Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-14
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,
6-5. The following information is for Rainbow National Bank:
Interest income
$2,250.00
Interest expense
1,500.00
Total assets
45,000.00
Securities losses or gains
21.00
Earning assets
40,000.00
Total liabilities
38,000.00
Taxes paid
16.00
Shares of common stock outstanding
5,000
Noninterest income
$800.00
Noninterest expense
900.00
Provision for loan losses
250.00
Please calculate:
ROE
ROA
Net interest margin
Earnings per share
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
Net noninterest margin
Net operating margin
Net income $405
ROE = = = 0.058or5.8percent
Totalequitycapital $45,000 – $38,000
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-16
Net income $425
ROA = = = 0.00943or 0.943percent
Totalassets $45,000
Net income $425
Earningspershare = = = $0.0849pershare
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
$2,182.50
Interest expense
$1,455.00
Total assets
$45,000.00
Securities losses or gains
$21.00
Earning assets
$40,000.00
Total liabilities
$38,000.00
Taxes paid
$16.00
Shares of common stock outstanding
5,000
Noninterest income
$776.00
Noninterest expense
$873.00
Provision for loan losses
$250.00
Common equitysharesoutstanding 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?
Total assets $25
ROE = ROA × = 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.
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-17
$25
New ROE = 1.188 percent × = 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
12.5 = 11.875 percent).
This represents no change in ROE. The bank’s management has been efficient, in this case, in
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
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-18
Net income after taxes $20 million
ROE = = = 0.133 or 13.33 percent
Equity capital $150 million
$150 million
( )
14.67 percent – 13.33 percent
Change in ROE = = 10 percent
13.33 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?
$165 million
( )
12.12 percent – 13.33 percent
13.33 percent
c. Can you determine what will happen to ROE if both operating revenues and expenses
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-19
$18 million
ROE = = 0.12 or 12 percent
$150 million
( )
12 percent – 13.33 percent
13.33 percent
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?
$135 million
( )
14.81 percent – 13.33 percent
Change in ROE = = 11.11 percent
13.33 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?
Total assets
ROE ROA 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:
Total assets
12 percent 0.8 percent 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
$ 30.00
Total operating revenues
135.00
Total assets
1,750.00
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
Total equity capital accounts
170.00
a.
Net income $30 million
Net profit margin = = = 0.2222 or 22.22 percent
Total operating revenue $135 million
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
Net Income
After-Tax
Total
Operating
Revenues
Total Assets
Total
Liabilities
1
$2.65
$26.50
$300.00
$273.00
2
2.75
30.10
315.00
288.00
3
3.25
39.80
331.00
301.00
4
3.65
47.50
347.00
314.00
5
4.00
55.90
365.00
329.00
Determine the figures for ROE, profit margin, asset utilization, and equity multiplier for this
Year
ROA
1
2
3
4
5
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-21
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.
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:
Total equity capital $250 million
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-22
e.
Net income $29 million
ROE = = = 0.116 or 11.6 percent
Totalequitycapital $250 million
Alternative Scenarios:
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?
$950 $950
Asset management efficiency ratio = = 0.2932 or 29.32 percent
$2,700 × 1.2 $3,240 =
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
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
$ 75
Interest expense
61
Provision for loan losses
6
Security gains (or losses)
2
Noninterest expense
8
Noninterest income
5
Extraordinary net gains
1
Total assets
1,000
a.
Interest income – Interest expenses
Net interest margin = Totalassets
$75 – $61 $14
= = 0.014 or 1.40%
$1,000 $1,000 =
b.
Noninterest income – Noninterest expenses
Net noninterest margin = Totalassets
$5 – $8 –$3
= = 0.003 or –0.3%
$1,000 $1,000 =−
c.
Net income $8
ROA = = = 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
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-24
Net interest income
16
16
16
16
16
Provision for loan losses
2
1
1
0
0
Net interest income after
14
15
15
16
16
Loan loss provision
Noninterest income
4
4
3
2
1
Noninterest expense
8
7
7
6
5
Net noninterest income
(4)
(3)
(4)
(4)
(4)
Income before taxes
10
12
11
12
12
Income taxes owed
1
1
0
1
0
Net income after taxes
9
11
11
11
12
but before gains (losses)
Net securities gains (losses)
2
2
1
0
0
Net income
11
13
12
11
12
Total assets
885
880
875
860
850
ROA
1.24%
1.48%
1.37%
1.28%
1.41%
Mountain’s ROA has remained consistent, in the range of 1.24 percent to 1.48 percent, over the
last five years.
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
Chapter 06 – Measuring and Evaluating the Performance of Banks and Their Principal Competitors
6-25
detailed than the example provided in the text as Tables 6-5 through 6-9. These exhibits are for