We derive a new series expansion formula for the scale matrix for Markov additive processes with a constant drift and general finite-activity one-sided jumps. This generalizes the series expansion formula of the scale function obtained in Landriault & Willmot (Scand. Actuar. J., 2020) for the Cramer-Lundberg process. Its applications in ruin theory and sequential testing are discussed. Joint work with J. Ivanovs (Aarhus University).