Blue Ridge Bank has a PM of 12 percent,an interest income to total assets ratio of 6.00 percent,and a noninterest income to assets ratio of 1.50 percent. Blue Ridge also has $9 in assets per dollar in equity capital. Blue Ridge's ROE is

Question

Quizplus · Accepted Answer

Blue Ridge Bank's ROE can be calculated using the following formula:

ROE = PM x EM

Where PM is the profit margin (net income divided by total revenue), and EM is the equity multiplier (total assets divided by equity capital).

First, we need to calculate Blue Ridge's net interest margin (NIM), which is the difference between interest income and interest expenses divided by total assets:

NIM = (Interest income - Interest expenses) / Total assets

Since we know Blue Ridge's interest income to total assets ratio is 6.00%, but we don't know their interest expenses, we can assume that their NIM is also 6.00% (since interest expenses are likely to be a smaller percentage of total assets than interest income).

Next, we can calculate Blue Ridge's return on assets (ROA), which is the sum of NIM and the noninterest income to assets ratio:

ROA = NIM + Noninterest income / Total assets
ROA = 6.00% + 1.50%
ROA = 7.50%

Finally, we can calculate Blue Ridge's ROE using the equity multiplier:

EM = Total assets / Equity capital
EM = 9

ROE = ROA x EM
ROE = 7.50% x 9
ROE = 67.50%

However, we need to adjust our ROE calculation to take into account Blue Ridge's PM of 12%. This means that 12% of their revenue is turned into net income. Therefore, we need to multiply their ROE by 0.12 to get their actual return on equity:

ROE = 67.50% x 0.12
ROE = 8.10%

Therefore, the correct answer is choice (C), 8.10%.

Blue Ridge Bank Has a PM of 12 Percent,an Interest