The bank knows the property to be financed and therefore also the value it assigns to the property. The price you pay for it does not matter to the bank.
Therefore a) you contribute the property as equity with a value X specified by the bank or b) you may have to provide more equity than the property is worth to the bank.
Therefore it does not matter for the financing.
I simply do not understand your problem, however I am not willing to explain it again. Just read the posts calmly once.