LONDON -- You normally expect companies in the FTSE 100 (INDEX: ^FTSE) to be boring, solid and dependable. But several companies in the index are far from that. There are several "make or break" shares where management actions, or simply fate, could ultimately determine whether they are very good investments or very poor investments.

The three most obvious are:

  • BP (LSE: BP.L), where the final settlement of the Deepwater Horizon oil spill liability and resolution of uncertainty around its Russian joint venture could send the shares in either direction.
  • Aviva (LSE: AV.L), which rewards shareholders with one of the highest dividends in the FTSE 100 and has turnaround potential, but is dogged by its exposure to the eurozone and risk of a dividend cut.
  • AstraZeneca (LSE: AZN.L), which pays a generous dividend but faces the prospect of its earnings falling off a cliff.

When companies have such a binary outcome, there are two ways of thinking about the valuation at which its shares trade. One is that the price reflects the balance of bulls and bears on the stock. The other is that the price is a weighted average based on the probability of either outcome.

BP has two big issues on its plate. One is to raise enough capital to settle the as-yet-unknown final bill for the Deepwater Horizon spill. The other is to sort out what it does in Russia.

It recently announced a $1.2 billion refinery sale, which brings the total of disposals since 2010 to $26.5 billion against a $38 billion target. That's good progress, but the total will not be achieved without cutting into BP's earnings power and reserves.

Almost a quarter of BP's production comes from its 50-50 Russian joint venture. It has been dogged by tensions with the local partners, who currently are blocking dividend payments. BP could yet be forced out on poor terms, or alternatively secure the strategically attractive scenario of a joint venture with the state-owned oil company.

Aviva's prospects have brightened since CEO Andrew Moss was shown the door, and executive chairman John McFarlane has grabbed the bull by the horns. With a strategy of cutting out underperforming businesses and layers of management deadwood, he has moved fast to divest operations and raise capital.

Eyes are now on its U.S. business, which it bought for $2 billion in 2006. Although plans for its sale are unconfirmed by management, the market would be pleased if McFarlane pulls off a deal, even though it's likely to raise less than half the original cost.

But Aviva's exposure to eurozone markets remains a drag, and its capital position is too tight for the dividend to be entirely safe. Last week Standard and Poor's downgraded Aviva's debt one notch from A to A- because of the significant risks and costs of the turnaround plan.

In a defensive sector and paying a high dividend, AstraZeneca seems to be the textbook high-yield share. The flip side of that is its well-documented patent cliff, and the risk that it fails to find replacement income streams for when its mainstream drugs lose patent protection.

That's become more pressing as the company has struggled to generate new drug formulas. Like Aviva, the company saw its CEO ousted earlier this year. Also like Aviva, the temporary replacement -- in this case former finance director and interim CEO Simon Lowth -- has raised investors' hopes.

AstraZeneca's participation alongside Bristol-Myers Squibb in the acquisition of biotech company Amylin seemingly demonstrates a bigger appetite for M&A activity. That may be what the company needs to keep it in business long term rather than operating in run-off mode. Eventually, that would manifest itself in a falling share price, which the generous dividend would not compensate for.

One major investor who does have faith in the company's future, backed by a very sizable holding, is dividend expert Neil Woodford. He has put over 20% of Invesco Perpetual's high income fund into just three pharmaceutical companies, including AstraZeneca. You can learn more of his investing style and allocation in a free Motley Fool report, "8 Shares Held by Britain's Super-Investor," which you can download here.

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Tony Reading owns shares in Aviva and AstraZeneca but no other shares mentioned in this article. The Motley Fool has a disclosure policy. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. Try any of our Foolish newsletter services free for 30 days.