No doubt Facebook has overpaid for acquisition of Instagram by buying it out for $1 Billion. However it is a well thought out marriage as facebook has not been making any revenue from mobile segment and Instagram caters exclusively for mobile segment and its app is a craze among youth.
When a business sees synergy, it may overpay for a brand because the acquyirer knows that dividends of the marriage are going to be hefty or may be non linear as instagram will get a Facebook makeover soon.