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I would search the "For Sale" forum for 186Cs that were sold in the past year or so and see what the asking price was (a quick PM to the seller might get you the actual price).

I would suggest contacting a dealer of used tubas such as Baltimore Brass or Dillon Music for a professional appraisal. They can provide a document stating the typical value of such an item that should be valid for insurance or tax purposes.

I sold a Miraphone 186 CC last year to a NYC pro. Price was $3400 including original hard case. I think the horn dated to around 1976 and was in good condition. Hope this helps. Sorry about your fire.