Bank of America (BAC 1.53%) popped by over 3% after it announced Tuesday morning that it had resubmitted its capital plan to the Federal Reserve.

The news was welcomed by investors, who were glad to see the bank is still pushing to increase the amount of capital it returns to shareholders. So, what effect does the bank's previously reported error have on the company's health? And what can we expect to happen in the coming weeks and months?

The "error" wasn't as bad as it sounded at first
On April 28, Bank of America disclosed a $4 billion accounting error which forced the company to withdraw its capital plan and put its hopes for a higher dividend and buyback on hold for a bit. The actual cause for the error and who was responsible are still unclear, but the mix-up is fairly simple to understand.

Essentially, banks are supposed to take unrealized gains and losses from certain debt securities out of their capital ratio calculations, but it turns out some realized gains and losses were being stripped out as well on securities the bank inherited as part of the Merrill Lynch acquisition.

While a $4 billion error might sound pretty devastating to the bank's capital ratios, it really wasn't. Bank of America also announced it completed a third-party review of its capital ratio reporting and calculation procedures. The bank ended up making only a very small change of less than 0.01% to its reported capital ratios for the third quarter, which is also a big reason for the positive reaction by investors.

What is the new plan to return capital?
No one really knows, but what Bank of America has told us is that it'll be more conservative than their original submission, which called for up to $4 billion in share buybacks and a quarterly dividend raise from $0.01 to $0.05 per share.

We may not know for certain until the Fed either approves or rejects the plan, but the fact that management is acting in a very shareholder-friendly way is a good sign for shareholders, even with a reduction in the anticipated return of capital. The company could have scrapped the plan entirely and waited until next year to boost the return of capital, much like Citigroup decided to do upon the rejection of its plan.

Where do we go from here?
The Fed has 75 days to review the plan, which means we should know the outcome by August 10 at the absolute latest. The bank already passed the "stress test" so there is little reason to think the capital plan will be rejected this time, since the capital ratios barely changed and they are requesting an even smaller increase in capital distribution.

As discussed earlier in May, Bank of America shareholders may need to wait a bit longer than they originally thought, but they will be rewarded for their patience as the company's issues get worked out, and that's just what we're seeing here.

Whatever happens, it'll go a long way to renewing investor confidence and putting the financial crisis in the past. A $4 billion buyback plan translates to about 2.5% of the company's total outstanding shares, which would be impressive even if it gets reduced somewhat.

And a $0.05 dividend would mean an annual yield of 1.3%, not a great payout by any means, but a definite step in the right direction. My best guess: The bank will keep its dividend request intact and make cuts from the buyback plan. Dividends are the much more visible way companies return capital to their shareholders, and banks want to send a clear message to investors that they are healthy enough to start paying respectable amounts of money to shareholders again.

Even though the dividend payment itself would still be small on a historic basis, the approval of the new amount by the Fed would go a long way toward building confidence in Bank of America and the banking sector in general.