If a company increases its cash dividends, what happens to the value
of the stock of the company?

"Is An Increase In Dividend Good Or Bad For The Shareholders?

The answer is, it depends. Using the previously stated definition of
dividend, paying it suggests that the company must, at least, have
"excess" cash on hand. Thus, the question boils down to: what should a
company do with its "excess" cash? Such a company has two
alternatives: either invest the money in projects (internal expansion
or acquisitions) or distribute it to shareholders. The choice between
these two alternatives is simple: if the company has good projects
(i.e., those with Net Present Value > 0), then it should invest in
these projects as they would create value to shareholders. Otherwise,
the company should distribute the "excess" cash to shareholders in the
form of dividends.

Thus, when a company increases its regular cash dividend it is
typically saying one of two things. One, using the "burden" argument
outlined above, the company must be saying (or signaling) that it
expects to be profitable in the future and thus the increase in
dividend is not a "burden." The second scenario, using the "good
projects" argument above, is that the investors may interpret the move
as a signal that the company does not have profitable projects and
thus it is distributing "excess" cash. Obviously, if the market
believes the first argument, then stock prices tend to increase;
prices decline if they believe that the company is facing the second
scenario."

"Dividend: Cash Vs. Stock Repurchase" By Alex Tajirian, Morevalue.com
(2001) http://www.morevalue.com/glossary/restrict/Dividend-PGE.html

"On the stock's ex-dividend date, its price will drop by the amount of
the dividend."

"Investment Glossary" Pershing LLC (2004)
http://www.netxclient.com/universal2/invest_glosry_DitDn.htm

Search terms:  Increase "cash dividend" stock value

This is definitely helpful. I've been trying to find out the
relationship between stocks and dividends for a while now. Thank you!
I'm curious how long it took you to find a good answer?

To answer your question directly:

If a company increases its cash dividends, what happens to the value
of the stock of the company?

Typically if a company gives a dividend, the stock drops by the amount
they gave, so the net gain is usually nothing.  As the google answer
person said, it could show they are doing good and the stock would
rise for other reasons.  But take the Microsoft dividend of last year.
 If the stock was at $28 a share and they issue a $3 per share
dividend, when that occurs the stock will be worth $25 and you will
have $3 of cash in your hand, as the market will reflect that
microsoft has that much less cash which made up the value of the
stock.