As General Electric's (NYSE:GE) stock price swooned during the past year, it became increasingly clear that the venerable industrial conglomerate would get booted from the Dow Jones Industrial Average. On Tuesday afternoon, the committee that manages the Dow index announced the inevitable change. On June 26, GE will be replaced in the Dow by pharmacy retail giant Walgreens Boots Alliance (NASDAQ:WBA).

The committee listed a number of reasons for making this switch. However, the most important one was simply that GE stock has fallen too far to be worth keeping in the index. As a result, GE's removal from the Dow shouldn't be seen as a warning sign for investors.

The Dow loses its last original member

General Electric was one of the 12 companies that made up the first iteration of the Dow Jones Industrial Average in 1896, and it has been in the index continuously since 1907. By contrast, all of its peers from the original Dow index are long gone.

A GE gas turbine

The Dow Jones index is about to lose its last original member. Image source: General Electric.

In terms of its business operations, GE still deserves to be a Dow component. Even if the company sells or spins off various divisions over the next two years as expected, annual revenue will likely remain at $100 billion or more -- well above the average for the Dow. Furthermore, GE remains a driving force in three big end markets: power, aviation, and healthcare.

However, the Dow is a price-weighted index. This means each company's impact on the index is proportional to its stock price. GE has a far lower stock price than every other Dow component, even though General Electric doesn't have the lowest market cap in the index. As a result, GE stock's movements have hardly any impact on the Dow these days.

In fact, GE recently accounted for just 0.36% of the index's weight, compared to 3.33% for the average Dow component. (Notably, if GE stock had held its ground over the past year, rather than plunging by 55%, it would still be the lowest-priced stock in the index.)

GE Chart

General Electric Stock Performance, data by YCharts.

By contrast, Boeing has an index weight of nearly 10%. GE stock would have to surge 26% just to boost the Dow by the same amount it would gain from a 1% uptick in Boeing's stock price. In other words, GE already plays virtually no role in the Dow, so there was no reason to leave it in the index.

Walgreens Boots Alliance is a sensible replacement

In choosing Walgreens to replace GE in the Dow Jones Industrial Average, the committee noted that consumer goods and healthcare are increasing in importance to the U.S. economy relative to industrial production. The top three pharmaceutical companies are all Dow components already, as is health insurance giant UnitedHealth, but Walgreens Boots Alliance captures a unique slice of the U.S. healthcare market.

Indeed, along with top rival CVS Health, Walgreens dominates the U.S. pharmacy business with roughly 10,000 locations. Analysts estimate that its annual revenue will surpass $130 billion this year. This clearly makes it a worthy member of the Dow.

Most importantly, Walgreens stock is priced around $65: five times higher than GE stock. That's still below average for the Dow, but at least Walgreens Boots Alliance will have a meaningful starting index weight of around 1.8%.

This doesn't affect GE stock's value

GE stock fell more than 1% in after-hours trading on Tuesday, extending its losses from the regular trading session and briefly dropping below the multiyear low of $12.73 set back in late March. Given that the stock already seemed to be dramatically undervalued, this seems like a golden opportunity for long-term investors.

Surprisingly, stocks that are booted from the Dow tend to perform better after they leave the index. And ultimately, business performance is the key determinant of stock price performance, so being in a particular index isn't important.

GE stock's inability to get back on track is certainly frustrating for many investors. However, it is being held back by poor sentiment more than anything else. If GE continues to execute on its turnaround plan over the next few years, the stock could zoom higher. As a result, I am considering adding to my GE stock holdings later this month.

Adam Levine-Weinberg owns shares of General Electric. The Motley Fool recommends CVS Health and UnitedHealth Group. The Motley Fool has a disclosure policy.