Solution manual bank management and financial services 9th edition by rose, peter chap015

Chapter 15 - The Management of Capital

CHAPTER 15
THE MANAGEMENT OF CAPITAL
Goal of This Chapter: The purpose of this chapter is to discover why capital—particularly equity
capital—is so important for financial institutions, to learn how managers and regulators assess
the adequacy of an institution’s capital position, and to explain the ways that management can
raise new capital.
Key Topics in This Chapter
•
•
•
•
•
•
•

The Many Tasks of Capital
Capital and Risk Exposures
Types of Capital In Use
Capital as the Centerpiece of Regulation
Basel I and Basel II
Capital Regulation in the Wake of the Great Recession/Basel III
Planning to Meet Capital Needs
Chapter Outline

I.
II.

III.

IV.

Introduction
The Many Tasks Capital Performs
A.
Cushion Against Risk of Failure
B.
Provides Funds Needed to Begin Operations
C.
Promotes Public Confidence
D.
Provides Funds for Future Growth and New Services
E.
Regulator of Growth
F.
Capital Plays a Role in Mergers
G.
Limits How Much Risk Exposure Banks and Competing Firms Can Accept
Capital and Risk
A.
Key Risks in Banking and Financial Institutions’ Management
1.
Credit Risk
2.
Liquidity Risk
3.
Interest Rate Risk
4.
Operational Risk
5.

Exchange Risk
6.
Crime Risk
B.
Defenses against Risk
1.
Quality Management
2.
Diversification
a.
Portfolio Diversification
b.
Geographic Diversification
3.
Deposit Insurance
4.
Owners' Capital
Types of Capital in Use
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Chapter 15 - The Management of Capital

V.

VI.

VII.

VIII.

A.
Common Stock
B.
Preferred Stock
C.
Surplus
D.
Undivided Profits
E.
Equity Reserves
F.
Subordinated Debentures
G.
Minority Interest in Consolidated Subsidiaries
H.
Equity Commitment Notes
Relative Importance of Different Sources of Capital
One of the Great Issues in the History of Banking: How Much Capital Is Really Needed?
A.
Regulatory Approach to Evaluating Capital Needs
1.
Reasons for Capital Regulation
2.
Research Evidence
The Basel Agreement on International Capital Standards: A Continuing Historic Contract
among Leading Nations
A.
Basel I
1.

Tier 1 (Core) Capital
2.
Tier 2 (Supplemental) Capital
3.
Calculating Risk-Weighted Assets
4.
Calculating the Capital-to-Risk-Weighted Assets Ratio
B.
Capital Requirements Attached to Derivatives
1.
Bank Capital Standards and Market Risk
2.
Value at Risk (VaR) Models Responding to Market Risk
3.
Limitations and Challenges of VaR and Internal Modeling
C.
Basel II
1
Pillars of Basel II
2.
Internal Risk Assessment
3.
Operational Risk
4.
Basel II and Credit Risk Models
5.
A Dual (Large-Bank, Small-Bank) Set of Rules
6.
Problems Accompanying the Implementation of Basel II
D.

Basel III: Another Major Regulatory Step Underway, Born in Global Crisis
Changing Capital Standards Inside the United States
A.
FDIC Improvement Act
B.
Prompt Corrective Action
1.
Well capitalized
2.
Adequately capitalized
3.
Undercapitalized
4.
Significantly undercapitalized
5.
Critically undercapitalized
Planning to Meet Capital Needs
A.
Raising Capital Internally
1.
Dividend Policy
2.
How Fast Must Internally Generated Funds Grow?
B.
Raising Capital Externally
1.
Selling Common Stock

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IX.

2.
Selling Preferred Stock
3.
Issuing Debt Capital
4.
Selling Assets and Leasing Facilities
5.
Swapping Stock for Debt Securities
Choosing the Best Alternative for Raising Outside Capital
Summary of the Chapter
Concept Checks

15-1. What does the term capital mean as it applies to financial institutions?
Funds contributed to a financial institution primarily by its owners, consisting mainly of stock,
equity reserves, surplus, and retained earnings, plus any long-term debt issued that qualifies
under regulations.
15-2. What crucial roles does capital play in the management and viability of a financial firm?
Capital provides the long-term, permanent funding that is needed to construct facilities and
provide a base for the future expansion of assets. Capital also absorbs operating losses until
management has a chance to correct the institution's problems. From a regulatory perspective
capital limits the growth of risky assets. Capital promotes public confidence and reassures
creditors concerning an institution’s financial strength. Also, capital provides funds for the
development of new services and facilities. Recently, capital has also played a key role in the
rapid growth of mergers among financial firms.
15-3. What are the links between capital and risk exposure among financial-service providers?

Capital functions as a cushion to absorb losses until management can correct the problems
generating those losses. Institutions face many different kinds of risk: (1) crime risk, (2) interest
rate risk, (3) credit risk, (4) liquidity risk, (5) exchange risk and (6) operational risk. Capital
represents the ultimate line of defense against these risks when all other defenses fail.
15-4. What forms of capital are in use today? What are the key differences between the
different types of capital?
The principal forms of bank capital include common and preferred stock, surplus, undivided
profits, equity reserves, subordinated debentures, minority interest in consolidated subsidiaries,
and equity commitment notes. Common stock represents the par value of common equity shares
outstanding, while surplus is the amount paid over par value for the stock when it is sold.
Preferred stock is a special type of ownership where dividends are fixed and stockholders
generally do not have a vote on major activities undertaken by the firm. Retained earnings or
undivided profits are the accumulated earnings of the firm kept to reinvest back in the company.
Subordinated debentures are long term debt instruments that do not represent ownership claims
and are contributed by outside investors. Equity reserves represents the funds set aside for
contingencies, such as legal action against the institution, reserve for dividend expected to be
paid but not yet declared, or shrinking fund to retire stock or debt in the future. Minority interests

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in consolidated subsidiaries are one in which financial firms hold ownership shares in other
businesses. Equity commitment notes are one in which debt securities are repaid from the sale of
stock.
15-5. Measured by volume and percentage of total capital, what are the most important and
least important forms of capital held by U.S.-insured banks? Why do you think this is so?
The most important form of capital is surplus, accounting for about two-thirds of all long-term
debt and equity capital. This is followed by retained earnings and capital reserves representing

about one-fifth of U.S. banks’ capitalization. The remainder is divided up among all other types
of capital, including long-term debt (subordinated notes and debentures) at close to 10 percent
and the par value of common stock at close to 3 percent. Preferred stock is relatively
insignificant at less than 1 percent of the U.S. banking industry’s capital.
Bank holding companies have issued substantial quantities of subordinated debt in recent years
because such notes are callable shortly after issue and carry either fixed or floating interest rates.
Common stock represents what owners contribute originally when they buy the stock to begin
with. Retained earnings represent the growth in earnings that accumulate in the firm over time.
What the owners contribute to the firm and the wealth that accumulates over time is the true
cushion against loss that capital represents.
15-6. How do small banks differ from large banks in the composition of their capital accounts
and in the total volume of capital they hold relative to their assets? Why do you think these
differences exist?
Small banks rely mainly on surplus value of their stock and retained earnings (undivided profits)
and very little on long-term debt (subordinated notes and debentures), whereas large banks rely
on surplus value of stock, retained earnings, and long term debt. This is because, large
institutions have the ability to sell their capital instruments in the open market, while the smallest
institutions, have only limited access to the financial market. Small banks have a difficult time
placing their equity and debt securities in the market and thus, rely more heavily on internal
capital (i.e. retained earnings). Moreover, many authorities in the field believe that generally the
smallest banks should maintain the thickest cushion of capital relative to their asset size because
they are not as well diversified as their large counterparts, both geographically and by product
line, and, therefore, run a greater risk of failing.
15-7 What is the rationale for having the government set capital standards for financial
institutions as opposed to letting the private marketplace set those standards?
The government's interest in set capital standards stems from its efforts to stabilize the financial
system, limit risk of failures, preserve public confidence, and avoid drains on the federal
insurance system. Capital requirements have long been subject to government regulation, though
bankers frequently argue that the market, rather than regulators, should determine how much
capital a financial institution should hold. The fear among regulators, however, is that financial

institutions would hold too little capital to avoid failures and also that the private market cannot
adequately assess their need for capital.

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15-8. What evidence does recent research provide on the role of the private marketplace in
determining capital standards?
The results of recent studies are varied, but most find that the private marketplace is more
important than government regulation in determining the amount and type of capital financial
institutions must hold. However, recently government regulation appears to have become nearly
as important as the private marketplace by tightening capital regulations and imposing minimum
capital requirements, especially in the wake of the great credit crisis of 2007–2009.
15-9. According to recent research, does capital prevent a financial institution from failing?
If capital is large enough to absorb operating losses it can prevent failure for some time, at least
until the capital is all used up. However, there is no solid, undisputed evidence of a significant
relationship between the size of the capital-to-asset ratio and the incidence of failure.
15-10. What are the most popular financial ratios regulators use to assess the adequacy of bank
capital today?
The prime capital-adequacy ratios, under Basel I, which the regulators use to assess are, Tier 1
risk-based capital ratio, which is equals core capital to risk-weighted assets, and total risk-based
capital ratio, which is equals total capital to risk-weighted assets.
15-11. What is the difference between core (or tier 1) capital and supplemental (or tier 2)
capital?
Core capital is the permanent capital of a bank, consisting mainly of common stock and surplus,
undivided profits (retained earnings), qualifying noncumulative perpetual preferred stock,
minority interest in the equity accounts of consolidated subsidiaries, and selected identifiable
intangible assets less goodwill, and other intangible assets. Supplemental capital (or tier 2) is a

secondary form of bank capital, which includes the allowance (reserves) for loan and lease
losses, subordinated debt capital instruments, mandatory convertible debt, intermediate-term
preferred stock, cumulative perpetual preferred stock with unpaid dividends, and equity notes
and other long-term capital instruments that combine both debt and equity features.
15-12. A bank reports the following items on its latest balance sheet: allowance for loan and
lease losses, $42 million; undivided profits, $81 million; subordinated debt capital, $3 million;
common stock and surplus, $27 million; equity notes, $2 million; minority interest in
subsidiaries, $4 million; mandatory convertible debt, $5 million; identifiable intangible assets, $3
million; and noncumulative perpetual preferred stock, $5 million. How much does the bank hold
in Tier 1 capital? In Tier 2 capital? Does the bank have too much Tier 2 capital?
The Tier 1 capital items include:
Common stock and
surplus

$27 million

The Tier 2 capital items include:
Allowance for loan and
lease losses

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$42 million


Chapter 15 - The Management of Capital

Undivided profits
Noncumulative
perpetual preferred

stock
Identifiable
intangible assets
Minority interest in
subsidiaries
Total Tier 1 capital

81 million

Subordinated debt capital
Mandatory convertible
debt

5 million

3 million
5 million

Equity notes
3 million
4 million
$120 million

2 million
Total Tier 2 capital

$52 million

The bank does not have too much Tier 2 capital. Tier 2 capital can be up to 100 percent of the
amount of Tier 1 capital and hence can still count toward meeting its capital requirements.

15-13. What changes in the regulation of bank capital were brought into being by the Basel
Agreement? What is Basel I? Basel II?
Capital requirements today are set by regulatory agencies and, for banks in leading countries
today, under rules laid out in the Basel Agreement on International Bank Capital Standards.
These government agencies set minimum capital requirements and assess the capital adequacy of
the financial firms they regulate.
Capital regulation aimed primarily at the largest international banks and formally began with a
multinational agreement known as Basel I. This set of international rules required many of the
largest banks to separate their on-balance-sheet and off-balance-sheet assets into risk categories
and to multiply each asset by its appropriate risk weight to determine total risk-weighted assets.
The ratio of total regulatory capital relative to risk-weighted assets and off-balance-sheet
commitments was an indicator of the strength of each international bank’s capital position.
Weaknesses in Basel I led to a Basel II agreement to be gradually phased in. This approach to
capital regulation required the world’s largest banking firms to conduct a continuing internal
assessment of their individual risk exposures, including stress testing. Thus, each participating
bank would calculate its own unique capital requirements based upon its own unique risk profile.
Smaller banks would use a simpler, standardized approach to determining their minimum capital
requirements similar to the rules of Basel I.
15-14. First National Bank reports the following items on its balance sheet: cash, $200 million;
U.S. government securities, $150 million; residential real estate loans, $300 million; and
corporate loans, $350 million. Its off-balance-sheet items include standby credit letters, $20
million, and long-term credit commitments to corporations, $160 million. What are First
National's total risk-weighted assets? If the bank reports Tier 1 capital of $30 million and Tier 2
capital of $20 million, does it have a capital deficiency?
(Note: There are three categories of standby credit letters with different conversion factors and
credit risk weights (See Table on p. 499-500), we have assumed the standby credit letters in this
discussion question are backing the issue of state and local government general obligation
bonds.)

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We first convert the off-balance-sheet items to their credit-equivalent amounts:
Off-Balance-Sheet Items:
Standby credit letters: $20 million × 0.20 = $4 million
Long-term commitments to corporations: $160 million × 0.50 = 80 million
Then we can risk-weight all assets as follows:
Risk-Weighted Assets
Cash
$200 million × 0 =
U.S. government securities:
$150 million × 0 =
Standby credit letters:
$4 million × 0.20 =
Residential real estate loans:
$300 × 0.50 =
Corporate loans:
$350 × 1.00 =
Long-term credit commitments:
$80 × 1.00 =
Total risk-weighted assets =

$ 0.00 million
0.00 million
0.80 million
150.00 million
350.00 million
80.00 million

$580.80 million

The bank has total capital of:
Tier 1 capital = $30 million
Tier 2 capital = $20 million
$50 million
The bank's capital to risk-weighted asset ratio is:
$50 million
= 0.086 or 8.6 percent .
$580.80 million
The ratio exceeds the minimum requirement of 8 percent. Moreover, more than 4 percent of the
8.6 percent in capital is Tier 1 capital, so the bank satisfies the capital requirements.
15-15. How is the Basel Agreement likely to affect a bank's choices among assets it would like
to acquire?
Under the capital standards brought into being by the Basel Agreement, differing risk weights
will apply to different kinds of bank assets. Each dollar of high-risk assets, such as corporate
loans and home mortgages, requires a greater proportion of bank capital pledged behind it than a
dollar of low-risk assets, such as government securities. Banks desiring to keep their capital costs
as low as possible and to reduce their credit risk exposure will move toward government
securities and away from corporate loans and home mortgage loans. They will also shift the

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Chapter 15 - The Management of Capital

proportion of investment in off-balance sheet items as they legally bind credit commitments
made by the banks to their customers.
15-16. What are the most significant differences among Basel I, II, and III? Explain the
importance of the concepts of internal risk assessment, VaR, and market discipline.

Basel I used a “one size fits all” approach to determine a bank’s capital requirements. Basel II
recognizes that different banks have different risk exposures and should be subject to different
capital requirements. It also broadens the types of risk considered for determining capital
requirements, including credit, market, and operational risk. Capital requirements laid down in
Basel I and II apparently were inadequate in the face of the latest credit crash. Also, Basel II had
resulted in less total capital and a weaker mix of capital, worsening what turned into a global
credit catastrophe. Basel III was hence designed to head off future financial crises. Basel III calls
for greater total capitalization (a higher percentage relative to assets) plus a stronger definition of
what belongs and does not belong in a bank’s capital accounts.
Internal risk assessment refers to an innovation in Basel II which allows banks to measure their
own risk exposure and determine how much capital they needed to meet that exposure. These
measurements are subject to review by the regulators to ensure that they are reasonable. The VaR
model is one of the models used to determine a bank’s risk exposure. It measures the price or
market risk of a portfolio of assets whose value may decline due to adverse movements in the
financial markets or interest rates. Market discipline refers to the market determining the bank’s
risk exposure. The market’s collective actions of buying and selling a bank's securities (like
subordinate debt) in the financial market provide an independent assessment of the bank's
financial condition. Since such debt is not guaranteed, the buyers of such securities would be
very vigilant about the bank’s financial condition.
15.17. What steps should be part of any plan for meeting a long-range need for capital?
The four key phases of planning to meet a bank's capital needs are as follows:
1. Develop an overall financial plan
2. Determine the amount of capital that is appropriate given the goals, planned service offerings,
acceptable risk exposure, and state and federal regulations
3. Determine how much capital can be generated internally through profits retained in the
business
4. Evaluate and choose that source of external capital best suited to the institution’s needs and
goals
15-18. How does dividend policy affect the need for capital?
Relying on the growth of earnings to meet capital needs means that a decision must be made

concerning the amount of earnings retained in the business versus the amount paid out to
stockholders in the form of dividends. For this reason, the management decides an appropriate
retention ratio. A retention ratio set too low results in slower growth of internal capital, which
may increase the failure risk and retard the expansion of earning assets. A retention ratio set too

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Chapter 15 - The Management of Capital

high can result in a cut in stockholders’ dividend income. Other factors held constant, such a cut
would reduce the market value of stock issued by a financial institution. Hence, the optimal
dividend policy is one that maximizes the value of the stockholders’ investment.
15-19. What is the ICGR, and why is it important to the management of a financial firm?
The Internal capital growth rate (ICGR) is ratio of retained earnings to the equity capital of the
firm. It shows that if we want to increase internally generated capital, we must increase earnings
(through a higher profit margin, asset utilization ratio, and/or equity multiplier) or increase the
earnings retention ratio, or both.
To illustrate, the ICGR indicates how fast a firm can allow its assets to grow and still keep its
capital-to-asset ratio fixed. If the assets grow by a percentage above the ICGR, there is a
possibility of capital-to-assets ratio to fall. If it falls far enough, the regulatory authorities may
insist that capital be increased. Thus, it makes ICGR an important factor to keep a check on the
firm’s earnings and its retention ratio.
15-20. Suppose that a bank has a return on equity capital of 12 percent and that its retention
ratio is 35 percent. How fast can this bank's assets grow without reducing its current ratio of
capital to assets? Suppose that the bank's earnings (measured by ROE) drop unexpectedly to only
two-thirds of the expected 12 percent figure. What would happen to the bank's ICGR?
The relevant formula is:
ICGR = ROE × Retention Ratio
ICGR = 0.12 × 0.35 = 0.042 or 4.2 percent.

The bank’s assets can grow at a rate of 4.2% percent without reducing the capital-to-assets ratio.
If ROE unexpectedly drops to only two-thirds of the expected 12 percent figure, the ICGR
becomes:
ICGR = [ 0.12 × 0.667 ] × 0.35 = 0.028 or 2.8 percent.
15-21. What are the principal sources of external capital for a financial institution?
The principal sources through which a financial firm can raise external capital are by selling
common stock, selling preferred stock, issuing debt capital, selling assets, leasing certain fixed
assets, or swapping stock for debt securities.
15-22. What factors should management consider in choosing among the various sources of
external capital?
The alternative that management should choose will depend primarily on the impact each source
would have on returns to stockholders, usually measured by earnings per share (EPS). Other key

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Chapter 15 - The Management of Capital

factors to consider are the institution’s risk exposure, the impact on control by existing
stockholders, the state of the market for the assets or securities being sold, and regulations.
The management while considering in choosing among the various sources of external capital
should also consider following factors individually. Drawing upon common and preferred stock
increases the borrowing capacity and provides permanent capital, but it can result in ownership
and earnings dilution. Debt capital is generally to boost EPS due to the financial leverage, but
debt also adds to failure and earnings risk and may make it more difficult to sell stock in the
future. Selling assets and leasing capital usually creates a substantial inflow of cash. Swapping
stock for debt securities strengthens its capital and saves the cost of future interest payments on
the notes.
Problems and Projects
15-1. The management at Sage National Bank located in Key West, Florida, is calculating the

key capital adequacy ratios for its third-quarter reports. At quarter-end, the bank’s total assets are
$95 million and its total risk-weighted assets including off-balance-sheet items are $75 million.
Tier 1 capital items sum to $4 million, while Tier 2 capital items total $2.5 million. Calculate
Sage National’s leverage ratio, total capital-to-total assets, core capital-to-total risk-weighted
assets, and total capital-to-total risk-weighted assets. Does Sage National meet the requirement
stipulated for a bank to qualify as adequately capitalized? In which of the five capital adequacy
categories created by U.S. federal regulators for PCA purposes does Sage National fall? Is Sage
National subject to any regulatory restrictions given its capital adequacy category?
Total assets
Total risk-weighted assets including offbalance-sheet items

$95.00 million
75.00 million

Tier 1 capital
Tier 2 capital

4.00 million
2.50 million

Leverage ratio =

Tier 1 capital
Total asset

Leverage ratio =

$4 million
= 0.0421or 4.21percent
$95 million

Total capital-to-total assets ratio =

( Tier 1 capital + Tier 2 capital )
Total assets

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Chapter 15 - The Management of Capital

Total capital-to-total assets ratio =

( $4 million + $2.5 million ) = 0.0684 or 6.84 percent
$95 million

Core capital-to-total risk-weighted assets =

Tier 1capital
Risk weighted assets including off-balance-sheet items

Core capital-to-total risk-weighted assets =

$4 million
= 0.0533or 5.33percent
$75 million

( Tier 1 capital

Total capital-to-total risk-weighted assets =

+ Tier 2 capital )

Risk weighted assets including off-balance-sheet items
( $4 million + $2.5 million ) = 0.0867 or 8.67 percent .
Total capital-to-total risk-weighted assets =
$75 million
Yes, Sage National Bank meets the requirement of having a minimum ratio of total capital to risk
weighted assets of at least 8 percent, a ratio of Tier 1 capital to risk-weighted assets of at least 4
percent, and a leverage ratio of at least 4 percent stipulated for a bank to qualify as adequately
capitalized. Sage National Bank falls in “adequately capitalized” category among the five capital
adequacy categories created by U.S. federal regulators for PCA purpose. Sage National Bank is
subject to a regulatory restriction of not accepting broker-placed deposits without regulatory
approval.
15-2. Please indicate which items appearing on the following financial statements would be
classified under the terms of the regulatory requirement for ( a ) Tier 1 capital or ( b ) Tier 2
capital.

Allowance for loan
and lease losses
Subordinated debt under
two years to maturity
Intermediate-term
preferred stock
Qualifying noncumulative
perpetual preferred stock
Cumulative perpetual preferred
stock with unpaid dividends

Subordinated debt capital

instruments with an original average
maturity of at least five years
Common stock
Equity notes
Undivided profits
Mandatory convertible debt
Minority interest in the equity
accounts of consolidated
subsidiaries

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Chapter 15 - The Management of Capital

Tier 1
Qualifying noncumulative
perpetual preferred stock
Common stock
Undivided profits
Minority interest in the equity
accounts of consolidated
subsidiaries

Tier 2
Allowance for loan and lease
losses
Subordinated debt under
two years to maturity
Intermediate-term preferred stock

Cumulative perpetual preferred
stock with unpaid dividends
Subordinated debt capital
instrument with an original
maturity of at least five years
Equity notes
Mandatory convertible debt

15-3. Under the terms of the Original Basel Agreement, what risk weights apply to the
following on-balance-sheet and off-balance-sheet items?

Residential real estate loans
Cash
Commercial loans
U.S. Treasury securities
Deposits held at other banks
GNMA mortgage-backed
securities
Standby credit letters for
commercial paper
Federal agency securities
Municipal general obligation bonds
Investments in subsidiaries
FNMA or FHLMC issued
or guaranteed securities

Credit card loans
Standby letters of credit for municipal
bonds
Long-term unused commitments to make

corporate loans
Currency derivative contracts
Interest-rate derivative contracts
Short-term (under one year) loan
commitments
Bank real property
Bankers’ acceptances
Municipal revenue bonds
Reserves on deposit at the Federal
Reserve banks

The items which would appear in the 0 percent (Zero credit risk), 20 percent (Low credit risk),
50 percent (Moderate credit risk) and 100 percent (Highest credit risk) risk weight categories are:
0 percent
Cash
U.S. Treasury
securities

20 percent
Deposits held at other
banks
Federal agency
securities

50 percent
Residential real
estate loans
Long-term unused
commitments to
make corporate

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100 percent
Commercial loans
Standby credit letters
for commercial
paper


Chapter 15 - The Management of Capital

GNMA mortgagebacked securities
Short- term (under
one year) loan
commitments
Reserves on deposit
at the Federal
Reserve banks

loans
Currency derivative
contracts
Interest-rate
derivative contracts

Municipal general
obligation bonds
FNMA or FHLMC
issued or guaranteed

securities
Standby letters of
credit for municipal
bonds

Municipal revenue
bonds

Investments in
subsidiaries
Credit card loans
Bank real property
Bankers’
acceptances

15-4. Using the following information for Gold Star National Bank, calculate that bank’s ratios
of Tier 1 capital-to-risk-weighted assets and total-capital-to-risk-weighted assets. Does the bank
have sufficient capital according to Basel I?
On-Balance-Sheet Items (Assets)
Cash
U.S Treasury
securities
Deposit balances
due from other
banks
Loans secured by
first liens on
residential property
(1- to 4- family
dwellings)

Loans to
corporations
Total assets

Off-Balance-Sheet Items
Standby letters of credit
backing repayment of
commercial paper
$ 20.5 million
Long-term unused loan
commitments to corporate
customers
25.5 million

$ 4.0 million
30.6 million

Total off-balance-sheet
items

4.0 million

46.0 million

66.0 million

Tier 1 capital

7.5 million

105.3 million
$209.9 million

Tier 2 capital

5.8 million

Gold Star National Bank's required level of capital under the new international capital standards
would be determined from:
The credit-equivalent amount of each off-balance-sheet (OBS) items:
Standby letters of credit backing repayment of
commercial paper
Long-term unused loan commitments to
corporate customers

$20.5 million × 1.00 = $20.5 million
$25.5 million × 0.50 = 12.75 million

On-Balance-Sheet Items and Credit-Equivalent Off-Balance Sheet Items:

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Chapter 15 - The Management of Capital

0 Percent Risk-Weighting Category
Cash
U.S Treasury securities
Total

$4 million
$30.6 million
$34.6 million

× 0.00 = $0.00 million

20 Percent Risk-Weighting Category
Deposit balances due from other banks

$4.0 million

× 0.20 = $0.80 million

50 Percent Risk-Weighting Category
Loans secured by first liens on
residential property

$66.0 million

× 0.50 = $33.00 million

100 Percent Risk-Weighting
Category
Loans to corporations
Standby letters of credit backing
repayment of commercial paper
Long-term unused loan commitments
to corporate customers
Total
Total risk-weighted assets held by this

bank

$105.3 million
$20.5 million
$12.75 million
$138.55 million

×1.00 = $138.55 million
$172.35 million

The bank's capital ratio is:

Tier 1 capital-to-total risk-weighted assets =

Tier 1capital
Risk-weighted assets including off-balance-sheet items

Tier 1 capital ÷ Risk-weighted assets = $7.5 million ÷ $172.35 million
= 4.35 percent
Total capital ÷ Risk-weighted Assets = $13.3 million ÷ $172.35 million
= 7.72 percent
The ratio of Tier 1 capital-to-risk-weighted assets is just above the minimum rate of 4 percent.
However, the combined Tier 1 plus Tier 2 capital of 7.72 percent of risk-weighted assets is below
the d 8 percent. Hence, the bank will have to raise new capital or reduce its risky assets under
Basel I.
15-5. Please calculate Red River National Bank’s total risk-weighted assets, based on the
following items that the bank reported on its latest balance sheet. Does the bank appear to have a
capital deficiency?

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Chapter 15 - The Management of Capital

Cash
Domestic interbank deposits
U.S. government securities
Residential real estate loans
Commercial loans
Total assets
Total liabilities
Total capital

$

75 million
130 million
250 million
375 million
520 million
$1,350 million
$1,250 million
$100 million

Off-balance-sheet items include:

Standby credit letters that back municipal
general obligation bonds
Long-term unused loan commitments to
private companies

$ 87 million
145 million

The risk-weighted assets of Red River National Bank would be calculated as follows:
The credit-equivalent amount of each off-balance-sheet (OBS) items:
Standby credit letters that back municipal
general obligation bonds
Long-term unused loan commitments to
private companies

$87 million × 0.20 = $17.4 million
$145 million × 0.50 = $72.5 million

On-Balance-Sheet Items and Credit-Equivalent Off-Balance Sheet Items:
0 Percent Risk-Weighting Category
Cash
U.S government securities
Total
20 Percent Risk-Weighting Category
Domestic interbank deposits
Standby credit letters that back municipal
general obligation bonds
Total

$75.00 million
$250.00 million
$325.00 million

× 0.00 = $0 million

$130.00 million
17.40 million
$147.40 million

50 Percent Risk-Weighting Category

15-15

× 0.20 = $29.48 million


Chapter 15 - The Management of Capital

Residential real estate loans

$375.00 million

100 Percent Risk-Weighting Category
Commercial loans
Long-term unused loan commitments to
private companies
Total
Total risk-weighted assets held by this bank

× 0.50 = $187.50 million

$520.00 million
$72.50 million
$592.50 million

× 1.00 = $592.50 million
$809.48 million

Red River's overall capital-to-assets ratio is:
Total Capital
Total Risk-Weighted Assets

=

$100 million
$809.48 million

=

0.1235 or 12.35 percent

Based on the risk weighted assets, it does not appear that Red River has a capital deficiency as
the capital to risk-weighted assets ratio is above the minimum requirement of 8 percent. In fact
Red River is in a position to generate more assets by utilizing some part of the extra capital of
4.35 percent.
15-6. Suppose Red River National Bank, whose balance sheet is given in problem 5, reports the
forms of capital shown in the following table as of the date of its latest financial statement. What
is the total dollar volume of Tier 1 capital? Tier 2 capital? Calculate the Tier 1 capital-to-riskweighted- assets ratio, total capital-to-risk-weighted-asset ratio, and the leverage ratio. According
to the data given in Problems 5 and 6, does Red River have a capital deficiency? What is its PCA
capital adequacy category?

Red River National Bank has the following Tier 1 and Tier 2 capital items and totals:
Tier 1 Capital
Common stock (par value)

Surplus
Undivided profits
Total Tier 1 capital

Tier 2 Capital
$5 million Allowance for loan losses
$15 million Subordinated debt capital
$30 million Intermediate-term preferred stock
$50 million
Total Tier 2 capital

$25 million
$20 million
$5 million
$50 million

Hence, the Tier 1 capital-to-risk-weighted- assets ratio is calculated as follows:
Tier 1 capital
Total risk-weighted assets

=

$50 million
$809.48 million

15-16

=

0.0618 or 6.18 percent

Chapter 15 - The Management of Capital

Total capital-to-risk-weighted-asset ratio is calculated as follows:
Total capital
Total risk-weighted assets

=

$50 million + $50 million
$809.48 million

=

0.1235 or 12.35 percent

The leverage ratio is calculated as follows:
Tier 1 capital
Total assets

=

$50 million
$1,350 million

=

0.0370 or 3.70 percent

This bank has sufficient Tier 1 capital and since its Tier 2 capital amount is exactly 100 percent
of Tier 1 capital amount, it satisfies the requirements of Basel I. Also, its PCA capital adequacy
category would be “well capitalized” as it has a ratio of capital to risk-weighted assets of more
than 10 percent and a ratio of Tier 1 (or core) capital to risk-weighted assets of more than 6
percent. However, its leverage ratio (Tier 1 capital to average total assets) does not meet the
required standard of at least 5 percent.
15-7. Richman Savings Association has forecast the following performance ratios for the year
ahead. How fast can Richman allow its assets to grow without reducing its ratio of equity capital
to total assets, assuming its performance holds reasonably steady over the period?
Profit margin of net income over operating revenue
Asset utilization (operating revenue ÷ assets)
Equity multiplier
Net earnings retention ratio

16.00%
8.25%
10x
60.00%

Internal capital growth rate = Profit margin of net income over operating revenue × Asset
utilization × Equity multiplier × Net earnings retention ratio
= 0.16 × 0.0825 × 10 × 0.60
= 0.0792 or 7.92 percent
Its assets cannot grow any faster than 7.92 percent over the period without reducing its ratio of
equity capital to total assets.
15-8. Using the formulas developed in this chapter and in Chapter 6 and the information that
follows, calculate the ratios of total capital to total assets for the banking firms listed below.
What relationship among these banks’ return on assets, return on equity capital, and capital-toassets ratios did you observe? What implications or recommendations would you draw for the
management of each of these institutions?

15-17


Chapter 15 - The Management of Capital

Name of Bank
First National Bank of
Hopkins
Safety National Bank
Ilsher State Bank
Mercantile Bank and Trust
Company
Lakeside National Trust

Net Income ÷ Total
Assets
(or ROA)
1.25%

Net Income ÷ Total
Equity Capital (or ROE)

1.2%
0.9%
0.25%

13%
11%
3%

−0.5%

−7%

15%

The basic relationship needed in this problem is:
Net income after tax
Equity capital
Net income after tax
Equity capital =
ROE
ROE =

And,
Net income after taxes
Total Assets
Net income after taxes
Total Assets =
ROA
ROA=

Hence, the capital-to-asset ratio can be calculated as follows:
Capital-to-asset ratio =

ROA
ROE

Therefore, the ratio of total capital to total assets for the banks named in the problem must be:

Name of Bank
First National
Bank of Hopkins
Safety National Bank
Ilsher State Bank
Mercantile Bank and
Trust Company
Lakeside National Trust

Net Income ÷
Total Assets
(or ROA)

Net Income ÷
Total Equity
Capital (or
ROE)

ROA ÷ ROE

1.25%
1.20%
0.90%

15.00%
13.00%
11.00%

8.33%
9.23%

8.18%

0.25%
−0.50%

3.00%
−7.00%

8.33%
7.14%

15-18


Chapter 15 - The Management of Capital

If an institution’s ratio of equity capital to total assets drops to 2 percent or less, a depository
institution is considered “critically undercapitalized”. In this case, none of the banks appear to
have a serious capital deficiency problem. However, the bank with the lowest capital to total
assets ratio is also the one with a negative return on assets and return on equity. It implies that the
negative earnings may be eroding the capital position of this bank.
15-9. Over the Hill Savings has been told by examiners that it needs to raise an additional $8
million in long-term capital. Its outstanding common equity shares total 5.4 million, each bearing
a par value of $1. This thrift institution currently holds assets of nearly $2 billion, with $135
million in equity. During the coming year, the thrift’s economist has forecast operating revenues
of $180 million, of which operating expenses are $25 million plus 70% of operating revenues.
Among the options for raising capital considered by management are (a) selling $8
million in common stock, or 320,000 shares at $25 per share; (b) selling $8 million in preferred
stock bearing a 9 percent annual dividend yield at $12 per share; or (c) selling $8 million in 10year capital notes with a 10 percent coupon rate. Which option would be of most benefit to the
stockholders? (Assume a 34% tax rate.) What happens if operating revenues are more than

expected ($225 million rather than $180 million)? What happens if there is a slower-thanexpected volume of revenues (only $110 million instead of $180 million)? Please explain.
(a)
Sale of
Common Stock
at $25 per share
Estimated operating revenues
Estimated operating expenses

(b)
Sale of 9%
Preferred Stock
at $12 per share

(c)
Sale of 10%
Capital Notes

$180,000,000
$151,000,000

$180,000,000
$151,000,000

$180,000,000
$151,000,000

Net revenues
Interest expense on capital notes

$29,000,000

-

$29,000,000
-

$29,000,000
$800,000

Before-tax income
Estimated income taxes

$29,000,000
$9,860,000

$29,000,000
$9,860,000

$28,200,000
$9,588,000

After-tax income
Preferred stock dividends

$19,140,000
-

$19,140,000
$720,000

$18,612,000

-

Net income for common stockholders

$19,140,000

$18,420,000

$18,612,000

Shares of common stock outstanding

5,720,000

5,400,000

5,400,000

Earnings per share of common stock

$3.35

$3.41

$3.45

In this case, sale of capital notes with a coupon rate of 10 percent would generate the highest
EPS for the bank's shareholders.

15-19

Chapter 15 - The Management of Capital

Because of the dilution effect of issuing stock, if operating revenues rise to $225 million, the
situation will be as shown below:
(a)
Sale of
Common Stock
at $25 per share
Operating revenues
Operating expenses

(b)
Sale of 9%
Preferred Stock
at $12 per share

(c)
Sale of 10%
Capital Notes

$225,000,000
$182,500,000

$225,000,000
$182,500,000

$225,000,000
$182,500,000

Net revenues
Interest on capital notes

$42,500,000
-

$42,5000,000
-

$42,500,000
$800,000

Before-tax income
Estimated income taxes

$42,500,000
$14,450,000

$42,500,000
$14,450,000

$41,700,000
$14,178,000

After-tax income
Preferred stock dividends

$28,050,000
-

$28,050,000
$720,000

$27,522,000
-

Net income for common
stockholders

$28,050,000

$27,330,000

$27,522,000

Shares of common stock
outstanding

5,720,000

5,400,000

5,400,000

$4.90

$5.06

$5.1

Earnings per share of
common stock

Again capital notes would be the best option, although the preferred stock can also be considered
this time as it also generates a slightly less earnings per share.

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Chapter 15 - The Management of Capital

If operating revenues drop to $110 million, then the situation will be as shown below:
(a)
Sale of
Common Stock
at $25 per share

(b)
Sale of 9%
Preferred Stock
at $12 per share

(c)
Sale of 10%
Capital Notes

Operating revenues
Operating expenses
Net revenues

Interest on capital notes

$110,000,000
$102,000,000
$8,000,000
-

$110,000,000
$102,000,000
$8,000,000
-

$110,000,000
$102,000,000
$8,000,000
$800,000

Before-tax income
Estimated income taxes

$8,000,000
$2,720,000

$8,000,000
$2,720,000

$7,200,000
$2,448,000

After-tax income

Preferred stock dividends

$5,280,000
-

$5,280,000
$720,000

$4,752,000
-

Net income for common
Stockholders

$5,280,000

$4,560,000

$4,752,000

Shares of common Stock
outstanding

5,720,000

5,400,000

5,400,000

$0.92

$0.84

$0.88

Earnings per share of
common stock

In this case, to raise the required sum of $8 million, issuing common stock is the best alternative
from the point of view of the common stockholders.

15-21