What is the value of a 1948 New Zealand Penny?
There was no 1948 New Zealand Penny minted.
The highest value New Zealand Penny is easily the 1956 Penny, but there are two varieties. The 1956 Penny with the high value shows Queen Elizabeth II with no shoulder straps. A very distant second would be the 1941, 1942 and 1954 Pennies. The high value is only ascribed to coins in mint uncirculated condition.
New Zealand Pennies were issued from 1940 until 1964. A limited collector set was issued in 1965. Decimal currency was introduced in 1967. Depending on their condition and any peculiarities, a New Zealand Penny could be worth anything from $1 to $2,000 NZD. A complete set of New Zealand Pennies from 1940 to 1965 in average condition might get $35 NZD.
With the possible exception of traders tokens (with the traders business name on them), there were no "New Zealand" Pennies minted prior to 1940. Any Pennies circulating in New Zealand prior to 1940 would have been mostly British Pennies and some Australian Pennies. It is possible that you have a British Penny, as the do not explicitly say the country of origin on them.
Current New Zealand coins are 10c, 20c, 50c, $1 and $2. Previously, the lowest denomination for a New zealand decimal coin was 1 cent. The lowest denomination ever for a New Zealand coin was a halfpenny (pre-decimal times). Unlike england, New Zealand has never had a farthing (equal to a quarter of a penny).
The first New Zealand Pennies were minted in 1940. Any Pennies circulating in New Zealand prior to 1940 would have been mostly British Pennies and some Australian Pennies. Since New Zealand was "discovered" and claimed by Captain Cook in 1769, it is extremely unlikely that there would be any New Zealand coinage.
A New Zealand 1940 bronze Penny (George VI), uncirculated and in absolute mint condition could fetch up to $65 NZD. If it has been circulated but still in good condition, it might fetch anything from $2 to $35 NZD. There were 5.424 million minted. A reputable coin dealer will be able to give a more accurate valuation. NOTE - 1940 was the first year of issue of the New Zealand Penny.