I can't emphasize enough how important this upcoming week is for Bank of America (BAC 3.38%) and its millions of shareholders.

On Monday, the nation's 19 largest banks prostrate themselves before the Federal Reserve in the annual stress test, a rite of passage for lenders seeking to return capital to shareholders. If B of A fares well and gets the go-ahead to increase its dividend payout or repurchase shares, then it's safe to assume that its shares will skyrocket. But if not ... well, you can probably do the math.

Are you stressed yet?
The stress test is part of the Fed's Comprehensive Capital Analysis and Review, which evaluates the "capital planning processes and capital adequacy of the largest bank holding companies." Its purpose is to determine "whether firms would have sufficient capital in times of severe economic and financial stress to continue to lend to households and businesses."

It works like this. The Fed assumes a high-stress scenario -- last year, this included a peak unemployment level of 13%, a 50% drop in equity prices, and a 21% decline in housing prices. It then determines whether the institutions at issue would maintain capital ratios above the regulatory minimum levels. Those that are able to do so, assuming they've requested it, are allowed to increase the amount of capital they return to shareholders via dividends and/or stock buybacks.

In 2012, the majority of institutions, 15 out of 19, passed the test, with many -- including JPMorgan Chase (JPM 1.64%) and Wells Fargo (WFC 3.17%), among others -- getting the all-clear to distribute more of their earnings. Suffice it to say, the four that failed the test -- Citigroup (C 1.49%), Ally Financial, SunTrust Banks (STI), and MetLife (MET 1.63%) -- weren't among the latter group.

While B of A was among the banks that passed, it hadn't requested approval to increase its dividend and therefore didn't receive it. The reason it didn't ask probably had something to do with the Fed's demoralizing "rejection" of its analogous request in 2011. I use quotation marks because the Fed didn't formally reject B of A; it simply asked the company to resubmit the request later that year, which B of A prudently chose not to do.

So what about this year's tests?
This go-around, it's anticipated that virtually every bank will seek approval to increase the amount of capital they return to shareholders. According to sources cited by The Wall Street Journal, Citigroup will ask for permission to initiate its first share buyback since 2007 -- though the request is expected to be "minimal." Both JPMorgan Chase and Wells Fargo will move to pony up. As will Fifth Third (FITB 6.27%), an Ohio-based regional lender that had a similar request denied last year.

The only one that's almost certainly not among these is Morgan Stanley (MS 1.39%), which has intimated that it'll use any excess capital to consummate the purchase of Smith Barney, a brokerage unit that it jointly owns with Citigroup.

While many analysts, myself included, assume that B of A is among the banks that will seek to return more capital, its CEO, Brian Moynihan, has been tight-lipped about whether it will, in fact, request approval to do so. He's declined to comment on the matter in multiple interviews with the media.

Working in its favor is that it's now the best capitalized too-big-to-fail bank, with a Basel III Tier 1 capital ratio of 8.97% -- JPMorgan comes in at 8.4%, Citigroup at 8.6%, and Wells Fargo at 8.02%. Working against B of A, however, is its erratic earnings stream, which Moynihan says the bank is "working to get through." In the third quarter of 2012, for example, B of A reported a mere $340 million in net income. A year earlier, it booked $6.2 billion in quarterly earnings.

Will B of A raise its dividend?
At least in the opinion of Meredith Whitney, the noted bank analyst who presciently predicted that Citigroup would have to slash its dividend in 2007, B of A will up its payout. Referring to B of A recently on CNBC, Whitney noted that she "hadn't seen an opportunity like this in four or five years." According to her, the bank's strong capital position and projected earnings will allow it to "quadruple" its dividend payouts this year -- though, to be fair, its dividend currently stands at only $0.01 per share.

For what it's worth, moreover, I agree completely -- though I wouldn't venture a guess about the magnitude of a potential increase. In the third quarter of this year, my stance on B of A changed dramatically, going from a reluctant apologist to an unabashed bull. In my opinion, and even in the face of its recent run-up in price, this bank is a buy all day long.