Question

This question is designed to inspire you to think about the effects of COVID19

on the management of a commercial bank.

Suppose a bank’s original T-account is de-

picted as follows:

Table 1: T-Account for Bank A in February 2020

Assets

Liabilities plus Equity

Loans: $ 800

Deposits: $1200

Securities: $ 400

Borrowings: $400

Reserves: $ 600

Equity: ?

The interest rate on loans is 8%, the average return for securities is 5%, the interest rate

on reserves is 2%, the interest rate on deposits is 1%, the interest rate on borrowings is

1.5%.

Please answer the following questions based on the information shown in Table 1.

1. Please calculate the equity value, the leverage ratio, the capital ratio and the return

on equity?

2. In March 2020, the financial risk becomes higher because of the outbreak of the

COVID19.The bank decides to raise the loan rate to 12%. The return on securities

declines to -5% because of the stock market crash. At the same time, the Federal

Reserve lowered the interest rate on a commercial bank’s borrowing to 0.5%.The

interest rate on deposits and reserves are also lowered to 0.5%. With the new

interest rates, what is the new return on equity if the balance sheet is still as

described in Table 1.

3. The outbreak of COVID19 in March 2020 may affect the management of a com-

mercial bank in the following ways. First, the value of securities decreases to $320

because the stock price plunged significantly. Second, $50 loans get defaulted be-

cause the borrowers’ financial situation deteriorates. Third, depositors needs to

withdraw $200 dollars to maintain their living. With the above three changes,

what does the commercial bank’s new balance sheet look like? Is the bank going

to be insolvent? What is the new capital ratio? Based on your calculation of the

capital ratio, is the bank facing a higher or lower risk of going bankruptcy?

Answer 1

Let's structure the balance sheet:

Assets	$	Liabilities & Equity	$
Reserves	600	Deposits	1,200
Loans	800	Borrowing	400
Securities	400	Bank Capital = Equity	????
Total Assets	1,800	Total Liabilities	1,800

Part (1)

The equity value = Bank capital = Total assets - total liabilities = 1,800 - (12,00 + 400) = 200

The leverage ratio = Total assets / Total equity = 1,800 / 200 = 9

The capital rato = Total equity / total assets = 1/Leverage rato = 1/9 = 0.1111

Please see the table below. Please see the seocnd row to understand the mathematics.

Assets	$	Interest / Return rate	Interest income / Return	Liabilities & Equity	$	Interest rate	Interest expense
	A	B	C = A x B		D	E	F = D x E
Reserves	600	2%	12	Deposits	1,200	1%	12
Loans	800	8%	64	Borrowing	400	1.50%	6
Securities	400	5%	20	Bank Capital = Equity	200	0%	-
Total Assets	1,800	Total income	96	Total Liabilities	1,800	Total expenses	18

Net income = total income - total expenses = 96 - 18 = 78

Return on equity = Net income / total equity = 78 / 200 = 39.00%

Part (2)

Assets	$	Interest / Return rate	Interest income / Return	Liabilities & Equity	$	Interest rate	Interest expense
	A	B	C = A x B		D	E	F = D x E
Reserves	600	0.5%	3	Deposits	1,200	0.5%	6
Loans	800	12.0%	96	Borrowing	400	0.5%	2
Securities	400	-5.0%	(20)	Bank Capital = Equity	200	0.0%	-
Total Assets	1,800	Total income	79	Total Liabilities	1,800	Total expenses	8

Net income = total income - total expenses = 79 - 8 = 71

Return on equity = Net income / total equity = 71 / 200 = 35.50%

Part (3)

Assets	Feb 20 balance	Change	Mar 20 balance	Liabilities & Equity	Feb 20 balance	Change	Mar 20 balance
	A	B	A + B		D	E	D + E
Reserves	600		600	Deposits	1,200	(200)	1,000
Loans	800	(50)	750	Borrowing	400		400
Securities	400		320	Bank Capital = Equity	200	-	-

Equity = total assets - total liabilities = (600 + 750 + 320) - (1,000 + 400) = 270

Hence, the new balance sheet will look like as shown below:

March 2020 balance sheet

Assets	$	Liabilities & Equity	$
			D + E
Reserves	600	Deposits	1,000
Loans	750	Borrowing	400
Securities	320	Bank Capital = Equity	270
Total Assets	1,670	Total Liabilities	1,670

Since the bank capital = equity = 270 > 0; the bank is going to be remain solvent.

the new capital ratio = total equity / total assets = 270 / 1,670 = 0.1617

Based on your calculation of the capital ratio, is the bank facing a higher or lower risk of going bankruptcy?

The capital ratio has increased and therefore improved and the leverage ratio ( = inverse of capital ratio) has decreased and therefore improved. So, overall the bank has now more equity capital, improved capital and leverage ratio, and hence the bank is now facing a lower risk of going bankruptcy.