Apple doesn’t need help from Progressive when it comes to selling products. But Apple could really profit by studying how Progressive deals with the companies’ common problem, one that most firms would be thrilled to have: more cash flow than it needs.

Progressive has an intelligent, rational, and transparent way to deal with the surplus cash that its operations generate. Apple doesn’t. It has fumbled around, trying half-heartedly to make Wall Street and good governance types happy, but in the process managing to ensnare itself in a nasty debate about whether it’s shortchanging its shareholders by hoarding cash.

As a result, what should have been a normal, boring Apple shareholder meeting next week has become a confrontation between Apple and some sharp-elbowed Wall Street types who want Apple to goose its stock price by giving $50 billion (or more) worth of new preferred stock to its common shareholders.

Apple is likely to ultimately prevail in a shareholder vote to eliminate its board’s right to issue preferred stock without getting shareholder approval. But its Street adversaries have spun their story so effectively that what Apple says is a classic good-governance move has resulted in the company’s image getting whacked.

Progressive has no such problems. It pays its shareholders (who include me) an ultra-rational dividend: a variable, once-a-year payment based on the success of its business. It uses the same “Gainshare” formula to determine employee bonuses. You can track the numbers, monthly, on Progressive’s website, which describes the formula in detail. The company also pays occasional extra dividends and episodically buys back shares. Dividends vary widely year by year, ranging from a total of $2.145 a share for 2007 to zero for 2008 to $1.2845 for last year.

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As a result, Progressive (PGR) is well-capitalized but doesn’t have oceans of surplus capital sloshing around on its balance sheet. Should things go bad, Progressive isn’t committed to making dividend payments that it can’t afford, as some giant banks were when the economic meltdown started six years ago. And as Apple (AAPL) could be in the future.

Apple, which had a stunning $137 billion of cash on its balance sheet at year-end, began to pay a dividend last year. It currently pays $2.65 a quarter (about $10 billion a year), a number that seems to have been plucked out of thin air. The same is true of the $45 billion total that Apple says it plans to return to shareholders over three years via dividends and stock buybacks.

Playing things by ear and instinct has worked great for Apple when it comes to creating and marketing high-profit-margin, gotta-have-it products. But it doesn’t work great as a capital allocation process.

So when Apple’s stock price fell sharply, it became vulnerable to a proposal by one of its holders, Greenlight Capital. Greenlight, which unlike Apple is skilled at Wall Street jousting, has gone public with a proposal for Apple to “enhance shareholder value” by giving holders at least $50 billion of preferred stock (with a dividend of at least 4%).

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If Apple announced such a distribution, which is a bit over $50 a share, Greenlight estimates it would add about $30 a share to the company’s stock price. That math seems right to me. However, that one-time gain would be more than wiped out when the preferred was distributed. And the preferred could cause problems down the road, by which time Greenlight and its followers would be long gone.

The preferred would be a permanent annual drain of $2 billion of after-tax money. Today, Apple can easily afford that. Or even $4 billion a year, if it issued $100 billion of preferred. Plus there’s also the $10 billion of regular annual dividends Apple is committed to. But who knows what the future holds for its trendy, hit-driven business? Committing to pay $12 billion or more of dividends annually is a big, big commitment.

But what about that $137 billion of cash? Well, a big chunk of it — $94  billion — is held by offshore subsidiaries, and can’t be used to pay dividends unless Apple pays U.S. income tax on it. Fat chance of that happening unless Uncle Sam declares a tax repatriation holiday.

I’ve praised Progressive’s dividend policy several times since the firm adopted it in 2007 — but so far, alas, no firm has followed Progressive’s lead. Apple should, but almost certainly won’t. Too bad. When it comes to dealing with surplus cash, you can’t do better than to go with the folks who brought us Flo.