What I have trouble understanding is how cost relates to actual value.
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In a nutshell...the Cost Approach is one of the three generally accepted methods for appraising real estate.
Lets say there's someone of like mind that desires a house similar to yours. Since there are no others around and yours happens to be for sale, their options are 1.) Build one like yours or 2.) Buy yours.
They know that it will cost $300K to build one like yours (just a number thrown out there, insert any you like). They start thinking. Let's see...Yours is 10 yrs. old, the furnace/AC, plumbing/wiring are 10 yrs. old, windows/doors/flooring, etc. are all 10 yrs. old. How much of a discount from new is required to entice them to purchase yours considering the physical depreciation? Is $250K a good price? $230K? You get the idea?
Normally I agree and don't really care about the cost, I only care about the value as perceived by the buyers of similar properties. However, in the case of new construction or unique homes without reasonable comps, the cost approach can be given a lot of weight in an appraisal.
The other two options for appraisers are the Income Approach or the Market (Sales Comparison) Approach.
Income Approach? I doubt that your house would be considered a good income producing property.
Sales comparison? The lack of similar houses mostly rules this one out but appraisers can distill some supporting data from the market.