Shares of International Business Machines (IBM -0.56%) tumbled late last year after the company abandoned its ambitious 2015 earnings target. Revenue has been declining, in part due to IBM divesting some of its weaker businesses, and the unrelenting rise in EPS during the past decade has slowed dramatically.

While IBM is viewed by some as a company stuck in the past, unable to keep up with a changing IT landscape from the rise of cloud computing to the growing importance of mobile, the company has made a lot more progress than many realize. At a recent IBM Investor Briefing, the company laid out its plan for a return to prosperity, built on strong growth in what IBM calls strategic imperatives.

With core businesses relatively stable and extremely profitable, resources are being shifted toward cloud, analytics, mobile, and security. Here is what investors need to know about the plan for growth at IBM.

A trillion-dollar opportunity
The strategic imperatives already account for $25 billion of revenue, or about 27% of the top line, more than doubling since 2010. In 2014, this group of businesses grew in the double digits, and it has a higher mix of software compared to the rest of the business, which carries higher margins than either services or hardware.

Here is an overview of these strategic imperatives:

Source: IBM

IBM expects these businesses to grow in the double digits for the long-term, and the company is shifting $4 billion in spending this year to target these growth opportunities. By 2018, IBM predicts that these strategic imperatives will make up more than 40% of the total business, generating approximately $40 billion in annual revenue.

IBM estimates that the cloud, including software, services, and related hardware, will offer a $400 billion market opportunity by 2018, growing at a 23% compounded annual rate. In 2014, IBM derived $7 billion of revenue from its cloud businesses, with half of that delivered as a service. The cloud business grew by 60% in 2014, and IBM is highly rated as a provider of hybrid and private cloud implementations.

Data analytics is the largest component of the strategic imperatives, generating $17 billion of revenue in 2014, up 7% year-over-year. Analytics is an area where IBM is investing heavily, particularly in its cognitive computing system, Watson. Through its BlueMix cloud platform, IBM offers Watson and other analytics software as a service, all running on SoftLayer, the cloud infrastructure company IBM acquired in 2013. IBM estimates that the market opportunity for data analytics will reach $315 billion by 2018, growing at a 7% compounded annual rate.

The final part of the strategic imperative initiative is engagement, which comprises mobile, social, and security software and services. The mobile business generated about $1 billion of revenue during 2014, with a high-profile deal with Apple to build enterprise applications for iOS standing out. The social business also generated $1 billion of revenue, while the security business generated in excess of $1.5 billion of revenue. Total engagement revenue grew by 35% during 2014, and IBM expects the market opportunity to reach $290 billion by 2018, growing at a 10% compounded annual growth rate.

All told, the total opportunity for IBM is in excess of $1 trillion. Of course, IBM will capture just a small part of this market, focusing on the highest-value portions, but the growth potential is significant nonetheless.

Why IBM will succeed
IBM is a company worth far more than the sum of its parts: 80% of IBM revenue comes from customers that pay for services, software, and hardware, giving IBM an enormous advantage when it comes to selling new software and services. This is where the real strength of the business model comes from.

A few pieces of data included in the investor presentation really drive home the scope of its business: 90% of the world's top 100 banks use IBM solutions, 80% of the top 50 retailers worldwide run their businesses on IBM systems, and 225 state and local governments use IBM mainframe systems to run critical processes.

With the core IBM business unlikely to grow, quickly ramping up these newer segments will be essential, and the enormous customer base gives the company a meaningful advantage. Overall, long-term financial model calls for low single-digit revenue growth and high single-digit EPS growth, driven by an expansion of software and service margins and a 2% to 3% annual share count reduction via buybacks.

These targets are realistic, and with the stock currently trading for about 10 times earnings, IBM is selling at a very pessimistic price. Of course, the company will need to execute on its plans, but I see little reason to doubt Big Blue.