a. Tax Management = \text =\frac{\text { Net Income }}{\text { Efficiency Ratio Net Income Before Taxes and Securities Transactions }}
=\frac{\$ 29 \text { million }-\$ 8 \text { million }}{\$ 29 \text { million }}-\frac{\$ 21 \text { million }}{\$ 29 \text { million }}
= 0.724 or 72.4 percent.
b. Expense Control Efficiency Ratio \text =\frac{\text { Net Income Before Taxes and Securities Gains }}{\text { Total Operating Revenues }}
c. Asset Management Efficiency Ratio (Asset Utilization) \text =\frac{\text { Total Operating Revenues }}{\text { Total Assets }}
=\frac{\$ 650 \text { million }}{\$ 1,750 \text { million }}=0.371 \text { or } 37.1 \text { percent. }
d. Funds Management Efficiency Ratio \text =\frac{\text { Total Assets }}{\text { Equity Capital }} =\frac{\$ 1,750 \text { million }}{\$ 170 \text { million }}=10.29x
e. \text { ROE }=\frac{\text { Net Income after Taxes }}{\text{Equity Capital}}=\frac{\$ 21 \text { million }}{\$ 170 \text { million }}=0.124 \text { or } 12.4%
=\frac{[(\$ 29 \times 1.20)-\$ 8}{\$ 1,750} * \frac{\$ 1,750}{\$ 170} = \frac{\$ 34.8-\$ 8}{\$ 1,750} * \frac{\$ 1,750}{\$ 170}
= 0.0153 * 10.3 = 0.1576 or 15.76%
This represents a 27% increase in ROE, from 12.4% to 15.76%. Since the equity multiplier did not change, this increase in ROE is due to the increase in ROA, from 1% to 1.26%.
Alternative Scenario b: If total assets climb by 20 percent, what will happen to Paintbrush’s efficiency ratio and ROE
Asset Management Efficiency Ratio =\frac{\$ 650}{\$ 1750 * 1.2}=\frac{\$ 650}{\$ 2100}=.31 \text { or } 31 \text { percent. }
This represents a decrease of 16.4%.
Funds Management Efficiency Ratio =\frac{\$ 2100}{\$ 170}=12.35 \text { times }
This represents an increase of 20%.
ROE would not change since the decrease in the asset management efficiency ratio is offset by the increase in the funds management efficiency ratio.
Alternative Scenario 3: What effect would a 20 percent higher level of equity capital have upon Paintbrush’s ROE and its components?
\frac{\text { Funds Management }}{\text{Efficiency Ratio}}= \frac{\text { Total Assets }}{\text{Equity Capital}}=\frac{\$ 1750 \text { million }}{\$ 170×1.20 \text { million }}=\frac{\$1.750 { }}{\$204} = 8.58
ROE = Tax Management Efficiency Ratio * Expense Control Efficiency Ratio * Asset Management Efficiency Ratio *Funds Management Efficiency Ratio
= 0.724 * 0.045 * 0.371 * 8.58 = 0.1037 or 10.37%
\text { Change in ROE = } \quad \frac{10.37 \%-12.4 \%}{12.4 \%}=-0.164 \text { or a } 16.4 \% \text { decrease }