Coins are not etched, they are struck or minted. Etching uses acid to dissolve metal or another substance from on top of a substrate. Unfortunately they have no numismatic value other than 1 cent. Some novelty-item collectors will pay a premium for one that's still attached to its original packaging.
These "Lincoln Facing Kennedy" pennies were made by private companies -- mostly in the 1970's -- that took a normal penny and stamped a portrait of President Kennedy facing President Lincoln on the front of the coin. They were normally attached to some kind of card that listed the "Astonishing Coincidences" between the two presidents. The card was usually stamped with a company name & address, and they were often given out as an advertising gimmick by small businesses to attract customers.
Note that some of the "amazing coincidences" require stretching history quite a bit.
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These "Lincoln Facing Kennedy" pennies were made by private companies -- mostly in the 1970's -- that took a normal penny and stamped a portrait of President Kennedy facing President Lincoln on the front of the coin. They were normally attached to some kind of card that listed the "Astonishing Coincidences" between the two presidents. The card was usually stamped with a company name & address, and they were often given out as an advertising gimmick by small businesses to attract customers. You can see a list of these "Astonishing Coincidences" here : http:/www.workingmancoins.comHistoryLinKenFacts.jpg Dan Moore The Working Man's Rare Coins http://www.workingmancoins.com Note that at least some of these "coincidences" involve more than a little stretching of historical facts.
The engraving of Kennedy was added by a third party after the coin left the Mint. These were quite common in the 60's and 70's. As such, they have little to no extra value, at least in the coin collecting world.
These novelty items sell for a dollar or two if they are attached the the card that lists the "Astonishing Coincidences" between the two presidents. Without the card, maybe a quarter. These coins are engraved or stamped with the Kennedy image after leaving the Mint. Although this modification technically does not deface the coin - it's still recognizable enough to be legal tender - the modification destroys most collectible value. Please see the many other similar questions for an explanation of how these novelty pieces are made. They have no numismatic value, I'm afraid. Most of the "amazing coincidences" are especially amazing because they stretch history more than a little bit.
It's not a Mint issue. A private company took a genuine cent and stamped Kennedy's profile on it as a novelty item. It has no numismatic value, so it was worth 1 cent yesterday, is worth that today, and will be worth that tomorrow.
These "Lincoln Facing Kennedy" pennies were made by private companies mostly in the 1970's that took a normal penny and stamped a portrait of President Kennedy facing President Lincoln on the front of the coin. They were normally attached to some kind of card that listed the "Astonishing Coincidences" between the two presidents. The card was usually stamped with a company name & address, and they were often given out as an advertising gimmick by small businesses to attract customers.
If you check a history book, some of these "coincidences" require a bit of fact-stretching.
Also coins are not carved, they're struck or minted. "Carving" would require that each one be made separately by someone with carving tools - not a very efficient way to make coins in today's world!
These coins aren't US Mint products. A private company took a genuine cent and stamped Kennedy's profile on it as a novelty item. Although this modification technically doesn't deface the coin - it's still recognizable enough to be legal tender - the modification destroys most collectible value.
These novelty items sell for a dollar or two if they are attached the the card that lists the "Astonishing Coincidences" between the two presidents. Without the card, maybe a quarter. Many of the "coincidences" are especially astonishing because they stretch history more than a little bit.
Answer
It's not a Mint issue. It has no numismatic value, so it was worth 1 cent yesterday, is worth that today, and will be worth that tomorrow.
"Etched"
These coins are sometimes incorrectly said to be "etched" with a picture of JFK. Etching is a special technique involving the use of acid to remove metal from a surface. The images on these coins are simply stamped using a metal punch.
These were mass-produced as novelties (not by the US Mint) and are practically worthless unless you happen to collect JFK stuff.
It isn't "worth" anything, but if glued to a card listing the "amazing similarities" shared by these two assassinated Presidents, they sell for about $1.