Question #$3$: Capital Adequacy Management $[12$ Points$]$

The balance sheets for two financial institutions: Logan Bank and Sawyer Savings and Loan are provided below.

Balance Sheet: Logan Bank

$\backslash$table$[[$Assets$,$Liabilities$]]$

Page $2$ of $4$

$\backslash$table$[[$Reserves:$,$$$28$ million,Checkable Deposits:,$$180$ million$],[$Loans:$,$$$173$ million,Bank Capital:,$$21$ million$]]$

Balance Sheet: Sawyer Savings and Loan

$\backslash$table$[[$Assets$,$Liabilities,$],[$Reserves:$,$$$28$ million,Checkable Deposits:,$$188$ million$],[$Loans:$,$$$173$ million,Bank Capital:,$],[,,,$$$13$ million$]]$

$($a$)$ Suppose that both banks had $$15$ million worth of residential loans that defaulted and the banks are now forced to write off the loans $($these loans are no longer considered assets$).$ Illustrate the new balance sheets after the residential loans are written off for both Logan Bank and Sawyer Savings and Loan. $[4$ Points$]$

$($b$)$ Sawyer Savings and Loans had less bank capital than Logan Bank. What is the upside for Logan Bank in having more bank capital? $[2$ Points$]$

$($c$)$ Calculate the equity multiplier $($EM$)$ for both Logan Bank and Sawyer Savings and Loan. Use the initial total assets for both banks in your calculations. Round vour answer to $2$ decimal places. $[2$ Points$]$

$($d$)$ What does return on equity $($ROE$)$ measure? Calculate the ROE for both Logan Bank and Sawyer Savings and Loan if the return on assets $($ROA$)$ is equal to $0\mathrm{.}3\%$ for both banks. What is the downside for Sawyer Savings and Loan in having more bank capital? $[4$ Points$]$