During the financial crisis, many banks issued warrants as part of the Troubled Asset Relief Program. Others issued warrants to entice investors to make riskier, but potentially more profitable, bets on a bank's stock.

Bank of America's (NYSE:BAC) warrants have been especially popular among investors. In this article, I'll explain the complicated nature of its stock warrants, and how much investors can make by buying Bank of America's warrants instead of the common stock. (If you need to freshen up on the mechanics of stock warrants, first read this article on how warrants work.)

How Bank of America's A warrants work
Bank of America's A warrants give investors the right to buy one share of Bank of America at \$13.30 per share on January 16, 2019. The ticker for this warrant varies by broker, but a common ticker has been Bank of America .

One interesting twist with the A warrants is the anti-dilution provision. The anti-dilution provision reduces the exercise price and increases the number of shares each warrant represents, to account for a dividend that is greater than the dividend at the time the warrants were issued.

Currently, Bank of America's stock pays a \$0.05 quarterly dividend, which is greater than the \$0.01 dividend paid at the time the warrants hit the market, triggering the anti-dilution provision.

Because of this provision, the exercise price of each warrant is currently in decline. According to a recent disclosure, Bank of America's A warrants now have a exercise price of \$13.267 per share.

Date

Exercise Price

Shares per Warrant

Initial sale (January 2009)

\$13.30

1.0

September 2014 (current)

\$13.267

1.0

Source: Bank of America.

In all reality, the published numbers above are rounded. The terms of the warrants require Bank of America to round the exercise price to one-tenth of a cent, and shares to one-tenth of a share.

To give you a picture of what these numbers look like without this rounding, I created the following table, using the formulas provided by Bank of America.

Date

Exercise Price

Shares per Warrant

Initial sale

\$13.30

1.00

September 2014

\$13.267302

1.002465

Source: Bank of America, with calculations completed by the author.

Notice the change in the shares per warrant when the figures are not rounded. The numbers are not rounded on each adjustment, only when reporting the number of shares each warrant represents.

Said another way, the number of shares warrants entitle their owners to buy goes up with each dividend, but the true economic impact only occurs at discrete intervals (1.1, 1.2, 1.3, and so on).

Given the mathematical relationship between dividends and the anti-dilution adjustment, the dividend will have to increase substantially, or the share price decline dramatically, in order for the warrants to be worth more than 1 share each at expiration.

Unfortunately, modelling the returns for these warrants is all but impossible to do perfectly. One would have to know Bank of America's stock price when it pays every future dividend, as well as the future dividend it pays. However, we can model returns based on the current rounded exercise price, and rounded shares per warrant, to generate a conservative return assumption at various stock prices in the future.

How much can you make?
The table below shows the expected profit based on varying prices for Bank of America's stock on January 16, 2019.

Future Stock Price

A Warrant Return

Stock Return

\$5.00

-100%

-63%

\$10.00

-100%

-37%

\$15.00

-76%

-5%

\$20.00

-8%

26%

\$25.00

61%

58%

\$30.00

129%

89%

The table above assumes a starting share price of \$16, and a common stock dividend of \$0.05 until January 2019. The warrant exercise price and shares per warrant are assumed to stay constant from their rounded September 2014 values.

Bank of America's B Warrants
Bank of America's B warrants are far more speculative than the A warrants. The B warrants, available under the ticker Bank of America (NYSE: BAC.WSB), allow investors to buy Bank of America shares at a price of \$30.79 on or before October 28, 2018.

Additionally, the warrants have an anti-dilutive provision to adjust the exercise price and shares per warrant, but only if the quarterly dividend exceeds \$0.32 per share.

Date

Exercise Price

Shares per Warrant

Initial sale in 2008 (current)

\$30.79

1.00

The anti-dilutive provision has not been triggered, and it is unlikely it will any time soon, given the current dividend of just \$0.05 per quarter. The table below shows the potential profits for the B warrants.

Future Stock Price

Warrant Return

Stock Return

\$15.00

-100%

-1%

\$20.00

-100%

25%

\$25.00

-100%

58%

\$30.00

-100%

89%

\$35.00

426%

120%

\$40.00

1,051%

151%

The table above assumes a starting share price of \$16, and a common stock dividend of \$0.05 until October 2018. The warrant exercise price and shares per warrant are assumed to stay constant at their current, September 2014 values.

As you can see, B warrants require a much greater return on Bank of America common stock than the A warrants in order to be profitable. Shares will need to roughly double from their share price in September 2014 to justify their exercise.

Naturally, the B warrants will likely create a much bigger profit or loss than the A warrants, due to the exceptionally high exercise price.

The bottom line
Bank of America's stock warrants can be an intriguing way to play the recovery of one of America's largest banks. The A warrants may be the most compelling, given that they have the longest-dated expiration, the lowest exercise price, and a currently active anti-dilution provision that is reducing the exercise price while increasing the number of shares each warrant represents.

In the future, this article will be updated to record the effects of the anti-dilution provision, as well as the changing profit potential for each warrant. Bookmark this page for future updates.

Jordan Wathen has no position in any stocks mentioned. The Motley Fool recommends Bank of America. The Motley Fool owns shares of Bank of America. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.