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Go on line and Google what folks are asking for Stelling banjos.
Pay attention to features like originality, condition, "fancy" things like inlays, gold plate, engraving, etc. Also if an original or at least good quality hardshell case comes with it.
Personally I'm not familiar with a "Foggy Mountain" model, so it would be good to Google search that too. Stelling is a very fine brand, now out of business, and there is a broad market for Stellings. In good original condition you could be looking at value measured in thousands of dollars. Let us know where in the world you live -- that affects selling price a lot.
Review the Classified ad section here on the BHO too.
Many folks post some photos of banjos here with a question just like yours. "What is this?" "How much might it be worth?" Etc.
Another approach is to take lots of clear, well lit, close up photos of the banjo from all angles (including inside) and send to them to a reputable banjo seller who would give you a written appraisal at an agreed-on fee. Such an appraisal will cost in excess of $100.
You can always use an auction approach, and let interested buyers tell you what they think it's worth.
Good luck.
Google led me to this old post right here on the BHO about the Stelling Foggy Mountain Banjo. Written by Geoff Stelling hisownself!
"The Foggy Mountain was introduced as a clawhammer banjo in Jan. 1990 available as both an openback and a resonator model. We made 30 with serial numbers from 001 thru 030. The first five had a squarish peghead shape sort of but not exactly like the Bowtie Gibson. From #006 through #030 made on 9-4-91 they all had the same shape as our Crusader model. From 9-19-91 the Foggy Mountain was continued with a regular Stelling serial number starting at #FM3788, but the flange still had Foggy Mountain stamped under the tailpiece instead of Stelling and the tone rings were more like a tension hoop size with a radiused top edge and a 45 degree angle wedge fit bottom edge. The last Foggy Mountain was #3851 made on 3-12-92. After that, we tried a low priced model called the White Dove that had the same peghead shape and tone ring configuration as the Foggy Mountain but it also had the Stelling logo on the peghead. I don't have the figures for exactly how many of them we made, but Lynwood Lunsford played one with Jimmy Martin and Lost and Found and his own band the Misty Valley Boys with great success.
Geoff Stelling"
Seems like a unique model -- there might be some interest in it! Lack of a full weight tone ring might limit the market a bit though.
You might do a comparison between it and other Stelling banjos and try to see what those banjos of similar components are selling for, as well as the age. Not being one of the better-known examples of Stellings, it might help in your ad to mention what the wood in the banjo is. I think most of the pots in Stellings were similar to the time of production but woods and inlay patterns, etc. would be different.
Bobby
My take on KCJ’s suggestion: Start with the highest price that might be plausible. You can drop a price, but can’t go the other way. Say you’ll consider offers. See if you get any. That will give you a low-end estimate. Then wait a week and drop the price weekly until either the banjo sells or you feel the range is just too low.