There are a lot of things to be considered in doing a CMA and what the banks appraiser would need to consider. You really should have an agent that has experience in your area visit your home and see all that it has to offer. That will enable an agent to complete an acurate CMA. That will give you a good idea of what your home could be worth in today's market. You should also shop for your loan. Just because you have a mortgage with one bank doesn't mean you need to stay with that bank for your refi. There are a few lenders out there who are offering really great refi programs right now as well. I hope your plans work out for you and you get to build that horse barn. I am in the process of purchasing a horse as I have always dreamed of. I will need to board for a while until I can accomidate my horse(s).
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You would need a local Realtor, or maybe the Realtor who sold you your home to do comps on your home to let you know what the appox. value of it would be. (Ask for a CMA).
This will give you an idea if your home will appraise at the 394,000.00 you need.
Unfortunately, an appraisal in 2006 is meaningless in today's market - since you're looking to refinance, I would sit down with your mortgage company or bank (whoever you are going to use for refinancing) and ask them whether the house qualifies, since your lender will probably not accept an appraisal done by anyone other than the appraiser they choose, and will charge you for an appraisal fee and a second appraisal to be done even if you get your own done first to see if the house appraises.
If you just want a general idea (i.e., a Comparative Market Analysis of the house) giving you a basic idea of current comparable sales in your neighborhood, your best bet is to call a local realtor and ask them. They can give you a rough idea - but only the lender's appraisal will count.