25. ABC Bank has the following measures of bank profitability: EM = 14 and ROA = 1.05%. XYZ Bank measures are EM = 12.3 and ROA = 1.15%. Which bank has a higher ROE? A. ABC Bank B. XYZ Bank C. Both banks have the same ROE D. None of the above
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The formula for ROE is: $ROE = EM \times ROA$ For ABC Bank, EM = 14 and ROA = 1.05% = 0.0105. $ROE_{ABC} = 14 \times 0.0105 = 0.147 = 14.7\%$ Show more…
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X-Bank reported an ROE of $15 \%$ and an ROA of $1 \%$ How well capitalized is this bank?
Profitability remains a challenge for banks and thrifts with less than $2 billion of assets. The business problem facing a bank analyst relates to the factors that affect return on assets (ROA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 20 community banks include the ROA (%), the efficiency ratio (%), as a measure of bank productivity (the lower the efficiency ratio, the better), and total risk-based capital (%), as a measure of capital adequacy. Complete parts (a) through (g) below. a. State the multiple regression equation. Let X1i represent the efficiency ratio (%) and let X2i represent the total risk-based capital (%). Yi = 2.73 + (- 0.0223)X1i + (- 0.0083)X2i (Round the constant to two decimal places as needed. Round the coefficients to four decimal places as needed.) b. Interpret the meaning of the slopes, b1 and b2, in this problem. Choose the correct answer below. A. For each increase of 1% in the ROA, the Efficiency Ratio is estimated to increase by b1% and the Risk-Based Capital is estimated to increase by b2%. B. For a given Risk-Based Capital, for each increase of 1% in the Efficiency Ratio, the ROA is estimated to increase by b1%. For a given Efficiency Ratio, for each increase of 1% in Risk-Based Capital, the ROA is estimated to increase by b2%. C. For each increase of 1% in both the Efficiency Ratio and the Risk-Based Capital, the ROA is estimated to increase by (b1 + b2)%. D. The slopes, b1 and b2, cannot be interpreted individually. c. Predict the mean ROA when the efficiency ratio is 70% and the total risk-based capital is 10%. 1.08 % (Round to two decimal places as needed.) d. Construct a 95% confidence interval estimate for the mean ROA when the efficiency ratio is 70% and the total risk-based capital is 10%. % <= muY|X <= % (Round to one decimal place as needed.)
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X-Bank reported an ROE of $16 \%$ and an ROA of $1.32 \%$ What is the equity multiplier? How well capitalized is this bank?
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