As an analyst of a medium-sized commercial bank, you have been asked to forecast next

year’s performance. In June you were provided with information about the sources and

uses of funds for the upcoming year. The bank’s sources of funds for the upcoming year

are as follows:

Source of funds dollar amount (in mill) Interest rate

DollSOuar Amount Interest Rate

Source of Funds (in Millions) to Be Offered

Demand deposits $5,000 0%

Time deposits 2,000 6%

1-year NCDs 3,000 T-bill rate_1%

5-year NCDs 2,500 1-year NCD rate_1%

Dollar Amount Loan Loss

Us

The bank also has $1 billion in capital.

The bank’s uses of funds for the upcoming year are as follows:

j

Loans to small businesses $ 4000 T-bill rate+6% 2%

Loans to large businesses 2000 T-bill rate+4% 1

Consumer loans 3000 T-bill rate+7% 4

Treasury bills 1000 T-bill rate 0

Treasury bonds 1500 T-bill rate+2% 0

Corporate bonds 1100 Treasury bond rate+2% 0

USES OF FUNDS DOLLAR AMT INTEREST RATE LOAN LOSS

The bank also has $900 million in fixed assets. The interest rates on loans to small and

large businesses are tied to the T-bill rate and will change at the beginning of each new

year. The forecasted Treasury bond rate is tied to the future T-bill rate, based on the expectation that an upward-sloping yield curve will exist at the beginning of next year. The corporate bond rate is tied to the Treasury bond rate, allowing for a risk premium of

2 percent. Consumer loans will be provided at the beginning of next year, and interest

rates will be fixed over the lifetime of the loan. The remaining time to maturity on all

assets except T-bills exceeds three years. As the one-year T-bills mature, the funds are to

be reinvested in new one-year T-bills (all T-bills are to be purchased at the beginning of

the year). The bank’s loan loss percentage reflects the percentage of bad loans. Assume

that no interest will be received on these loans. In addition, assume that this percentage

of loans will be accounted for as loan loss reserves (assume that they should be subtracted when determining before-tax income).

The bank has forecasted its noninterest revenues to be $200 million and its noninterest

expenses to be $740 million. A tax rate of 34 percent can be applied to the beforetax

income in order to estimate after-tax income. The bank has developed the following

probability distribution for the one-year T-bill rate that will exist as of the beginning of

next year:

Possible T-Bill Rate Probability

8% Possible T-Bill Rate 30% Probability

9 50

10 20

Questions

1 Using the information provided, determine the probability distribution of return on

assets (ROA) for next year by completing the following table:

Interest Rate Scenario

(Possible T-Bill Rate) Forecasted ROA Probability

Interest rate scenario Forecasted ROA Probability

8%

9

10

2 Will the bank’s ROA next year be higher or lower if market interest rates are higher?

(Use the T-bill rate as a proxy for market interest rates.) Why? The information provided

did not assume any required reserves. Explain how including required reserves

would affect the forecasted interest revenue, ROA, and ROE.

3 The bank is considering a strategy of attempting to attract an extra $1 billion as oneyear

negotiable certifi cates of deposit (NCDs) to replace $1 billion of five-year NCDs.

Develop the probability distribution of ROA based on this strategy:

Inate Forecasted ROA Based on the

Scenario Strategy of Increasing One-Year NCDs Probability

Inter rate Forecast ROA based on Strategy of increasing one year NCDS Probabil

8%

9

10

4 Is the bank’s ROA likely to be higher next year if it uses the strategy of attracting more

one-year NCDs?

5 What would be an obvious concern about a strategy of using more one-year NCDs

and fewer five-year NCDs beyond the next year?

6 The bank is considering a strategy of using $1 billion to offer additional loans to

small businesses instead of purchasing T-bills. Using all the original assumptions pro-

vided, determine the probability distribution of ROA (assume that noninterest expenses

would not be affected by this change in strategy).Columns (three of them) Interest Rate Scenario (possible T-Bill rate), Forcasted ROA if an extra $1 Billion is used for loans to small businesses, Probability

Interest Rate Scenario Forecasted ROA if an Extra $1 Billion

(Possible T-Bill Rate) Is Used for Loans to Small Businesses Probability

8%

9

10

7 Would the bank’s ROA likely be higher or lower over the next year if it allocates the

extra funds to small business loans?

8 What is the obvious risk of such a strategy beyond the next year?

9 The strategy of attracting more one-year NCDs could affect noninterest expenses and

revenues. How would noninterest expenses be affected by the strategy? How would

noninterest revenues be affected by the strategy?

10 Now assume that the bank is considering a strategy of increasing its consumer loans

by $1 billion instead of using the funds for loans to small businesses. Using this information along with all the original assumptions provided, determine the probability

distribution of ROA. Columns (three of them) Interest Rate Scenario (possible T-Bill rate), Possible ROA if an extra $1 Billion is used for consumer loans, Probability

nterest Rate Scenario Possible ROA if an Extra $1 Billion

(Possible T-Bill Rate) Is Used for Consumer Loans Probability

8%

9

10

11 Other than possible changes in the economy that may affect credit risk, what key factor

will determine whether this strategy is beneficial beyond one year?

12 Now assume that the bank wants to determine how its forecasted return on equity

(ROE) next year would be affected if it boosts its capital from $1 billion to $1.2 billion.

(The extra capital would not be used to increase interest or noninterest revenues.)

Using all the original assumptions provided, complete the following table: Columns (four of them) Interest Rate Scenario (possible T-Bill rate), Forcasted ROE if capital = $1 Billion, Forcasted ROE if capital = $1.2 Billion, Probability

Iterest Rate Scenario Forecasted ROE if Forecasted ROE if

(Possible T-Bill Rate) Capital _ $1 Billion Capital _ $1.2 Billion Probability

8%

9

10

Briefly state how the ROE will be affected if the capital level is increased.

year’s performance. In June you were provided with information about the sources and

uses of funds for the upcoming year. The bank’s sources of funds for the upcoming year

are as follows:

Source of funds dollar amount (in mill) Interest rate

DollSOuar Amount Interest Rate

Source of Funds (in Millions) to Be Offered

Demand deposits $5,000 0%

Time deposits 2,000 6%

1-year NCDs 3,000 T-bill rate_1%

5-year NCDs 2,500 1-year NCD rate_1%

Dollar Amount Loan Loss

Us

The bank also has $1 billion in capital.

The bank’s uses of funds for the upcoming year are as follows:

j

Loans to small businesses $ 4000 T-bill rate+6% 2%

Loans to large businesses 2000 T-bill rate+4% 1

Consumer loans 3000 T-bill rate+7% 4

Treasury bills 1000 T-bill rate 0

Treasury bonds 1500 T-bill rate+2% 0

Corporate bonds 1100 Treasury bond rate+2% 0

USES OF FUNDS DOLLAR AMT INTEREST RATE LOAN LOSS

The bank also has $900 million in fixed assets. The interest rates on loans to small and

large businesses are tied to the T-bill rate and will change at the beginning of each new

year. The forecasted Treasury bond rate is tied to the future T-bill rate, based on the expectation that an upward-sloping yield curve will exist at the beginning of next year. The corporate bond rate is tied to the Treasury bond rate, allowing for a risk premium of

2 percent. Consumer loans will be provided at the beginning of next year, and interest

rates will be fixed over the lifetime of the loan. The remaining time to maturity on all

assets except T-bills exceeds three years. As the one-year T-bills mature, the funds are to

be reinvested in new one-year T-bills (all T-bills are to be purchased at the beginning of

the year). The bank’s loan loss percentage reflects the percentage of bad loans. Assume

that no interest will be received on these loans. In addition, assume that this percentage

of loans will be accounted for as loan loss reserves (assume that they should be subtracted when determining before-tax income).

The bank has forecasted its noninterest revenues to be $200 million and its noninterest

expenses to be $740 million. A tax rate of 34 percent can be applied to the beforetax

income in order to estimate after-tax income. The bank has developed the following

probability distribution for the one-year T-bill rate that will exist as of the beginning of

next year:

Possible T-Bill Rate Probability

8% Possible T-Bill Rate 30% Probability

9 50

10 20

Questions

1 Using the information provided, determine the probability distribution of return on

assets (ROA) for next year by completing the following table:

Interest Rate Scenario

(Possible T-Bill Rate) Forecasted ROA Probability

Interest rate scenario Forecasted ROA Probability

8%

9

10

2 Will the bank’s ROA next year be higher or lower if market interest rates are higher?

(Use the T-bill rate as a proxy for market interest rates.) Why? The information provided

did not assume any required reserves. Explain how including required reserves

would affect the forecasted interest revenue, ROA, and ROE.

3 The bank is considering a strategy of attempting to attract an extra $1 billion as oneyear

negotiable certifi cates of deposit (NCDs) to replace $1 billion of five-year NCDs.

Develop the probability distribution of ROA based on this strategy:

Inate Forecasted ROA Based on the

Scenario Strategy of Increasing One-Year NCDs Probability

Inter rate Forecast ROA based on Strategy of increasing one year NCDS Probabil

8%

9

10

4 Is the bank’s ROA likely to be higher next year if it uses the strategy of attracting more

one-year NCDs?

5 What would be an obvious concern about a strategy of using more one-year NCDs

and fewer five-year NCDs beyond the next year?

6 The bank is considering a strategy of using $1 billion to offer additional loans to

small businesses instead of purchasing T-bills. Using all the original assumptions pro-

vided, determine the probability distribution of ROA (assume that noninterest expenses

would not be affected by this change in strategy).Columns (three of them) Interest Rate Scenario (possible T-Bill rate), Forcasted ROA if an extra $1 Billion is used for loans to small businesses, Probability

Interest Rate Scenario Forecasted ROA if an Extra $1 Billion

(Possible T-Bill Rate) Is Used for Loans to Small Businesses Probability

8%

9

10

7 Would the bank’s ROA likely be higher or lower over the next year if it allocates the

extra funds to small business loans?

8 What is the obvious risk of such a strategy beyond the next year?

9 The strategy of attracting more one-year NCDs could affect noninterest expenses and

revenues. How would noninterest expenses be affected by the strategy? How would

noninterest revenues be affected by the strategy?

10 Now assume that the bank is considering a strategy of increasing its consumer loans

by $1 billion instead of using the funds for loans to small businesses. Using this information along with all the original assumptions provided, determine the probability

distribution of ROA. Columns (three of them) Interest Rate Scenario (possible T-Bill rate), Possible ROA if an extra $1 Billion is used for consumer loans, Probability

nterest Rate Scenario Possible ROA if an Extra $1 Billion

(Possible T-Bill Rate) Is Used for Consumer Loans Probability

8%

9

10

11 Other than possible changes in the economy that may affect credit risk, what key factor

will determine whether this strategy is beneficial beyond one year?

12 Now assume that the bank wants to determine how its forecasted return on equity

(ROE) next year would be affected if it boosts its capital from $1 billion to $1.2 billion.

(The extra capital would not be used to increase interest or noninterest revenues.)

Using all the original assumptions provided, complete the following table: Columns (four of them) Interest Rate Scenario (possible T-Bill rate), Forcasted ROE if capital = $1 Billion, Forcasted ROE if capital = $1.2 Billion, Probability

Iterest Rate Scenario Forecasted ROE if Forecasted ROE if

(Possible T-Bill Rate) Capital _ $1 Billion Capital _ $1.2 Billion Probability

8%

9

10

Briefly state how the ROE will be affected if the capital level is increased.

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