In British currency, the smallest unit is one penny, and the coin worth one cent is a "penny," plural "pence." A "halfpenny" (currently written as one word, no hyphen) had a value of half a cent. (Halfpennies have not been issued since 1984).
The "lf" is not pronounced and the "a" has a long "a" sound, as if spelled "haypenny." Sometimes this is indicated by spelling it with an apostrophe, "ha'penny."
I'm not sure about the use of the hyphen, but with many, many compound words you will find that a) older sources use the hyphen; b) modern sources tend to leave out the hyphen; c) some conservative modern sources will still use the hyphen. I'm sure that is what is happening here.
You would not write "half penny." You would either write "halfpenny," "ha'penny," or "half-penny." You could write "half of a penny." Thus, it would be quite natural to write,
"As its name suggests, a halfpenny is worth half of a penny."