The billionaire Koch brothers made a name for themselves backing conservative causes, but the lesser-known private-equity division of their sprawling industrial conglomerate appears to be more motivated by investment returns than politics.

Meredith Corp. is using an investment from Koch Equity Development LLC, or KED as the private-equity unit is known, to help fund its pending purchase of magazine publisher Time Inc. KED agreed to invest $650 million to support the $1.85 billion purchase, announced Sunday.

The...