The dealership I went through got very "huffy" about it. They did not like it at all and gave some attitude. But then they did eventually match it.
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I almost did exact same process as you back in Jan of 23. Only difference was dealership would only allow me to put $3000 on credit card (for points and pay off at end of month). I paid the other $2000 in cash for my $5,000 down payment. My sales guy was very easy to work with and was very familiar with the credit union I got my loan through. The dealership appeared to not care that I declined the financing through Ford and went with the much lower rate offered by credit union. They honored the price that was on the original DORA document including X plan pricing. They didn't try to upsell me on anything (not aggressively anyway).Ask the dealer and they can let you know ahead of time if they’ve worked with that lender before which makes it so fast and easy. I put my down payment directly to the dealer on a credit card (to get points) they let you charge up to $5000 at my dealership- drove away with my truck and let my bank handle the rest. I’ve gone to other dealers that do not let you do this- but that might be unusual because every dealer I’ve told that to scoffs. Anyways- when that happened I just refinanced at my own bank once my plates came in.