There are a lot of variables needed to understand what a 40% increase actually means in dollars. It may be an exorbitant increase, but it also may actually be a relatively small increase.
appraised value of your property.
Since I left the city in the early 90s I have built two homes in raw land in rural areas. In both cases the only permit was for drilling a well and in the first place, the septic. For the water wells there was no inspection - just a report to the State. For the septic there was no inspection because everyone knew XXXX XXXX and his one man band company and he did wonderful work as long as it was 30-50 year old technology.
But to appraisals for tax purposes, I knew pulling permits is a multifaceted issue. First, after paying for the permits themselves and maybe some kind of bureaucratic review, the permit mainly serves to give notice to the assessors office for a follow-up for personal property taxes. There was not permit required to put up an out building and bring REA power into it but if a home got built afterward, OK? In both homes I have been on site when the assessors (always two) showed up, unannounced and literally years after the construction was done. Tape measurers in hand, a camera and 'the clip board' with checkboxes. At the first place I wasn't necessarily cheating but I wasn't 'greasing the wheels either.' All was good and cordial until they asked if I had ventilation fans in the bathrooms. I got angry and asked if I was paying taxes to exhaust stink from the bathrooms?!? It got tense from there.
In the current case the assessors got locked out of access to a place behind and saw tire tracks. They thought they'd ask for the lock combo to the neighbor's property (which I didn't know of course) - then they saw the homestead. "Um, new construction, huh? Well we have to do what we do." All was good until I saw them measuring the chicken house and was not too subtle. "Oh, we thought this was a storage shed." A storage shed is a taxable improvement. There there chickens in the run and clucking the whole time. In our area, AG stuff is not a capital/taxable improvement.
All of this to say when all is said and done the assessor folk go back to their office to correlate the check boxes and develop a comparable to recent sales. Sounds reasonable - that's how all assessors do it, right? The problem is what they have available for comparison or 'comps.'
If none they develop their own. You can argue about a bathroom fan or being off grid but you can not argue the entire basis of the valuation as being comparable to a recent sale if there are none.
The above is all assessor stuff.
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I mentioned earlier about assessed value and levy. After you are done arguing about the home and out buildings and the bathroom fans these are completely different things: land characterization and usage. Your home may be given given 5 +/- acres. The rest SHOULD be something different from the homestead.
Maybe your time is worth so much it is not worth researching.