1

4. Use the following information for questions a) – c) A bank currently just meets its...

Question

4. Use the following information for questions a) – c) A bank currently just meets its...

4. Use the following information for questions a) – c)

A bank currently just meets its total capital requirements of 8%. The bank currently has a dividend payout ratio of 25%. Assets are expected to grow at 5%.

a) What is the required ROA to support the growth in assets?

b) If the bank expects its ROA to be 0.5%, what is the maximum dividend payout ratio to support the increase in assets?

c) If the bank expects its ROA to be 0.5% and the bank does not wish to change its dividend payout ratio from 25%, how much new equity capital (as a percent of total assets) must the bank issue to support the growth in assets?

Answers

Growth = ROA x (1 - dividend payout ratio) / Capital requirement

Part (a)

5% = ROA x (1 - 25%) / 8%

Hence, ROA = 5% x 8% / (1 - 25%) = 0.53%

Part (b)

5% = 0.5% x (1 - dividend payout ratio) / 8%

Hence, dividend payout ratio = 1 - 5% x 8% / 0.5% = 20.00%

Part (c)

Let Z be the new equity capital (as a percent of total assets) the bank must issue to support the growth in assets

Growth = [ROA x (1 - dividend payout ratio) + Z] / Capital requirement

5% = [0.5% x (1 - 25%) + Z] / 8%

Hence, capital requirement = Z = 5% x 8% - 0.5% x (1 - 25%) = 0.0250%


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