# How are ROE, ROA and the assets to equity ratio related?

Q32. Financial leverage
How are ROE, ROA and the assets to equity ratio related?

A32.
(1) Return on equity (ROE)
= Return on assets (ROA) x Assets to equity ratio
(2) Return on assets (ROA)
= Net income / Average total assets
(3) Assets to equity ratio
= Financial leverage ratio
= Average total assets / Average stockholders’ equity
(4) Return on equity (ROE)
= Net income / Average stockholders’ equity
= (Net income / Average total assets) x (Average total assets / Average stockholders’ equity)
= Return on assets (ROA) x Assets to equity ratio

[Entity 32-a]
Net income = \$120,000
Average total assets = \$600,000
Average stockholders’ equity = \$300,000
Return on assets (ROA)
= \$120,000 / \$600,000 = 20%
Assets to equity ratio
= \$600,000 / \$300,000 = 2.0
Return on equity (ROE)
= \$120,000 / \$300,000 = 40%
Return on equity (ROE)
= Return on assets (ROA) x Assets to equity ratio
= 20% x 2.0 = 40%

[Entity 32-b]
Net income = \$120,000
Average total assets = \$600,000
Average stockholders’ equity = \$400,000
Return on assets (ROA)
= \$120,000 / \$600,000 = 20%
Assets to equity ratio
= \$600,000 / \$400,000 = 1.5
Return on equity (ROE)
= \$120,000 / \$400,000 = 30%
Return on equity (ROE)
= Return on assets (ROA) x Assets to equity ratio
= 20% x 1.5 = 30%

[Note]
ROA is same for both Entity 32-a and Entity 32-b. (20% = 20%)
Assets to equity ratio is higher for Entity 32-a than for Entity 32-b. (2.0 > 1.5)
ROE is higher for Entity 32-a than for Entity 32-b. (40% > 30%)
Entity 32-a is financially more leveraged than Entity 32-b.