The huge crash in oil prices last year caused profits to collapse for most exploration and production companies. These are companies involved in discovering and developing oil and gas, and their bottom lines are highly reliant on a supportive oil price. Two of the biggest E&P companies are Occidental Petroleum (OXY 0.58%) and ConocoPhillips (COP 0.39%). Both companies have similar business and production profiles. And, both companies are attractive dividend payers -- Occidental yields 3.5%, and ConocoPhillips pays a 4.2% dividend. But the big question now is whether investors can count on these juicy dividends.

As exploration and production giants, both Occidental and ConocoPhillips are being hit hard by the oil collapse. This calls into question whether their dividends can survive the crisis, since a number of energy stocks have slashed their payouts in recent weeks. Here's a closer look at two high-profile dividend stocks in the oil sector.

Dividends appear safe, despite the oil collapse
Based on the oil crash, it was clear that earnings reports from exploration and production companies were inevitably going to be ugly across the board. Indeed, Occidental lost $3.4 billion last quarter, compared to a $1.6 billion profit in the same quarter of 2013, because its worldwide realized crude oil prices declined by 28% year over year, from $99 per barrel to $71 per barrel. For the year, core earnings per share fell 15% to $4.83 per share.

Likewise, ConocoPhillips also had a rough year. The company booked a $39 million loss in the fourth quarter, which depressed its full-year results. Full-year 2014 earnings were $6.9 billion, or $5.51 per share, compared with full-year 2013 earnings of $9.2 billion, or $7.38 per share. This represented a 25% decline in profits, year over year.

The strain on both Occidental and ConocoPhillips was magnified because neither company cut production, despite sliding oil prices throughout the latter half of the year. Last quarter, domestic oil production increased by 19,000 barrels per day year over year, due mostly to 42% growth in oil production from its Permian Basin operations. Occidental isn't laying off the gas pedal anytime soon: 2015 production is set to grow 6%-10% from 2014 levels. Meanwhile, ConocoPhillips' production excluding its Libyan operations grew 4%, and it expects to achieve 2%-3% production growth in 2015.

Fortunately, both ConocoPhillips and Occidental have maintained their dividends through the crash, despite the losses incurred last quarter.

Capital discipline is painful, but necessary
Along with their earnings results, both companies announced steep cuts to their capital spending budgets. This makes complete sense of course, because neither company can continue to produce at a loss.

Occidental's 2015 budget is set at $5.8 billion in planned capital spending, which represents a 33% reduction from last year. For its part, ConocoPhillips reduced its expected 2015 capital expenditures to $11.5 billion from $13.5 billion previously announced -- a 15% reduction. It's not surprising to see Occidental slash its budget by a greater amount, since it was more aggressive than ConocoPhillips in accelerating production in the past few years.

While these measures will impact both companies' production in the future, it is a necessary step in light of the massive decline in oil prices. If and when oil prices recover, there will be room for higher spending. Capital discipline should also help keep cash flow high and allow them to continue paying their dividends, even if oil prices stay low. However, it may not be feasible for either company to increase its dividends in the current environment, given that both were free cash flow negative last year. Of course, if oil prices rise once again, this would change.

The key takeaway is that while the oil crash wreaked havoc on Occidental's and ConocoPhillips' fundamentals, their dividends remain secure. This is a good sign that both companies are committed to their dividends.