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.
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