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?
Homework 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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