In this paper a simple age-structured model is constructed to analyze how a wildlife population creating hunting value, but also damage costs, is influenced by predation. The model may exemplify a moose population causing forest browsing damage and exposed for predation by wolf or other big carnivores within a Scandinavian institutional setting. However, it can also fit to other ecological and institutional settings as in North America and other parts of Europe. Two age classes of the prey population, immature and mature animals, are included. The paper provides several results, including a characterizing of the optimal harvesting scheme, and how the harvest and stock composition are influenced by damage costs. It is also shown how the damage costs influence the economic loss of predation. The paper also demonstrates that these results may be rather sensitive to certain conditions, including the timing of the events (e.g., damage costs and predation) over the year cycle.