Question

Suppose Melvin’s Bank starts with the balance sheet in Table 9.4A and the income statement in Table 9.2. Show how the balance sheet and income statement change in each of the following scenarios. Also calculate the new ROA, ROE, and rate sensitivity gap.

a. The bank issues $20 of new stock and uses the proceeds to make loans.

b. Britt moves $25 from his savings account to his checking account.

c. The bank is hired to manage the assets of a wealthy person, for which it is paid $10 a year.

d. The bank lends $5 of reserves to another bank in the federal funds market. (Assume the federal-funds rate is the same as the Treasury-bill rate.)

e. The bank replaces $10 of its loans with floating-rate loans, which pay the Treasury-bill rate plus 2 percent.

INCOME STATEMENT

For the year ended December 31, 2021

Interest Income Securities 4% ($30) $1.20

Loans 8% ($80) $6.40

Total $7.60

Noninterest Income $5.00 (letters of credit)

TOTAL INCOME $12.60

Interest Expense 4% ($50) $2.00 (savings accounts)

Noninterest Expense $6.00 (salaries, etc.)

TOTAL EXPENSE $8.00

PROFITS (Income – Expense) $4.60 ROA = profits assets = $4.60 $120 = 3.8% ROE = profits capital = $4.60 $20 = 23%

MELVIN’S BANK BALANCE SHEET

December 31, 2020

Assets

Reserves 10

Securities 30

Loans 80

Liabilities and Net Worth

Checking Deposits 50

Nontransaction Deposits 50

Net Worth 20

Answer 1

Answer :

Showing how the balance sheet and income statement change in each of the following scenarios. Also calculating the new ROA, ROE and rate sensitivity gap

(a).

Balance sheet

Assets	Amount	Liabilities and Net worth	Amount
Reserves	$10	Checking deposits	$50
Securities	$30	Nontransaction deposits	$50
Loans	$100	Net worth	$40
Total	$140	Total	$140

By this scenario, it has affect on income statement, because the additional loans generate new interest income for the bank. Interest income will raise by as follows

Interest income = 8%($20) = $1.60

Profit = Total income + Interest income - Total expense

Profot = $12.60 + $1.60 - $8.00 = $6.20

Calculating the ROA, ROE and Rate Sensitivity Gap

ROA = Ptofit / Assets

ROA = $6.20 / $140 = 4.4%

ROE = Profit / Net worth

ROE = $6.20/$40 = 15.5%

Rate - Sensitivity gap = Rate - Sensitivity assets - Rate - Sensitivity Liabilities

Rate - Sensitivity = $30 (T - bills) - $50 (Savings accounts)

Rate - Sensitivity gap = - $20

(b)

Balance sheet

Assets	Amount	Liabilities and Net worth	Amount
Reserves	$10	Checking deposits	$75
Securities	$30	Nontransaction deposits	$25
Loans	$80	Net worth	$20
Total	$120	Total	$120

By this scenatio, it has effect on income statment, Because the interest expense are lower, interest expense will decreases by as follows

Interest Expense = 4%($25) = $1

It will lower the total expenses to $7.00

Profit = $12.60 - $7.00 = $5.60

Calculating the ROA, ROE and Rate - Sensitivity Gap

ROA = Profits / Assets

ROA = $5.60 / $120 = 4.7%

ROE = Profits / Net worth

ROE = $5.60 / $20 = 28%

Rate - Sensitivity gap = Rate - Sensitivity Assets - Rate - Sensitivity Liabilities

Rate - Sensitivity gap = $30 (T - bills) - $25(Savings accounts)

Rate - Sensitivity gap = $5

(c).

Assets management is an offf balance sheet activity (OBS). By this scenario, it has affect on income statement, but not on balance sheet. Non interest income raises by $10

Profit = $22.60 - $8.00 = $14.60

Calculating the ROA, ROE and Rate - Sensitivity Gap

ROA = Profits / Assets

ROA = $14.60/$120 = 12.2%

ROE = Profits / Net worth

ROE = $14.60 / $20 = 73%

Rate - Sensitivity gap = Rate - Sensitivity Assets - Rate - Sensitivity Liabilities

Rate - Sensitivity gap = $30 (T - bills) - $50(Savings accounts)

Rate - Sensitivity gap = $20

(d).

Balance sheet

Assets	Amount	Liabilities and Net worth	Amount
Reserves	$5	Checking deposits	$50
Securities	$30	Nontransaction deposits	$50
Loans	$80	Net worth	$20
Federal Funds Loan	$5	-	-
Total	$120	Total	$120

By this scenario, it has affect on income statment, but not on the balance sheet. Interest income raises by as follows,

Interest income = 4% ($5) = $0.2

Profit = $12.80 - $8.00 = $4.80

Calculating the ROA, ROE and Rate - Sensitivity Gap

ROA = Profits / Assets

ROA = $4.80 / $120 = 4%

ROE = Profits / Net worth

ROE = $4.80 / $20 = 24%

Rate - Sensitivity gap = Rate - Sensitivity Assets - Rate - Sensitivity Liabilities

Rate - Sensitivity gap = $35 (T - bills) - $50(Savings accounts)

Rate - Sensitivity gap = $15

(e).

Balance Sheet

Assets	Amount	Liabilities and Net worth	Amount
Reserves	$10	Checking deposits	$50
Securities	$30	Nontransaction deposits	$50
Loans	$80	Net worth	$20
Total	$120	Total	$120

By this scenario, it has affect on income statement, but not on balance sheet. Interest income on loans is as follows

Interest income loan = 8%($70) + 6%($10) = $6.20

Profit = $12.40 - $8.00 = $4.40

Calculating the ROA, ROE and Rate - Sensitivity Gap

ROA = Profit / Assets

ROA = $4.40 / $120 = 3.67%

ROE = Profit / Net worth

ROE = $4.40/$20 = 22%

Rate - Sensitivity gap = Rate - Sensitivity Assets - Rate - Sensitivity Liabilities

Rate - Sensitivity gap = $40(T - bills) - $50(Savings accounts)

Rate - Sensitivity gap = $10

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