Considering appraisals in analyzing deals

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I was wondering about how to analyze a property’s value when it comes to appraisals or how I should be using appraisals as info. What’s the difference between a tax appraisal and (I’m not sure what to call it) a market appraisal? For instance a duplex I bought to house hack appraised at 192,000 and the county appraisal was around 145,000. Does the county appraisal being lower give me some bargaining power? The reason I’m asking is because I’m talking about doing a partnership with a co worker and he seems awfully concerned about what the county appraised a property at, yet I hadn’t put too much thought into it when I bought my house hack. Any comments appreciated. Thanks.

The tax appraisal is only meaningful in regard to the taxes assessed on your property.  So low is better and people fight hard to get lower tax appraisals.  If you want to see how meaningful the tax appraisal is, try selling it to the government for the value they appraised it at... never happen.  

The CMA (competitive market analysis) is a much better yardstick of value, since it benchmarks your property versus the sales price of competitive properties sold in the recent past in your neighborhood. At the end of the day, a property is only worth what a willing buyer will pay for it.