THE WALL STREET JOURNAL.

By DAVID BENOIT And BEN FOX RUBIN

Carl Icahn on Wednesday urged Dell Inc. shareholders to head to court to force founder Michael Dell to pay more, in the activist investor's latest effort to ruffle a buyout slated for a shareholder vote next week.

The billionaire investor has taken up the mantle of getting a Delaware judge to appraise the value of Dell, a ruling that could lead to those who join him getting more than the $13.65-a-share buyout—or possibly less. The decision to seek an appraisal suggests Mr. Icahn is resigning himself to the possibility shareholders vote in favor of the buyout next week, as his plan would only affect shareholders if the deal passes.

At the same time, because a shareholder has to vote against the deal to seek an appraisal, if enough shareholders attempt the maneuver it could block the deal.

In Delaware, a shareholder is allowed to seek a judge's opinion on what the long-term intrinsic value of a company is, instead of outright accepting a merger offer. If a judge were to determine that Dell shares are worth more than $13.65, the buyout group would be forced to deliver the extra amount, with interest, to those shareholders who sought the appraisal.

The shareholders also take the risk that a judge could rule the shares are worth less, and they would also have to wait the time it takes a judge to decide—potentially years. Also, owning appraisal rights could potentially be an issue for some institutional shareholders who have strict rules about holding only public shares.

Appraisal cases that make it to a judge's rule are rare, with only a few each year, people in the industry said.

Mr. Icahn's plea to shareholders says "those who seek appraisal may get lucky" and presents the move as a can't-lose option because shareholders can withdraw their request up to 60 days after the merger and still get the $13.65-a-share buyout price.

"We believe if you seek appraisal, you will receive more," the letter says.

"As I said all along, I believe it's worth well more than $13.65" a share, Mr. Icahn said in an interview Wednesday. "It looks like it's going to be a very close vote, but if Dell wins, going for appraisal rights is a no-brainer."

Mr. Icahn, Dell's second-largest shareholder behind Mr. Dell, has repeatedly criticized the bid by Mr. Dell and private-equity firm Silver Lake Partners to take Dell private for $24.4 billion, saying the proposal undervalued Dell's shares with its $13.65-a-share price tag.

Mr. Icahn revealed a position in Dell after the buyout agreement was announced Feb. 5. In a recent filing, Mr. Icahn estimated his firm spent about $2 billion acquiring the position in Dell, which would mean an average of $13.12 a share. Part of his stake is in options, which makes his final cost unclear.

Dell shares lost 3 cents to close at $13.33 in 4 p.m. trading in New York Wednesday.

Shareholder-advisory group Institutional Shareholder Services Inc., as well as Glass, Lewis & Co. and Egan-Jones Proxy Services, this week recommended Dell stockholders vote for the buyout offer, improving the odds of the deal passing.

In his latest letter to shareholders, Mr. Icahn says he would seek to settle the appraisal with Mr. Dell and Silver Lake—who have their own risk in any court proceeding—within the 60-day grace period, a situation he says may allow a shareholder to "have your cake and eat it too."

One possible point in his favor: Often, deal agreements include a clause that allows buyers to back out of a deal if too many shareholders seek an appraisal. However, there is no such clause in the Dell agreement, which means the buyout group assumed the risk of such an occurrence.

Gary Lutin and the Shareholder Forum, a shareholder-advisory group, set up a public trust earlier this year that would support Dell investors seeking appraisal rights and said Wednesday that at least reserving an appraisal right seems to be an obvious step to many in the forum.

"Fair-market value is almost always more than auction price, especially in a situation like Dell in which you have very sophisticated private-equity firms who are unlikely to pay more for a company than its professionally determined long-term going concern value," Mr. Lutin said.

—Shira Ovide contributed to this article.

Write to David Benoit at david.benoit@dowjones.com and Ben Fox Rubin at ben.rubin@dowjones.com

A version of this article appeared July 11, 2013, on page B4 in the U.S. edition of The Wall Street Journal, with the headline: Icahn Maneuvers For Dell Appraisal.