Question

Return on equity can be expressed as the product of

Select one:

a. Return on assets and profit margin

b. Return on assets and total asset turnover

c. Return on assets and the equity multiplier

d. None of the given answers

Answer 1

Return on Equity is measured by dividing Net Income by Shareholder's equity.
Return on Equity (ROE) = Net Income / Shareholders' Equity.

Return on Equity (ROE) can also be expressed as the product of
Return on assets and the equity multiplier
Explanation
Return on Assets is given by the formula: Net Income/ Total Assets
Equity Multiplier is given by the formula: Total Assets/ Shareholder's Equity
Hence, Return on Assets * Equity Multiplier can be expressed as
(Net Income/ Total Assets) * (Total Assets/ Shareholder's Equity)
which is equal to Net Income/ shareholder's Equity
Therefore, we can say ROE = Return on Assets * Equity Multiplier
Hence, option (c) is correct.

Option (a) is incorrect. Product of Return on Assets and Profit margin is not equal to Return on Equity.
We know, Return on Assets is given by formula: Net Income/ Total Assets
and Profit Margin is given by formula: Net Income/ Sales
Hence, when we multiply Return on Assets and Profit Margin, we get
Net Income/Total Assets * Net Income/ Sales
which is equal to (Net Income)*(Net Income)/Total Assets * Sales
Hence, Incorrect.

Similarly, option (b) is also incorrect. Product of Return on Assets and total assets turnover is not equal to Return on Equity.
We know, Return on Assets is given by formula: Net Income/ Total Assets
and Total Assets Turnover is given by formula: Net Sales/ Total Assets
Hence, when we multiply Return on Assets and Total Assets Turnover, we get
Net Income/Total Assets * Net Sales/ Total Assets
which is equal to (Net Income)*(Net Sales)/Total Assets * Total Assets
Hence, Incorrect.

Option (d) is incorrect as we do have a correct answer which is option (c).