Does the good news conveyed by the announcement of a dividend increase mean that a firm can increase its stock price in the long run simply by paying cash dividends?

True

Explanation:

Yes, as there is an increase in dividend with the same expected return, share price increases using dividend growth model.

As for example current dividend = $5

And expected return = 10%

Price of share = 5/10% = $50

In case dividend is increased to $10 then share market price = $10/10% = $100

Now, with an increase in dividend rate, there is an increase in market price accordingly company can raise dividend in order to raise the share price accordingly.

Further, this might not be possible when dividend is fixed for the period as dividend is fixed with no further growth rate the price will also be fixed. So every time when the price is to be increased, the dividend has to be increased.

Therefore, above statement is true.