Using the formulas developed in this chapter and in Chapter 6 and the information that follows, calculate the ratios of total capital to total assets for the banking firm listed below. What relationship among these banks’ return on assets, return on equity capital, and capital-to- assets ratios did

Question

Using the formulas developed in this chapter and in Chapter 6 and the information that follows, calculate the ratios of total capital to total assets for the banking firm listed below. What relationship among these banks’ return on assets, return on equity capital, and capital-to- assets ratios did you observe? What implications or recommendations would you draw for the management of each of these institutions?

Accepted Answer

Name of Bank	Net Income/Total Assets (or ROA)	Net Income/Total Equity Capital (or ROE)
First National Bank of Hopkins	1.40%	15%
Safety National Bank	1.20%	13%
Ilsher State Bank	0.90%	11%
Mercantile Bank and Trust Company	0.50%	6%
Lakeside National Trust	-0.50%	-7%

The basic relationship needed in this problem is

[latex] ext { ROE }=\frac{ ext { Net Income After Taxes }}{ ext { Equity Capital }} =\frac{ ext { Net Income After Taxes } *}{ ext { Total Assets }} \frac{ ext { Total Assets }}{ ext { Equity Capital }}[/latex]

= [latex] ext { ROA }* \frac{ ext { Total Assets }}{ ext { Equity Capital }}[/latex]

In which case:

[latex]\frac{ ext { Total Assets }}{ ext { Equity Capital }}=\frac{ ext { ROE }}{ ext { ROA }}[/latex] and [latex]\frac{ ext { Equity Capital }}{ ext { Total Assets }}=\frac{ ext { ROA }}{ ext { ROE }}[/latex]

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.

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

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