In May, Delta Air Lines (NYSE:DAL) announced plans to dramatically increase its share repurchase activity in order to return cash to shareholders and take advantage of its surprisingly low stock price.

Investors cheered the news at the time. However, Delta stock quickly fell into a rut again, as unit revenue declines started to accelerate at Delta and several of its peers. By the end of last week, Delta stock had fallen to $40, more than 20% below the 52-week high achieved earlier this year.

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Delta Air Lines YTD Stock Chart, data by YCharts

In response to this weakness in its stock price, Delta has increased its buyback activity even more than projected. This is allowing Delta to capitalize on its stock swoon to create long-term value for its shareholders.

Delta plans a buyback increase
Delta came into 2015 with a $2 billion buyback plan in place, scheduled to run through 2016, of which $850 million had already been completed. The company then spent $425 million during Q1 to buy back 9.3 million shares, leaving it with $725 million remaining on its buyback program.

During the May presentation in which Delta laid out its new capital allocation targets, the company revealed that it was on pace to complete the last $725 million of its $2 billion buyback by the end of Q2 -- i.e. a year and a half early. This was enabled by Delta's surging earnings and free cash flow, attributable to the solid domestic economic climate and falling oil prices.

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Delta's profit has been rising quickly. Photo: The Motley Fool

At that time, Delta unveiled an even bigger buyback program. Delta intends to repurchase another $5 billion of stock by 2017. This could allow it to retire as much as 15% of its outstanding shares.

Overachieving, once again
As predicted, Delta did complete the last $725 million of its old buyback program during Q2. But that's not all. In an investor update filed last week, Delta noted that it had returned more than $1 billion to shareholders through dividends and buybacks last quarter.

Delta's quarterly dividend amounts to a little less than $75 million. Including the $725 million needed to finish the old buyback program would have brought Delta's capital returns to $800 million in Q2. Thus, Delta must have also used at least $200 million of its new $5 billion buyback authorization last quarter.

Thus, Delta has ramped up its buyback activity at a stunning pace. It has now repurchased at least $1.35 billion of stock in the first half of 2015. That's as much as it spent on buybacks in the previous two years, combined.

Delta's buybacks will create value
Delta's management has good reason to ramp up the buyback pace. Delta stock is incredibly cheap right now -- it trades for about 9 times projected 2015 earnings and less than 8 times projected 2016 earnings. This represents a roughly 50% valuation discount to the S&P 500.

Earnings estimates have declined significantly in the past few months, as a modest rebound in oil prices, the strong dollar, and sluggish demand in some international markets have slowed Delta's earnings growth. If this continued, it could eventually make Delta stock seem like much less of a bargain.

However, fuel prices have pulled back since peaking in early May and Delta is taking action to shore up unit revenue by cutting capacity in some of the weakest overseas markets. This should drive strong profit growth in the second half of 2015 and throughout 2016. Delta's rapid pace of buybacks will provide an additional boost to EPS growth.

By taking advantage of its currently depressed stock price to buy back lots of stock, Delta is paving the way for faster EPS growth. As investors become more comfortable that the revenue environment is stabilizing, Delta stock could start to close the valuation gap with the broader market. That provides plenty of upside for long-term investors.

Adam Levine-Weinberg is long January 2017 $40 calls on Delta Air Lines, The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.