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Firm a and firm b have debt-total asset ratios of 33 percent and 23 percent and returns on total assets of 7 percent and 10 percent, respectively. what is the return on equity for firm a and firm b? (

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The Return on Equity for firm a and firm b is 13%

Return on Equity

A metric of financial performance known as return on equity (ROE) is obtained by dividing net income by shareholders' equity. ROE is referred to as the return on net assets since shareholders' equity is determined by subtracting a company's debt from its assets. ROE is regarded as a barometer of a company's profitability and how well it produces profits. The management of a firm is more effective at generating income and growth from its equity financing the higher the ROE. Any corporation can calculate its ROE in percentage form if its net income and equity are both positive figures. Before dividends given to common shareholders, after payouts to preferred shareholders, and before interest paid to lenders, net income is computed.

Return on equity=

Net Income/Equity = Net Income/Asset x Asset/Equity = Return on Asset x Asset x Asset - Equity ratio

For Firm A, return on asset is 7%, asset-equity ratio= 1/(1-debt-asset ratio)=1/ (1-33%)=1.49

Return on equity=1.49[tex]\times 7%=10.45%[/tex]%

=10.45%

For Firm B, return on asset is 10%, asset-equity ratio=1/(1-debt-asset ratio)=1/(1-23%)=1.30

Return on equity= 1.30[tex]\times[/tex]10% = 13%

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