Turmoil is the best word to describe the situation at the top of Occidental Petroleum (OXY -2.37%). Despite commendable efforts by the company's CEO, Stephen Chazen, to grow production while cutting costs, Occidental just can't seem to shake the rumors that the board of directors – led by chairman and former CEO Ray Irani – has been wanting to give Chazen the axe.

News like this is just more cannon fodder for investors who have seen Occidental's share price drop for the past two years in spite of the massive boom in U.S. oil and gas. What is even more surprising about this slide is that there have been several promising operating results coming out of the company for the past couple of quarters. It's very possible that Occidental can't gain any traction in the market because of investor sentiment, so what is a company like it to do? Let's take a quick look at a couple ideas that the company is floating.

Buy back the bullish
With share prices down almost 25% since Chazen took the reigns in 2011, the company has looked at almost any idea possible to get increased shareholder value. The problem is, though, that none of these ideas has seemed to stick so far. Even when the company announced it was raising its dividend by more than 18% back in February, the news gained little traction against the story that the board was pursuing a succession plan for Chazen.

Now, with share prices so low, the company is considering a buyback program. Few details were given regarding the idea on the company's most recent conference call, but then again the company said it has explored myriad ideas, ranging from spinning off its midstream assets into an MLP to splitting the domestic and international segments of the company in two. While companies like Phillips 66 (PSX -1.84%) and Marathon Petroleum (MPC -1.83%) have shown that spinning off midstream assets can be a great way to unlock value, its hard to tell if Occidental's assets would garner that much attention. 

Any way you shake it, these kinds of moves could give a nice injection of shareholder value, but they are only one-time deals that might not lead to long-term-value creation.

Wrap it up?
One of the more intriguing moments during the most recent earnings presentation was when Chazen addressed the notion that selling the entire company would take one phone call. If the idea of selling a company with a total enterprise value of $69 billion with only one phone call sounds a bit strange, you are probably right. If you were to think of the candidates that would be able to make such a deal, then the idea that only one or two could do it makes sense.

The idea of buying a company this size isn't completely unprecedented. Back in 2009, ExxonMobil (XOM -1.04%) bought XTO Energy for over $41 billion. Granted, Exxon may have overpaid for that acquisition, but Occidental is certainly in that range. Furthermore, Occidental's positions in the Permian Basin and the Bakken could be very attractive to some of these integrated oil majors who have stated they want to focus more on domestic production rather than some of the riskier plays overseas.

The chances of Occidental being sold is very unlikely, but the idea that the CEO of the company would even be willing to address this kind of question goes to show how much the company is willing to look at anything to grow shareholder value.

What a Fool believes
If you want to increase shareholder value, then why don't we ask what the shareholders of Occidental want. Clearly back in 2011, when shareholders disapproved of Irani's lavish executive pay and sent him packing, investors were looking for a change to the corporate culture. After the announcement that the company was investigating a CEO succession plan, several of the company's activist investors stood up and backed Chazen as the right man for the job. Now with rumors picking up again about tension among the board of directors, those same activist investors are now looking for Irani and several other members of the board to step down. 

Sometimes, a shake-up of the C-suite or the board can be just what the doctor ordered. When Aubrey McClendon announced his retirement as CEO of Chesapeake Energy (CHKA.Q), the company's shares jumped 9%. The move allowed the company to worry less about the media circus surrounding McClendon's legal battles, and focus on bringing the balance sheet back into order. Perhaps Occidental is due for a similar fate.