Attached is the pdf with the questions. Ignore the copy and pasted format

Consider the following balance sheet for Wachovia Bank (in millions):

Balance Sheet (unit: $ millions)

Assets Liabilities

Floating-rate mortgages

(currently 10% annually)

30-year fixed-rate loans

(currently 7% annually)

Total Assets

50

50

100

1-year time deposit

(currently 5% annually)

3-year time deposits

(currently 8% annually)

Equity

Total Liabilities and equity

70

20

10

100

a. What is Wachovia?s expected net interest income at year-end?

b. What will net interest income be at year-end if interest rates rise by 2%?

c. Using the one-year cumulative repricing gap model, what is the expected net interest

income for a 2 percent increase in in interest rates?

d. What will net interest income be a year-end if interest rates on RSAs increase by 2 percent

but interest rate on RSLs increase by 1 percent? Is it reasonable for changes in interest rates

on RSAs and RSLs to differ? Why?

2. Two banks are being examined by regulators to determine the interest rate sensitivity of their

balance sheets. Bank A has assets composed solely of a 10 year $1 million loan with a coupon

rate and yield of 12 percent. The loan is financed with a 10 year, $1 million CD with a coupon

rate and yield of 10 percent. Bank B has assets composed solely of a 7-year, 12 percent zerocoupon

bond with a current (market) value of $894,006.20 and a maturity (principal) value of

$1,976,362.88. The bond is financed with a 10-year, 8.275 percent coupon, $1,000,000 face

2

value CD with a yield to maturity of 10 percent. The loan and the CDs pay interest annually,

with principal due at maturity.

a. If market interest rates increases 1 percent (100 basis points), how do the market values of

the assets and liabilities of each bank change? That is, what will be the net effect on the

market value of the equity for each bank?

b. What accounts for the differences in the changes in market value of equity between the two

banks?

c. Verify your results above by calculating the duration for the assets and liabilities of each

bank, and estimate the changes in value for the expected change in interest rates.

Summarize your results.

3. Consider the following balance sheet of GWSB bank. Assume that the bank does not have off

balance sheet commitments.

Assets Liabilities and Equities

Cash and Reserves $ 5 Deposits $ 111

Treasury Securities 10 10 year subordinate Debts 16

Commercial Loan (BB+) 15 Perpetual noncumulative

Preferred shares

1

Single Family Mortgages 40 Common stock 2

Consumer Loans 35 Retained Earnings 4

Commercial Loans (CCC+) 24 Total Liabilities and Equities $ 134

Allowance for Loan Losses ($ 10)

Physical Assets $15

Total Assets $134

Risk Weight of Assets

Assets Risk Weight

Cash and Reserves 0%

Treasury Securities 0%

3

Commercial Loan (BB+) 100%

Single Family Mortgages 50%

Consumer Loans 100%

Commercial Loans (CCC+) 150%

Physical Assets 100%

Tier 1 vs. Tier 2 capital

10 year subordinate Debts Tier 2

Perpetual noncumulative Preferred shares Tier 1

Common stock Tier 1

Retained Earnings Tier 1

Reserve for Loan Losses Tier 2

Using the information given about risk weights and capital categories, calculate the following

three capital adequacy ratios (leverage ratio, tier 1 capital ratio and total risk based capital

ratio).

4. GWSB bank has $20 million in assets, with risk adjusted assets of $10 million. Tier 1 capital is

$500,000 and Tier II capital is $400,000. How will each of the following transactions affect the

value of the Tier I and total capital ratios? What will be the new value of each ratio be? (Use the

information on risk weights and capital tiers in Question 3 if necessary.)

The current value of the Tier I ratio is 5 percent and the total ratio is 9 percent.

a. The bank repurchases $100,000 of common stock with cash.

b. The bank issues $2 million of CDs and uses the proceeds to issue single family mortgage loans.

c. The bank receives $500,000 in deposits and invests them in T-bills.

d. The bank issues $800,000 in common stock and lends it to help finance a new shopping mall.

The developer has A+ credit rating. (Hint: the real estate loan will have 50% risk weight.)

e. The bank issues $1 million in non-qualifying preferred stock and purchases general obligation

mutual bonds. (Hint: non-qualifying preferred stocks are counted as Tier 2.)

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f. Homeowners pay back $4 million of single family mortgages and the bank uses the proceeds

to build new ATMs. (Hint: ATMs are physical assets.)

5. Tree Row Bank has assets of $150 million, liabilities of $135 million, and equity of $15 million.

The asset duration is six years and the duration of the liabilities is four years. Market interest

rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with Treasury bond

futures contracts, which currently have a price quote of $95 per $100 face value for the

benchmark 20-year, 8 percent coupon bond underlying the contract, a market yield of 8.5295

percent, and a duration of 10.3725 years.

a. Should the bank go short or long on the futures contracts to establish the correct macrohedge?

b. How many contracts are necessary to fully hedge the bank?

c. Verify that the change in the futures position will offset the change in the cash balance sheet

position for a change in market interest rates of plus 100 basis points and minus 50 basis

points.

d. If the bank had hedged with Treasury bill futures contracts that had a market value of $98

per $100 of face value and a duration of 0.25 years, how many futures contracts would have

been necessary to fully hedge the balance sheet?

e. What additional issues should be considered by the bank in choosing between T-bond or Tbill

futures contracts?

Department of Finance School of Business Spring, 2017 FINA 3301: Money and Capital Markets (rev 4/26/17) Problem Set 3 (Due on May 1st) 1. Consider the following balance sheet for Wachovia Bank (in millions): Balance Sheet (unit: $ millions) Assets Liabilities Floating-rate mortgages 1-year time deposit (currently 10% annually) 50 (currently 5% annually) 70 30-year fixed-rate loans (currently 7% annually) 20 3-year time deposits 50 (currently 8% annually) Equity Total Assets 100 Total Liabilities and equity 10 100 a. What is Wachovia's expected net interest income at year-end? b. What will net interest income be at year-end if interest rates rise by 2%? c. Using the one-year cumulative repricing gap model, what is the expected net interest income for a 2 percent increase in in interest rates? d. What will net interest income be a year-end if interest rates on RSAs increase by 2 percent but interest rate on RSLs increase by 1 percent? Is it reasonable for changes in interest rates on RSAs and RSLs to differ? Why? 2. Two banks are being examined by regulators to determine the interest rate sensitivity of their balance sheets. Bank A has assets composed solely of a 10 year $1 million loan with a coupon rate and yield of 12 percent. The loan is financed with a 10 year, $1 million CD with a coupon rate and yield of 10 percent. Bank B has assets composed solely of a 7-year, 12 percent zerocoupon bond with a current (market) value of $894,006.20 and a maturity (principal) value of $1,976,362.88. The bond is financed with a 10-year, 8.275 percent coupon, $1,000,000 face 1 value CD with a yield to maturity of 10 percent. The loan and the CDs pay interest annually, with principal due at maturity. a. If market interest rates increases 1 percent (100 basis points), how do the market values of the assets and liabilities of each bank change? That is, what will be the net effect on the market value of the equity for each bank? b. What accounts for the differences in the changes in market value of equity between the two banks? c. Verify your results above by calculating the duration for the assets and liabilities of each bank, and estimate the changes in value for the expected change in interest rates. Summarize your results. 3. Consider the following balance sheet of GWSB bank. Assume that the bank does not have off balance sheet commitments. Assets Cash and Reserves Liabilities and Equities $ 5 Deposits $ 111 Treasury Securities 10 10 year subordinate Debts 16 Commercial Loan (BB+) 15 Perpetual noncumulative 1 Preferred shares Single Family Mortgages 40 Common stock 2 Consumer Loans 35 Retained Earnings 4 Commercial Loans (CCC+) 24 Total Liabilities and Equities Allowance for Loan Losses Physical Assets Total Assets ($ 10) $15 $134 Risk Weight of Assets Assets Cash and Reserves Treasury Securities Risk Weight 0% 0% 2 $ 134 Commercial Loan (BB+) Single Family Mortgages Consumer Loans Commercial Loans (CCC+) Physical Assets 100% 50% 100% 150% 100% Tier 1 vs. Tier 2 capital 10 year subordinate Debts Perpetual noncumulative Preferred shares Common stock Retained Earnings Reserve for Loan Losses Tier 2 Tier 1 Tier 1 Tier 1 Tier 2 Using the information given about risk weights and capital categories, calculate the following three capital adequacy ratios (leverage ratio, tier 1 capital ratio and total risk based capital ratio). 4. GWSB bank has $20 million in assets, with risk adjusted assets of $10 million. Tier 1 capital is $500,000 and Tier II capital is $400,000. How will each of the following transactions affect the value of the Tier I and total capital ratios? What will be the new value of each ratio be? (Use the information on risk weights and capital tiers in Question 3 if necessary.) The current value of the Tier I ratio is 5 percent and the total ratio is 9 percent. a. The bank repurchases $100,000 of common stock with cash. b. The bank issues $2 million of CDs and uses the proceeds to issue single family mortgage loans. c. The bank receives $500,000 in deposits and invests them in T-bills. d. The bank issues $800,000 in common stock and lends it to help finance a new shopping mall. The developer has A+ credit rating. (Hint: the real estate loan will have 50% risk weight.) e. The bank issues $1 million in non-qualifying preferred stock and purchases general obligation mutual bonds. (Hint: non-qualifying preferred stocks are counted as Tier 2.) 3 f. Homeowners pay back $4 million of single family mortgages and the bank uses the proceeds to build new ATMs. (Hint: ATMs are physical assets.) 5. Tree Row Bank has assets of $150 million, liabilities of $135 million, and equity of $15 million. The asset duration is six years and the duration of the liabilities is four years. Market interest rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with Treasury bond futures contracts, which currently have a price quote of $95 per $100 face value for the benchmark 20-year, 8 percent coupon bond underlying the contract, a market yield of 8.5295 percent, and a duration of 10.3725 years. a. Should the bank go short or long on the futures contracts to establish the correct macrohedge? b. How many contracts are necessary to fully hedge the bank? c. Verify that the change in the futures position will offset the change in the cash balance sheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points. d. If the bank had hedged with Treasury bill futures contracts that had a market value of $98 per $100 of face value and a duration of 0.25 years, how many futures contracts would have been necessary to fully hedge the balance sheet? e. What additional issues should be considered by the bank in choosing between T-bond or Tbill futures contracts? 4