for a song

Very cheaply, for little money, especially for less than something is worth. For example, "I know a man ... sold a goodly manor for a song" (Shakespeare, All's Well That Ends Well, 3:2). This idiom alludes to the pennies given to street singers or to the small cost of sheet music. [Late 1500s]

The adverb has one meaning:

Meaning #1: for a relatively small amount of money
  Synonyms: for a bargain price, at a low price