The coin shown is only worth one cent. Something that's really rare but damaged can still have a nice value. Every coin is different and can be tough to put a value on. Some would not care for a damaged coin but others may be Ok with it.
I am something of a proponent of damaged coins. My 09-S, VDB cent has a damaged rim but is otherwise An XF coin. I bought it for a song. I own several early coppers that have damage as defined by the TPG’s but each are lovely coins in their own right. I will always choose an eye appealing “damaged” coin over a lower quality “problem free” coin. I love eye appeal and really like the cost savings.
The coin pictured was only worth one cent before it was damaged. A damaged collectable coin will most likely retain some value. How much value depends on the individual coin and the extent of the damage.
As a general rule of thumb, any problem coin, damaged or some other problem, will be worth anywhere from 20-80% of what a problem free example will be worth.
@ldhair ... @ZoidMeister ...I agree. @Trella Davis ...it really depends on the extent of the damage. Your coin appears to be an 82D large date copper. The extent of the damage shown (good pics, btw) does not show any underlying zinc, so you can be fairly certain it weighs 3.11g. That said, if a key date wheat cent, a 1922 no D for example, had minor damage then it could still have a nice price tag, depending...imo...Spark
Most of them are face value. Old, rare, precious metal coins are worth at least the metal value and sometimes more depending on the demand for that coin/year/mm. But because of the damage it won't get a very high price. Which is to be expected as condition is a major price consideration. As for the OP coin, 1982-D large date it was worth 1 cent before damage, and 1 cent after damage. Don't confuse this coin which was produced in the billions with the 1982-D small date copper transitional error. (2 known?)
Here is the biggest tragedy that I have seen for a damaged coin. This is a 1792 half disme. Many collectors think that it was the first U.S. coin. At any rate it is obvious that this piece has a big problem, a hole. Many collectors rate that as the most catastrophic of all defects. This piece sold in a Heritage auction for $37,500. If it had not had the hole, it would have brought $130 to $150 thousand. The collector demand for this piece is such that collectors are willing to pay this much for a heavily damaged piece.
Their lowest value is face value but it all depends on the coin, it's grade and what condition it's in.
There are more 1792 half dismes with holes than you might think. The thing that made this piece unusual was that the rest of the coin was really nice. Usually they have many other problems along with the hole.
Even in that condition the large date is 100% legible. There are a few other markers, the shape of the 8's. the distance from the rim, here is the two types of 2's:
