Congratulations, Apple (Nasdaq: AAPL).

After reporting an astounding quarter on Tuesday, the tech giant's shares surged enough to surpass ExxonMobil (NYSE: XOM) as the largest publicly traded company on Earth based on market capitalization. As I write, Apple and Exxon are now both worth around $416 billion, with Apple ahead by a few hairs.

But hold on -- there's a difference between the two. Exxon paid out $131 billion in dividends over the last 20 years. Apple has paid a trivial sum, and ceased paying dividends entirely in 1996. While Exxon writes shareholders checks every quarter, Apple keeps cash in the bank, pushing its market capitalization up by default. If Exxon had been equally as stingy with its dividend policy, it would be the larger company today by far.

Another way to look at it: After subtracting cash and cash equivalents, Exxon's business is worth around $405 billion; Apple's, about $315 billion.

These calculations are somewhat meaningless. Apple does have a larger market cap. But thinking about a company's value in these weird, abstract terms brings up a very real and important topic: the role dividends play in accruing value to shareholders.

I'm an unapologetic cheerleader of companies that pay large dividends because the historic evidence is, in my view, unambiguous: Companies that pay higher dividends produce greater returns than those that do not.

Recently, Fool colleague Chris Baines took issue with this stance. Using the same logic I outlined comparing Apple to Exxon above, Chris noted that whether a company pays a dividend or not is technically meaningless, since cash not paid to investors increases shareholder equity and pushes a company's market capitalization up. He wrote:

As a shareholder, it's your cash regardless of whether it's given to you in higher shareholders' equity per share (which increases the share price $1 for $1) or a cash dividend. You can always sell shares to create a dividend in whatever amount you wish.

There's a name for this, Chris points out: The Modigliani-Miller capital structure irrelevance theorem. "According to Modigliani and Miller," he wrote, "there's no wrong answer in a perfect and efficient capital market. ... Your choice is irrelevant."

Chris took another shot more recently:

Morgan claims that dividend payers have historically outperformed nondividend payers. This is absolutely true. ... What I dispute is that these companies outperformed because they paid dividends, and that therefore managements are putting their shareholders in "peril" by not paying more in dividends. Morgan's academic studies prove that dividend payouts and outperformance are correlated, not that dividend payouts cause outperformance.

But that's not quite right. The studies do, in fact, show causation -- that companies that pay higher dividends produce greater returns because they pay higher dividends.

The issue here is what a company's management does with cash that isn't paid out as dividends. If used efficiently for well-timed share buybacks or smart acquisitions, retaining cash can be a wonderful thing.

Some companies do this well. Most, however, don't. And as investor Rob Arnott has pointed out (link opens PDF), that renders some of Modigliani and Miller's assumptions dubious:

Implicit in this view is a world of perfect capital markets. For instance, this reasoning assumes that investment policy is unaltered by the amount of dividends paid, that information is equal and shared (meaning the dividend does not convey managers' private information), that tax treatment is the same for retained or distributed earnings, that managers act in the best interests of the shareholders, that markets are priced efficiently, and so forth. When the assumption of perfection is relaxed, a host of behavioral or information-based hypotheses arise as potential explanations for how the market's payout ratio might relate to expected future earnings growth.

Chris gives this point some attention. "In the real world, companies look at taxes, transaction costs, and other factors as they come up with an optimal capital structure," he writes. But he then dismisses its importance: "Such tweaking may allow a company to benefit from such frictions. But you certainly won't be able to retire on it."

Arnott shows, however, that dividend policy is vitally important to a company's returns. Counterintuitively, low dividend payouts are associated with low future earnings growth expectations, and vice versa. Why? Because companies that retain earnings rather than pay them out as dividends are habitually tempted to engage in "inefficient empire building and the funding of less-than-ideal projects and investments, leading to poor subsequent growth, whereas high payout ratios lead to more carefully chosen projects," Arnott writes. And the market knows it.

This may not seem applicable to Apple, since management isn't using a significant amount of retained cash to invest (yet). But that doesn't mean cash held on its balance sheet creates the same value as a dividend paid to shareholders.

Chris writes that cash held on the balance sheet "increases the share price $1 for $1." But it almost certainly does not. Cash held on a balance sheet is often discounted by the market. And for good reason: As Arnott's data show, there's an uncomfortably high probability that a company will squander its cash on poor investments.

Chris writes, "According to M&M, there is no harm in [hoarding cash] as long as the cash is invested in something with returns commensurate with the risk." The problem is, much of it eventually is not. With the exception of a small number of companies that have exceptional track records of investing retained earnings, a dollar in shareholders' pockets is worth more than a dollar a company holds in the bank and promises to look after for you. This alone likely explains why Apple trades at a fairly low P/E ratio, particularly since it has no real track record of making mega-acquisitions.

Back to the original point: Is Apple the world's largest publically traded company? Yes. But it could potentially be worth so much more if opened up to the possibility of dividends. When -- or if -- that will happen, don't hold your breath. As Chief Financial Officer Peter Oppenheimer said on a conference call this week, "We're not letting [the cash] burn a hole in our pockets."

Fool contributor Morgan Housel owns shares of ExxonMobil. Follow him on Twitter @TMFHousel. The Motley Fool owns shares of Apple. Motley Fool newsletter services have recommended buying shares of Apple. Motley Fool newsletter services have also recommended creating a bull call spread position in Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not 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.