Let's say the firm was expected to pay a $100/share dividend, but instead pays a dividend of $110. Like the example above, we would expect to see the stockholder's value fall to $890 ($1,000 - $110 = $890). Again, the stockholder still has $1,000; $890 in the firm and $110 in cash. In practice though, we see that instead of the stock dropping to $890, it falls to say, only $895. Thus the stockholder's value is now; $110 + $895 = $1,005.

Why did they gain $5 in value, just by issuing the dividend?