Question

happy bank starts with $200 in bank capital. It then takes in $800 in deposits. It keeps 10 percent ( 1/10th ) of deposit 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 npercent 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 bank's capital decline? which change is larger? why?

Answer 1

(a)

Reserve = Deposit x 10% = $800 x 10% = $80

Balance sheet is as follows.

ASSETS	$	LIABILITIES & CAPITAL	$
Reserves	80	Deposits	800
Loan	920	Capital	200
TOTAL	1,000	TOTAL	1,000

(b)

Leverage ratio = Capital / Total assets = $200 / $1,000 = 0.2 = 20%

(c)

After default, decrease in bank loan and decrease in capital will equal ($920 x 10%) = $92.

New Balance sheet is as follows.

ASSETS	$	LIABILITIES & CAPITAL	$
Reserves	80	Deposits	800
Loan	828	Capital	108
TOTAL	908	TOTAL	908

(d)

% Decrease in total asset = $92/$1,000 = 0.092 = 9.2%

% Decrease in capital = $92/$200 = 0.46 = 46%

% decrease in capital is much larger because total asset was much higher than initial capital, so the same amount of fall caused by bad loans resulted in a higher % decrease in capital compared to that in total assets.