2. Leverage and returns

The following tables show the balance sheets of two banks: Big Bank and Small Bank.

Big Bank Balance Sheet
Assets	Liabilities and Net Worth
Reserves	$100,000	Checking deposits	$300,000
Loans outstanding	$250,000	Stockholders' equity	$50,000
Total	$350,000	Total	$350,000

Small Bank Balance Sheet
Assets	Liabilities and Net Worth
Reserves	$0	Checking deposits	$0
Loans outstanding	$500,000	Stockholders' equity	$500,000
Total	$500,000	Total	$500,000

is a levered bank, while is an unlevered bank.

Assume that both banks offer an annual rate of 2% on checking deposits and charge an annual rate of 4% on loans.

For Big Bank , the annual interest cost on deposits is

, and the annual return on loans is

. Hence, Big Bank earns a net profit of

, which represents a rate of return of

(Hint: Round to 1 decimal place.) on stockholders' equity.

For Small Bank, the annual interest cost on deposits is

, and the annual return on loans is

. Hence, Small Bank earns a net profit of

, which represents a rate of return of

(Hint: Round to 1 decimal place.) on stockholders' equity.

Suppose that the value of loans in both banks declines by 10%. The amount of loans outstanding for Big Bank decreases from $250,000 to

, which represents a loss of

(Hint: Round to 1 decimal place.) of stockholders' equity. The amount of loans outstanding for Small Bank decreases from $500,000 to

, which represents a loss of

(Hint: Round to 1 decimal place.) of stockholders' equity.

Therefore, provides a higher rate of return to its investors, and exposes its investors to greater risk in the event of a decline in the value of loans.