Solution manual bank management and financial services 9th edition by rose, peter chap006

Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

CHAPTER 6
MEASURING AND EVALUATING THE PERFORMANCE OF BANKS AND THEIR
PRINCIPAL COMPETITORS
Goal of This Chapter: The purpose of this chapter is to discover what analytical tools can be
applied to a bank’s financial statements so that management and the public can identify the most
critical problems inside each bank and develop ways to deal with those problems.
Key Topics in this Chapter







Stock Values and Profitability Ratios
Measuring Credit, Liquidity, and Other Risks
Measuring Operating Efficiency
Performance of Competing Financial Firms
Size and Location Effects
Appendix: Using Financial Ratios and Other Analytical Tools to Track Financial Firm
Performance—The UBPR and BHCPR
Chapter Outline

I.
II

Introduction:
Evaluating Performance
A.

Determining Long-Range Objectives
B.
Maximizing the Value of the Firm: A Key Objective for Nearly All FinancialService Institutions
C.
Profitability Ratios: A Surrogate for Stock Values
1.
Key Profitability Ratios
2.
Interpreting Profitability Ratios
D.
Useful Profitability Formulas for Banks and Other Financial-Service Companies
E.
Return on Equity and Its Principal Components
F.
The Return on Assets and Its Principal Components
G.
What a Breakdown of Profitability Measures Can Tell Us
H.
Measuring Risk in Banking and Financial Services
1.
Credit Risk
2.
Liquidity Risk
3.
Market Risk
a.
Price Risk
b.
Interest Rate Risk
4.

Foreign Exchange and Sovereign Risk
5.
Off-Balance-Sheet Risk
6.
Operational (Transactional) Risk
7.
Legal and Compliance Risks
8.
Reputation Risk

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

9.
Strategic Risk
10.
Capital Risk
I.
Other Goals in Banking and Financial-Services Management
III.
Performance Indicators among Banking’s Key Competitors
IV.
The Impact of Size on Performance
A. Size, Location, and Regulatory Bias in Analyzing the Performance of Banks and
Competing Financial Institutions
V.
Summary of the Chapter
Appendix to the Chapter - Using Financial Ratios and Other Analytical Tools to Track FinancialFirm Performance-The UBPR and BHCPR

Concept Checks
6-1. Why should banks and other corporate financial firms be concerned about their level of
profitability and exposure to risk?
Banks in the U.S. and most other countries are like private businesses that must attract capital
from the public to fund their operations. If profits are inadequate or if risk is excessive, they will
have greater difficulty in obtaining capital and their funding costs will grow, eroding
profitability. Bank stockholders, depositors, and bank examiners representing the regulatory
community are all interested in the quality of bank performance. The stockholders are primarily
concerned with profitability as a key factor in determining their total return from holding bank
stock, while depositors (especially large corporate depositors) and examiners typically focus on
bank risk exposure.
6-2. What individuals or groups are likely to be interested in these dimensions of performance
for a financial institution?
The individuals or groups likely to be interested in the dimensions i.e., profitability and risk are –
other banks lending to a particular bank, borrowers, large depositors, holders of long-term debt
capital issued by banks, bank stockholders, and bank examiners representing the regulatory
community.
6-3.

What factors influence the stock price of a financial-service corporation?

A bank's stock price is affected by all those factors affecting its profitability and risk exposure,
particularly its rate of return on equity capital and risk to shareholder earnings. Research
evidence over the years has found that the stock prices of financial institutions is sensitive to
changes in market interest rates, currency exchange rates, and the strength or weakness of the
economy. A bank can raise its stock price by working to achieve policies that increase future
earnings, reduce risk, or pursue a combination of both actions.
6-4. Suppose that a bank is expected to pay an annual dividend of $4 per share on its stock in
the current period and dividends are expected to grow 5 percent a year every year, and the

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

minimum required return-to-equity capital based on the bank's perceived level of risk is 10
percent. Can you estimate the current value of the bank's stock?
In this constant dividend growth rate problem, the current value of the bank's stock would be:
Po =

D1 4  (1+0.05) 4.2
=
=
=$84
(r-g) (0.10-0.05) 0.05

6-5. What is return on equity capital, and what aspect of performance is it supposed to
measure? Can you see how this performance measure might be useful to the managers of
financial firms?
Return on equity capital is the ratio of net income over total equity capital. It represents the rate
of return earned on the funds invested in the bank by its stockholders. They expect to earn a
suitable profit over the risk of their investment.
Return on equity capital can also be calculated using the return on assets as follows:
Total assets
ROE = ROA 
Total equity capital
This ROE–ROA relationship illustrates the fundamental trade-off between risk and return. This
equation reminds us that the return to a financial firm’s shareholders is highly sensitive to how its
assets are financed—the proportion of debt and owner’s capital used. Constructing a risk-return
trade-off table can help the managers understand how much leverage (debt relative to equity)

must be used to achieve a financial institution’s desired rate of return to its stockholders.
6-6
Suppose a bank reports that its net income for the current year is $51 million, its assets
total $1,144 million, and its liabilities amount to $926 million. What is its return on equity
capital? Is the ROE you have calculated good or bad? What information do you need to answer
this last question?
The bank's return on equity capital should be:
ROE 

=

Net income
Total equity capital

$51 million
 0.2339 or 23.39 percent
$1,144 million  $926 million

In order to evaluate the performance of the bank, you have to compare its ROE to the ROE of
some major competitors or the industry average.
6-7
What is the return on assets (ROA), and why is it important? Might the ROA measure be
important to banking’s key competitors?

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Return on assets is the ratio of net income over total assets. The rate of return secured on a bank's

total assets indicates the efficiency of its management in generating net income from all of the
resources (assets) committed to the institution. This would be important to banks and their major
competitors.
6-8. A bank estimates that its total revenues will amount to $155 million and its total expenses
(including taxes) will equal $107 million this year. Its liabilities total $4,960 million while its
equity capital amounts to $52 million. What is the bank's return on assets? Is this ROA high or
low? How could you find out?
The bank's return on assets would be:
ROA 

=

Net income
Total Assets

$155 million  $107 million
 0.0096 or 0.96 percent
$4,960 million  $52 million

The size of this bank's ROA should be compared with the ROA's of other banks similar in size
and location to determine whether this bank's ROA is high or low.
6-9. Why do the managers of financial firms often pay close attention today to the net interest
margin and noninterest margin? To the earnings spread?
The net interest margin (NIM) indicates how successful the bank has been in borrowing funds
from the cheapest sources and in maintaining an adequate spread between its returns on loans
and security investments and the cost of its borrowed funds. If the NIM rises, loan and security
income must be rising or the average cost of funds must be falling or both. A declining NIM is
undesirable because the bank's interest spread is being squeezed, usually because of rising
interest costs on deposits and other borrowings and increased competition today.
In contrast, the noninterest margin reflects the banks spread between its noninterest income (such

as service fees on deposits) and its noninterest expenses (especially salaries and wages and
overhead expenses). For most banks the noninterest margin is negative. Management will usually
attempt to expand fee income, while controlling closely the growth of noninterest expenses in
order to make a negative noninterest margin less negative.
The earnings spread measures the effectiveness of the bank's intermediation function of
borrowing and lending money, which, of course, is the bank's primary way of generating
earnings. As competition increases, the spread between the average yields on assets and the
average cost of liabilities will be squeezed, forcing the bank's management to search for
alternative sources of income, such as fees from various services the bank offers.
6-10. Suppose a banker tells you that his bank in the year just completed had total interest
expenses on all borrowings of $12 million and noninterest expenses of $5 million, while interest
income from earning assets totaled $16 million and noninterest revenues totaled $2 million.
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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Suppose further that assets amounted to $480 million, of which earning assets represented 85
percent of that total while total interest-bearing liabilities amounted to 75 percent of total assets.
See if you can determine this bank's net interest and noninterest margins and its earnings base
and earnings spread for the most recent year.
The bank's net interest and noninterest margins must be:
Net interest margin =

=

 Interest income - Interest expense 
Total assets

$16 million - $12 million

= 0.00833
$480 million

 Noninterest revenues 


Provision for loan and lease losses - Noninterest expenses 

Net noninterest margin =
Total assets
=

$2 million - $5million
= -0.00625
$480 million

The bank's earnings spread and earnings base are:
Earnings spread =

=

$16 million
$12 million
= 0.0059
$480 million × 0.85 $480 million × 0.75

Earnings base =

=

Totalinterest income
Total interestexpense
Total earning assets
Total interest-bearing liablities

Total earning assets
Total assets

$480 million -  $480 million  0.15 
$480 million

= 0.85 or 85 percent

6-11. What are the principal components of ROE, and what does each of these components
measure?
The principal components of ROE are:
a. The net profit margin or the Net after-tax income to Total operating revenues which reflects
the effectiveness of a bank's expense control program and service pricing policies;

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

b. The degree of asset utilization or the ratio of Total operating revenues to Total assets which
measures the effectiveness of the bank's portfolio management policies, especially the mix and
yield on assets; and,
c. The equity multiplier or the ratio of Total assets to Total equity capital which measures a
bank's use of leverage in funding its operations: the sources chosen to fund the financial
institution (debt or equity).

6-12. Suppose a bank has an ROA of 0.80 percent and an equity multiplier of 12X. What is its
ROE? Suppose this bank's ROA falls to 0.60 percent. What size equity multiplier must it have to
hold its ROE unchanged?
The bank's ROE is:
ROE = 0.80 percent ×12 = 9.60 percent.
If ROA falls to 0.60 percent, the bank's ROE and equity multiplier can be determined from:
ROE = 9.60 percent = 0.60 percent × Equity multiplier
Equity Multiplier 

9.60 percent
 16X
0.60 percent

6-13. Suppose a bank reports net income of $12, pre-tax net income of $15, operating revenues
of $100, assets of $600, and $50 in equity capital. What is the bank's ROE? Tax-management
efficiency indicator? Expense control efficiency indicator? Asset management efficiency
indicator? Funds management efficiency indicator?
The bank's ROE must be:
ROE =

$12
= 0.24 or 24 percent
$50

Its tax-management, expense control, asset management, and funds management efficiency
indicators are:
Tax Management Effeciency Indicator =

$12
= 0.8or 80 percent

$15

Expense Control Effeciency Indicator =

$15
= 0.15or15percent
$100

Asset Management Effeciency Indicator =

$100
= 0.1667 or16.67 percent
$600

Fund Management Effeciency Indicator =

$600
= 12x
$50

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Alternative calculation for ROE:
= 0.8 × 0.15 × 0.1667 × 12
= 0.24 or 24 percent

6-14. What are the most important components of ROA, and what aspects of a financial

institution’s performance do they reflect?
The principal components of ROA are:
a. Total Interest Income less Total Interest Expense divided by Total Assets, measuring a bank's
success at intermediating funds between borrowers and lenders.
b. Provision for Loan Losses divided by Total Assets, which measures management's ability to
control loan losses and manage a bank's accrual expense.
c. Noninterest Income less Noninterest Expenses divided by Total Assets, which indicates the
ability of management to control salaries and wages, other noninterest costs of operations and
generate income from handling customer transactions.
d. Applicable Taxes divided by Total Assets, which is an index of tax management effectiveness,
measures the financial firm’s share of the cost of government securities.
6-15. If a bank has a net interest margin of 2.50%, a noninterest margin of −1.85%, and a ratio
of provision for loan losses, taxes, security gains, and extraordinary items of −0.47%, what is its
ROA?
The bank's ROA must be:
ROA = Net interest margin + Noninterest margin – Ratio of provision for loan
losses, taxes, security gains, and extraordinary items
ROA = 2.5 percent + (−1.85 percent) – (−0.47 percent) = 1.12 percent
6-16. To what different kinds of risk are banks and their financial-service competitors subjected
today?
a. Credit Risk: the probability that the loans and securities the bank holds will not pay out as
promised.
b. Liquidity Risk: the probability that the bank will not have sufficient cash on hand in the
volume needed precisely when cash demands arise.
c. Market Risk: the probability that the market value of assets held by the bank will decline due
to falling market prices. Market risk is composed of both price risk and interest rate risk.

6-7

Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Price Risk: the probability or possibility that the value of bond portfolios and
stockholders’ equity may decline due to market prices movement against the financial
firm.
Interest-Rate Risk: the possibility or probability that the interest rates will change,
subjecting the bank to incur a lower margin of profit or a lower value for the firm’s
capital.
d. Foreign Exchange and Sovereign Risk: the uncertainty that due to fluctuation in currency
prices, assets denominated in foreign currencies may fall, forcing the write-down of these assets
on its Balance Sheet.
e. Off-Balance-Sheet Risk: the probability that the volume of off-balance-sheet commitments far
exceeds the volume of conventional assets.
f. Operational (Transactional) Risk: the uncertainty regarding a financial firm’s earnings due to
failures in computer systems, employee misconduct, floods, lightening strikes and other similar
events.
g. Legal and Compliance Risk: the uncertainty regarding a financial firm’s earnings due to
actions taken by our legal system or due to a violation of rules and regulations.
h. Reputation Risk: the uncertainty due to public opinion or the variability in earnings due to
positive or negative publicity about the financial firm.
i. Strategic Risk: the uncertainty in earnings due to adverse business decisions, lack of
responsiveness to industry changes, and other poor decisions by management.
j. Capital Risk: the risk that the value of the assets will decline below the value of the liabilities.
All of the other risks listed above can affect earnings and the value of the assets and liabilities
and therefore can have an effect on the capital position of the firm.
6-17. What items on a bank's balance sheet and income statement can be used to measure its
risk exposure? To what other financial institutions do these risk measures seem to apply?
There are several alternative measures of risk in banking and financial service firms. Capital risk
is often measured by bank capital ratios, such as the ratio of total capital to total assets or total
capital to risk assets. Credit risk can be tracked by such ratios as net loan losses to total loans or

relative to total capital. Liquidity risk can be followed by using such ratios as cash assets and
government securities to total assets or by purchased funds to total assets. Interest-rate risk may
be indicated by such ratios as interest-sensitive assets to interest-sensitive liabilities or the ratio
of money-market assets to money-market borrowings.
These risk measures also apply to those nonbank financial institutions that are private, profit
making corporations, including stockholder-owned thrift institutions, insurance companies,

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

finance and credit card companies, security broker and dealer firms, mutual funds, and hedge
funds.
6-18. A bank reports that the total amount of its net loans and leases outstanding is $936
million, its assets total $1,324 million, its equity capital amounts to $110 million, and it holds
$1,150 million in deposits, all expressed in book value. The estimated market values of the
bank's total assets and equity capital are $1,443 million and $130 million, respectively. The
bank's stock is currently valued at $60 per share with annual per-share earnings of $2.50.
Uninsured deposits amount to $243 million and money-market borrowings total $132 million,
while nonperforming loans currently amount to $43 million and the bank just charged off $21
million in loans. Calculate as many of the risk measures as you can from the foregoing data.
1. Liquidity Risk:
Net Loans and Leases
$936 million
=
= 0.706949or 70.69 percent
Total Assets
$1,324 million
2. Interest Rate Risk:

Uninsured Deposits
$243million
=
= 0.211304 or 21.13percent
Total Deposits
$1,150 million
3. Capital Risk:
Equity Capital
$130 million
=
= 0.09009 or 9.01percent
Risk Assets
$1,443 million
Stock Price
$60

 24
Earnings per Share $2.50
Book Value of Assets
$1,324 million
=
= 0.917533or 91.75 percent
Market Value of Assets
$1,443 million
4. Credit Risk:
Nonperforming Assets
$43million
=
= 0.04594or 4.59 percent
Net Loans and Leases

$936 million
Charge-offs of Loans
$21million
=
= 0.022436 or 2.24 percent
Total Loans and Leases
$936 million
5. Price Risk:

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Book Value of Assets
$1,324 million
=
= 0.917533or 91.75 percent
Market Value of Assets
$1,443 million

Problems and Projects
6-1. An investor holds the stock of Last-But-Not-Least Financials and expects to receive a
dividend of $4.75 per share at the end of the year. Stock analysts recently predicted that the
bank’s dividends will grow at approximately 3 percent a year indefinitely into the future. If this
is true, and if the appropriate risk-adjusted cost of capital (discount rate) for the bank is 14
percent, what should be the current price per share of Last-But-Not-Least Financials’ stock?
P0 

D1

4.75

 $43.18
 r  g   0.14  0.03

6-2. Suppose that stockbrokers have projected that Jamestown Savings will pay a dividend of
$2.50 per share on its common stock at the end of the year; a dividend of $3.25 per share is
expected for the next year, and $4.00 per share in the following two years. The risk-adjusted cost
of capital for banks in Jamestown’s risk class is 15 percent. If an investor holding Jamestown’s
stock plans to hold that stock for only four years and hopes to sell it at a price of $50 per share,
what should the value of the bank’s stock be in today’s market?
P0 

2.50
3.25
4
4
50




2
3
4
 1  0.15  1  0.15  1  0.15   1  0.15  1  0.15 4

P0 = $38.14 per share.
6-3
Oriole Savings Association has a ratio of equity capital to total assets of 9 percent. In

contrast, Cardinal Savings reports an equity-capital-to-asset ratio of 7 percent. What is the value
of the equity multiplier for each of these institutions? Suppose that both institutions have an
ROA of 0.67 percent. What must each institution’s return on equity capital be? What do your
calculations tell you about the benefits of having as little equity capital as regulations or the
marketplace will allow?
Oriole Savings Association has an equity-to-asset ratio of 9 percent which means its equity
multiplier must be:
1
1
=
= 11.11X
0.09
 Equity Capital 


Assets



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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

In contrast, Cardinal Savings has an equity-to-asset ratio of 7 percent which means it has an
equity multiplier of:
1
1
=
= 14.29X

0.07
 Equity Capital 


Assets


With an ROA of 0.67 percent Oriole Savings Association would have an ROE of:
ROE = 0.67 × 11.11x = 7.44 percent.
With an ROA of 0.67 percent Cardinal Savings would have an ROE of:
ROE = 0.67 × 14.29x = 9.57 percent
In this case Cardinal Savings is making greater use of financial leverage and is generating a
higher return on equity capital as compared to Oriole Savings Association.
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
$50
Interest and dividends on securities
6
Total interest income
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
Total noninterest expenses
Net noninterest income

10
5
20

Pretax operating income
Securities gains (or losses)
Pretax net operating income
Taxes
Net operating income
Net extraordinary income

6-11

10*
5
2
17
-2
8

2
10
2
8
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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Net income
*Note: the bank currently has 40 FTE employees.

7

Smiling Merchants National Bank
Report of Condition
Assets
Liabilities
Cash and deposits due from banks $100 Demand deposits
Investment securities
150 Savings deposits
Federal funds sold
10 Time deposits
Net loans
700 Federal funds purchased
(Allowance for loan losses = 25)
Total liabilities
(Unearned income on loans = 5)
Equity capital
Net Fixed Assets

50 Common stock
Surplus
Total assets
980 Retained earnings
Total Capital
Total earnings assets
860 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?
1.

ROE =

2.

ROA =

3.

4.

Net income
$7
=
= 0.0778 or 7.78 percent
Total equity capital
$90

Net income
$7
=

= 0.00714 or 0.71 percent
Total assets
$980
Net interest income
$10
Net interest margin =
=
= 0.0120 or 1.02 percent
Total assets
$980
Net noninterest margin =

Net noninterest income
-$2
=
= -0.00204 or -0.20 percent
Total assets
$980

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

5.

Net operating margin =
=

6.

$8
= 0.008163 or 0.82 percent
$980

Earnings spread =
=

Total operating revenues - Total operating expenses
Total assets

Totalinterest income
Totalinterest expenses
Total earnings assets Totalinterest-bearing liabilities

$56
$46
= 0.002103 or 0.21 percent
$860 $650

7.

Net profit margin =

Net income
$7
=
= 0.092105 or 9.21 percent
Total operating revenues
$54

8.

Asset utilization =

Total operating revenues
$76
=
= 0.077551 or 7.76 percent
Total assets
$980

9.

Equity multiplier =

Total assets
$980
=
= 10.89x
Total equity capital
$90

10.

Tax Management =

11.

Expense control effeciency =

12.

Asset managment effeciency ratio =
=

Net income
$7
=
= 0.7 or 70 percent
Pretax net operating income
$10
Pretax net operating income
$10
=
= 0.131579 or 13.16 percent
Total operating revenue
$76
Total operating revenues
Total assets

$76
= 0.07755 or 7.76 percent
$980

13.

Funds Managment Effeciency Ratio =

14.

Operating effeciency ratio =

Total assets
$980
=
= 10.89x
Total equity capital
$90

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.
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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

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
tax-management 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
Taxes paid
Shares of common stock outstanding
Noninterest income
Noninterest expense
Provision for loan losses

$2,250.00

1,500.00
45,000.00
21.00
40,000.00
38,000.00
16.00
5,000
$800.00
900.00
250.00

Please calculate:
ROE
ROA
Net interest margin
Earnings per share

6-14


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

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
=
= 0.009or 0.90 percent
Total assets
$45,000
Net interest income
$750
=
= 0.01667 or1.67 percent
Total assets
$45,000

Net interest margin =

Earnings per share =

Net income
$405
=
= $0.081per share
Common equity shares outstanding
5,000

Net noninterest margin =

Net noninterest income
-$350
=
= -0.0078or -0.78percent
Total assets
$45,000

Total operating revenues-Total operating expenses
$400
=
Total assets
$45,000
= 0.00889 or 0.89 percent

Net operating margin =

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
Shares of Common Stock outstanding

Noninterest income
Noninterest expense
Provision for loan losses
ROE =

$2,317.50
$1,545.00
$45,000.00
$21.00
$40,000.00
$38,000.00
$16.00
5,000
$824.00
$927.00
$250.00

Net income
$425
=
= 0.06064 or 6.06 percent
Total equity capital
$45,000 - $38,000

6-15


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

ROA =

Net income
$425
=
= 0.00943or 0.943percent
Total assets
$45,000

Earnings per share =

Net income
$425
=
= $0.0849 per share
Common equityshares 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 equityshares outstanding
5,000

6-6. Zebra Group holds total assets of $25 billion and equity capital of $2 billion and has just
posted an ROA of 0.95 percent. What is the financial firm’s ROE?
ROE = ROA × 

Total assets
$25
= 0.95 percent ×
= 0.11875 or 11.875 percent
Total equity capital
$2

Alternative Scenarios:
a.
Suppose Zebra Group finds its ROA climbing by 25 percent, with assets and equity
capital unchanged. What will happen to its ROE? Why?
ROA increases by 25 percent, with no change in assets or equity capital.
Therefore, the new ROA = 0.95 × 1.25 = 0.01188 or 1.188 percent.
6-16

Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

$25
= 0.14844 or 14.84 percent
$2
This represents a 25 percent increase in ROE. With no changes in assets or equity, the investors'
funds are more effectively utilized, generating additional income and making the bank more
profitable.
New ROE = 1.188 percent ×

b:
On the other hand, suppose the bank’s ROA drops by 25 percent. If total assets and equity
capital hold their present positions, what change will occur in ROE?
ROA decreases by 25 percent, with no change in equity or assets.
Therefore, the new ROA = 0.95 × 0.75 = 0.007125 or 0.7125 percent.
New ROE = 0.7125 percent ×

$25
= 0.08906 or 8.91 percent
$2

This represents a 25% decrease in ROE. The bank's management has been less efficient, in this
case, in managing their lending and/or investing functions or their operating costs.
c.
If ROA at Zebra Group remains fixed at 0.95 percent but both total assets and equity
double, how does ROE change? Why?
ROA is constant at 0.95 percent, and Total assets double in size to $50 billion and equity capital
doubles in size to $4 billion.

Therefore, the equity multiplier (i.e. total assets ÷ equity capital) remains the same (E.M. =
$50 ÷ $4 = 12.5X). As a result, ROE does not changes from the original situation (0.95 percent ×
12.5 = 11.875 percent).
This represents no change in ROE. The bank's management has been efficient, in this case, in
managing their lending and/or investing functions or their operating costs.
d.
How would a decline in total assets and equity by half (with ROA still at 0.95 percent)
affect the bank’s ROE?
This, of course, is just the reverse of scenario c. Since the changes in both assets and equity
capital are the same, the ratio of the two (i.e., the equity multiplier) remains constant. As a result,
there is again no change in ROE.
6-7. OK State Bank reports total operating revenues of $150 million, with total operating
expenses of $125 million, and owes taxes of $5 million. It has total assets of $1.00 billion and
total liabilities of $850 million. What is the bank’s ROE?
Net income after taxes = $150 million − $125 million − $5 million = $20 million
Equity capital = $1.00 billion − $850 million = $150 million

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Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

ROE =

Net income after taxes
$20 million
=
= 0.133 or 13.33 percent
Equity capital
$150 million

Alternative Scenarios:
a.
How will the ROE for OK State Bank change if total operating expenses, taxes, and total
operating revenues each grow by 10 percent while assets and liabilities remain fixed?
Total operating revenues = $150 million × 1.10 = $165 million
Total operating expenses = $125 million × 1.10 = $137.5million
Tax liability = $5 million × 1.10 = $5.5 million
Net income after taxes = $165 - $137.5 - $5.50 = $22 million
ROE =

$22 million
= 0.1467 or 14.67 percent
$150 million

Change in ROE =

 14.67 percent - 13.33 percent 
13.33 percent

= 10 percent

b.
Suppose OK State’s total assets and total liabilities increase by 10 percent, but its
revenues and expenses (including taxes) are unchanged. How will the bank’s ROE change?
Total assets increase by 10% (Total assets = $ 1.0 × 1.10 = $1.1 billion)
Total liabilities increase by 10% (Total liabilities = $850 million × 1.10 = $935
Revenues and expenses (including taxes) remain unchanged.
Equity capital = $1.1 billion − $935 million = $165 million
ROE =

$20 million
= 0.1212 or 12.12 percent
$165 million

Change in ROE =

 12.12 percent - 13.33 percent 
13.33 percent

= -9.09 percent

c.
Can you determine what will happen to ROE if both operating revenues and expenses
(including taxes) decline by 10 percent, with the bank’s total assets and liabilities held constant?
Total revenues decline by 10% (Total revenues = $150 million × 0.90 = $135million)
Total expenses decline by 10% (Total expenses = $125 million × 0.90 = $112.5 million)
Tax liability declines by 10% (Tax liability = $5 × 0.9 = $4.5 million)
Assets and liabilities remain unchanged (Therefore, equity remains unchanged)
Net income after tax = $135 million – 112.5 million − $4.5 million = $18

6-18


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

$18 million
= 0.12 or 12 percent
$150 million
 12 percent - 13.33 percent  = -10 percent

Change in ROE =
13.33 percent
ROE =

d.
What does ROE become if OK State’s assets and liabilities decrease by 10 percent, while
its operating revenues, taxes, and operating expenses do not change?
Total assets = $1.0 billion × 0.9 = $900 million
Total liabilities = $850 million × 0.9 =$765 million
Equity capital = $900 million − $765 million = $135 million
ROE =

$20 million
= 0.1481 or 14.81 percent
$135 million

Change in ROE =

 14.81 percent - 13.33 percent 
13.33 percent

= 11.11 percent

6-8. Suppose a stockholder-owned thrift institution is projected to achieve a 0.90 percent ROA
during the coming year. What must its ratio of total assets to equity capital be if it is to achieve
its target ROE of 12 percent? If ROA unexpectedly falls to 0.80 percent, what assets-to-capital
ratio must it then have to reach a 12 percent ROE?
ROE  ROA 

Total assets

Total equity capital

Total assets
ROE
12 percent
=
=
= 13.33x
Total equity capital
ROA
0.90 percent
If ROA unexpectedly falls to 0.80 percent and target ROE remains 12 percent:
12 percent  0.8 percent 

Total assets
Total equity capital

Total assets
12 percent
=
= 15x
Total equity capital
0.80 percent
6-9. Conway County National Bank presents us with these figures for the year just concluded.
Please determine the net profit margin, equity multiplier, asset utilization ratio, and ROE.
Net income
Total operating revenues
Total assets

$

30.00
135.00
1,750.00

6-19


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Total equity capital accounts

170.00

Net income
$30 million
=
= 0.2222 or 22.22 percent
Total operating revenue
$135 million

a. Net profit margin =

b. Asset utilization =

Total operating revenue
$135 million
=
= 0.0771 or 7.71 percent
Total assets

$1, 750 million

c. Equity multiplier =

Total assets
$1,750 million
=
= 10.29x
Total equity capital
$170 million

d. Net profit margin =

Net income
$30 million
=
= 0.1765 or 17.65 percent
Total equity capital
$170 million

6-10. Runnals National Bank has experienced the following trends over the past five years (all
figures in millions of dollars):

Year
1
2
3
4
5

Net Income
After-Tax
$2.65
2.75
3.25
3.65
4.00

Total
Operating
Revenues
$26.50
30.10
39.80
47.50
55.90

Total Assets
$300.00
315.00
331.00
347.00
365.00

Total
Liabilitie
s
$273.00
288.00
301.00

314.00
329.00

Determine the figures for ROE, profit margin, asset utilization, and equity multiplier for this
bank. Are any adverse trends evident? Where would you recommend that management look to
deal with the bank’s emerging problem(s)?
Year
1
2
3
4
5

Profit
Margin
10.00%
9.14%
8.17%
7.68%
7.16%

Asset
Utilization
8.83%
9.56%
12.02%
13.69%
15.32%

Equity

Multiplier
11.11x
11.67x
11.03x
10.52x
10.14x

ROA
0.88%
0.87%
0.98%
1.05%
1.10%

ROE
9.81%
10.19%
10.83%
11.06%
11.11%

If we look at the entire five-year period, Runnal's profit margin has declined constantly. This can
be viewed as troublesome when we note that net income and total operating revenues have
nearly doubled during the five-year period. Two potential areas that management should
investigate are (1) the mix of funding sources and (2) non-interest expenses.
Runnal’s asset utilization has shown a constant growth trend over the five years due to careful
allocation of assets towards the highest yielding loans and investments while avoiding excessive
6-20

Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

risk. The bank’s equity multiplier increased in the first year and started reducing the subsequent
years as its equity capital increased in all the years.
Runnal experiences an increase in ROE over the years as the expanding asset utilization offsets
decreases in net profit margin and equity multiplier. Since ROE has grown much more rapidly
than ROA, we should be concerned that Runnal is increasing its liability sources of funding,
thereby increasing its leverage to keep its ROE growing. This can cause serious problems with
its income as interest rates rise, driving up its cost of funds.
With regard to its noninterest expenses, if these are growing faster than the bank's noninterest
income, then there is greater pressure on the bank's net interest margin to offset the increasing
negative spread between noninterest income and noninterest expenses.
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.
a.

=

Tax management efficiency =

Net income
Pretax net operating income

$37 million - $8 million
$29 million
=
= 0.7838 or 78.38 percent
$37 million
$37 million
Pretax net operating income
Total operating revenue

b.

Expense control efficiency =

=

$37 million
= 0.0389 or 3.89 percent
$950 million
Total operating revenue
Total assets

c.

Asset management efficiency =

=

$950 million
= 0.3519 or 35.19 percent

$2,700 million

d.

Fund management efficiency =

Total assets
$2,700 million
=
= 10.8x
Total equity capital
$250 million

6-21


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

e.

ROE =

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.

6-22


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

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.
6-12. Using this information for Eagle Bank and Trust Company (all figures in millions),
calculate the bank's net interest margin, noninterest margin, and ROA.
Interest income
Interest expense
Provision for loan losses
Security gains (or losses)
Noninterest expense
Noninterest income
Extraordinary net gains
Total assets
a. Net interest margin =

=

$

75

61
6
2
8
5
1
1,000

Interest income - Interest expenses
Total assets

$75 - $61
$14
=
 0.014 or 1.40%
$1,000
$1,000

b. Net noninterest margin =

=

Noninterest income - Noninterest expenses
Total assets

$5 - $8
-$3
=
  0.003 or -0.3%
$1,000

$1,000

c. ROA =

Net income
$8
=
= 0.008 or 0.80 percent
Total assets $1,000

6-13. Mountain Savings reported these figures (in millions) on its income statement for the past
five years. Calculate the institution’s ROA in each year. Are there any adverse trends? Any
favorable trends? What seems to be happening to this institution?

Gross interest income
Interest expenses

Current
Year
$40
24

6-23

One
Year
Ago
$41
25

Two
Years
Ago
$42
26

Three
Years
Ago
$43
27

Four
Years
Ago
$44
28


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

Net interest income
Provision for loan losses
Net interest income after
Loan loss provision
Noninterest income
Noninterest expense
Net noninterest income
Income before taxes
Income taxes owed

Net income after taxes
but before gains (losses)
Net securities gains (losses)
Net income
Total assets
ROA

16
2
14

16
1
15

16
1
15

16
0
16

16
0
16

4
8
(4)

10
1
9

4
7
(3)
12
1
11

3
7
(4)
11
0
11

2
6
(4)
12
1
11

1
5
(4)
12
0

12

2
11
885
1.24%

2
13
880
1.48%

1
12
875
1.37%

0
11
860
1.28%

0
12
850
1.41%

Mountain's ROA has remained consistent, in the range of 1.24 percent to 1.48 percent, over the
last five years.
The gross interest income has consistently declined over the last five years. However, the

company has also managed to decrease interest expenses at the same rate. A similar trend is seen
in the movement of noninterest income and noninterest expense, offsetting the effects of each
other. Thus, the company has been able to maintain a constant level of net income from
operations.
Growth in interest and noninterest income has been in level with the growth in interest and
noninterest expense, as well as a reduction in the allowance for loan losses, resulting in a
constant level of net income from operations.
6-14. An analysis of the BHCPR reports on BB&T is presented in this chapter’s appendix. We
examined a wide variety of profitability measures for that bank, including ROA, ROE, net profit
margin, net interest and operating margins, and asset utilization. However, the various measures
of earnings risk, credit risk, liquidity risk, market risk (price risk and interest rate risk), and
capital risk were not discussed in detail. Using the data in Tables 6-5 through 6-9, calculate each
of these dimensions of risk for BB&T for the most recent two years and discuss how the bank’s
risk exposure appears to be changing over time. What steps would you recommend to
management to deal with any risk exposure problems you observe?
Note to instructors: The Bank Holding Performance Report (BHCPR) is provided to each bank
by the Federal Financial Institutions Examination Council. The BHCPR is prepared from the call
reports of condition and income that are filed quarterly by all banks. It (the BHCPR) is for the
use of regulators and management to assess how well the bank is performing relative to its
internal goals and its peer group.
The user's guide to the BHCPR is available from the FFIEC for a nominal fee and details the
various ratios and comparative data contained in the BHCPR. The actual BHCPR is much more

6-24


Chapter 06 - Measuring and Evaluating the Performance of Banks and Their Principal Competitors

detailed than the example provided in the text as Tables 6-5 through 6-9. These exhibits are for
illustrative purposes and do not contain all the information that is necessary to calculate all the

risk measures described in the text. The instructor may find it helpful to use BHCPRs provided
by a few local banks in class discussions. Those actual BHCPRs allow the students to calculate
the full range of risk and return measures and expand discussion of the concepts and ratios
considerably.

6-25