How do I "capture" the equity in a purchase to use towards LTV?

[Tyler H.]

For all you investors that pick up property below "market value"... Is there a way to PURCHASE an apartment and utilize that "equity" as part of my down payment?

EASY EXAMPLE. 

REO Apartment that APPRAISES for 1M

I acquire for a purchase price of 900K.

So assuming I could find 80%LTV, and I HAVE 10%, Is it possible to use that extra equity for my remaining 10%?

I understand traditionally banks will go off of COST/PURCHASE PRICE if it is lower, but maybe others have experience / suggestions. 

If not, what solutions do  I have? Use HM or bridge loan for aquisition, wait 6 months, than refi?

THANKS