It depends on the quality of the original internationalization work. If everything is implemented correctly, then it will be similar to adding support for a new European language - most of the work will be translation and testing.
However, if you've only tested the software with European languages, you might find a lot of problems with your original internationalization work. In particular you might need to consider:
- bi-directional text
- ligatures (joinining the characters)
- rendering (characters change shape depending on their position in the word)
- number and date formats formats
- specialized input methods
- cultural differences (for icons etc)
- file encodings
- testing
If you have custom code that implements software features in a way that isn't fully localizable then you need to budget for fixing this too.
If you have manuals, help text and other collateral that also needs to be translated, then the software cost might not be such a large proportion of the total budget.
Also, if you have plans to perform localization for any Far Eastern languages (Japanese, Chinese, Korean, ...) you might consider sharing the cost across those projects, since many of the issues will be similar.
One final point - maintaining the localization for future releases might cost substantially more than providing it in the first place.