None.
If you are an informed customer, you are presenting a well prepared, line by line deal terms for either a yes or a no. The price should not change regardless of your financing as that would be tied selling, which would be illegal.
You loose the so called negotiating power, by visiting a dealership, by going in blind and hoping the dealer has your best fiduciary interests in mind, by not understanding the product you are about to buy or not knowing what you want to buy, not reading the contract at your own pace, or by simply being emotional in a business transaction.
The internet age has lessened the information asymmetry that existed as the dealers primary tool in negotiations.