Meredith Corp. agreed to acquire Time Inc. for $2.8 billion including debt, swallowing the once-mighty home of Fortune and Sports Illustrated after the internet age wreaked havoc on even the most prestigious magazine titles.

The $18.50-a-share offer is an all-cash one, Meredith said in a statement Sunday. The deal gives Meredith, publisher of Better Homes & Gardens, a larger audience at a time when publishers need to get bigger to compete with Facebook and Google in advertising.

The acquisition also gives the billionaire Koch brothers, who agreed to support Meredith’s offer with an equity injection of $650 million, a foothold in the struggling magazine industry.

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