THE WALL STREET JOURNAL.

By DAVID BENOIT, KIRSTEN GRIND and SHARON TERLEP

Relenting to pressure from all sides, Michael Dell agreed Friday to personally pay more to take ownership of the company that bears his name.

Mr. Dell and his partner on the deal, private-equity firm Silver Lake, are now offering a 13-cent special dividend to shareholders, plus a raised price of $13.75 for each share. The increases add $350 million to what had been a $24.4 billion deal for Dell Inc.

In exchange, the special Dell board committee negotiating the deal agreed to adjust the shareholder voting rules in ways that advocates and critics of the takeover alike say should help it get across the finish line.

Mr. Dell himself is funding the special dividend, according to people familiar with the deal.

The buyout, controversial with Dell shareholders since it was announced in early February, still isn't assured. Investor Carl Icahn, its most-vocal detractor, on Thursday filed suit in Delaware Court of Chancery seeking to bar any change in voting rules. A hearing on that case is scheduled for Monday, Aug. 12, according to people involved in it.

On Friday, Mr. Icahn said "an increase of a mere 13 cents is an insult to shareholders" and he said the special committee "is improperly putting its thumb on the scales in favor of Mr. Dell's offer."

It is unclear if shareholders will be satisfied with and pass the improved offer. Mr. Icahn, for one, has argued the voting changes could in fact generate additional "no" votes.

Franklin Mutual Advisers, one of Dell's large institutional investors, plans to vote in favor of the new Dell deal, Peter Langerman, Franklin's chief executive said Friday. "We're not jumping up and down," said Mr. Langerman, who said Franklin earlier voted against the buyout. "But if the vote were today or tomorrow we would say yes."

Mr. Langerman and his team met with Mr. Dell last month and aired their concerns about the deal and its price, he said. "We were quite vocal in terms of dissatisfaction with the process and the price," Mr. Langerman said. Franklin is a unit of money-manager Franklin Resources Inc.

Donald Yacktman, president of Yacktman Asset Management, said Friday he still opposes the Dell buyout. "From the word go, we've made a statement about where we've stood and we're not going to change that," said Mr. Yacktman, whose firm is also a large Dell shareholder.

The fabric of the new deal shows the determination of Mr. Dell, the company's founder, chairman and chief executive, to see it through. Last week the buyout group had offer to raise its $13.65 bid to $13.75, saying it was their "best and final" offer. In his own letter to shareholders last week Mr. Dell said, "I am at peace either way and I will honor your decision."

Mr. Dell and the partner heading the deal for Silver Lake, Egon Durban, spent time at their nearby homes in Hawaii working out new terms, said people familiar with the talks.

The new deal also calls for a third-quarter dividend of eight cents a share that might not have been paid had the buyout closed according to an earlier schedule.

The buyout group proposed the eight-cent payout on Wednesday, according to a person familiar with the matter. The Dell board said the quarterly dividend wasn't enough, and by Wednesday evening they'd agreed on adding the 13-cent special dividend, people familiar with the matter said. The details were hammered out late into Thursday night.

All in, the offer-price increase and the dividends amount to a value of $13.96 a share for holders not affiliated with Mr. Dell, a 2.3% increase from the original offer. Dell shares rose 5.6% to $13.68 in Friday trading, the highest since April and a sign investors think the deal will get done.

Dell shareholders will get a chance to vote on the new proposal on Sept. 12. Friday's deal also includes a new "record date," of Aug. 13, the date that determines which Dell stockholders can cast votes on the deal.

The voting-rule change means only shares that are actually voted count, altering an earlier clause that had abstentions counting as "no" votes. That clause proved problematic when turnout for the vote wasn't as high as the buyout group and special committee had hoped. When they didn't have the confidence they had the votes to get the deal passed, the special committee delayed the vote twice.

Alex Mandl, chairman of the special committee, said Friday the new voting standard is "in the best interests of Dell shareholders" and "has enabled us to secure substantial additional value." He said the voting change was warranted because when the sides struck a deal there was only a choice between "a going-private transaction and a continuation of the status quo."

Now, he says, the "nature" of shareholders' choice has changed because an alternative has emerged, a reference to Mr. Icahn's competing plan for Dell to borrow and pay out money to shareholders.

Southeastern Asset Management Inc., aligned with Mr. Icahn in the fight, responded it was "amazed" at Mr. Mandl's justification, saying he was using their opposition to justify lowering the voting requirement for Mr. Dell and Silver Lake.

A new record date could also help the buyout group by attracting short-term shareholders, known as merger arbitragers, who buy shares with the hopes of securing gains when deals get completed.

Dell, founded by Mr. Dell nearly 30 years ago, has struggled to keep pace with the latest technology trends. Mr. Dell has envisioned refocusing the company on serving corporate clients rather than selling consumer computers. Shareholders who have protested the deal have had many of the same goals but felt the original $13.65-a-share price undervalued the company and that the buyout unfairly cut them out of potential upside in any Dell revival.

The resistance to the original deal proved more than Mr. Dell could overcome, even as certain key developments went his way. In April, industry-research firm IDC issued a surprisingly bleak report on global PC shipments, potentially lending credence to the board's inclination to sell the company.

Later that month, private-equity giant Blackstone Group LP, which had considered an offer greater than $14.25 a share, backed away after getting spooked at Dell's business prospects during due-diligence research. That move, and the lack of any other bidders for the whole company, gave the committee and buyout group leverage to say no higher offer was in sight. Then in July three shareholder-advisory firms urged investors to take the $13.65-a-share offer.

Still, all of these favorable factors weren't enough to overcome the assault by Southeastern and Mr. Icahn. The investing pair have said if the buyout vote failed, they would put up their own slate of directors at Dell's annual meeting to try to oust the board, including Mr. Dell. They have proposed a plan in which the company would borrow money and pay shareholders $14 a share and a warrant for as many as 1.1 billion shares out of about 1.76 billion shares outstanding.

They have urged Dell's board to hold the buyout vote at the same time as the annual meeting, to give shareholders an option to choose their proposal, Mr. Dell's, or neither.

On Friday morning, the Dell board made clear it had no such intentions, setting the annual meeting for Oct. 17.

—Shira Ovide, Peg Brickley and Joann S. Lublin contributed to this article.

Write to David Benoit at david.benoit@dowjones.com, Shira Ovide at shira.ovide@wsj.com and Kirsten Grind at kirsten.grind@wsj.com

A version of this article appeared August 3, 2013, on page B1 in the U.S. edition of The Wall Street Journal, with the headline: Michael Dell Sweetens Offer.