance company. I once worked at an unscrupulous dealer who refused to sign up customers through Ford Motor Credit in order to maximize profits.
Things like extended warranties and gap insurance may be things you would like to have for your vehicle, but there is markup in them. You can save money by negotiating the price of everything you buy in the finance office.
So when you pay cash for an automobile, you don't pay an interest rate, and most of the time warranties and insurance aren't even pitched to you, so you pay less money overall for the vehicle. But if the dealer knows up front that you are paying cash, they will try to save as much profit as possible on the front end of the deal, which could result in you paying more for the price of the automobile then if you had financed. If you are paying cash for a vehicle, don't tell the dealer until you have negotiated the price on the vehicle.