Suppose a stockholder-owned thrift institution is projected to achieve a 1.10 percent ROA during the coming year. What must its ratio of total assets to equity capital be if it is to achieve its target ROE of 12 percent? If ROA unexpectedly falls to 0.80 percent what assets-to-capital ratio must it

Question

Suppose a stockholder-owned thrift institution is projected to achieve a 1.10 percent ROA during the coming year. What must its ratio of total assets to equity capital be if it is to achieve its target ROE of 12 percent? If ROA unexpectedly falls to 0.80 percent, what assets-to-capital ratio must it then have to reach a 12 percent ROE?

Accepted Answer

ROE = ROA * (Total Assets/Equity Capital)

[latex]\frac{ ext { Total Assets }}{ ext { Equity Capital }}=\frac{ ext { ROE }}{ ext { ROA }}=\frac{12 \%}{1.10 \%}=10.91 x[/latex]

If ROA unexpectedly falls to 0.80% and target ROE remains 12%:

[latex]12 \%=.80 \% \quad * \quad \frac{ ext { Total Assets }}{ ext { Equity Capital }}[/latex]

[latex]\frac{ ext { Total Assets }}{ ext { Equity Capital }}=\frac{12 \%}{.80 \%}=15 x[/latex]

Question 6.P.8: Suppose a stockholder-owned thrift institution is projected ...

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