With nothing more than a passing glance, it would be easy to assume International Business Machines (IBM -0.89%) -- you know it better as just IBM -- is struggling. While the company topped its fourth-quarter earnings estimates, reported revenue was flat year over year. The technology giant also announced plans to lay off around 3,900 workers, joining the chorus being sung by so many of its tech peers. The stock tumbled on Thursday following Wednesday's post-close release of all this news.

A more thorough look at last quarter's results, however, paints a more bullish picture than the one most investors are currently seeing.

IBM's different parts are part of a greater whole

If you're struggling to put your finger on the pulse of what exactly IBM does these days, you're not alone. Mainframes are mostly a thing of the past, and the company is no longer at the forefront of the personal computer industry. IBM does offer a variety of cybersecurity, cloud management, and artificial intelligence tools, but doesn't seemingly lead any of those markets (although it is a respected player in the hybrid cloud space).

And yet the organization is as relevant -- and necessary -- today as it ever was. It's just difficult to see because its solutions are all-encompassing and don't readily fit into one narrow category.

With that in mind, investors may want to think of the new-and-improved IBM as a top-to-bottom technology solutions provider, where every individual aspect of its business fuels other parts of its business. As CFO James Kavanaugh touched on in Wednesday's earnings call, "Our approach to hybrid cloud is platform-centric. As we land a platform, we get a multiplier effect across software, consulting, and infrastructure."

Translation: Sales of hybrid cloud hardware generate sales of software, and that drives cloud services and consulting revenue. Kavanaugh's pointed out in the past, in fact, that every $1 worth of hybrid cloud platform sales produces between $3 and $5 in software sales and between $6 and $8 of cloud consulting and services revenue. And the company's consulting services and software spur the initial interest in its hardware.

A complicated offering? Perhaps a little. That's not a bad thing though. The more complicated a solution is, the more likely it is IBM's customers will stick with the company rather than abandon a major investment in everything IBM brings to the table.

With that as the backdrop, it's clear from last quarter's results that the business model is working very, very well, fueling the company's biggest and most profitable business.

An optimal mix of profit-driving sales

While IBM's evolved business model might be tough to define, it's not tough to see it's working. Take a look at this snippet from well into the company's Q4 press release. Software now makes up more than 40% of IBM's top line, and more than 81% of that revenue is turned into operating profit. Both are leading metrics for the organization. Neither figure would be nearly as impressive, though, were it not for sales of infrastructure.

Software is IBM's single-biggest business, generating the bulk of its operating profits.

Note: Dollar figures are in millions. Image source: IBM's Q4-2022 press release.

At the same time, while not nearly as potent as the company's software business, consulting services account for nearly 30% of IBM's total sales, indirectly supporting the usage of its high-margin software business.

And these numbers are getting better over time. Two years back, software (labeled as cloud and cognitive software at the time) only made up about one-third of IBM's top line and sported slightly lower gross margins.

IBM's software arm continues to grow, adding inordinately more to the company's bottom line.

Note: Dollar figures are in millions. Image source: IBM's Q4-2020 press release.

The math evident in these two division breakdowns jibes with Kavanaugh's "multiplier" message: A little bit of hardware business drives a lot of software business, and at least some service business.

Yes, operating margins for IBM's consulting and systems business are being pressured by the same rising costs impacting its peers. This headwind, however, is more than offset by the already-high and improving margins for its biggest and best business. Based on the data from the images above, in fact, software alone is now responsible for more than 60% of IBM's operating income.

Connect the dots, not only is IBM's dividend even better protected than it may seem on the surface, the company may be understating this year's projected $1 billion increase in last year's free cash flow of $9.3 billion.

IBM is a great opportunity ... for certain investors

If you're looking for great growth, this isn't the stock for you. IBM just doesn't have the sort of cutting-edge technology in its portfolio that's capable of driving double-digit percentage revenue growth. And even if it did, the company is still a behemoth that makes for tougher year-over-year comparisons.

If you're looking for current income with a decent chance of some tech-like growth, though, IBM's current dividend yield of 4.7% is respectable, and you should know that last quarter's lack of revenue growth is solely the result of adverse exchange rates. On a constant-currency basis, last quarter's top line actually improved by 6%, capping off full-year revenue growth that was the best IBM investors have seen since 2011.

The stock's post-earnings sell-off is a buying opportunity.