Question 6.P.7: OK State Bank reports total operating revenues of $150 milli...

Net Income after Taxes = $150 million -$130 million -$5 million = $15 million

Equity Capital = $1.00 billion – $900 million = $100 million

Alternative Scenario a: How will the ROE for OK State Bank change if total operating expenses, taxes and total operating revenues each grow by 10 percent while assets and liabilities stay fixed.

Total revenues = $150 million * 1.10 = $165 million

Total expenses = $130 million * 1.10 = $143million

Tax liability = $5 million * 1.10 = $5.5 million

Net Income after Taxes = $165 – $143- $5.50 = $16.5 million

ROE = $16.5 million/$100 million = 0.165 or 13.2%

Change in ROE = (16.50%-15%)/15% = 10%

Alternative Scenario b: Suppose OK State’s total assets and total liabilities increase by 10 percent, but its revenues and expenses (including taxes) are unchanged. How will the bank’s ROE change?

Total assets increase by 10% (Total assets = $ 1.0 * 1.10 = $1.1 billion)

Total liabilities increase by 10% (Total liabilities = $900 million * 1.10 = $990

Revenues and expenses (including taxes) remain unchanged.

Solution: Equity Capital = $1.1 billion – $990 million = $110 million

.1364

\text { Therefore change in ROE }=\frac{13.64 \%-15 \%}{15 \%}=\frac{-1.36 \%}{15 \%} = -.0909%

(ROE decreases by 9.09%)

Alternative Scenario c: Can you determine what will happen to ROE if both operating revenues and expenses (including taxes) decline by 10 percent, with the bank’s total assets and liabilities held constant?

Total revenues decline by 10% (Total revenues = $150 million * 0.90 = $135million)

Total expenses decline by 10% (Total expenses = $130 million * 0.9 = $117 million)

Tax liability declines by 10% (Tax liability = $5 * 0.9 = $4.5 million)

Assets and liabilities remain unchanged (Therefore, equity remains unchanged)

Solution: Net Income after Tax = $135 million – 117 million – $4.5 million = $13.5

\text { Therefore change in ROE }=\frac{13.5 \%-15 \%}{15 \%}=\frac{-1.5 \%}{15 \%} = -.10

(ROE decreases by 10%)

Alternative Scenario d: What does ROE become if OK State’s assets and liabilities decrease by 10 percent, while it’s operating revenues, taxes and operating expenses do not change?

Total assets = $1.0 billion * 0.9 = $900 million

Total liabilities = $900 million * 0.9 =$810 million

Equity capital = $900 million – $810 million = $90 million

ROE = \frac{\$ 15}{\$ 90} = .1667

16.67 percent