SYDNEY, Sept 29 (Reuters) - In what could be a cautionary tale for Alcoa Inc, global miner BHP Billiton's decision to spin off non-core businesses into a separate company is yet to pay off for shareholders. Alcoa announced on Monday it will break itself in two, separating a faster growing plane and car parts business from traditional alumina and aluminum production as shareholders seek higher returns amid a commodity slump. BHP used a similar rationale for ring-fencing select operations in Australia, southern Africa and South America into what became South 32 last May to concentrate on its most profitable commodities. South32 shares fell to a record low on Tuesday of A$1.38, more than a third below its listing price. BHP stock, at A$21.61 at Australia's Tuesday close, is the lowest in seven years. "The argument is that these things create simpler structures where management can better... More