When IBM (NYSE:IBM) CEO Ginni Rometty took the helm on Jan. 1, 2012, she was faced with a daunting task: bringing the technology giant into the 21st century. New technologies like cloud computing were just beginning to catch on, and IBM was still tethered to a floundering hardware business. For investors, both before and since Rometty's appointment as CEO, it's been a ho-hum couple of years.

When Rometty took over, IBM's stock was sitting at $186.30 a share. Today? Though it's risen above the $200-a-share range once or twice, IBM is still around $189 per share. Yes, IBM continues to offer shareholders a 2.3% dividend yield, but its stagnant stock price undercuts IBM's solid dividend. The problem has been, and continues to be, transitioning a $189 billion behemoth from a 20th-century, hardware-driven company to a cutting-edge technology leader. The good news is there are several reasons for investor optimism as IBM heads into 2015.

Keeping its head in the cloud

As Rometty stated during IBM's Q2 earnings report, it's in the process of a "transformation." For a company of IBM's size, that's a little like asking an ocean liner to execute a U-turn. IBM investors need look no further than Microsoft (NASDAQ:MSFT) to see just how difficult it is for tried-and-true technology leaders to transform their business.

Though IBM's last quarter was disappointing to many, primarily because of flat revenues compared with last year, there were several bright spots. One area in particular should have IBM shareholders and prospective investors intrigued: the cloud. IBM's cloud services revenues nearly doubled, to an annual run-rate of $2.8 billion. That's not quite Microsoft's $4.4 billion annually in cloud revenues, but it's certainly a step in the right direction.

Like Microsoft, IBM is in the enviable position to offer a great deal more than simply cloud hosting, a business that is already commoditized. The cloud will be won by those, like IBM, that provide ancillary cloud services. Rometty and team are just getting started in the cloud, and nearly $3 billion in sales puts it near the top of the cloud provider's list.

Big data will become big business

The sheer volume of information available to businesses today is mind-boggling, which should be great news for business execs. The difficulty is figuring out how to collate, analyze, and utilize all that information, or big data. Sometimes, too much of a good thing is a bit overwhelming. Thankfully for investors, IBM has positioned itself as a leader in providing big data solutions, including investing in artificial intelligence solutions like its Watson super-computer.

New data from research firm Gartner also bodes well for fans of IBM. According to its latest study on big data, 73% of the surveyed tech gurus told Gartner they either already have invested in big data solutions or plan to do so. Of those 73%, however, a mere 13% have actually written a big data-related check for their organization. In other words, more and more IT leaders see the benefits of big data, but most haven't taken the plunge, yet. And IBM is at the forefront of what looks to be an industry ready to take off.

Managing expenses

Flat revenues last quarter disappointed some IBM investors, even though earnings jumped a whopping 42% on a GAAP basis. How? Rometty's cost-cutting initiatives are beginning to take hold. You may recall earlier this year that IBM announced a sweeping round of layoffs that affected as many as 13,000 employees. No one likes to see folks losing their jobs, but from an investor's perspective, IBM needed to better align its people with its transformation.

Last quarter, IBM pared $6.8 billion in expenses, a 15% decline from a year-ago. It may not be pleasant, but the harsh reality is that a dramatic change in business focus requires drastic measures. It was only a short time ago Microsoft CEO Satya Nadella announced his own plans to cut his workforce – a whopping 18,000 over the next year -- to better align it with his, "mobile-first, cloud-first" emphasis.

Final Foolish thoughts
Not to be discounted, IBM investors can also toss in its shift to mobile as a key growth driver, as its latest "enterprise mobility" alliance with Apple demonstrates. It's been a long time coming, and it's not over by any means, but IBM is showing signs of life in new, fast-growing lines of business. And its lackluster performance is good news for investors who appreciate value. As of now, IBM's forward price-earnings ratio is a mere 9.5, easily one of the cheapest in its industry. For patient, long-term investors, there are several reasons to consider IBM.

Tim Brugger has no position in any stocks mentioned. The Motley Fool recommends Apple and Gartner and owns shares of Apple, IBM, and Microsoft. Try any of our Foolish newsletter services free for 30 days. We Fools don't 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.