How does a dividend payment of 50 flow through the three statements?

No effect — dividends are not an expense but an equity transaction. Cash flow statement: financing cash flow −50, Δ cash −50. Balance sheet: cash −50 (assets), retained earnings −50 (equity). The balance sheet balances. Important in an IB context: dividends reduce equity, and therefore also equity value in a DCF and SOTP. For dividend stocks (Allianz, Munich Re, Siemens), dividend policy is a primary valuation driver via the DDM.

Proposed dividends are NOT booked as a liability on the balance sheet under IFRS (disclosure only); under local GAAP they are booked as a 'liability to shareholders' once the AGM approves them.