We investigate Markov-modulated stochastic recursive equations. This class includes multi-type branching processes with immigration as well as linear stochastic equations. Conditions are established for the existence of a stationary solution and expressions for the first two moments of this solution are found. Furthermore, the transient characteristics of the stochastic recursion are investigated: we obtain the first two moments of the transient solution as well. Finally, to illustrate our approach, the results are applied to the performance evaluation of packet forwarding in delay-tolerant mobile ad-hoc networks.