Shout (noun and verb), in Australia, New Zealand, and England, refers to an act of spontaneous giving.
Its primary use is in pub culture, where one person in a group elects to pay for a round of drinks for that group.
It may be that person's polite way of leaving the group to go elsewhere.
In Australian culture one person shouts the first round, then each in turn is expected to shout the next or if they wish to stop drinking the shout the round without buying themselves a drink. This is the sequence described in the Industrial Relations Court of Australia during the Garsid v Hazeltin Air Services(1997). 
By extension, it can refer to paying for another person's purchase; something they have chosen or will choose for themselves, as distinct from a gift or present.
Typical constructions are:
Historically, the term "shout" was used by Rolf Boldrewood in "A Colonial Reformer" (1877), Henry Lawson in his poem "The Glass on the Bar" (1890), Jack Moses in "Beyond the City Gates" (1923) and Dal Stivens in "The Courtship of Uncle Henry" (1946).
References.
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