Mouse, if you are talking in terms of the initial purchase of the property the lender bases the Loan to Value off the lesser of the purchase price or appraised value. For example If you bought this $485K house for a purchase price of $450K than the lender the day of closing goes off of the $450K amount. Also if you put $45K as a down payment against a purchase price of $450K that would be considered 10% down.
However depending on your credit if you are looking to buy this home for $450K and would like to take a new second mortgage out after closing for up to $485K it can be done. There are Home equity lines of credit that allow you to take a second lien out up to 100% of your homes appraised value. You need excellent credit to do this and it is a completely separate transaction from your purchase mortgage. I hope that makes sense.
Now if you try for a conventional or sub-prime mortgage they will require that this property is owned for at least 6 months and in most extreme cases 12 months before you can use the appraised value over the purchase price. I have dealt with customers in the past that bought say a $485K house for $450K and did some repairs to justify why the house is worth more than what they bought it for a month ago. A lender will want to see that an appraiser notes what type of work was done to cause such a rapid increase in value.
One issue that lenders unfortunately deal with is when someone buys a $485K house for lets say $300K. After they close on the purchase they take a 2nd mortgage out for the full $485K and walk away from the property with $185K cash and let the home go into foreclosure. People that take advantage of this type of situation make it much more difficult for borrowers to obtain easy financing when their intentions for the cash out are good.
I hope this information makes some sense to you, and if you have any other questions please feel free to ask.