The main character in Kurt Vonnegut, Jr.'s 1965 book, God Bless You, Mr. Rosewater, is an eccentric philanthropist. He thinks it's unfair that babies don't all start with an equal playing field.

'I think it's a heartless government that will let one baby be born owning a big piece of the country, the way I was born, and let another baby be born without owning anything.'

To rectify this perceived injustice, he sends one share of stock to each newborn child in the country.

Wouldn't that be a nice start?

Don't get me wrong. I know a single share of stock doesn't amount to much. Even a share of $850-plus Google (Nasdaq: GOOG) stock wouldn't go too far if you had to live off of it.

But there is a well-known way that you can stretch your investment -- even if it starts as a single share -- to where it can more than provide for any needs you might have.

Unfortunately, it's my experience that not too many investors take advantage.

The Secret To Lasting Income

So how can you make your investment -- no matter how small initially -- turn into something that you can actually afford to live on? Simple: Reinvest its dividends.

I know. It's not groundbreaking. But are you actually doing it?

Unless you absolutely need the cash now, reinvesting is invaluable.

Dividends are one of the most powerful wealth-building tools in an investor's arsenal because of the phenomenon of compounding. By reinvesting your dividend checks (instead of cashing them), you can buy more shares, which lead to even larger dividend checks. These larger checks can then be used to buy even more shares and so on. In time, even a small stake in such stocks can grow into a tidy sum.

(Reinvesting your dividends is a cinch. In fact, many dividend payers do it automatically -- and if they don't, just give your broker a call and he'll take care of it for you in a matter of seconds.)

Take a look at my chart to see what happens to a $20,000 investment earning a 7% annual yield that's reinvested.

As you can see, steady compounding yields amazing results over the long haul.

Thanks to the power of reinvested dividends and dividend growth, after 10 years your portfolio could be generating $5,299 in annual income -- that's +278.5% more income when compared to an investor who doesn't reinvest.

In fact, it could be generating an effective yield of 26.5% based on your initial $20,000 investment after 10 years.

It doesn't take Warren Buffett to see how quickly your income stream can grow when you invest this way.

How To 'Cheat' To Greater Income

There is a little trick you can use to make the entire process go a little faster. If you look at my chart, you'll notice that the tallest column (representing the most income) is 'cheating' a little.

You see, it represents your income if you reinvest... and your investment sees +5% annual dividend growth. Investing -- and then reinvesting -- in stocks with rising dividend payments essentially puts your income growth into overdrive.

But if you have a portfolio full of stocks with steadily rising payments, it also means you're costing yourself even more if you don't reinvest your dividends. Keep that in mind the next time you're checking up on your income portfolio.