Its board approved the sale on Monday. The deal would cost Cloverdell Investment, an affiliate of Warburg, about Rs 560 crore (Rs 5.6 billion).
According to the agreement, Pantaloon Retail India, along with its wholly owned subsidiary Future Value Retail, would sell its stake in FCH.
The deal is proposed at Rs 162 per share, an 18 per cent premium to Friday's closing price.
FCH scrip closed at Rs 143.55 on the Bombay Stock Exchange on Monday, up 4.78 per cent over Friday's close.
Warburg Pincus would buy a 40 per cent stake in the first tranche and 14 per cent in the second.
Subsequently, it would make an open offer for the remaining stake.
The company would also infuse Rs 100 crore (Rs 1 billion) of primary capital through a preferential allotment by Future Capital, said a company statement.
At present, the debt on Future Group's books stands at Rs 5,800 crore (Rs 58 billion).
The stake sale to Warburg Pincus would help Future Group reduce its debt by Rs 4,300 crore (Rs 43 billion),
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