Question

You must show all your work. Problem 1: Based on the balance sheet and income statement below, calculate the ROA, ROE, and rate sensitivity gap for each question below. For each question, begin with the original numbers when calculating your answers. Show your work in each case. (20 pts) Suppose Melvin's Bank starts with the balance sheet and the income statement as shown below: Melvin's Bank - Initial Balance Sheet Liabilities and Net Worth Assets $10 $40 Checking Deps Non-transaction deposits Reserves $40 $20 $100 $20 Securities $70 $100 Net Worth Loans Total Total Melvin's Bank - Income Statement Securities (2%) Loans (8 %, fixed rate) Total Interest Income $3.00 Letters of Credit $1.00 Other fees $4.00 Total Non-interest Income Total Income Savings accounts (4 %) $6.40 Non-interest expense $ Total Expense $ Profits (Net Earnings)

Answer 1

income statement

Securitiies (2%* 20)	0.4
Loans (8% * 70)	5.6
Total Interest		6.0
Letter of credit	3.0
other fee	1.0	4.0
Total income (A)		10.0
Savings account (4%*40) (ie non transaction)		1.6
non-interest expense		6.4
Total expense (B)		8.0
Profit (A-B)		2.0

a.

• ROA = profits/ assets => 2/100*100 = 2%
• ROE= profits/networth => 2/20*100 = 10%
• Rate sensitivity = rate sensitive assets - rate sensitive liabilities => $ 20 - $ 40 = $ -20.

b. Income increases by $ 20* 8% = $ 1.6. So new income is 2.0+1.6 = 3.6. Assets and liabilities will increase by $20 respectively. So assets = 100 + 20 = 120. Net worth rises by $ 20. So net worth = 20 + 20 = 40

• ROA = 3.6/120*100 = 3%
• ROA = 3.6/40*100 = 9%
• Rate sensitivity = 20 - 40 = -20

please comment for any query on this problem.