Question

Leverage

Consider the following balance sheets of two banks. These two banks have equal amounts of assets but are leveraged differently. Assume that there is no regulatory capital requirement.

Balance Sheet of Arch Bank
Assets		Liabilities and Net Worth
Outstanding Loans	$100,000	Deposits (Liabilities)	$80,000
		Capital (Net worth)	20,000
Total	$100,000	Total	$100,000

Balance Sheet of Medes Bank
Assets		Liabilities and Net Worth
Outstanding Loans	$100,000	Deposits (Liabilities)	$95,000
		Capital (Net worth)	5,000
Total	$100,000	Total	$100,000

Which bank has a lower leverage ratio?

(Arch Bank/Medes Bank)

Suppose both banks' assets increase by 10% to $110,000. Assume that the liabilities of both banks remain the same. Arch Bank's capital increases by (10%/40%/50%/150%) , and Medes Bank's capital increases by(10%/40%/150%/200% ) . Therefore, if the value of assets is rising and liabilities do not change, a higher leverage ratio results in a(smaller/greater) percentage increase in capital.

Now suppose all the items on the balance sheets of both banks return to their initial values. Suddenly, the banks realize that loans they made are riskier than they thought, and the total value of their assets declines by 5% to $95,000. Again, assume that the liabilities of both banks remain the same. Arch Bank's capital decreases by (5%/20%/25%/75%) , and Medes Bank's capital decreases by(5%/20%/75%/100%) . Therefore, if the value of assets is falling, a higher leverage ratio means a(smaller/greater) percentage decrease in capital.

Under this second scenario, which bank is closer to insolvency?

(Arch Bank/Medes Bank)

Answer 1

(a) Leverage = Loans / Capital

Arch: $100,000 / $20,000 = 5

Medes: $100,000 / $5,000 = 20

Arch bank has lower leverage.

(b) Capital of both banks will increase by $10,000.

% increase, Arch = $10,000 / $20,000 = 0.5 or 50%

% increase, Medes = $10,000 / $5,000 = 2, or 200%

So, higher leverage results in greater % increase in capital (for Medes).

(c) Asset & capital fall by $5,000 for both banks.

% decrease, Arch = $5,000 / $20,000 = 0.25, or 25%

% decrease, Medes = $5,000 / $5,000 = 1, or 100%

Higher leverage means greater % decrease in capital.

(d) Medes is closer to insolvency since its capital is falling by higher percentage.