In one example, a network device determines a set of candidate loop-free alternate (LFA) next hops for forwarding network traffic from the network device to a multi-homed network by taking into account a first cost associated with a second path from a first border router to the multi-homed network and a second cost associated with a second border router to the multi-homed network, wherein the multi-homed network is external to an interior routing domain in which the network device is located. The network device selects an LFA next hop from the set of candidate LFA next hops, to be stored as an alternate next hop for forwarding network traffic to the multi-homed network, and updates forwarding information stored by the network device to install the selected LFA next hop as the alternate next hop for forwarding network traffic from the network device to the multi-horned network.