That is a good question and one that I have been asked-especially lately.  The simple answer is no.  When a property is purchased it establishes the market value- even when you are getting a good deal.  When a loan is issued it is based upon the lower of: appraised value or purchase price.  So using your example above the loan will be based upon the purchase price of $120k. 

The long answer to this, like most things, there are exceptions.  There are many programs through local goverments that are doing loans to rehab properties- something to check into.  Then through FHA they have a program called the 203(k)- which allows to finance some repairs into properties.  Below are some guidelines on this program if it is applicable.

This program (203(k))can be used to accomplish rehabilitation and/or improvement of an existing one-to-four unit dwelling in one of three ways:

To purchase a dwelling and the land on which the dwelling is located and rehabilitate it.

To purchase a dwelling on another site, move it onto a new foundation on the mortgaged property and rehabilitate it.

To refinance existing liens secured against the subject property and rehabilitate such a dwelling.

To purchase a dwelling and the land on which the dwelling is located and rehabilitate it, and to refinance existing indebtedness and rehabilitate such a dwelling, the mortgage must be a first lien on the property and the loan proceeds (other than rehabilitation funds) must be available before the rehabilitation begins.

To purchase a dwelling on another site, move it onto a new foundation and rehabilitate it, the mortgage must be a first lien on the property; however, loan proceeds for the moving of the house cannot be made available until the unit is attached to the new foundation.

Eligible Improvements

Luxury items and improvements are not eligible as a cost rehabilitation. However, the homeowner can use the 203(k) program to finance such items as painting, room additions, decks and other items even if the home does not need any other improvements. All health, safety and energy conservation items must be addressed prior to completing general home improvements.

Required Improvements

All rehabilitation construction and/or additions financed with Section 203(k) mortgage proceeds must comply with the following:

A. Cost Effective Energy Conservation Standards

(1) Addition to existing structure. New construction must conform with local codes and HUD Minimum Property Standards in 24 CFR 200.926d.

(2) Rehabilitation of Existing Structure. To improve the thermal efficiency of the dwelling, the following are required:

a) Weatherstrip all doors and windows to reduce infiltration of air when existing weatherstripping is inadequate or nonexistent.

b) Caulk or seal all openings, cracks or joints in the building envelope to reduce air infiltration.

c) Insulate all openings in exterior walls where the cavity has been exposed as a result of the rehabilitation. Insulate ceiling areas where necessary

d) Adequately ventilate attic and crawl space areas. For additional information and requirements, refer to 24 CFR Part 39.

(3) Replacement Systems.

a) Heating, ventilating, and air conditioning system supply and return pipes and ducts must be insulated whenever they run through unconditioned spaces.

b) Heating systems, burners, and air conditioning systems must be carefully sized to be no greater than 15 percent oversized for the critical design, heating or cooling, except to satisfy the manufacturer's next closest nominal size.

B. Smoke Detectors. Each sleeping area must be provided with a minimum of one (1) approved, listed and labeled smoke detector installed adjacent to the sleeping area.

The answer is NO!  We get this question a lot, mostly from 1st time buyers with little money down and some debt.  They have seen their friends buy homes, then refinance later to payoff credit cards, while home values were going up.  This is understandably an interesting concept, however you cannot borrow more than the value of the home's purchase price ( with few exceptions for certain loans allowing for closing costs to be included in the amount financed ).  The purchase price dictates the maximum loan amount on a purchase, not the appraised value.

Buying a foreclosed home does not guarantee a substantial equity position results, however it is common.  If a buyer were to be fortunate enough to find a property sold as a foreclosure, or short sale, or other kind of distress, there is potential for substantial equity gains in the near term as many are sold well below even the current, depressed market value.  We have been seeing many examples of 1st time buyers purchasing short sale homes & bank owned properties at a very nice discount to the appraised values.  If you are fortunate enough to end up with this type of deal, most lenders will allow a cash out refinance using the appraised value of the home after a 12 month period.  If refinancing will allow a homeowner to "convert" or trade some of their "bonus equity" into monthly debt savings at this point, then that may be a great outcome for that individual.

One tip that may help a buyer payoff some debt now, would be to negotiate a purchase contract with the seller that provides for them to pay all of the buyers closing costs.  This frees up cash that would otherwise be needed by the buyer to close, & would allow the buyer to redirect those funds towards reducing their current debt.  This may ultimately make them a stronger, more qualified buyer due to the reduction in debt ratio.  Current FHA guidelines allow for a minimum of 3.5% down, & up to 6% of the purchase price can be allocated as seller concession for buyers costs. 

In the case of the original question the example could look like this:

Offer $127,700 with the condition that the seller agrees to pay $7662 ( 6%) towards closing costs.  Use any additional funds to buy the interest rate down with discount points, put down 3.5%, & apply the rest of your cash towards paying down debt.  The seller would net $120,038.  The home's appraised value of $150,000 would be fine, & still provide the borrower with $26,770 in "instant equity".  Within a short period of time this buyer would possibly be able to refinance this loan into a conventional loan, without PMI, & this would potentially allow for additional savings subject to market interest rates at that time.

On any purchase money mortgage, only monies needed to actually buy the home can be considered in financing.  That said, if there are repairs needed, the property may qualify for the Federal Hosing Administration's 203k rehab loan.  96.5% of the purchase price and repair costs can be incorporated into the loan.  In your situation, the loan would be based on a purchase price of $120,000, so the will be the value used in determining the loan amount.  The appraised value of the home does not come into play.

If you do need to have some repairs done to the property, then the appraised value will be based upon the after repairs value.  And with the FHA 203k loan, the work is generally completed AFTER the transfer of the property.  The full blown 203k which involves a consultant allows for a 6 month time frame to get the repairs done.  The streamlined 203k has a cap of $35,000 for repairs and a shorter time frame, usually 60 days, is allowed.

That said, a possibility exists, that down the road, you may be able to take cash out to pay off other debts.  BUT, with the ever changing underwriting guidelines, this is not something you should count on as being available.  A refinance will consider the actual appraised value, although FHA will use the purchase price as the value for 12 months.

Nope.  It doesn't work like that.  When you're buying a house, the loan-to-value ratio is based on the lower of the purchase price or the property's appraised value.  Moreover, any pre-approval you get is only an indication on the part of the lender that you are sufficiently credit-worthy to qualify for a loan and that your income is sufficient to qualify for a given monthly payment.  A proper pre-approval letter will, in addition to stating the maximum loan amount for which you qualify, state the maximum loan-to-value (calculated using the lower of the purchase price or appraised value) permitted under the program for which you are pre-approved.  Similarly, a loan commitment for a property "yet to be chosen" will be subject to that and other conditions. 

There was a time when a couple of lenders would loan up to 107% of the purchase price of a property and allowed the excess 7% to go towards closing costs and paying off existing debts.  Such programs, like so many others, however, have gone the way of the dodo bird.