Question 15.P.8: Using the formulas developed in this chapter and in Chapter ...

The basic relationship needed in this problem is

= \text { ROA }* \frac{\text { Total Assets }}{\text { Equity Capital }}

In which case:

\frac{\text { Total Assets }}{\text { Equity Capital }}=\frac{\text { ROE }}{\text { ROA }} and  \frac{\text { Equity Capital }}{\text { Total Assets }}=\frac{\text { ROA }}{\text { ROE }}

Therefore the ratio of total capital to total assets for the banks named in the problem must be:

First National Bank of Hopkins = 0.014/0.15 = 0.0933 or 9.33%.

Safety National Bank = 0.012/0.13 = 0.0923 or 9.23%

Ilsher State Bank = 0.009/0.11 = 0.0818 or 8.18%

Mercantile Bank and Trust Company = 0.005/0.06 = 0.0833 or 8.33%

Lakeside National Bank = -0.005/-0.07 = 0.0714 = 7.14%

None of the banks appear to have a serious capital deficiency problem. However, the bank with the lowest capital to total assets ratio is also the one with a negative return on assets and return on equity. The negative earnings may be eroding the capital position of this bank.