Depends on what the coin is made out of.
The coin has absolutely no collector value because it wasn't made by the US Mint. Any value comes from the material the coin was made out of. If the coin was gold plated, it would be worth a couple cents at most. If the coin was solid gold, it would be worth the value of the gold, but no more.
The Liberty head design was used on over several different coins in 1878. Please post a new question with the coin's denomination, with the wording "What is the value of an 1878 US (coin denomination)?" e.g. What is the value of an 1878 US silver dollar? or What is the value of an 1878 US 10 dollar gold piece.
Only one genuine 1849 $20 gold piece is known, and it was designed by James Barton Longacre, not George T. Morgan. Any other supposed $20 gold piece with that date is either a fantasy coin, a replica, or an outright fake.
If it's a Morgan Mint copy, then it's gold plated at best -- no collector value -- maybe a couple dollars novelty value.
Morgan dollars are silver, not gold.
For the source and detailed information concerning this subject, click on the related links section indicated below.
It's gold plated but not gold. The only good news is that the underlying coin is 90% silver so as of 01/2011 it's worth maybe $18 to $20 for the silver. If you think about it, $20 gold pieces were smaller than Morgan dollars so putting that much gold (about $25 worth at the time) into a $1 coin wouldn't have made a lot of "cents".
It's still worth about $36.00 just for the silver, the gold maybe 5 cents. The plating actually killed the collectible value of the coin.
The US struck a gold and silver one dollar coin in 1878, post new question as to type of coin.
I think it is rather expensive as it is a collectible year and not many made with that amount of gold.
Providence mint
What is the value of a one fourth ounce gold austrian 500 schilling piece?
These usually sell in internet auctions for about $1500.