It is feasible to go for a refinance when you have built up at least 10% equity in your home (For Fannie Mae owned mortgages, the value is 5%). It is also possible for you to choose the option if your equity is less than 5%, but you may have to pay a certain amount of cash in order to make up for the difference in equity.
Be Realistic. Lenders have tightened up loan requirements, so you'll need a good credit score and at least some equity in your home to refinance. To figure out how much equity you have, subtract the total amount that you owe on all of your existing mortgages from how much you think your home is worth. If your credit is severely impaired or you owe more than the value of your home, you probably won't be able to refinance right now.
When you do a cash-out refinance you are leveraging the equity in your home in order to receive a lump sum of cash at closing. Many individuals and families use this type of loan if they want to remodel their home, or they have kids that are attending college soon. Veterans and other military personnel can now take advantage of a 100% cashout refinance thanks to the Veterans Benefits Improvement Act of 2008.
Pull your credit report from the bureaus and review it for any negative items (late pays, collections etc) and inaccurate detail. Try to dispute negative items and remove them from the report. If required pay off any unpaid debt. Otherwise, you won't get a low rate and may not even qualify. Of course there are lenders in the subprime market who may offer you a bad credit refinance loan, but it's better to avoid them as they'll possible charge higher rates and fees.