Nice coin, David! And valuable, too.
Carlo Felix (or Felice) was king of the old Italian State of Sardinia from 1821 to 1831. The state issued gold coins in 20, 40, and 80 lire denominations, as follows:
20 LIRE: 21 mm diameter, 0.187 troy ounces gold
40 LIRE: 26 mm diameter, 0.373 troy ounces gold
80 LIRE: 33 mm diameter, 0.749 troy ounces gold
The way to evaluate coins like this is in two steps. First, find the basic gold value, then add the collector premium over basic value.
Use a web site such as Kitco.com to find the current price of gold. For instance, the price is currently $1307 US dollars per troy ounce, but it will be different tomorrow ~~ look it up. Multiply the gold price by the gold weight to get the basic value. A 20 lire coin, for instance, evaluates to 0.187 x 1307 = $244 US dollars basic value.
When it comes to collector premium, there will be no premium over basic value if the coin is damaged, bent, cleaned, holed, or otherwise compromised. The premium is, roughly, 50 dollars for worn or average circulated coins. But the premium goes way up for coins that are uncirculated, or nearly uncirculated.
Here are approximate collector premiums to add to the basic value for uncirculated specimens. The sum of basic value plus premium equals the catalog value of the coin. Use our Important Terminology page to interpret catalog values. These are very approximate values and any uncirculated coin as old as this one should be thoroughly examined and evaluated by an expert to come up with a final worth.
20 LIRE fully uncirculated
mint mark is an anchor: $200 premium added to basic value
mint mark is L or P: $300
40 LIRE fully uncirculated
mint mark is an anchor: $800 premium added to basic value
mint mark is L or P: $600
80 LIRE fully uncirculated
mint mark is an anchor: $800 premium added to basic value
mint mark is L or P: $600
coins dated 1828P: $1200
coins dated 1831P with no anchor: $1800
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