Imagine hearing this from your financial advisor: “I’ve got a great stock for you. It’s down -20%, the company lost $7 billion this year, and its reputation stinks.”

You’d probably get up and walk out the door, right?

But what if, just before you slammed it shut, the advisor managed to blurt out, “Wait, this stock is on sale for half price and could more than double your money”?

You just might go back, sit down and listen to the rest of the pitch.

And you’d hear a bunch of things, some good, some bad. The bad part, in addition to the tanking stock and hefty losses, is the company helped precipitate the financial crisis and got billions of dollars in bailout money.

More recently, it admitted to signing off on thousands of foreclosures without even reviewing them — the “robo-signing” scandal you’ve probably heard about. The recession spurred such an avalanche of loan defaults that some big-name banks resorted to simply pushing foreclosure documents through just to keep up, regardless of whether foreclosure was actually warranted.

The culprit I’m referring to is the largest consumer bank in terms of assets in the United States, Bank of America (NYSE: BAC).

After all the bad press, it would be easy just to dismiss BofA as unworthy. But since the point of investing is to make money, I suggest looking past the ugliness for a moment and considering why this might actually be a great stock for the long-term.

I’ve got four good reasons for you…

1. The company’s turning over a new leaf. New President and CEO Brian Moynihan has been trying to salvage BofA’s image since taking over the company in January 2009. For example, he has publicly backed financial industry reform and consumer protections, openly agreed that banks shouldn’t be considered “too big to fail” and looked for ways to improve service, such as scaling back penalty fees. He has also become known for consulting frequently with front-line employees to get first-hand reports of what customers are saying.

Regarding the robo-signing situation, Barbara Desoer, President of Mortgage, Home Equity and Insurance Services at BofA, has said the bank will improve its foreclosure procedures by doing a better job of gathering accurate information on each case and of selecting and monitoring the law firms it uses to process foreclosures. In the meantime, it’s reviewing and resubmitting affidavits for more than 100,000 foreclosures it had previously initiated.

2. There’s still big earnings potential. During the next five years, analysts predict BofA will post annual earnings growth of 9% to 13% from sources like the company’s wealth management services through Merrill Lynch, its investment banking division and, of course, its gigantic deposit base and loan business. The strong presence of the company’s consumer banks in high-growth areas like California, Florida and Texas will help earnings immensely. I should also note that the earnings estimates I’ve reported incorporate a -$2 billion decrease in annual revenue starting in the third quarter of 2011, which is related to costs for complying with the new financial reform legislation.

3. The stock is very cheap. BofA’s stock has a low price-to-book (P/B) ratio of 0.57, meaning investors can essentially buy its assets for $0.57 on the dollar. The historical average P/B of 1.2 and a book value per share of $21.17 put shares of BofA at a fair market value in the $25 range. Right now, it’s only trading at $11.75 — more than a 50% discount.

4. You can make a lot of money. Like I said, isn’t that why we invest? Assuming earnings projections for BofA prove accurate, its stock is positioned for total returns of +15% to +20% a year out to 2015, which translates to an absolute return of 75% to 105% in the next four years. That kind of growth potential is hard to ignore, and I wouldn’t be surprised if the stock exceeded those estimates.

Action to Take –> Although Bank of America may never fully recover its reputation or completely rebuild its pre-crisis empire, it would be a mistake for competitors or investors to underestimate it. Bad name or not, BofA is still the biggest consumer bank in the United States, it’s fundamentally sound and its earning power is enormous — it’s just going through a bad time now because of its role in the financial crisis and the robo-signing scandal.

But, as you know, the best time to buy a good stock is often when it’s out of favor, as BofA currently is. So consider putting aside any negative feelings you have about the company and picking up some of its shares while they’re on a major sale. If the projections are accurate, and I think they are, then you’ll be well-rewarded.