New to BP: Funding Question

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Only a couple years into my RE investing career here and want to leverage the collective knowledge of BP. I'm under contract to purchase a 4-unit for 307k. I believe the building will appraise for 335k-350k and I'm still waiting for the appraisal to come in. After talking to my broker, the lender obviously still wants 25% down on sales price and not based on appraised value, which I have no problem with and have the 77k available and ready to go. The more I thought about this, I thought why not go get a bridge loan for 230K and pay for the building in cash and then the very next day, perform delayed financing backed by Fannie @ 75% LTV since I'm this is only my 2nd property. Worse case scenario, it appraises for close to my sales price and I still pay my original 77K down. Medium case scenario, it appraises for 335K, at 75% LTV is 251K refinanced loan so my down payment is 56K. Best case scenario, it appraises for 350K, at 75% LTV is 263K refinanced loan so my down payment is 44K. If I'm right, this put more money in my pocket for weathering the storm. If I'm wrong, I still pay the 77K down, which I was going to do anyways. I realize bridge or other hard loans are not free and will add a few thousand to this deal. I figured I would have my traditional lender and a bridge/HML lender both perform appraisals and then I determine the best course. Thoughts?

Well, it appears that the delayed financing LTV is 70% rather than the 75% I suggested above. Can someone confirm this is the case for even those that own 4 or less properties?