Second National Bank is forecasting a return on equity of 15 percent for this year.The board of directors wants to maintain its current policy of paying the bank's stockholders 40 percent of any net earnings the bank will earn.How fast can the bank's assets grow this year without jeopardizing its ratio of capital to assets?
A)15 percent
B)9 percent
C)8 percent
D)6 percent
E)None of the options is correct.

Question

Quizplus · Accepted Answer

To maintain the current ratio of capital to assets, the bank's growth rate should be such that the increase in total equity matches the increase in total assets.
Let's assume that the bank currently has total assets worth $100 and total equity worth $10 (i.e., the capital ratio is 10 percent).

If the bank aims to achieve a return on equity of 15 percent, it needs to earn a net income of $1.5 (i.e., 15% of $10).

If the bank maintains its policy of paying 40 percent of net earnings to shareholders, it will pay out $0.6 (i.e., 40% of $1.5) as dividends and retain $0.9 as earnings.

Now, if the bank grows its assets by x percent, the new total assets will be $100*(1+x), and the new total equity will be $10+0.9. We need to solve for x such that the new equity/assets ratio equals the current ratio of 10 percent:

(10 + 0.9) / (100*(1+x)) = 10%

Solving for x gives us:

x = 9%

Therefore, the bank can grow its assets by 9 percent this year without jeopardizing the capital/asset ratio. Any higher growth rate would reduce the ratio and potentially make it difficult for the bank to meet its capital requirements.

Second National Bank Is Forecasting a Return on Equity of 15