The firm had previously agreed to pay $2bn for its portfolio company, a value which caused several shareholders to call in a law firm in the belief it undervalued the stock.
Insight and new partner Vector Capital will now pay $25.75 per share for the software company, beating the $25.50 per share offer from Dell.
Some shareholders had complained the previous $23 per share offer was too low considering the stock was trading at $24.63 at the time, and hit $26.44 in January.
Chairman and CEO Vinny Smith, who will continue to lead the company after the closing of the proposed transaction, will have at least 84 per cent of his shares rolled over into the surviving privately-owned entity.
The transaction will be financed through a combination of a $187m equity commitment from both Insight and Vector, the share rollover and $1.195bn of debt financing commitments from JP Morgan, RBC Capital and Barclays Capital.
Insight and Vector will see a four-fold increase in its termination fee to $25 million, if Quest breaks the deal for a superior offer, up significantly from the $4.2m termination clause in the previous merger agreement.
The transaction is expected to close in the third quarter of 2012.
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