Wal-Mart (NYSE:WMT) turned 50 earlier this month and if you judge by the numbers, the game-changing retail colossus that entrepreneur Sam Walton launched in Bentonville, Ark. is aging very well. So why would many shareholders — including multiple pension funds — like to see an extreme makeover?

First the good news: since CEO Michael Duke took the helm in February 2009, WMT shares have risen 61% — on par with the Dow’s rise over that same time frame. The company’s first-quarter earnings reported in May beat the Street: profit rose 10% to more than $3.7 billion on revenue of $112.3 billion — more than 8% higher than the same quarter last year.

Same-store sales — always a critical measure of strength for retailers — rose by 2.6% in the most recent quarter, WMT’s best same-store growth since 2009. And at international stores, sales grew by nearly 11%. In the retail industry, results like those are not too shabby.

So what prompted a near revolt by WMT shareholders at the company’s annual meeting in June? A bribery scandal involving the company’s Mexican subsidiary, a criminal probe by the Justice Department (DOJ) and a Securities and Exchange Commission (SEC) investigation over that scandal. Additionally, there have been shareholder lawsuits focused on what WMT executives knew about the alleged bribery and when they knew it.

Here’s the Cliff Notes version of the bribery backstory: In 2005, an executive at Wal-Mart de Mexico approached the legal department at company headquarters with details of a formal campaign to gain permits throughout Mexico by bribing officials.

In the following days and weeks, WMT headquarters reportedly uncovered some $24 million in suspect payments, on top of evidence that Wal-Mart de Mexico had intentionally tried to keep the payments secret from the company’s top bosses in Bentonville.

But instead of notifying law enforcement officials in the U.S. or Mexico, company leaders initiated a cover-up, according to a New York Times investigative article published in April. While the alleged bribery was reported on the watch of Duke’s predecessor, H. Lee Scott Jr., the Times story alleged that Duke was kept in the loop in his role as the head of Wal-Mart International.

Since then, the vultures have been circling Wal-Mart headquarters in general — and Duke’s office in particular. Not counting company executives and members of the Walton family, 30% of Wal-Mart shareholders voted against the reelection of Duke and three other board members — including Sam’s son S. Robson “Rob” Walton.

Other reports have raised the possibility that Duke and other key executives could be charged with criminal violations of the Foreign Corrupt Practices Act. At the very least, the company is likely to face considerable fines if it is proved to have covered up payoffs to foreign officials.

And Duke could be in the investigators’ crosshairs. When he took over as CEO in 2009, Duke said Wal-Mart already had disclosed all possible cases of fraud. Wal-Mart Vice-Chairman Eduardo Castro-Wright, who ran the Mexico business between 2001 and 2005, retired on July 1, making Duke an attractive target for shareholders’ wrath as well. Several pension funds already have filed lawsuits against WMT over the scandal.

The biggest casualty of the bribery investigations may be the newly tarnished perception of Wal-Mart’s ethics. WMT may need an executive shakeup to polish its corporate image. If Wal-Mart embarks on an extreme leadership makeover to put the Mexico scandal behind it, this is how the shake-up might look:

Out:

• Michael Duke: When things go wrong, somebody has to take the fall. With Castro-Wright out of the picture, Duke is the most logical choice.
• Lee Scott: Scott, the Wal-Mart CEO who headed the company when the bribery issues were first sent up the chain of command, is still a board member. I’d expect him to retire sooner rather than later.

Maybe:

• Douglas McMillion. McMillon has got Wal-Mart in his blood — he’s an Arkansas boy who joined the company as a summer associate in the distribution center back in 1984 and came back full time after earning his MBA. He was president and CEO of Sam’s Club from 2006 to 2009, leaving to take over Wal-Mart International when Duke became CEO of the company. McMillion, who generated $46 billion in sales from Sam’s Club in less than three years, would be a great choice as CEO if his role in International doesn’t hurt him.

In:

• William Simon. Simon, who joined Wal-Mart in 2006 from Brinker International, has brought innovation to the company’s U.S. operations and could be a good fit to head the company if it chooses not to look outside for a big name. Since becoming CEO of Wal-Mart U.S. in 2010, Simon has presided over 3,900 stores and 1.2 million employees.
• Jim Walton. The youngest son of founder Sam Walton is the ultimate insider. He owns (directly or indirectly) more than 48% of Wal-Mart stock and joined the board in 2005. In addition to having a seat on the WMT board, Walton is Chairman and CEO of family-owned Arvest Bank, where Jim had his first job as a teller. He would be a solid choice to take over if Rob steps down.

Bottom Line

With Mal-Mart under investigation by U.S. and Mexican authorities — and shareholders up in arms about the company’s business ethics — now is not the time to initiate a new position in WMT. The various facets of the bribery scandal will take time to play out and the stock will probably lose some altitude as it does. Patience could pay off in the second half of the year.

As of this writing, Susan J. Aluise did not hold an interest in any of the stocks named here.