When companies have cash to spare, they can reward shareholders by repurchasing their stock. Shares represent small ownership stakes in the underlying business, similar to how slices of pizza make up a whole pie. And when shares are repurchased and retired, it's like a pizza being cut into fewer slices. It makes each remaining share represent a bigger part of the whole pie and, therefore, it's more valuable. It's why buybacks can be a big deal.

With this in mind, fintech company Olo (OLO 1.01%), premium movie-theater chain Imax (IMAX 2.11%), and luxury-furniture retailer RH (RH -0.54%) have share-repurchase plans that are truly eye-catching. Here they are, presented from the smallest plan to the largest.

1. Olo: $100 million authorization

Olo provides order-digitization services to restaurants and has become a clear leader in the space. It seems like all of the big restaurant chains are Olo customers, and it's why this growth stock once commanded a lofty market capitalization of over $6 billion. However, it has recently come back down to a more reasonable market cap of just $1.3 billion.

Olo's management believes it can increase its business 100-fold by onboarding more customers, earning more revenue per digital order with products like Olo Pay, and with digital orders becoming a larger part of the overall sales mix in the long term. And because it has this vision, it believes its shares are undervalued today, which is why it just authorized a repurchase plan of $100 million. That's roughly 8% of shares outstanding.

There's plenty of reason to be optimistic about an Olo investment. But there's also reason for caution. Specifically, it's done very well at attracting top customers. But some of these have the resources to bring Olo's services in-house. This recently happened with sandwich chain Subway. It's not something I expect to happen often; I believe restaurants would rather focus on food than technology. But it's something that can happen nonetheless.

Moreover, it's possible that Olo's expenses will go up in coming years, specifically with sales and marketing. Having already attracted so many big chains, its focus will logically turn to smaller chains, which still cost money to attract but have smaller upside because operations are small by comparison.

We may already be seeing this playing out to some extent. Through the first two quarters of 2022, Olo's sales and marketing expenses have more than doubled year over year, whereas revenue is only up around 23%. That said, this line item is still less than 20% of revenue, which isn't unusual for a growth company trying to increase its business 100-fold.

Olo is well capitalized with $465 million in cash, cash equivalents, and short-term investments -- roughly one-third of its total valuation. Therefore, it seems like the market is already discounting this stock, factoring in the risks. Buying back $100 million in stock would make the valuation even more attractive. And that's why a share repurchase plan of this magnitude could positively move the needle for Olo shareholders.

2. Imax: $225 million authorization

As of this writing, Imax has a market capitalization of $900 million. And as of Sept. 7, it's authorized to spend $225 million buying back stock. That's 25% of shares outstanding, which is a large plan and signals that management believes its stock is undervalued.

The stock may indeed be undervalued. Consider that it's down more than 60% from its all-time high way back in 2015. However, recent shifts in consumer behavior might better favor its premium-experience positioning from here.

Studios are increasingly releasing fewer movies to the box office overall. But the movies being released are bigger-budget films. A majority of these films are optimized for Imax screens. This might explain why the company's market share of the box office has climbed to 5.1% in 2022, compared to its historical average of about 3%.

Some might argue that recent shifts at the box office are related to the pandemic and will return to normal in time. However, I believe that the relatively recent rise of streaming services is redirecting studio budgets, meaning box-office trends are more permanent. In short, long-term shifts seem to be in Imax's favor.

If the company executes its $225 million share repurchase plan, it will help boost shareholder value. But investors should control their expectations. Management tends to move slowly, averaging just $35 million in buybacks annually over the past five years. Therefore, don't expect the boost from this $225 million plan to happen all at once.

3. RH: $2.45 billion authorization

Whereas Imax has a history of repurchasing shares at a slow, steady pace, RH has the opposite reputation. In 2017, it was authorized to buy back around 30% of its stock, which led to shares skyrocketing over 300% in under a year. And it could execute a plan of this magnitude yet again.

RH has a market cap of $6.5 billion as of this writing. On June 2, the company announced it was authorized to repurchase $2.45 billion in stock. Management then immediately went to work and has already spent $255 million for 1 million shares. But that still leaves almost $2.2 billion to work with, or over 30% of outstanding shares. And if management increases its speed, it could really move this stock.

RH trades at a trailing price-to-earnings ratio of just 9, which is cheap on an absolute basis. However, the market is rightly concerned about its positioning as a luxury furniture retailer as the U.S. economy slows down. The company is already feeling the effects. In 2021, net revenue was up 32% year over year. But net revenue is only up 5% year to date. And management thinks full-year revenue will actually drop by as much as 18% by year's end.

With financial results rapidly deteriorating, you might think RH would want to hoard cash instead of repurchasing shares. However, there's more to keep in mind. The company doesn't believe in discounting merchandise to stimulate sales growth. Therefore, it won't be slashing prices at the expense of profits. To the contrary, even with slumping sales, it expects to remain profitable on an operating basis. And if there's no cash burn, there's no reason to stingily hoard its money. It can execute its share-repurchase plan if it wants to.

Of the three stocks here, RH is the one I'd buy today. To be clear, I wouldn't invest in any of these companies for the share-repurchase plans alone. That's a shorter-term consideration, whereas investors should focus on long-term business fundamentals.

In that regard, Imax is promising. But after years of underperformance, it needs to prove it's ready to shine. Similarly, Olo has been public for less than two years and it's still establishing its track record with public shareholders.

By comparison, RH has a long history of market-beating results, which gives me greater confidence it can endure a slowdown in the economy and emerge strong when the economy (eventually) improves.