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

Question

The following tables show the balance sheets of two banks: Big Bank and Small Bank. is a levered bank, while is an unlevered bank. Assume that both banks offer an annual rate of 4% on checking deposits and charge an annual rate of 8% on loans. 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 on stockholders' equity. 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 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 stockholders' equity. The amount of loans outstanding for Small Bank decreases from $500,000 to, which represents a loss of 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.

Explanation / Answer

Big Bank is a levered bank, while Small Bank is an unlevered bank.*

*The bank which has greater debt to equity is levered which in this case is the Big Bank.

For Small Bank, the annual interest cost on deposits is $0, and the annual return on loans is $40000 ($500000 x 8%). Hence, Small Bank earns a net profit of $40000, which represents a rate of return of 8.0% ($40000/$500000) on stockholders' equity.

For Big Bank, the annual interest cost on deposits is $12000 ($300000 x 4%), and the annual return on loans is $20000 ($250000 x 8%). Hence, Big Bank earns a net profit of $8000 ($20000 - $12000), which represents a rate of return of 16.0% ($8000/$50000) 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 $250000 to $225000 [$250000 - (10% x $250000)], which represents a loss of 4.0% [(8% x $25000)/$50000] of stockholders' equity. The amount of loans outstanding for Small Bank decreases from $500000 to $450000 [$500000 - (10% x $500000)], which represents a loss of 0.8% [(8% x $50000)/$500000] of stockholders' equity.

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

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