By Tiisetso Motsoeneng JOHANNESBURG (Reuters) - South African conglomerate Bidvest has offered about $515 million for the shares it does not already own in drugmaker Adcock Ingram in a new attempt to build a big presence in the pharmaceutical market. The deal would give Bidvest a substantial presence in the generic market, which is set to grow as the government prepares a national health insurance plan that would rely on the use of cut-price versions of branded drugs. Bidvest already owns a 34.5 percent stake in the drugmaker, which it acquired a year ago, scuppering a rival bid from Chile's CFR Pharmaceuticals. Adcock is trailing rivals as it struggles with slowing sales, over-reliance on a heavily regulated home market and factories that are running below capacity. Under the latest offer, Bidvest would pay about 6 billion rand ($515 million), or 52 rand per share, which represents a 3.6 percent premium to Adcock's closing price on Friday. Shares in Adcock jumped as much as 6.6 percent during the session. By 1410 GMT, the stock had given up some its gains to trade 4.3 percent higher at 52.34 rand. "OPPORTUNISTIC" Adcock reported a 38 percent rise to 83.8 cents in half-year headline earnings per share on Monday, a sign that a turnaround plan that include cost cuts and adopting a centralised business model is gaining traction. It has not commented on the Bidvest approach. "Considering the potential turnaround of the company, I think it is definitely an opportunistic bid," said Simon Mather, analyst at Barclays, who has a "neutral" rating on the stock. "In a more optimistic scenario about the prospects of Adcock, we got to a fair value of 69.5 rand per share provided management is able to orchestrate a meaningful turnaround of the business." Bidvest's offer values Adcock at around 9.1 billion rand -- below its enterprise value of about 10 billion rand, according to Thomson Reuters data. Bidvest has been trying to take control of Adcock since 2013, seeing an opportunity to turn around an underperforming company and add painkillers and cough syrups to its stable of products. Last year, it sank a 12.8 billion rand, or 74.5 rand per share, takeover offer for Adcock from CFR by building a blocking stake that gave it the current holding. In March 2013, Bidvest offered a 10 percent premium for a 60 percent stake in Adcock, a bid spurned by Adcock's board at the time as opportunistic. ($1 = 11.7232 rand)