Question

1. A commercial bank’s T-account in 2020 is shown as below: Table 2: T-Account for Bank A in 2018 Assets Liabilities plus Equity Loans: $ 800 Deposits: $900 Securities: $ 100 Borrowings: $0 Cash Reserves: $ 60 Equity: ?

The bank pays 8% for the bank deposit to the depositors; the average interest rate on the loans is 15%; the cash reserves does not pay any interest; and the returns to its securities is 10%.

(1) Calculate the value of equity, the value of capital ratio and the leverage ratio?

(2) Calculate the return on equity.

(3) Calculate the capital ratio and return on equity again if deposits is 800 and more equity is used to finance for the assets? By comparing your answer with

(2), when equity increases, whether the return on equity would increase or decrease?

Answer 1

Answer:

(1) Value of Equity=Value of Assets-Value of Liabilities.

Here Assets=Loans $800+Securities $100+Cash reserves $60=$960.

Liabilities=Deposits $900.

Value of Equity=$960-$900=$60.

Value of Capital ratio=Equity(Capital)/Assets*100=60/960*100=6.25%.

Value of Leverage ratio=Total liabilities/Total Assets=$900/$960=0.9375.

(2)

Return on equity=Return/Equity*100.

Return=Interest received-Interest paid.

Interest received is 15 % on loan of $800=$120 and 10% on securities of $100=$10.

Total interest received=$120+$10=$130.

Interest paid=8% on deposits of $900=$72.

Return=$130-$72=$58

Return on equity=$58/$60*100=96.67%.

(3)

If deposits are $800 and Equity is $160 then

Value of Capital ratio=Equity(Capital)/Assets*100=160/960*100=16.67%.

Return on equity=Return/Equity*100.

Return=Interest received-Interest paid.

Interest received is 15 % on loan of $800=$120 and 10% on securities of $100=$10.

Total interest received=$120+$10=$130.

Interest paid=8% on deposits of $800=$64.

Return=$130-$64=$66

Return on equity=$66/$160*100=41.25%.

When equity increases return on equity decreases.