return on equity can be calculated as roa × equity multiplier. what is another way to express this equation?

Another way to express the equation

ROE=ROA×Equity Multiplier\text{ROE}=\text{ROA}\times \text{Equity Multiplier}ROE=ROA×Equity Multiplier

is by substituting the equity multiplier with its equivalent in terms of debt and equity:

Equity Multiplier=Total AssetsShareholders’ Equity=1+DebtEquity\text{Equity Multiplier}=\frac{\text{Total Assets}}{\text{Shareholders' Equity}}=1+\frac{\text{Debt}}{\text{Equity}}Equity Multiplier=Shareholders’ EquityTotal Assets​=1+EquityDebt​

Therefore, the equation can be written as:

ROE=ROA×(1+DebtEquity)\boxed{ \text{ROE}=\text{ROA}\times \left(1+\frac{\text{Debt}}{\text{Equity}}\right) }ROE=ROA×(1+EquityDebt​)​

This expression highlights how financial leverage (debt relative to equity) amplifies the return on equity based on the return on assets