* Santander says has faith in Brazil long-term outlook
* CEO rules out strategy change with other listed units
* Sees offering of UK unit taking place in 'mid-term'
* Europe earnings rise as first-quarter profit up 8 pct
(Adds details of banks advising on deal)
MADRID/SAO PAULO, April 29 (Reuters) - Banco Santander SA launched a 4.7 billion euro ($6.5 billion) offer on Tuesday for the 25 percent of its Brazilian unit it does not already own, giving investors a chance to gain exposure to a budding recovery of the euro zone's largest bank.
Under the proposed deal, minority investors in Banco Santander Brasil SA would receive up to 665 million shares of the Madrid-based lender in a voluntary swap at the equivalent of 15.31 reais a share. That represents a 20 percent premium to Santander Brasil's closing price on Monday.
Santander, which is emerging from Europe's worst economic crisis in decades while still facing a weak Brazilian economy, hopes the buyout will help cut costs, boost returns and lure clients to Santander Brasil. Investors are undervaluing the potential of Santander Brasil, executives said.
"It's a take-it-or-leave-it offer to gain exposure to Santander's better momentum in Europe as we all recognise that much heavy lifting has to be done in Brazil," said Mohammed Mourabet, who oversees $900 million in assets for Victoire Brasil Investimentos in São Paulo.
Santander Brasil shares soared 21 percent on Tuesday, their biggest intraday gain since the lender went public in October 2009, underscoring the potential success of the deal. The buyout, announced the same day Santander reported an 8 percent rise in first-quarter profit, is an exception to its strategy of listing foreign units whenever possible to raise cash.
"The offer price seems reasonable given that it is well above what we consider to be Santander Brasil's stand-alone fair value," said Saúl Martínez, a senior banking industry analyst with JPMorgan Securities in New York.
Santander Brasil shares have lost nearly half their value since the IPO because the bank failed to deploy capital in profitable activities, outperform competitors and gain scale.
"We can do better, and this is a first step to begin charting a new course," Jesús Zabalza, chief executive of Santander Brasil, told investors on a call.
The buyout also reflects Santander's confidence in its finances ahead of Europe's toughest banking stress tests yet.
The plan would help group profits grow 7 percent in 2015 and in 2016, equivalent to a boost of 560 million euros in 2016.
Goldman Sachs Group Inc and UBS AG are advising Santander. Santander shares, up more than 13 percent this year, closed 1.5 percent higher at 7.154 euros in Madrid.
Most analysts expect the deal, which executives hope to conclude by October, to succeed.
Faltering growth in Brazil is weighing on profitability at Santander's Latin America division as Spain slowly emerges from one of its worst economic crisis ever. In the first quarter, Europe provided just over half of Santander's net income, which rose to 1.3 billion euros. Profit in continental Europe rose 64 percent quarter on quarter and 53 percent on the year.
Its UK unit, where revenue in pounds rose 13 percent from the first quarter of 2013 on a sharp rise in margins and an improving economy, was now on par with Brazil in providing a fifth of total profits, Santander said.
Santander CEO Javier Marin said in January that a long-expected public offering of its UK unit would not take place in 2014, but occur in the "mid-term."
In Brazil, Santander's profit dropped 27 percent from a year ago, while it rose 20.9 percent from the fourth quarter of 2013, taking into account currency fluctuations.
Profits at the parent company missed forecasts slightly. Non-performing loans in Spain and Brazil edged up slightly at the end of March from end December, even if at a group level the ratio dipped to 5.52 percent from 6.61 percent.
A buyout of minority shareholders of Santander's listed units in Mexico and Chile looks "unlikely at this point, simply because doing so doesn't appear to make the same kind of financial sense as it does in Brazil," JPMorgan's Martínez said.
($1 = 2.24 Brazilian reais)
(Additional reporting by Tomas Cobos and Steve Slater in London, and Aluísio Alves in São Paulo; Editing by Julien Toyer, Sophie Walker, John Stonestreet; Chizu Nomiyama and Steve Orlofsky)