Monetary reform came to South Korea in 1962 and old hwan pieces like yours were replaced with modern won issues.
James' coin is not very valuable. It is probably one US dollar or so. The coin pictured is pretty well worn, and would have trouble fetching a dollar from a collector. If your piece is in better condition, and if a collector really needs it to complete his or her set, your coin might sell for two dollars or a little more.
The coin bears a Dangun date, with a calendar starting at the legendary founding of Korea in 2333BC. If you can find a 10 hwan coin with a 4292 date (equivalent to 1959), it is more valuable. Most 4292 10 hwans are heavily circulated. An uncircluated example catalogs for $50 and up if dated 4292. There are many more 4294 (1961) coins in uncirculated condition and they are not as valuable.