For smart investors, it's a proven fact reinvesting dividends and letting your money compound over time is one of the most important ways to grow one's money. However, companies can also achieve a similar affect for shareholders in a much less direct way. Instead of paying out dividends, some managements believe capital can be put to much better use by buying back stock. This is a critical management decision companies like American Capital Agency (AGNC 0.21%) and many more have proven to provide incredible returns to shareholders.

Why a company buys back shares
There are several good reasons for a company to buy back its shares, but the general answer is because the company feels like it is the best use of their capital at the time.

For instance, look at the situation of the widely held mortgage REIT American Capital Agency(AGNC 0.21%), which has been aggressively buying back its shares. In fact, during the fourth quarter of 2013 alone, the company bought back 7% of the total outstanding shares. The logic behind the move was the company was trading for a discount of up to 25% off of its book value, so in theory the buyback was a better way to increase value as opposed to increasing the dividend or purchasing new assets.

What it means to investors
For investors, a good buyback program can have the same effect as a dividend reinvestment plan, and some companies buy back more shares (as a percentage of the total) than could ever reasonably be expected to be paid out as a dividend.

Let's say you own shares of a company that are currently worth $50 each. If that company buys back 5% of its shares each year, then those shares should increase in value by 5% every year, or to $52.50 after one year. If the company keeps this up year after year, then after 30 years the shares should be worth about $216. This is on top of any other gains in shareholder value, resulting from reinvesting dividends or growth in the company's profitability.

How to find the best buybacks
Most companies have a buyback program to an extent, and about 80% of S&P 500 companies buy back stock. However, some companies have drastically better buyback programs than others, and some offer great buybacks and dividends.

A good place to start is this list of the best stocks for total shareholder return (dividends plus buybacks) which was prepared by Goldman Sachs, and some of the returns on this list are pretty impressive.

For example, People's United Financial currently pays a 4.4% dividend yield, but offers shareholders a total return of almost 15% because of buybacks. During 2013, the company repurchased 33.4 million shares of common stock, which represents about 10.7% of the current total. So, just with dividends and buybacks, an investment in People's returned 15% in 2013, and this is not including any improvement in the bank's fundamentals.

Ameriprise Financial (AMP 0.79%) has been aggressively putting capital to work to boost investor confidence, and to take advantage of what management believes is a low valuation of its shares. Including dividends, the company's total yield is over 17%, and shares have climbed by almost 50% over the past year.

The best of both worlds
There are companies in every sector with excellent buyback programs, and most of them pay some type of dividend yield as well. An excellent strategy is to find companies whose shares are very cheap already (like the banking sector) and invest in those companies taking advantage by aggressively buying back shares. This produces a double-value investment because you are buying shares at a discount, and the company is using your profits to buy even more shares at a discount.