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Formula for Financial Leverage = total debt / equity
Equity = outstanding shares
So when a company buy back shares it reduces the equity (the denominator) which will increase the financial leverage.
e.g. Debt = 10m; Equity = 5m;
Financial Leverage = 10/5 = 2
Company buyback 3m
Financial Leverage = 10 / (5 – 3) = 5