Modigliani & Miller show thatdividend policy can also be considered irrelevant. Yet, unexpectedincreases in dividends are often closely followed by priceincreases, why?

To clarify, when a firm pays a dividend the stock priceshould drop by the amount of the dividend on the ex-dividend date.Let's say a firm has 5 stockholders, each holding 1 share. The firmowns $2,000 in cash and $3,000 in other assets. So the firm isworth $5,000 (it owes no debt). Each stockholder's claim isworth:

     $5,000/5 = $1000.

Now the firm declares a dividend of $100/share. Theymust pay out a total of: $100 x 5shares = $500. So after thedividend is paid the firm now has $1,500 in cash and $3,000 inother assets, for a total of $4,500. Dividing this by 5stockholders, we find that each stockholders claim is $900. Thesame as if we take $1,000 less $100 dividend to get $900. Thestockholder hasn't lost anything, he still has $1,000 in value,just $900 in the firm and $100 in cash now.

But what we actually often see in practiceis:

Let’s say the firm was expected to pay a $100/sharedividend, but instead pays a dividend of $110. Like the exampleabove, 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 thatinstead 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 thedividend?