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You have been hired to analyze the debt securities of your organization. The firm has outstanding loans and bonds. A quick review of the balance sheet shows the following:

Liability
Amount ($)

Nominal
Interest
(coupon)
Rate

Years to
Maturity

Selected Liabilities of the firm

Simple Loans

800

5%

1

Fixed-Payment Loans

5,000

12%

19

Long-term Bonds #1

500,000

10%

4

Long-term Bonds #2

1,080,000

10%

10

Liabilities Total

1,585,800

Market Price for Bond #1

930.50

Market Price for Bond #2

859.50

Face Value of Each Bond

1,000.00

Selected Current Assets of the firm

Marketable Securities:

Treasury Bills

100,000

Note: Treasury Bills have a $10,000 face value, which matures in one year. Each Treasury Bill has a cost of $9,580.00

1-How much interest would the firm pay each year on the simple-interest loan?

2-How much would you write a cheque for to pay off the loan in one year?

3-What is the monthly payment needed to pay off the fixed-payment loans?

4-What is the current yield for each bond if the current price is:

a-$930.50 for Bond #1?

b-$859.50 for Bond #2?

5-What is the expected yield to maturity for each bond?

a-Bond #1 selling for $930.50?

b-Bond #2 selling for $859.50

6-What is the rate of capital gain if both bonds sell for $900.00 in one year?

a-Bond #1 selling for $930.50 today?

b-Bond #2 selling for $859.50 today?

7-If the Yield to Maturity expected by investors changes to 11%:

a-What will be the market price of Bond #1?

b-What will be the market price for Bond #2?

c-What will be the dollar change in price for Bond #1?

d-What will be the dollar change in price for Bond #2?

e-What will be the percent change in price for Bond #1?

f-What will be the percent change in price for Bond #2?

g-Since the change in expected yield to maturity is the same, why is the amount of change different between the bonds?

8-If investors holding our 4-year bonds (Bond #1) receive interest income annually for four years, plus the face value of the bonds at maturity,

a-What will be the total interest earned on the bond over the next four years?

b-What will be the face value received at maturity?

Given the following projected income stream for Bond #1:

Projected Reinvestment Rates

Year

Coupon
Interest ($)

Face
Value ($)

10%

5%

1

100

2

100

10.00

5.00

3

100

21.00

10.25

4

100

1000

33.10

15.76

Total Income

400

1000

64.10

31.01

c-What is the total cash available over the next four years to the bond holder earning

ii-10%

iii-15%

d-What is the average annual rate of return for the bond holder earning

ii-10%

iii-15%

e-Why does the reinvestment rate affect the annual rate of return for the same bond?

f-If the expected rate of return on our bonds is 10%, what is the duration of Bond #1?

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28 Sep 2019

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Please can someone help me with this :

Minicase 1

Interest Rates, Bond Yields, and Duration

CONCEPTS IN THIS CASE

simple loans
fixed-payment loans
coupon bonds
present value
yield-to-maturity
current yield
nominal and real interest rates
rate of return
capital gain
interest-rate and reinvestment risk
duration

You have been hired to analyze the debt securities of your organization. The firm has outstanding loans and bonds. A quick review of the balance sheet shows the following:

Liability
Amount ($)

Nominal
Interest
(coupon)
Rate

Years to
Maturity

Selected Liabilities of the firm

Simple Loans

800

5%

1

Fixed-Payment Loans

5,000

12%

19

Long-term Bonds #1

500,000

10%

4

Long-term Bonds #2

1,080,000

10%

10

Liabilities Total

1,585,800

Market Price for Bond #1

930.50

Market Price for Bond #2

859.50

Face Value of Each Bond

1,000.00

Selected Current Assets of the firm

Marketable Securities:

Treasury Bills

100,000

Note: Treasury Bills have a $10,000 face value, which matures in one year. Each Treasury Bill has a cost of $9,580.00

How much interest would the firm pay each year on the simple-interest loan?

How much would you write a cheque for to pay off the loan in one year?

What is the monthly payment needed to pay off the fixed-payment loans?

What is the current yield for each bond if the current price is:

$930.50 for Bond #1?

$859.50 for Bond #2?

What is the expected yield to maturity for each bond?

Bond #1 selling for $930.50?

Bond #2 selling for $859.50

What is the rate of capital gain if both bonds sell for $900.00 in one year?

Bond #1 selling for $930.50 today?

Bond #2 selling for $859.50 today?

If the Yield to Maturity expected by investors changes to 11%:

What will be the market price of Bond #1?

What will be the market price for Bond #2?

What will be the dollar change in price for Bond #1?

What will be the dollar change in price for Bond #2?

What will be the percent change in price for Bond #1?

What will be the percent change in price for Bond #2?

Since the change in expected yield to maturity is the same, why is the amount of change different between the bonds?

If investors holding our 4-year bonds (Bond #1) receive interest income annually for four years, plus the face value of the bonds at maturity,

What will be the total interest earned on the bond over the next four years?

What will be the face value received at maturity?

Given the following projected income stream for Bond #1:

Projected Reinvestment Rates

Year

Coupon
Interest ($)

Face
Value ($)

10%

5%

1

100

2

100

10.00

5.00

3

100

21.00

10.25

4

100

1000

33.10

15.76

Total Income

400

1000

64.10

31.01

What is the total cash available over the next four years to the bond holder earning

10%

15%

What is the average annual rate of return for the bond holder earning

10%

15%

Why does the reinvestment rate affect the annual rate of return for the same bond?

If the expected rate of return on our bonds is 10%, what is the duration of Bond #1?

What is the yield to maturity on the Treasury Bills (a discount bond)?

What is the real rate of interest if the nominal rate is 10% and the inflation rate is 3%?

Copyright © 2000–2001 Addison Wesley Longman, a division of Pearson Education

Adaptation copyright © 2002 Pearson Education Canada

Exercise on Bond Valuation.

An investor has two bonds in her portfolio that have a face value of $1000 and pay a 10% annual coupon. Bond A matures in 15 years, while Bond B matures in 1 year.

What will the value of each bond be if the going interest rate is 5%, 8%, and 12%. ? Assume that only one more interest payment is to be made on Bond B at its maturity, and that 15 more payments are to be made on bond A.

Why does the longer-term bond price vary more than the price of the shorter-term bond when interest rates change ?

Please show your work solve problem in detail.

PROBLEMS, GRAPGHING

1. Suppose a candidate who runs on a platform of “soak the rich” wins the 2016 presidential election. After being elected, he or she persuades Congress to raise the top marginal tax rate on the federal personal income tax to 65%.

a. Use one graph to show the effect of this change in tax rates on the market for municipal bonds and another graph to show the effect on the market for U.S. Treasury bonds.

b. What happened to the interest rate spread between municipal bonds and U.S. Treasury bonds and why?

Suppose that, holding yield constant, investors are indifferent as to whether they hold bonds issued by the federal government or bonds issued by state or local governments (they consider the bonds the same with respect to default risk and liquidity). Suppose that state government issued console with $60 annual payments and that the federal government has also issued console with $60 annual payments.

a. If the federal and state consoles have both the same after-tax yields of 6%, what are their pretax yields? (Assume that the federal income tax rate is 36%)

2. Suppose it is 2020 and 1-year interest rate is 5 percent. You observe that the interest rate on 2-year bond is 4.5%. Assume there is no liquidity premium and the interest rates are determined according to expectation hypothesis of the yield curve

a. Based on the interest rates above, what is the expected 1-year interest rate, starting one year from today?

b. If the interest rate on 3-year bond is 4%., what is the expected 1-year interest rate starting 2 years from today?

c. If the interest rate on 4-year bond is 4%., what is the expected 1-year interest rate starting 3 years from today?

d. Draw the yield curve for the next four years.

e. Is the yield curve for the next four years upward sloping or downward sloping? Explain why

f. What might the yield curve today indicate about future interest rates?

g What might the yield curve today indicate about future economic activity? Explain why?

h. What might the yield curve indicate about the markets’ prediction for inflation rate in the next four years?

i. What might the yield curve indicate about monetary policy today?

j. What might the yield curve indicate about a long-term bonds price? Expected return on long-term bonds? Explain

k. Given the slope of the yield curve today, would you rather be lender or borrower in the next five years? Why?

3. The following is from an article in the Wall Street Journal, describing events in the market for Treasury securities on the given day: “Treasury prices were mixed, with the shorter end of the yield curve falling and the longer- dated Treasury rising in prices”.

a. Draw Treasury yield curve, showing the situation on that day as described in the sentence above.

Explain why prices of Treasury were mixed with the shorter end of the yield curve rising in prices and the longer- dated Treasury falling in prices.

Given the latest data on the state of the U.S. economy, assume that the Fed signals the next increase in the target for the federal funds. The increase won’t happen until the Fed’s meeting in summer of 2016.

Will the Treasury yield curve become more or less steep today?

Which of the following would you expect in the market for Treasury? Explain your choice

- There will be an increase in demand for bond today?

There will be a decrease in supply of bonds today?

There will be a decrease in demand for bonds today?

There will be an increase in supply of bonds today?

What will happen to the yields on Treasury? Explain

4. The table below shows current and expected future one-year interest rates, as well as current interest rates on n-year bonds

Year One-year Bond Rate N-Year Bond Rate Liquidity premium

1 2% 2% _______

2 3% 3% _______

3 4% 5% _______

4 6% 6% _______

5 7% 8% _______

Assume the expectation theory of the term structure and calculate interest rates in the term structure for maturities of one to five years.

Draw the yield curve for the next four years.

Is the yield curve for the next four years upward sloping or downward sloping? Explain why

What might the yield curve today indicate about future interest rates?

What might the yield curve today indicate about future economic activity? Explain why?

What might the yield curve indicate about the markets’ prediction for inflation rate in the next four years?

Calculate the liquidity premium for each n-year bond

What does the liquidity premium stay for?

Compare the liquidity premium in 2-year bond and 5-year bond. Why is the liquidity premium on 2-year bond lower than the liquidity premium on 5-year bond?

5. A Suppose that you are the manager of the Bank One. Assume required reserve ratio 10 percent. The bank has the following balance sheet:

Assets Liabilities

Reserves $ 65 million Deposits $ 400 million

Loans $ 425 million Bank capital $ 90 million

Is Bank One meeting the reserve requirement?

By how much can Bank One increase its loans?

Suppose Bank One suffers a deposit outflow of $40 million .Illustrate numerically the effect of the deposit outflow of $40 million on the bank’s deposits and reserves

Does the bank now hold excess reserves?

Is the bank meeting a required reserve ratio of 10 percent?

What action must you take to meet the reserve requirement? List three or more actions. work

If a borrower defaults on a loan of $10 million, will be the bank able to sustain the loss?

Why no, why yes?

If Bank One ROA is 7%, what is the bank profit? What is the bank ROE?

How can you increase the bank’s ROE, what trade –off do you face?

6. Suppose that you are the manager of the Bank One that has $30 million of fixed assets, $20 million of variable interest rate assets, $15 million of fixed liabilities and $25 million of variable interest rate liabilities.

a. Is the rate sensitivity gap positive or negative? Explain

b. Explain verbally and show numerically what will happen to the bank profits if interest rates rise by 4 percent.

c. What action would you take to reduce the bank’s interest-rate risk? Explain

d. Explain and show numerically what happens to the bank profit if interest rates fall by 4 percent

e. What action would you take to reduce the bank’s interest-rate risk? Explain

f. Given the bank assets and liabilities explain how you can use the interest rate swaps to reduce the bank interest rate risk. Would you trade variable- rate payments for fixed- rate payment? Why yes, why not?

7. Assume the following information about the banking system

Quantities in billions of dollars

Currency (C) = $762

Excess Reserves ( R ) = $66

Required reserves (RR) = $0

Checking deposits (D ) = $604

Give the numerical answer to the following questions:

a. What is the size of the monetary base?

b. What is the money supply in the economy?

c. What is the size of the money multiplier?

Assume that the currency to deposit ratio rises to 1.5

a. Compute the effect of the change in currency ratio on the money multiplier, m

b. What will be the money supply now given the monetary base?

If the Fed wants to keep the money supply at the initial level in part b, how must the Fed respond? Explain

Would the Fed adjust the money multiplier, the monetary base or both to keep the money supply at the initial level?

How much would the Fed buy or sell in the government bonds to keep the money supply at the initial level?

8. Assume that the MB = $828, Money supply = $1366, Currency in the circulation = $ $762, Deposit = $$604, the currency to deposits ratio c is 1.262, the excess reserve ratio is 0.109, the required reserve ratio is 0, and the money multiplier m= 1.650. The non-bank public shifts $40B from currency to deposits, and the Fed wishes to keep the money supply at the level of $1366 B. Explain verbally and show numerically the effect of the currency shift on the following

a. The level of reserves in the banking system

b. The monetary base

c. The size of the money multiplier

d. How should the Fed respond given his goal of keeping the money supply at the level of $1366? Explain

e. How much in the government bonds should the Fed buy or sell to keep the money supply at the level of $1366?

9. Use the graph of the market for reserves to analyze each of the following situations. Be sure that your graph clearly shows changes in the equilibrium federal funds rate, changes in the equilibrium level of reserves, any shifts in the demand and supply curves, and any change in equilibrium federal funds rate

Suppose that the Fed decides to increase the federal funds rate from 2%to 2.25%. Show graphically and explain verbally what policy tools the Fed can use to bring the change in the federal funds rate.

Suppose that the Fed decides to decrease the federal funds rate from 2.25%to 2.%. Show graphically and explain verbally what policy tools the Fed can use to bring the change in the federal funds rate.

Suppose that banks increase their demand for reserve. Show graphically and explain verbally how the Fed can offset this change in order to keep the equilibrium federal funds rate unchanged

Suppose there is a switch from currency into deposits, everything else held constant. Show graphically and explain verbally how the Fed can offset this change in order to keep the equilibrium federal funds rate unchanged

Suppose that the Fed decides to decrease the required reserve ratio. Show graphically and explain verbally how the Fed can offset this change in order to keep the equilibrium federal funds rate unchanged.

f. Suppose that banks decrease their demand for reserves. Show graphically and explain

verbally how the Fed can offset this change in order to keep the equilibrium federal funds

rate unchanged.

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