BP Na Kika platform, Gulf of Mexico. Source: BP website.

The steep drop in oil and gas prices during the past year has punished the major integrated energy companies. BP plc (NYSE: BP) is down 21% in the past year because of this. It's getting hit hard by fears over its underlying operations, as well as the potential outcome of the civil trial stemming from the 2010 Gulf of Mexico oil spill.

The company, however, is making progress on several of these issues, and at $40 per share, BP is a steal. Here's why I believe investors should buy U.K.-based BP instead of its two biggest U.S.-based rivals, ExxonMobil Corporation (NYSE: XOM) and Chevron Corporation (NYSE: CVX).

The pervasive negativity is overblown
BP isn't immune to the deterioration in the oil and gas markets. For example, BP's first-quarter profit fell 18% year over year, to $2.6 billion. Not surprisingly, the exploration and production business crumbled due to falling oil prices. Upstream profits collapsed 86% year over year.

Some of this was offset by BP's downstream segment, where profits more than doubled, to $2.2 billion. Downstream includes activities like refining, which actually benefits from volatility in commodity prices, because when oil prices fall, refining feedstock costs fall, as well, and margins widen. Moreover, BP was boosted by a surprise $200 million profit from its nearly 20% investment in Russian energy giant Rosneft, while analysts expected BP to actually post a loss from its Rosneft stake.

Overall, BP's results handily beat analyst estimates. Revenue fell 41% year over year, to $54.2 billion, but that topped projections by nearly $3 billion. Diluted earnings per share clocked in at $0.14, which was actually double what analysts expected.

Looking back further, BP's trailing 12 month profits totaled $2.8 billion, down 71% from the year-ago period. It's clear that the downturn in oil and gas prices has taken its toll.

But there's reason to believe BP's operations could improve going forward, as the price of oil has already rallied approximately 33% off its 2015 lows. This could be a major tailwind for BP as it has grown production recently. Last quarter, excluding Russia, BP grew production by 8%.

BP is aggressively ramping-up several projects. For example, oil production began in March on the Sunrise Phase I project in Canada. Total production is expected to reach 60,000 barrels per day at full capacity by the end of 2016. And the first of BP's planned start-ups for the current year, in Angola, is expected to ramp up very soon. .

At the same time, it seems very possible that the result of the civil trial won't be as bad as feared. BP's civil trial is still ongoing, and the big question is how much BP will ultimately be held liable. Judging by BP's depressed valuation, it seems that the market is pricing in the worst-case scenario, which would be close to $18 billion.

Earlier this year, a federal judge ruled that only 3.19 million barrels had spilled into the Gulf of Mexico. This was significantly lower than the government's calculation, and reduced the maximum financial penalty that BP could face from $17 billion to $13.7 billion. The actual fine will only be known at the conclusion of the trial, which won't be for a few months from now. Still, this is at least a promising sign that BP won't face the maximum penalty for the fine.

BP looks too cheap
BP has a depressed valuation and an elevated dividend yield when stacked up against its peers Chevron and ExxonMobil; but because BP is improving on its various challenges, it may be too cheap.

 Company ExxonMobil Chevron BP
Forward P/E 15 16 14
Enterprise Value to EBITDA 7.8 6.6 6.1
Dividend Yield 3.4% 4.2% 5.9%

Source: Yahoo! Finance

BP is significantly discounted when compared to its bigger peers, ExxonMobil and Chevron, on both an earnings and cash flow basis. While BP does have unique risks, such as its heavy exposure to Russia and the uncertainty pertaining to the civil trial, its discounted valuation offers an opportunity for investors that can see beyond these short term weaknesses. So does its extremely high dividend yield, which clocks in at nearly 6%. In fact, BP has the highest dividend yield of any integrated major, topping even Royal Dutch Shell plc and its 5.3% yield.

As a result, BP could very well prove its doubters wrong, and its current valuation might be too cheap given the progress it's making. In the meantime, investors are getting paid very well to wait.