Happy Bank starts with $200 in bank capital. It then takes in $800 in deposits.

Question

Happy Bank starts with $200 in bank capital. It then takes in $800 in deposits. It keeps 12.5 percent (1/8th) of deposits in reserve. It uses the rest of its assets to make bank loans.

a) Show the balance sheet of Happy Bank.

b) What is Happy Bank’s leverage ratio?

c) Suppose that 10 percent of the borrowers from Happy Bank default and these bank loans become worthless. Show the bank’s new balance sheet.

d) By what percentage do the bank’s total assets decline? By what percentage does the banks’ capital decline? Which change is larger? Why?

Explanation / Answer

If the bank keeps 1/8 of deposits in reserve and loans the rest, the balance sheet will be something like this

1)Assets
$100 Reserves
$900 Loans
$1000 Total
Liabilities
$800 Deposits
Net Worth (Assets - Liabilities)
$200

3)If 10% default, the balance sheet will be like this:

Assets
$100 Reserves
$810 Loans
$910 Total
Liabilities
$800 Deposits
Net Worth (Assets - Liabilities)
$110

4)The assets went from $1000 to $910, which is a 9% decline. "Capital" is net worth, which went from $200 to $110, which is a 45% decline. The difference is because the bank mostly using other people's money - the deposits - in order to make the loans.

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