7. If a bank\'s ROA is projected to be 1% this year, how much in assets for each

Question

7. If a bank's ROA is projected to be 1% this year, how much in assets for each $1 in capital is needed to achieve 10% ROE? What happens in ROA is expected to fall to 0.5%? 8. Bank L operates with an equity-to-asset ratio of 6%, while Bank S operates with a similar ratio of 10%. Calculate the equity multiplier for each bank and the corresponding return on equity if each bank earns 1.5% on assets. Suppose, instead, that both banks report an ROA of 1.2%. What does this suggest about financial leverage? 9. Explain how and why profitability ratios at small banks typically differ from those at large banks?

Explanation / Answer

7. ROA = Return on Assets = 1%

Now, ROE = Return on Equity = Profit / Equity = 10%

It means Profit = Equity * 10% = $1 (capital is Equity) * 10% = $1

So Profit needs to be $1

ROA = 1% (as stated above)

Profit / Assets = 1%

1 / Assets = 1%

Assets = 1/1% = $100

So There needs to be $100 in assets.

(B) If ROA is 0.5%

Profit / Assets = 0.5%

1 / Assets = 0.5%

Assets = 1/0.5% = $200

So There needs to be $200 in assets.

8. Equity / Assets = 6% (for Bank L)

Equity / Assets = 10% (for Bank S)

Equity Multiplier is total assets / total Equity

So for Bank L Equity multiplie = 100/6 = 16.67

for Bank S, Equity multiple = 100/10 = 10

Now, ROA = Profit / Assets = 1.5%

ROE = Return on Equity = ROA * Equity multiplier = Profit / Assets * Assets / Equity

Thus, ROE for Bank L = 1.5%*16.67 = 25%

ROE for Bank S = 1.5%*10 = 15%

Greater the Equity multiplier, greater is the leverage. So Bank L is more financially leveraged as compared to Bank S

Now, if ROA = 1.2%,

Thus, ROE for Bank L = 1.2%*16.67 = 20%

ROE for Bank S = 1.2%*10 = 12%

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