This is at a 5% discount to TTML's closing of Rs 8.01 per share on the BSE today.
Tata Sons Limited, one of the promoters, will be divesting 1.84% stake in the company through offer for sale on May 30 to meet the minimum public shareholding norms.
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Market regulator SEBI's norms require all listed private sector companies to have at least 25% public shareholding by June.
Based on the floor price, the promoters are expected to garner Rs 26.60 crore from the sale of shares.
"Tata Sons Limited proposes to sell an aggregate not exceeding 35,000,000 equity shares of Rs 10 each of TTML, representing approximately 1.84% of the paid up equity share capital of the company...On May 30, 2013," the company said in a filing to the BSE.
"...The floor price for the sale in terms of the SEBI OFS circulars shall be Rs 7.60 per equity share of TTML," the filing added.
SEBI recently relaxed norms for TTML's offer for sale (OFS) by promoters.
As per BSE, promoters currently hold 77.72% stake in the company while 22.28% is held by public.