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Our neighborhood is all custom homes. When our house was appraised for our loan, the comps. were also all ovewwr the board, but they used the features we had and they didn't, or vice versa to adjust the appraisal, so a house that is smaller by 400 sq ft would have adjusted our appraisal upwards, one larger by 400 sq ft would have adjusted our appraisal downwards. Ditto for features such as the number of bedrooms and bathrooms, garage and carport spaces, swimming pools, spas, fireplaces, etc. They TRY to get homes as similar to the one being appraised as possible, within the same area, but sometimes there simply is no real comparable home.
I agree that the chicken coop is unlikely to have affected the value unles it is a large, permanent structure, and then, unless in bad repair, is likely to increase the value.
Our property taxes are based more upon the land than the home, although there is a complicated formula that does partially consider the value of improvements. I had neighbors who used to live in Michigan, and remember them telling me that people there often kept the exterior in as poor appearance as possible, while keeping all upgrades internal to the house, so as to keep property taxes low.
If you look at zillow.com, and type in your address, it will show you a fair range of value for your house, based upon demographics of sales in your area, and also show you how the value has changed over hte last month, year, 5 years or 10 years.
I am betting that the price has gone down considerably based upon te overall prices for your area, and that without the improvements you have made, that it would be worth far less than it appraised for. That is assuming that the appraisal was reasonably accurate. If you think not, ask for a 2nd opinion using alternate comparison properties. They should be able to reuse the data they have from your home, and if requested within a small timeframe, you probably have the right to get it redone for free or at very low additional cost.