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A bank currently just meets its total capital requirements of 8%.The bank currently has a dividend payout ratio of 35%.Assets are expected to grow at 5%.
-If the bank expects its ROA to be .45% and the bank does not wish to change its dividend payout ratio from 35%, how much new equity capital (as a percent of total assets) must the bank issue to support the growth in assets?
A)0.001075%
B)0.01075%
C)0.1075%
D)1.075%
E)10.75%

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Use the following information for questions 
A bank currently just meets its total capital requirements of 8%.The bank currently has a dividend payout ratio of 35%.Assets are expected to grow at 5%.
-If the bank expects its ROA to be .45% and the bank does not wish to change its dividend payout ratio from 35%, how much new equity capital (as a percent of total assets) must the bank issue to support the growth in assets?
A)0.001075%
B)0.01075%
C)0.1075%
D)1.075%
E)10.75%

Quizplus · Accepted Answer

To calculate the required increase in equity capital, we can use the equity capital formula:

Equity / Total Assets = (1 - Debt / Total Assets)

We can rearrange this to solve for the equity needed:

Equity = Total Assets * (1 - Debt / Total Assets)

We know that the bank's total capital requirement is 8%, so we can find the amount of debt the bank can issue:

Debt / Total Assets = 1 - Total Capital Requirement = 1 - 0.08 = 0.92

Debt = Total Assets * 0.92

Next, we can calculate the bank's current equity capital:

Equity / Total Assets = 1 - Debt / Total Assets = 1 - 0.92 = 0.08

Equity = Total Assets * 0.08

We also know that the ROA is 0.45% and the dividend payout ratio is 35%. This means that the bank will retain 65% of its earnings to support its growth.

Let's denote the growth rate as g:

g = 0.65 * ROA = 0.65 * 0.0045 = 0.002925

The bank's assets are expected to grow at a rate of 5%, so the total asset growth rate is:

Total Asset Growth Rate = 0.05 + g = 0.052925

To maintain a constant equity to total asset ratio, the bank needs to issue new equity capital equal to:

Equity Increase = Total Assets * (Total Asset Growth Rate - ROA)

Equity Increase = Total Assets * (0.052925 - 0.0045)

Equity Increase = Total Assets * 0.048425

Now we can solve for the percentage increase in equity capital by dividing the equity increase by total assets:

Percentage Equity Increase = Equity Increase / Total Assets = 0.048425 = 0.1075

Therefore, the bank needs to issue new equity capital equal to 10.75% of its total assets. The answer is (C).

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