Looks like you bought the house in 2004 for $116k. I asssume you have paid down some principle since that time. I think your house will appraise for what you need out of it to refinance. An appraisal is really more about justifying a price than it is determining market value. I've found refi appraisals are usually a bit more liberal on value than for a purchase.
It is a good time to refi and save some money. If you need help in picking a lender, just let me know.
Best of luck!