FIN507 Bank Management
Solutions to Recommended Problems from Modules 2, 3, 4,5 & 6
Module 2 Recommended Problems: Chapter 3: #2, 3, & 5, Chapter 4: #1-4
3-2. Of the business activities listed here, which activities can be conducted through U.S.-regulated holding
companies today?
a. Data processing companies
b. Office furniture sales
c. Auto and truck leasing companies
d. General life insurance and property-casualty insurance sales
e. Savings and loan associations
f. Mortgage companies
g. General insurance underwriting activities
h. Professional advertising services
i. Underwriting of new common stock issues by nonfinancial corporations
j. Real estate development companies
k. Merchant banks
l. Hedge funds
Banks can perform most of the activities listed above. It may be easier to talk about the activities they cannot
do. They cannot sell office furniture and they cannot perform professional advertising services. They can do
just about everything else listed here.
3-3 You are currently serving as president and chief executive officer of a unit bank that has been operating
out of its present location for five years. Due to the rapid growth of households
3-5. First Security Trust National Bank of Boston is considering making aggressive entry into the People’s
Republic of China, possibly filing the necessary documents with the government in Beijing to establish future
physical and electronic service facilities. What advantages might such a move bring to the management and
shareholders of First Security? What potential drawbacks should be considered by the management and
board of directors of this bank?
China is a huge market and entering into the Chinese market now may give this bank an advantage over other
banks. They will already have the necessary contacts and understanding of the Chinese system when it
becomes a more open economy in the future. However, there is considerable risk. It could be years before the
economy becomes more open so profit opportunities might be slow to develop. In addition, the government
could change its mind about allowing foreign banks ownership in China and seize any assets held by foreign
banks. Finally, the system is dominated by large government owned banks and it may be difficult to compete
with these banks. The Chinese government could give preferential treatment to these government banks at
the expense of the private sector.
4-1. A group of businesspeople from Scott Island are considering filing an application with the state banking
commission to charter a new bank. Due to a lack of current banking facilities within a 10-mile radius of the
community, the organizing group estimates that the initial banking facility would cost about $3.3 million to
build along with another $500,000 in other organizing expenses and would last for about 25 years. Total
revenues are projected to be $400,000 the first year, while total operating expenses are projected to reach
$160,000 in year 1. Revenues are expected to increase 4 percent annually after the first year, while expenses
will grow an estimated 2 percent annually after year 1. If the organizers require a minimum of a 10 percent
annual rate of return on their investment of capital in the proposed new bank, are they likely to proceed with
their charter application given the above estimates?
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Revenues
Op Expense
$400,000
$160,000
$416,000
$163,200
$432,640
$166,464
$449,946
$169,793
$467,943
$173,189
$486,661
$176,653
$506,128
$180,186
$526,373
$183,790
$547,428
$187,466
$569,325
$191,215
$592,098
$195,039
$615,782
$198,940
$640,413
$202,919
$666,029
$206,977
$692,671
$211,117
$720,377
$215,339
$749,192
$219,646
$779,160
$224,039
$810,327
$228,519
$842,740
$233,090
$876,449
$237,752
$911,507
$242,507
$947,968
$247,357
$985,886
$252,304
$1,025,322
$257,350
Required Rate
of Return
0.10
Present value of future cash
flows @ 10%
Initial investment
Net
Present
Value
of
Investment
Net Profit
$240,000
$252,800
$266,176
$280,152
$294,754
$310,008
$325,942
$342,583
$359,962
$378,110
$397,059
$416,842
$437,494
$459,052
$481,554
$505,038
$529,547
$555,122
$581,807
$609,650
$638,698
$669,001
$700,611
$733,582
$767,972
$3,329,203
$3,800,000
($470,797)
Given the above information, the organizers are not likely to proceed given that the net present value of this
investment is negative. The return they are going to earn is less than the 10% they need to earn.
4-2. Norfolk Savings Bank is considering the establishment of a new branch office at the corner of 49th Street
and Hampton Boulevard. The savings association’s economics department projects annual operating
revenues of $1.6 million from fee income generated by service sales and annual branch operating expenses of
$800,000. The cost of procuring the property is $1.75 million and branch construction will total an estimated
$2.75 million; the facility is expected to last 20 years. If the savings bank has a minimum acceptable rate of
return on its invested capital of 15 percent, will Norfolk Savings likely proceed with this branch office project?
Year
Revenues
Op
Expense
Net Profit
1
$1,600,000
$800,000
$800,000
2
$1,600,000
$800,000
$800,000
3
$1,600,000
$800,000
$800,000
4
$1,600,000
$800,000
$800,000
5
$1,600,000
$800,000
$800,000
6
$1,600,000
$800,000
$800,000
7
$1,600,000
$800,000
$800,000
8
$1,600,000
$800,000
$800,000
9
$1,600,000
$800,000
$800,000
10
$1,600,000
$800,000
$800,000
11
$1,600,000
$800,000
$800,000
12
$1,600,000
$800,000
$800,000
13
$1,600,000
$800,000
$800,000
14
$1,600,000
$800,000
$800,000
15
$1,600,000
$800,000
$800,000
16
$1,600,000
$800,000
$800,000
17
$1,600,000
$800,000
$800,000
18
$1,600,000
$800,000
$800,000
19
$1,600,000
$800,000
$800,000
20
$1,600,000
$800,000
$800,000
Required
0.15
Rate
of
Return
Present value of Future
Cash Flows
Initial investment
Net Present Value of
Investment
$5,007,465
$4,500,000
$507,465
Norfolk is likely to proceed with this project because the net present value is positive. This means that the
interest rate that Norfolk will earn on this project is higher than the 15% they need to earn.
4-3. Forever Savings Bank estimates that building a new branch office in the newly developed Washington
township will yield an annual expected return of 12 percent with an estimated standard deviation of 10
percent. The bank’s marketing department estimates that cash flows from the proposed Washington branch
will be mildly positively correlated (with a correlation coefficient of + 0.15) with the bank’s other sources of
cash flow. The expected annual return from the bank’s existing facilities and other assets is 10 percent with a
standard deviation of 5 percent. The branch will represent just 20 percent of Lifetime’s total assets. Will the
proposed branch increase Forever’s overall rate of return? Its overall risk?
The estimated total rate of return would be:
E (R) = 0.20 (12%) + 0.80 (10%) = 10.4%
The risk attached to this overall return rate would be:
σ2 = (0.20)2 (0.10)2 + (.80)2 (0.05)2 + 2(0.20)(0.80)(0.15)(0.10)(0.05)
σ2 =0.00224
σ = 4.73%
Thus   4.73% and the branch will slightly increase the bank's expected return but slightly increase its overall
risk. The bank should proceed with this project.
4-4. The following statistics and estimates were compiled by Big Moon Bank regarding a proposed new branch
office and the bank itself:
Branch office expected return
Standard deviation of branch return
Existing bank’s expected return
Standard deviation of existing bank’s return
Branch asset value as a percentage of total bank assets
Correlation of net cash flows for branch and bank as a whole
= 15%
= 8%
= 10%
= 5%
= 16%
= +0.48
What will happen to Big Moon’s total expected return and overall risk if the proposed new branch project is
adopted?
The bank's total expected return is:
E (R) = 0.16 (15%) + 0.84 (10%)
=
10.80%
The bank's risk exposure is:
σ2 = (.15)2 (.082 + (.85) 2 (.05)2 + 2(.15)(.85)(.48)(.08)(.05)
σ2 = .00244
And thus σ = .049395 or 4.94%
The proposed project raises the savings banks expected return slightly and but slightly increase its overall risk.
The bank should proceed with this project.
Module 3 Recommended Problems: Chapter 5: #3-5, 10
5-3. If you know the following figures:
Total interest income
Total interest expenses
Total noninterest income
Total noninterest expenses
$140 Provision for loan losses
100 Income taxes
75
Increases in bank’s undivided profits
90
$5
4
6
Please calculate these items:
Net interest income
Net noninterest income
Pretax net operating income
Net income after taxes
Total operating revenues
Total operating expenses
Dividends paid to common stockholders
Net interest income
Net noninterest income
Pretax net operating income
Net income after taxes
Total operating revenues
Total operating expenses
Dividends paid to common stockholders
a.
b.
c.
d.
e.
f.
g.
$40a
−15b
20c
16d
215e
195f
10g
Total interest income − Total interest expense ($140 − $100)
Total noninterest income − Total noninterest expense ($75 − $90)
Net interest income + Net noninterest income − PLL ($40 – $15 − $5)
Pretax net operating income − Taxes ($20 − $4)
Interest income + Noninterest income ($140 + $75)
Interest expenses + noninterest expenses + Provision for loan losses ($100 + $90 + $5)
Net income after taxes − increases in bank’s undivided profits ($16 − $6)
5-4. If you know the following figures:
Gross loans
Allowance for loan losses
Investment securities
Common stock
Surplus
Total equity capital
Cash and due from banks
Miscellaneous assets
Bank premises and equipment, gross
Please calculate these items:
Total assets
Net loans
Undivided profits
Fed funds sold
Depreciation
Total deposits
$300
15
36
5
15
30
10
25
25
Trading-account securities
Other real estate owned
Goodwill and other intangibles
Total liabilities
Preferred stock
Nondeposit borrowings
Bank premises and equipment, net
$2
4
3
375
3
40
20
Total assets
Net loans
Undivided profit
Fed funds sold
Depreciation
Total deposits
a.
b.
c.
d.
e.
f.
$405a
$285b
$7c
$20d
$5e
$335f
Total liabilities + Total equity capital ($30 + $375)
Gross loans − Allowance for loan losses ($300 – $15)
Total equity capital – Preferred stock – Common stock – Surplus ($30 – $15 – $5 – $3)
This is the only asset missing so subtract all other assets from total assets
Bank premises and equipment, gross – bank premises and equipment, net ($25 – $20)
Total liabilities less nondeposit borrowings ($375 – $40)
5-5. The Sea Level Bank has Gross Loans of $800 million with an ALL account of $45 million. Two years ago the
bank made a loan for $12 million to finance the Sunset Hotel. Two million dollars in principal was repaid
before the borrowers defaulted on the loan. The Loan Committee at Sea Level Bank believes the hotel will sell
at auction for $7 million and they want to charge off the remainder immediately.
a.
The dollar figure for Net Loans before the charge-off is _____.
Net Loans = Gross Loans –ALL = $800 − $45 = $755 million
b.
After the charge-off, what are the dollar figures for Gross Loans, ALL and Net Loans assuming no
other transactions?
Gross Loans = $800 million – ($10 million − $7 million) = $797 million
ALL =$45 million – ($12 million− $2 million − $7 million) = $42 million (The amount of the loan that is bad)
Net Loans = Gross Loans – ALL = $797 − $42 = $755 million
c.
If the Sunset Hotel sells at auction for $10 million, how will this affect the pertinent balance sheet
accounts?
Gross loans and ALL would not change as the bank would recover all the money invested earlier.
5-10. Which of these account items or entries would normally occur on a bank’s balance sheet (Report of
Condition) and which on a bank’s income and expense statement (Report of Income)?
Federal funds sold
Addition to undivided profits
Credit card loans
Utility expense
Vault cash
Allowance for loan losses
Depreciation on premises and equipment
Commercial and industrial loans
Repayments of credit card loans
Common stock
Deposits due to banks
Leases of business equipment to customers
Interest received on credit card loans
Fed funds purchased
Savings deposits
Provision for loan losses
Service charges on deposits
Undivided profits
Mortgage owed on the bank’s buildings
Other real estate owned
Interest paid on money market deposits
Securities gains or losses
The items which would normally appear on a bank's balance sheet are:
Federal funds sold
Credit card loans
Vault cash
Allowance for loan losses
Commercial and Industrial Loans
Repayments of credit card loans
Common stock
Federal funds purchased
Deposits due to bank
Leases of business equipment to
customers
Savings deposit
Undivided profits
Mortgage owed on the bank’s
buildings
Other real estate owned
Additions to undivided profits
The items which would normally appear on a bank’s income statement are:
Interest received on credit card loans
Provision for loan losses
Depreciation
on
premises
and
equipment
Interest paid on money market
deposits
Securities gains or losses
Utility expense
Service charges on deposits
Module 4 Recommended Problems: Chapter 6: #4, 5, & 11
6-4. The latest report of condition and income and expense statement for Smiling Merchants National Bank
are as shown in the following tables:
Smiling Merchants National Bank (complete)
Income and Expense Statement (Report of Income)
Interest and fees on loans
Interest and dividends on securities
Total interest income
$50
6
56
Interest paid on deposits
Interest on nondeposit borrowings
Total interest expense
40
6
46
Net interest income
Provision for loan losses
Noninterest income and fees
Noninterest expenses:
Salaries and employee benefits
Overhead expenses
Other noninterest expenses
10
5
20
10*
5
2
Total noninterest expenses
Net noninterest income
17
-2
Pretax operating income
Securities gains (or losses)
Pretax net operating income
Taxes
Net operating income
Net extraordinary income
Net income
8
2
10
2
8
-1
7
*Note: the bank currently has 40 FTE employees.
Smiling Merchants National Bank
Report of Condition
Assets
Cash and deposits due from banks
Investment securities
Federal funds sold
Net loans
(Allowance for loan losses = 25)
(Unearned income on loans = 5)
Net Fixed Assets
$100
150
10
700
Total assets
980
Total earnings assets
860
50
Liabilities
Demand deposits
Savings deposits
Time deposits
Federal funds purchased
Total liabilities
Equity capital
Common stock
Surplus
Retained earnings
Total Capital
Interest-bearing deposits
$190
180
470
80
920
20
35
35
80
650
Fill in the missing items on the income and expense statement. Using these statements, calculate the
following performance measures:
ROE
ROA
Net interest margin
Net noninterest margin
Net operating margin
Earnings spread
Net profit margin
Asset utilization
Equity multiplier
Tax management efficiency
Expense control efficiency
Asset management efficiency
Funds management efficiency
Operating efficiency ratio
What strengths and weaknesses are you able to detect in Smiling Merchants’ performance?
ROE =
1.
Net income
$7
=
= 0.0778 or 7.78 percent
Total equity capital
$90
ROA =
2.
Net income
$7
=
= 0.00714 or 0.71 percent
Total assets
$980
Net interest margin =
3.
Net interest income
$10
=
= 0.0120 or 1.02 percent
Total assets
$980
Net noninterest margin =
4.
Net operating margin =
5.
=
6.
Totalinterest income
Totalinterest expenses
Total earnings assets Totalinterest-bearing liabilities
$56
$46
= 0.002103 or 0.21 percent
$860 $650
Net profit margin =
Net income
$7
=
= 0.092105 or 9.21 percent
Total operating revenues
$54
Asset utilization =
Total operating revenues
$76
=
= 0.077551 or 7.76 percent
Total assets
$980
Equity multiplier =
Total assets
$980
=
= 10.89x
Total equity capital
$90
7.
8.
9.
Total operating revenues - Total operating expenses
Total assets
$8
= 0.008163 or 0.82 percent
$980
Earnings spread =
=
Net noninterest income
-$2
=
= -0.00204 or -0.20 percent
Total assets
$980
Tax Management =
10.
Net income
$7
=
= 0.7 or 70 percent
Pretax net operating income
$10
11.
Expense control effeciency =
Pretax net operating income
$10
=
= 0.131579 or 13.16 percent
Total operating revenue
$76
Asset managment effeciency ratio =
12.
=
$76
= 0.07755 or 7.76 percent
$980
Total operating revenues
Total assets
Funds Managment Effeciency Ratio =
13.
Total assets
$980
=
= 10.89x
Total equity capital
$90
14.
Operating effeciency ratio =
Total operating expenses
$68
=
= 0.894737 or 89.47 percent
Total operating revenues
$76
Strengths:
ROE: Positive value reflects a high rate of return flowing to shareholders.
Net profit margin: Positive value reflects effectiveness of management in controlling cost and service pricing
policies.
Asset utilization: Positive value reflects a good portfolio management policies and yield on assets.
Equity multiplier: Positive value reflects efficient financial policies.
Expense control efficiency, asset management efficiency ratio, funds management efficiency ratio, operating
efficiency ratio also reflects a high operating efficiency and expense control.
Tax-management efficiency ratio: Positive ratio reflecting the use of security gains or losses and other taxmanagement tools (such as buying tax-exempt bonds) to minimize tax exposure etc.
Weaknesses:
ROA: Positive value (0.714%) reflects managerial efficiency and how successful management has been in
converting assets into net earnings. Since the positive value is only 0.714% it acts as a weakness for Smiling
Merchants National Bank.
Net noninterest margin: Negative value (−0.2%) reflects that net noninterest income is inline with noninterest
cost.
Net interest margin: Positive value (1.02%) reflects that management is not successful in achieving close
control over earning assets and in utilizing the cheapest sources of funding. Since the positive value is only
1.02% it acts as a weakness for Smiling Merchants National Bank.
Earnings spread: Positive value (0.21%) reflects a high competition, forcing management to try and find other
ways to make up for an eroding earnings spread.
6-5. The following information is for Rainbow National Bank:
Interest income
Interest expense
Total assets
Securities losses or gains
Earning assets
Total liabilities
$2,250.00
1,500.00
45,000.00
21.00
40,000.00
38,000.00
Taxes paid
Shares of common stock outstanding
Noninterest income
Noninterest expense
Provision for loan losses
16.00
5,000
$800.00
900.00
250.00
Please calculate:
ROE
ROA
Net interest margin
Earnings per share
Net noninterest margin
Net operating margin
ROE =
Net income
$405
=
= 0.058or 5.8 percent
Total equity capital
$45,000 - $38,000
ROA =
Net income
$405
=
= 0.009 or 0.90 percent
Total assets
$45,000
Net interest margin =
Earnings per share =
Net interest income
$750
=
= 0.01667 or1.67 percent
Total assets
$45,000
Net income
$405
=
= $0.081per share
Common equity shares outstanding
5,000
Net noninterest margin =
Net operating margin =
Net noninterest income
-$350
=
= -0.0078or -0.78 percent
Total assets
$45,000
Total operating revenues-Total operating expenses
$400
=
Total assets
$45,000
= 0.00889 or 0.89 percent
Alternative Scenarios:
a.
Suppose interest income, interest expenses, noninterest income, and noninterest expenses each
increase by 3 percent while all other revenue and expense items shown in the preceding table remain
unchanged. What will happen to Rainbow ROE, ROA, and earnings per share?
Interest income
Interest expense
Total assets
Securities losses or gains
Earning assets
Total liabilities
Taxes paid
$2,317.50
$1,545.00
$45,000.00
$21.00
$40,000.00
$38,000.00
$16.00
Shares of Common Stock outstanding
Noninterest income
Noninterest expense
Provision for loan losses
5,000
$824.00
$927.00
$250.00
ROE =
Net income
$425
=
= 0.06064 or 6.06 percent
Total equity capital
$45,000 - $38,000
ROA =
Net income
$425
=
= 0.00943or 0.943percent
Total assets
$45,000
Earnings per share =
Net income
$425
=
= $0.0849 per share
Common equity shares outstanding
5,000
b.
On the other hand, suppose Rainbow interest income and expenses as well as its noninterest income
and expenses decline by 3 percent, again with all other factors held constant. How would the bank’s ROE,
ROA, and per-share earnings change?
Interest income
Interest expense
Total assets
Securities losses or gains
Earning assets
Total liabilities
Taxes paid
Shares of common stock outstanding
Noninterest income
Noninterest expense
Provision for loan losses
$2,182.50
$1,455.00
$45,000.00
$21.00
$40,000.00
$38,000.00
$16.00
5,000
$776.00
$873.00
$250.00
ROE =
Net income
$386
=
= 0.05507 or 5.51percent
Total equity capital
$45,000 - $38,000
ROA =
Net income
$386
=
= 0.00857 or 0.857 percent
Total assets
$45,000
Earnings per share =
Net income
$386
=
= $0.0771per share
Common equity shares outstanding
5,000
6-11. Paintbrush Valley State Bank has just submitted its Report of Condition and Report of Income to its
principal supervisory agency. The bank reported net income before taxes and securities transactions of $37
million and taxes of $8 million. If its total operating revenues were $950 million, its total assets $2.7 billion,
and its equity capital $250 million, determine the following for Paintbrush Valley:
a. Tax management efficiency ratio.
b. Expense control efficiency ratio.
c. Asset management efficiency ratio.
d. Funds management efficiency ratio.
e. ROE.
Tax management efficiency =
a.
=
$37 million - $8 million
$29 million
=
= 0.7838 or 78.38 percent
$37 million
$37 million
Expense control efficiency =
b.
=
Net income
Pretax net operating income
Pretax net operating income
Total operating revenue
$37 million
= 0.0389 or 3.89 percent
$950 million
Asset management efficiency =
c.
=
Total operating revenue
Total assets
$950 million
= 0.3519 or 35.19 percent
$2,700 million
Fund management efficiency =
d.
ROE =
e.
Total assets
$2,700 million
=
= 10.8x
Total equity capital
$250 million
Net income
$29 million
=
= 0.116 or 11.6 percent
Total equity capital
$250 million
Alternative Scenarios:
a.
Suppose Paintbrush Valley State Bank experienced a 20 percent rise in net before-tax income, with its
tax obligation, operating revenues, assets, and equity unchanged. What would happen to ROE and its
components?
ROE = ROA ×
Total assets
Net income
Total assets
or
×
Total equity Total assets
Total equity
[  $37 × 1.20  - $8
$2,700
×
$2,700 $44.4 - $8 $2,700
or
×
= 0.1456 or 14.56 percent
$250
$2,700
$250
This represents a 25 percent increase in ROE, from 11.60 percent to 14.56 percent. Since the equity
multiplier did not change, this increase in ROE is due to the increase in ROA, from 1.07 percent to 1.35
percent.
b.
If total assets climb by 20 percent, what will happen to Paintbrush’s efficiency ratio and ROE?
Asset management efficiency ratio =
$950
$950
=
 0.2932 or 29.32 percent
$2,700 × 1.2 $3, 240
This represents a decrease of 16.67 percent.
Fund management efficiency =
$3,240 million
= 12.96x
$250 million
This represents a 20% increase.
ROE would not change since the decrease in the asset management efficiency ratio is offset by the increase in
the funds management efficiency ratio.
c.
What effect would a 20 percent higher level of equity capital have upon Paintbrush’s ROE and its
components?
Fund management efficiency =
$2,700
= 9x
$250  1.2
The fund management efficiency ratio decreases from 10.8x to 9x.
ROE = Tax management efficiency ratio × Expense control efficiency ratio × Asset management efficiency ratio
× Funds management efficiency ratio
= 78.38% × 3.89% × 35.19% × 9x = 0.097 or 9.7 percent
A 20 percent increase in equity will decrease the ROE by 16.67 percent from 11.6 percent to 9.7 percent.
Module 5 Recommended Problems: Chapter 7: #1, 3, 4, 10, 11, 13, & 17
7-1. A government bond is currently selling for $1,195 and pays $75 per year in interest for 14 years
when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity if purchased
today for $1,195?
The yield to maturity ( x ) equation for this bond would be:
$1,195 
$75
$75
$75
$75
$75
$1,075



 ... 

(1  YTM )1 (1  YTM ) 2 (1  YTM ) 3 (1  YTM ) 4
(1  YTM )13 (1  YTM )14
Using a financial calculator the YTM = 5.4703 percent.
7-3. U.S. Treasury bills are available for purchase this week at the following prices (based upon $100 par
value) and with the indicated maturities:
a.
b.
c.
$97.25, 182 days.
$95.75, 270 days.
$98.75, 91 days.
Calculate the bank discount rate (DR) on each bill if it is held to maturity. What is the equivalent yield to
maturity (sometimes called the bond-equivalent or coupon-equivalent yield) on each of these Treasury
Bills?
The discount rates and equivalent yields to maturity (bond-equivalent or coupon-equivalent yields) on
each of these Treasury bills are:
Discount Rates
Equivalent Yields to Maturity
a.
100 - 97.25
×
360
100 - 97.25 × 365
= 5.44%
= 5.67%
100
182
97.25
182
b
100 - 95.75
100
×
360
270
100 - 98.75
100
×
360
91
= 5.67%
100 - 95.75
95.75
×
365
270
= 6.00%
100 - 98.75
98.75
×
365
91
= 5.08%
c.
= 4.95%
7-4. Farmville Financial reports a net interest margin of 2.75 percent in its most recent financial report,
with total interest revenue of $95 million and total interest costs of $82 million. What volume of earning
assets must the bank hold? Suppose the bank’s interest revenues rise by 5 percent and its interest costs
and earnings assets increase by 9 percent. What will happen to Farmville’s net interest margin?
The relevant formula is:
Net interest margin = 0.0275 =
$95 mill.  $82 mill.
Total earning assets
Then, total earning assets must be $473 million.
If revenues rise by 5 percent, and interest costs and earnings assets rise by 9 percent, net interest margin
is:
Net interest margin =
$95(1.05)  $82(1.09)
473(1.09)
=
99.75  89.38
515.57
= 0.0201 or 2.01 percent
7-10 Sparkle Savings Association has interest-sensitive assets of $400 million, interest-sensitive liabilities
of $325 million, and total assets of $500 million. What is the bank’s dollar interest-sensitive gap? What is
Sparkle’s relative interest-sensitive gap? What is the value of its interest-sensitivity ratio? Is it asset
sensitive or liability sensitive? Under what scenario for market interest rates will Sparkle experience a
gain in net interest income? A loss in net interest income?
Dollar Interest-Sensitive Gap = ISA – ISL = $400 million − $325 million = $75 million
Relative IS Gap
=
Interest-Sensitivity Ratio
=
ISA
ISL
ISA – ISL
Bank Size
=
=
$400
$325
$75
$500
= 0.15
= 1.23
Here, the interest sensitivity gap is positive and asset sensitive as the interest sensitive assets are greater
than interest sensitive liabilities. Sparkle Savings Association, being an asset sensitive financial firm, will
have a positive relative IS gap and an interest-sensitivity ratio greater than 1. In case of a positive IS gap,
there will be a gain in net interest income if the market interest rates are rising. For a positive IS gap,
there will be a loss in net interest income, if the market interest rates are falling.
7-11 Snowman Bank, N.A., has a portfolio of loans and securities expected to generate cash inflows for
the bank as follows:
Expected Cash Inflows of
Principal and Interest
Payments
$1,275,600
746,872
341,555
62,482
9,871
Annual Period in Which Cash Receipts Are
Expected
Current year
Two years from today
Three years from today
Four years from today
Five years from today
Deposits and money market borrowings are expected to require the following cash outflows:
Expected Cash Outflows of
Principal and Interest
Payments
$1,295,500
831,454
123,897
1,005
-----
Annual Period during Which Cash Payments
Must Be Made
Current year
Two years from today
Three years from today
Four years from today
Five years from today
If the discount rate applicable to the previous cash flows is 4.25 percent, what is the duration of the
Snowman’s portfolio of earning assets and of its deposits and money market borrowings? What will
happen to the bank's total returns, assuming all other factors are held constant, if interest rates rise? If
interest rates fall? Given the size of the duration gap you have calculated, in what type of hedging should
Snowman engage? Please be specific about the hedging transactions needed and their expected effects.
Snowman has asset duration of:
$1,275,600  1   $746,872  2   $341,555  3   $62,482  4   $9,871  5 
DA 
=
(1  0.0425)1
(1  0.0425) 2
(1  0.0425) 3
(1  0.0425) 4
(1  0.0425) 5
$1,275,600   $746,872   $341,555   $62,482   $9,871 
(1  0.0425)1 (1  0.0425) 2 (1  0.0425) 3 (1  0.0425) 4 (1  0.0425) 5
$3, 754,097 / $2,273,192= 1.6515 years
Snowman has a liability duration of:
$1,295,500  1   $831,454  2   $123,897  3   $1,005  4 
(1  0.0425)1
(1  0.0425) 2
(1  0.0425) 3
(1  0.0425) 4
DL 
$1,295,500   $831,454   $123,897   $1,005 
(1  0.0425)1 (1  0.0425) 2 (1  0.0425) 3 (1  0.0425) 4
= $3,104,236 / $2,117,934 = 1.4657 years
Snowman's duration gap = Dollar-weighted duration of asset portfolio − Dollar-weighted duration of
liability portfolio = 1.6515 − 1.4657 = 0.1858 years.
Because Snowman's Asset Duration is greater than its Liability Duration, the bank has a positive duration
gap, which means that the bank's net worth will decrease if interest rates rise, because the value of the
liabilities will decline by less than the value of the assets. On the other hand, if interest rates were to fall,
this positive duration gap will increase the net worth. In this case, the value of the assets will rise by a
greater amount than the value of the liabilities.
Given the magnitude of the duration gap, the management of Snowman Bank, needs to do a
combination of things to close its duration gap between assets and liabilities. If the interest rates are
rising, it probably needs to try to shorten asset duration and lengthen liability duration to move towards
a negative duration gap. The opposite is true if interest rates are expected to fall. The bank can use
financial futures or options to deal with whatever asset-liability gap exists at the moment. The bank may
want to consider securitization or selling some of its assets, reinvesting the cash flows in maturities that
will more closely match its liabilities' maturities. The bank may also consider negotiating some interestrate swaps to change the cash flow patterns of its liabilities to more closely match its asset maturities.
7-13. Conway Thrift Association reports an average asset duration of 7 years and an average liability
duration of 4 years. In its latest financial report, the association recorded total assets of $1.8 billion and
total liabilities of $1.5 billion. If interest rates began at 5 percent and then suddenly climbed to 6
percent, what change will occur in the value of Conway’s net worth? By how much would Conway’s net
worth change if, instead of rising, interest rates fell from 5 percent to 4.5 percent?
The key formula is:

Change in net worth =  DA 

 

Δr
Δr
 A    DL 
 L
(1+r)
(1+r)
 

For the change in interest rates from 5 to 6 percent, change in net worth will be:

 

0.01
0.01
  7 
 1.8   1.4657 
 1.5
(1+0.05)
(1+0.05)

 

= – $0.12 billion – (–$0.05714 billion)
= – $0.06286 billion
On the other hand, if interest rates decline from 5 to 4.5 percent, change in net worth will be:

 

0.005
0.005
  7 
 1.8   1.4657 
 1.5
(1+0.05)
(1+0.05)

 

= + $0.06 billion – $0.02857 billion
= + $0.03143 billion
7-17 A government bond currently carries a yield to maturity of 6 percent and a market price of
$1,168.49. If the bond promises to pay $100 in interest annually for five years, what is its current
duration?
The duration of the bond is computed as follows:
($100 1) ($100  2) ($100  3) ($100  4) ($1,100  5)




4,950.98
(1  .06)1
(1  .06) 2
(1  .06)3
(1  .06) 4
(1  .06) 5
D 

$100
$100
$100
$100
$1,100
1,168.5




1
2
3
4
(1  .06) (1  .06) (1  .06) (1  .06) (1  .06) 5
Therefore, the current duration of the bond is 4.23 years.
Module 6 Recommended Problems: Chapter 8: #2-4, 7-10; Chapter 9: #1 & 5
8-2 Use the quotes of Eurodollar futures contracts traded on the Chicago Mercantile Exchange as shown
below to answer the following questions:
Open
High
Low
Eurodollar (CME)-$1,000,000; pts. of 100%
Jun 08 97.2725 97.2875 97.2025
Jly 08 97.2150 97.2250 97.0900
Aug 08 97.1200 97.1200 96.9500
Sep 08 97.1600 97.1850 96.8300
Dec 08 96.9750 97.0050 96.5500
Settle
Chg
High
97.2150
97.1200
96.9850
96.8850
96.6050
−.0520
−.1150
−.2150
−.2850
−.3800
98.2550
98.1850
98.2200
98.3350
98.2650
Lifetime
High/Low
Low
Low
Open Int
91.6800
97.0300
96.9500
91.6800
91.5700
1,264,397
13,725
2,929
1,453,920
1,384,300
Mar 09
Jun 09
Sep 09
Dec 09
Mar 10
96.8850
96.6900
96.4600
96.1650
95.9500
96.9200
96.7350
96.4900
96.2000
95.9850
96.4000
96.2200
96.0200
95.7750
95.5900
96.4550
96.2600
96.0450
95.8000
95.6150
−.4400
−.4500
−.4200
−.3700
−.3350
98.1850
98.0000
97.7700
97.5050
97.2750
91.5750
91.3100
91.2600
91.1600
91.4850
1,229,271
985,412
817,642
607,401
474,017
a.
What is the annualized discount yield based on the “low” index price for the nearest
March contract?
The annualized discount yield is (100 – 96.40) = 3.60 percent
b.
If your financial firm took a short position at the high price for the day for 15 contracts,
what would be the dollar gain or loss at settlement on June 09?
Selling at a high price, the firm will realize:
($1,000,000 × [1 − ((3.265 ÷ 100) × 90/360)] × 15 = $14,877,562.50
Value at settlement:
($1,000,000 × [1 − ((3.74 ÷ 100) × 90/360)] × 15 = $14,859,750.00
Therefore, the firm will realize a profit of $14,877,562.50 – $14,859,750.00 = $17,812.50.
c.
If you deposited the initial required hedging margin in your equity account upon taking the
position described in (b), what would be the marked-to-market value of your equity account at
settlement?
Initial margin paid = $750 × 15 = $11,250
Realized gain on short position = $17,812.5.
Thus, equity account balance will be: $11,250 + $17,812.50 = $29,062.50
8-3. What kind of futures or options hedges would be called for in the following situations?
a.
Market interest rates are expected to increase and your financial firm’s asset-liability managers
expect to liquidate a portion of their bond portfolio to meet customers’ demands for funds in the
upcoming quarter.
The financial firm can expect a lower price when they sell their bond portfolio if the interest rates
increase. To hedge, in this situation, the firm should short futures contracts on government securities.
The securities will be first sold at a higher price and then purchased when prices are low realizing a
profit, provided interest rate really does rise as expected. A similar gain could be made using put options
on government securities or on financial futures contracts.
b.
Your financial firm has interest-sensitive assets of $79 million and interest-sensitive liabilities of
$88 million over the next 30 days and market interest rates are expected to rise.
The financial firm interest-sensitive liabilities exceed its interest-sensitive assets by $9 million which
means the firm will be open to losses if interest rates rise. The firm could sell financial futures contracts
or use a put option on government securities or financial futures contracts approximately equal in dollar
volume to the $9 million interest-sensitive gap to hedge their risk.
c.
A survey of Tuskee Bank’s corporate loan customers this month (January) indicates that on
balance, this group of firms will need to draw $165 million from their credit lines in February and March,
which is $65 million more than the bank’s management has forecasted and prepared for. The bank’s
economist has predicted a significant increase in money market interest rates over the next 60 days.
The forecast of higher interest rates means the bank must borrow at a higher interest cost which, other
things held equal, will lower its net interest margin. To offset the expected higher borrowing costs the
bank's management should consider a short sale of financial futures contracts or a put option
approximately equal in volume to the additional loan demand. Either government securities or EuroCDs
would be good instruments to consider using in the futures market or in the option market.
d.
Monarch National Bank has interest-sensitive assets greater than interest-sensitive liabilities by
$24 million. If interest rates fall (as suggested by data from the Federal Reserve Board) the bank’s net
interest margin may be squeezed due to the decrease in loan and security revenue.
Monarch National Bank has interest-sensitive assets greater than interest-sensitive liabilities by $24
million. If interest rates fall, the bank's net interest margin will likely be squeezed due to the faster fall in
interest income. Purchases of financial futures contracts followed by a subsequent sale or call options
would probably help here.
e.
Caufield Thrift Association finds that its assets have an average duration of 1.5 years and its
liabilities have an average duration of 1.1 years. The ratio of liabilities to assets is .90. Interest rates are
expected to increase by 50 basis points during the next six months.
Caufield has asset duration of 1.5 years and liabilities duration of 1.1. A 50-basis point rise in moneymarket rates would reduce asset values relative to liabilities which mean its net worth would decline.
The bank should consider short sales of government futures contracts or put options on these securities
or on their related futures contracts.
8-4. Your financial firm needs to borrow $500 million by selling time deposits with 180-day maturities. If
interest rates on comparable deposits are currently at 3.5 percent, what is the cost of issuing these
deposits? Suppose interest rates rise to 4.5 percent. What then will be the cost of these deposits? What
position and types of futures contract could be used to deal with this cost increase?
Marginal deposit interest cost = Amount of new deposits to be issued × Annual interest rate ×
Maturity of deposit in days
Annual interest rate ×
360
At a rate of 3.5 percent, the interest cost is:
$500 million × 0.035 ×
30
= $8,750,000
360
At a rate of 4.5 percent, the interest cost would be:
$500 million × 0.045 ×
30
= $11,250,000
360
A short hedge could be used based upon Eurodollar time deposits, Federal funds futures contracts, or
LIBOR futures contract.
8-7. By what amount will the market value of a Treasury bond futures contract change if interest rates
rise from 5 to 5.25 percent? The underlying Treasury bond has a duration of 10.48 years and the
Treasury bond futures contract is currently being quoted at 113-06. (Remember that Treasury bonds are
quoted in 32nds.)
Change in value of a T-bond futures contract=
-10.48 ×
$113,187.5 × 0.0025
= -2,824.3
1 + 0.005
8-8. Morning View National Bank reports that its assets have a duration of 7 years and its liabilities
average 1.75 years in duration. To hedge this duration gap, management plans to employ Treasury bond
futures, which are currently quoted at 112-170 and have a duration of 10.36 years. Morning View’s latest
financial report shows total assets of $100 million and liabilities of $88 million. Approximately how many
futures contracts will the bank need to cover its overall exposure?


Total liability
 Dliabilities   Total assets
 Dassets 
Total assets


Number of future contracts needed =
Duration of the underlying security named in the futures contract 
Price of the futures contract
88


× 1.75  × $100,000,000
7 100

Number of futures contracts needed = 
= 468.338
10.36 × $112,531.25
Therefore, the bank needs to sell approximately 468 contracts to hedge the duration gap.
8-9 You hedged your financial firm’s exposure to declining interest rates by buying one September call on
Treasury bond futures at the premium quoted on April 15 as referenced in Exhibit 8-4.
a.
How much did you pay for the call in dollars if you chose the strike price of 11000? (Remember
that option premiums are quoted in 64ths.)
Price paid per call = 7.96875 × 1,000 = $7,968.75
b.
Using the following information for trades taking place on June 10. If you sold the call on June
10, due to a change in circumstances, would you have reaped a profit or loss? Determine the amount of
the profit or loss.
9-1. GoodLife National Bank placed a group of 10,000 consumer loans bearing an average expected gross
annual yield of 6 percent in a package to be securitized. The investment bank advising GoodLife
estimates that the securities will sell at a slight discount from par that results in a net interest cost to the
issuer of 4.0 percent. Based on recent experience with similar types of loans, the bank expects 3 percent
of the packaged loans to default without any recovery for the lender and has agreed to set aside a cash
reserve to cover this anticipated loss. Underwriting and advisory services provided by the investment
banking firm will cost 0.5 percent. GoodLife will also seek a liquidity facility, costing 0.5 percent, and a
credit guarantee if actual loan defaults should exceed the expected loan default rate, costing 0.6 percent.
Please calculate the residual income for GoodLife from this loan securitization.
Answer:
The estimated residual income for GoodLife National Bank is:
Gross Loan
Yield
6%
-
Liquidity
Facility
Fee
0.5%
Security
Interest Rate
4%
-
-
Credit
Enhancement
Fee
0.6%
Expected Default On
Packaged Loans
3%
-
=
-
Underwriting
And Advisory Fee
0.5%
Expected
Residual Income
-2.6%
9-5. What type of credit derivatives contract would you recommend for each of the following situations:
a. A bank plans to issue a group of bonds backed by a pool of credit card loans but fears that the
default rate on these credit card loans will rise well above 6 percent of the portfolio – the default
rate it has projected. The bank wants to lower the interest cost on the bonds in case the loan
default rate rises too high.
Answer:
The best solution to this problem is to use credit-linked notes. The interest payments on these
notes will change if significant factors change.
b. A commercial finance company is about to make a $50 million project loan to develop a new
gas field and is concerned about the risks involved if petroleum geologists’ estimates of the
field’s potential yield turn out to be much too high and the field developer cannot repay.
One possibility for solving this problem is to use a credit option. If the developer cannot repay
the loan then the option would pay off. They would lose their premium if the developer can
repay the loan but they are protected against significant loss.
c. A bank holding company plans to offer new bonds in the open market next month, but knows
that the company’s credit rating is being reevaluated by credit-rating agencies. The holding
company wants to avoid paying sharply higher credit costs if its rating is lowered by the
investigating agencies.
A credit risk option would be a good solution to this problem because it protects the bank from
higher borrowing costs in the future. If the borrowing costs rise above the spread specified in
the option contract, the contract would pay off.
d. A mortgage company is concerned about possible excess volatility in its cash flow off a group
of commercial real estate loans supporting the building of several apartment complexes.
Moreover, many of these loans were made at fixed interest rates, and the company’s economics
department has forecast a substantial rise in capital market interest rates. The company’s
management would prefer a more stable cash flow emerging from this group of loans if it could
find a way to achieve it.
One possibility to solve this problem would be to enter into a total return swap with another
bank. The other bank would receive total payments of interest and principal on this loan as well
as the price appreciation on this loan. The original bank would receive LIBOR plus some spread
in return as well as compensation for any depreciation in value of the loan.
e. First National Bank of Ashton serves a relatively limited geographic area centered upon a
moderate-sized metropolitan area. It would like to diversify its loan income but does not wish to
make loans in other market areas due to its lack of familiarity with loan markets outside the
region it has served for many years. Is there a derivative contract that could help the bank
achieve the loan portfolio diversification it seeks?
This bank could enter into a credit swap with another bank. This swap agreement means that
the two banks simply exchange a portion of their customers’ loan repayments. The purpose of
this type of swap agreement is to help the two banks diversify their market area with having to
make loans in an unfamiliar area and further spread out the risk.
US TREASURY BONDS (CBOT)
$100,000, pts & 64ths of 100 pct
Calls
Strike Price
Jul
Sep
10900
—
5-15
11000 3-34
4-31
11100 2-44
3-51
11200 1-59
3-12
11300 1-19
2-40
11400 0-52
2-09
11500 0-31
1-47
Dec
—
4-47
—
3-39
—
2-46
2-22
Jul
0-06
0-12
0-22
0-37
0-61
1-30
2-09
Puts
Sep
0-58
1-10
1-30
1-54
2-18
2-51
3-25
Dec
1-61
2-20
2-46
3-11
—
4-17
4-57
Selling price of the call: 4.484375 × 1,000= $4,484.40
Therefore, loss on sale of call= $4,484.40 – $7968.75= −$3,484.40
8-10 Refer to the information given for problem 9. You hedged your financial firm’s exposure to
increasing interest rates by buying one September put on Treasury bond futures at the premium quoted
for April 15 of the same year (see Exhibit 8-4).
a.
How much did you pay for the put in dollars if you chose the strike price of 11000? (Remember
that premiums are quoted in 64ths.)
Price of put per contract = 0.765625 × 1,000= $765.625
b.
Using the above information for trades on June 10, if you sold the put on June 10 due to a
change in circumstances would you have reaped a profit or loss? Determine the amount of the profit or
loss.
Selling price of put option: 1.15625 × 1,000 = $1,156.25
Therefore, gain on sale of put = $1,156.25 − 765.625= $390.625.
Source of solutions: Ross and Hudgins, 2013, Instructor Manual for Bank Management & Financial Services,
9th ed. New York, NY: Mc-Graw Hill, publisher.