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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) 0.2925%
B) 2.935%
C) 0.1075%
D) 1.075%
E) 1.367%

Question

Quizplus · Accepted Answer

To maintain an 8% capital requirement ratio with a 5% growth in assets, the bank needs to have an additional capital equivalent to 8% of the growth in assets. 
So, the required new equity capital = 8% * 5% = 0.4%
However, the bank already has a dividend payout ratio of 35%, which means it can distribute only (100% - 35%) = 65% of its earnings as dividends. Hence, to maintain the dividend payout ratio of 35%, the bank can only keep (100% - 65%) = 35% of its earnings as retained earnings. 
Therefore, to raise the required new equity capital of 0.4%, the bank must retain earnings of 0.4%/35% = 1.143% of its assets. 
Therefore, the answer is (0.4%/35%) = 0.1075% as a percentage of total assets, which is option C.

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