Question

(Time: 10 min) There are two banks with identical assets, but different liabilities as shown in the balance sheets below: Bank 1 Reserves million Loans $42 million Bonds $ 10 million Liabilities L) + Capital EO) Deposits 33 million Disc. La S 11 million Bank Capital (EQ $ 4 million Bank 2 Assets (A) Reserves $ 8 million Loans $ 42 million Bonds $ 10 million Liabilines (L) + Capital (EO Deposit $ 9 million Disc. Los $ 9 million Bank Capital (EQ $ 2 million Suppose that after a successful year the ROA=2% for each bank. • What is the return on equity (ROE) for Bank 1? Bank 2? (Fully explain your results in numbers and words.) • What do you think is the reason behind the differences in ROE across banks? (Fully explain.) tv

Answer 1

Hi,

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Question:

Answer:

ROE = Net Income/Shareholder Equity

Here,

Net Income = Final profit before dividend distribution

Shareholder Equity = Total Assets - Total Liabilities

[Assets = liabilities + shareholders' equity

shareholders' equity = assets - liabilities.]

As per the question:

ROA = 2%

We know that,

ROA =   Net Income/Average assets ( total Assets)

Now we come on the Bank 1:

Assets = 8 + 42 + 10 = $60 million

Liability = $56 million ( not considering EQ)

Shareholder Equity = Assets - Liabilities

= 60 - 56 = $4 million

ROA =   Net Income/Average assets ( total Assets)

2 =   Net Income/60

Net Income = 60*2 = $120 millions

ROE = Net Income/Shareholder Equity

ROE = 120/4 = 30

This means the company earned a 30% profit on every dollar invested by shareholders .

For bank 2:

Assets = $60 million

Liabilities = $58 millions

Shareholder Equity = Assets - Liabilities

= 60 - 58 = $2 million

ROA =   Net Income/Average assets ( total Assets)

2 = Net Income/60

Net Income = $120 million

ROE = Net Income/Shareholder Equity

120/2 = 60

ROE = 60

This means the company earned a 60% profit on every dollar invested by shareholders.

ROE of both the banks is different because of differences in shareholder equity. In the bank of A, EQ is larger than bank B so the shareholder equity is different in both the bank.

Thank You