The Federal Reserve announced on Wednesday that 28 banks have been given unconditional approval to increase their dividends and/or share buybacks over the next 12 months.

However, three of these banks -- namely, JPMorgan Chase, Goldman Sachs, and Morgan Stanley -- were granted approval to do so only after submitting adjusted capital plans that took into account the results of the first round of this year's stress tests, which were released last week.

A fourth bank, Bank of America (NYSE:BAC), received approval for its capital plans, though it must submit an updated plan by the end of the third quarter in order to "address certain weaknesses in its capital planning processes."

Finally, two international banks -- Deutsche Bank and Santander Holdings USA -- had their capital plans rejected based on qualitative grounds, related presumably to the accuracy and thoroughness of their capital planning processes. As a result, neither of these banks is allowed to make "any capital distribution unless expressly permitted by the Federal Reserve."

Of all the banks that passed, the biggest relief was likely felt by the executives at Citigroup (NYSE:C), which had failed two of the past three tests. CEO Michael Corbat even went so far recently as to stake his continued employment on this year's results, purportedly saying that he would resign if the bank failed.

Today's news clears Citigroup to raise its dividend for the first time since the financial crisis, long after many of its peers were given initial approval to do so.

The big question now is how much each of these banks will boost their quarterly distributions and share repurchase plans. Immediately after the Fed released its results, for instance, Bank of America said that it will repurchase an additional $4 billion in common stock over the course of the next year. This will undoubtedly come as a disappointment to shareholders waiting for a bigger dividend.

Many banks have been pining to increase the amount of capital that they return to shareholders since the crisis. Doing so not only rewards their titular owners, but also draws down their retained earnings, which has the benefit of boosting profitability -- i.e., return on equity.