ITIL. as well as ISO 20000, uses Financial Management for IT Services (Budgeting and accounting for service in ISO 20000) process to manage financial aspect of IT services . For these activities, help from someone with financial experience (e.g. from controlling) would be of great help. Close cooperation with corporate finance department is required.
Additionally, Continual Service Improvement is strongly related to finances (related to IT services) and their improvements. Improvements activities should be performed in scope of your usual improvement activities.