Chapter 3.pdf

Chapter 03 - Valuing Bonds

Chapter 03 Valuing Bonds Multiple Choice Questions

1. The following entities issue bonds to raise long-term loans except: A. The federal government B. State and local governments C. Companies D. Individuals

2. The type of bonds where the identities of bonds' owners are recorded and the coupon interest payments are sent automatically are called: A. Bearer bonds B. Government bonds C. Registered bonds D. None of the above

3. A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The interest payments are made annually. Calculate the price of the bond (in euros)if the yield to maturity is 3.5%. A. 100 B. 106.77 C. 106.33 D. none of the above

4. Generally, a bond can be valued as a package of: I) Annuity, II) Perpetuity, III) Single payment A. I and II only B. II and III only C. I and III only D. none of the above

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5. A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The interest payments are made annually. Calculate the yield to maturity of the bond (in euros) if the price of the bond is 106 euros. A. 5.00% B. 3.80% C. 3.66% D. none of the above

6. Generally, bonds issued in the following countries pay interest semi-annually. I) USA, II) UK, III) Canada, IV) Germany, & V) Japan A. I, II, III, & IV B. I, II, III, & V C. II, III, & IV only D. None of the above

7. If a bond is paying interest semi-annually, then: A. interest is paid once a year B. interest is paid every six moths C. interest is paid every three months D. none of the above

8. A 3-year bond with 10% coupon rate and $1000 face value yields 8% APR. Assuming annual coupon payment, calculate the price of the bond. A. $857.96 B. $951.96 C. $1000.00 D. $1051.54

9. A 5-year treasury bond with a coupon rate of 8% has a face value of $1000. What is the semi-annual interest payment? A. $80 B. $40 C. $100 D. None of the above

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10. A three-year bond has 8.0% coupon rate and face value of $1000. If the yield to maturity on the bond is 10%, calculate the price of the bond assuming that the bond makes semi-annual coupon interest payments. A. $857.96 B. $949.24 C. $1057.54 D. $1000.00

11. A four-year bond has an 8% coupon rate and a face value of $1000. If the current price of the bond is $878.31, calculate the yield to maturity of the bond (assuming annual interest payments). A. 8% B. 10% C. 12% D. 6%

12. A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123. Calculate the yield to maturity on the bond assuming annual interest payments. A. 10.0% B. 8.9% C. 7.0% D. None of the above

13. Which of the following statements about the relationship between interest rates and bond prices is true? I) There is an inverse relationship between bond prices and interest rates. II) There is a direct relationship between bond prices and interest rates. III) The price of short-term bonds fluctuates more than the price of long-term bonds for a given change in interest rates. (Assuming that coupon rate is the same for both) IV) The price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates. (Assuming that the coupon rate is the same for both) A. I and IV only B. I and III only C. II and III only D. None of the given statements are true

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14. Consider a bond with a face value of $1,000, a coupon rate of 6%, a yield to maturity of 8%, and ten years to maturity. This bond's duration is: A. 8.7 years B. 7.6 years C. 0.1 years D. 6.5 years

15. A bond with a face value of $1,000 has coupon rate of 7%, yield to maturity of 10%, and twenty years to maturity. The bond's duration is: A. 10.0 years B. 7.4 years C. 20.0 years D. 12.6 years

16. A bond with a face value of $1,000, coupon rate of 0%, yield to maturity of 9%, and ten years to maturity. This bond's duration is: A. 6.7 years B. 7.5 years C. 9.6 years D. 10.0 years

17. A bond with duration of 10 years has yield to maturity of 10%. This bond's volatility is: A. 9.09% B. 6.8% C. 14.6% D. 6.0%

18. A bond with duration of 5.7 years has yield to maturity of 9%. The bond's volatility is: A. 1.9% B. 5.2% C. 5.7% D. 9.0%

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19. If a bond's volatility is 10% and the interest rate goes down by 0.75% (points) then the price of the bond: A. decreases by 10% B. decreases by 7.5% C. increases by 7.5% D. increases by 0.75%

20. If a bond's volatility is 5% and the interest rate changes by 0.5% (points) then the price of the bond: A. changes by 5% B. changes by 2.5% C. changes by 7.5% D. none of the above

21. Volatility of a bond is given by: I) Duration/ (1 + yield) II) Slope of the curve relating the bond price to the interest rate III) Yield to maturity A. I only B. II only C. III only D. I and II only

22. The term structure of interest rates can be described as the: A. Relationship between the spot interest rates and the bond prices B. Relationship between spot interest rates and stock prices C. Relationship between spot interest rates and maturity of a bond D. None of the above

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23. Which of the following statements is true? I) The spot interest rate is a weighted average of yields to maturity II) Yield to maturity is the weighted average of spot interest rates and estimated forward rates III) The yield to maturity is always higher than the spot rates A. I only B. II only C. III only D. I and III only

24. A forward rate prevailing from period three through to period four can be: I) readily observed in the market place II) extracted from spot interest rate with 3 and 4 years to maturity III) extracted from 1 and 2 year spot interest rates A. I only B. II only C. III only D. I and III only

25. If the 3-year spot rate is 10.5% and the 2-year spot rate is 10%, what is the one-year forward rate of interest two years from now? A. 3.7% B. 9.5% C. 11.5% D. None of the above

26. If the 5-year spot rate is 10% and the 4-year spot rate is 9%, what is the one-year forward rate of interest four years from now? A. 14.1% B. 9.5% C. 1.0% D. 11.0%

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27. If the 4-year spot rate is 7% and the 3-year spot rate is 6%, what is the one-year forward rate of interest three years from now? A. 10.0% B. 6.5% C. 9.6% D. None of the above

28. Interest represented by "r2" is: A. Spot rate on a one-year investment (APR) B. Spot rate on a two-year investment (APR) C. Expected spot rate 2 years from today D. Expected spot rate one year from today

29. How can one invest today at the 2-year forward rate of interest? I) By buying a 2-year bond and selling a 1-year bond with the same coupon II) By buying a 1-year bond and selling a 2-year bond with the same coupon III) By buying a 1-year bond and then after a year reinvesting in a further 1-year bond A. I only B. II only C. III only D. II and III only

30. The expectations hypothesis states that the forward interest rate is the: I) expected future spot rate II) always greater than the spot rate III) yield to maturity A. I only B. II only C. III only D. II and III only

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31. If the nominal interest rate per year is 10% and the inflation rate is 4%, what is the real rate of interest? A. 10% B. 4% C. 5.8% D. None of the above

32. Mr. X invests $1000 at 10% nominal rate for one year. If the inflation rate is 4%, what is the real value of the investment at the end of one year? A. $1100 B. $1000 C. $1058 D. None of the above

33. What forward rate is embedded in a two year zero coupon bonds with a yield to maturity of 6% and a three year zero coupon bond and a yield to maturity of 6.5%? Assume both bonds are currently priced at par. A. 5.50% B. 6.00% C. 6.50% D. 7.50%

34. Which bond is more sensitive to an interest rate change of 0.75%? Bond A: YTM = 4.00%, Maturity = 8 years, Coupon = 6% or $60, Par Value = $1,000 Bond B: YTM = 3.50%, Maturity = 5 years, Coupon = 7% or $70, Par Value = $1,000 A. A B. B C. Both the same D. Cannot be determined

True / False Questions

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35. The yield to maturity on a bond is really its internal rate of return. True False

36. In the US, most bonds make coupon payments annually. True False

37. The duration of any bond is the same as its maturity. True False

38. The duration of a zero coupon bond is the same as its maturity. True False

39. The longer a bond's duration greater is its volatility. True False

40. The term structure of interest rate is the relationship between yield to maturity and maturity. True False

41. If the term structure of interest rate is flat the nine-year interest rate is equal to the ten-year interest rate. True False

42. Short-term and long-term interest rates always move in parallel. True False

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43. The expectations theory implies that the only reason for a declining term structure is that investors expect spot interest rates to fall. True False

44. The relationship between nominal interest rate and real interest rate is given by: (1 + rnominal) = (1 + rreal)(1 + inflation rate) True False

45. Treasury bonds do not have default risk, but are subject to inflation risk. True False

46. Indexed bonds were completely unknown in the U.S. before 1997. True False

47. The U.S. Treasury issues inflation-indexed bonds known as TIPs. True False

48. Forward rates are always higher than spot rates. True False

49. Defaulted bonds often pay some level of residual? True False

Short Answer Questions

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50. Briefly explain the cash flows associated with a bond to the investor.

51. Briefly explain the term "yield to maturity."

52. What is the relationship between interest rates and bond prices?

53. Discuss the concept of duration.

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54. Briefly discuss the concept of volatility.

55. Briefly explain what is meant by "the term structure of interest rates."

56. Briefly explain the expectations theory.

57. What is the relationship between real and nominal rates of interest?

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58. Define the term, "real interest rate."

59. What are TIPs? Briefly explain.

60. What is the relationship between spot and forward rates?

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Chapter 03 Valuing Bonds Answer Key

Multiple Choice Questions

1. The following entities issue bonds to raise long-term loans except: A. The federal government B. State and local governments C. Companies D. Individuals

Type: Easy

2. The type of bonds where the identities of bonds' owners are recorded and the coupon interest payments are sent automatically are called: A. Bearer bonds B. Government bonds C. Registered bonds D. None of the above

Type: Medium

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3. A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The interest payments are made annually. Calculate the price of the bond (in euros)if the yield to maturity is 3.5%. A. 100 B. 106.77 C. 106.33 D. none of the above The annual interest payment = (100) × (0.05) = 5 euros Price = PV; Using a financial Calculator: PMT = 5; I = 3.5; FV = 100; & N = 5; Compute: PV = 106.77 euros

Type: Medium

4. Generally, a bond can be valued as a package of: I) Annuity, II) Perpetuity, III) Single payment A. I and II only B. II and III only C. I and III only D. none of the above

Type: Easy

5. A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The interest payments are made annually. Calculate the yield to maturity of the bond (in euros) if the price of the bond is 106 euros. A. 5.00% B. 3.80% C. 3.66% D. none of the above The annual interest payment = (100) × (0.05) = 5 euros Using a financial Calculator: PMT = 5; FV = 100; & N = 5; & PV = -106 Compute: I = 3.66%

Type: Medium

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6. Generally, bonds issued in the following countries pay interest semi-annually. I) USA, II) UK, III) Canada, IV) Germany, & V) Japan A. I, II, III, & IV B. I, II, III, & V C. II, III, & IV only D. None of the above

Type: Medium

7. If a bond is paying interest semi-annually, then: A. interest is paid once a year B. interest is paid every six moths C. interest is paid every three months D. none of the above

Type: Easy

8. A 3-year bond with 10% coupon rate and $1000 face value yields 8% APR. Assuming annual coupon payment, calculate the price of the bond. A. $857.96 B. $951.96 C. $1000.00 D. $1051.54 PV = (100/1.08) + (100/(1.08^2)) + (1100/(1.08^3)) = $1051.54

Type: Medium

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9. A 5-year treasury bond with a coupon rate of 8% has a face value of $1000. What is the semi-annual interest payment? A. $80 B. $40 C. $100 D. None of the above Annual interest payment = 1000(0.08) = $80; Semi-annual payment = 80/2 = $40

Type: Easy

10. A three-year bond has 8.0% coupon rate and face value of $1000. If the yield to maturity on the bond is 10%, calculate the price of the bond assuming that the bond makes semi-annual coupon interest payments. A. $857.96 B. $949.24 C. $1057.54 D. $1000.00 PV = (40/1.05) + (40/(1.05^2)) + . . . + (1040/(1.05^6)) = $949.24

Type: Difficult

11. A four-year bond has an 8% coupon rate and a face value of $1000. If the current price of the bond is $878.31, calculate the yield to maturity of the bond (assuming annual interest payments). A. 8% B. 10% C. 12% D. 6% Use trial and error method. (80/1.12) + (80/(1.12^2)) + (80/(1.12^3)) + (1080/(1.12^4)) = $870.51. Therefore, yield to maturity is 12%. Or use a financial calculator: PV = -878.31; N = 4; PMT = 80; FV = 1000; COMPUTE: I = 12%

Type: Difficult

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12. A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123. Calculate the yield to maturity on the bond assuming annual interest payments. A. 10.0% B. 8.9% C. 7.0% D. None of the above Use a financial calculator: PV = -1123; FV = 1000; PMT = 100 and N = 5 and compute I = 7.0%

Type: Medium

13. Which of the following statements about the relationship between interest rates and bond prices is true? I) There is an inverse relationship between bond prices and interest rates. II) There is a direct relationship between bond prices and interest rates. III) The price of short-term bonds fluctuates more than the price of long-term bonds for a given change in interest rates. (Assuming that coupon rate is the same for both) IV) The price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates. (Assuming that the coupon rate is the same for both) A. I and IV only B. I and III only C. II and III only D. None of the given statements are true

Type: Difficult

14. Consider a bond with a face value of $1,000, a coupon rate of 6%, a yield to maturity of 8%, and ten years to maturity. This bond's duration is: A. 8.7 years B. 7.6 years C. 0.1 years D. 6.5 years PV = $865.80; Duration = [(55.56) + 2(51.44) + 3(47.63) + 4(44.10) + 5(40.83) + 6(37.81) + 7(35) + 8(32.42) + 9(30.01) + 10(490.99)]/(865.80) = 7.6 years

Type: Difficult

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15. A bond with a face value of $1,000 has coupon rate of 7%, yield to maturity of 10%, and twenty years to maturity. The bond's duration is: A. 10.0 years B. 7.4 years C. 20.0 years D. 12.6 years Step 1: N = 20; PMT = 70; FV = 1,000; I = 10; Compute PV = 744.59 Step 2: Duration = [((1)(70)/1.1) + ((2)(70)/1.1^2) + . . . + ((20)(1070)/1.1^20)]/744.59 = 10 years

Type: Difficult

16. A bond with a face value of $1,000, coupon rate of 0%, yield to maturity of 9%, and ten years to maturity. This bond's duration is: A. 6.7 years B. 7.5 years C. 9.6 years D. 10.0 years

Type: Difficult

17. A bond with duration of 10 years has yield to maturity of 10%. This bond's volatility is: A. 9.09% B. 6.8% C. 14.6% D. 6.0% Volatility (%) = Duration/(1 + yield) = 10/1.1 = 9.09%

Type: Difficult

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18. A bond with duration of 5.7 years has yield to maturity of 9%. The bond's volatility is: A. 1.9% B. 5.2% C. 5.7% D. 9.0% Volatility = 5.7/1.09 = 5.2

Type: Difficult

19. If a bond's volatility is 10% and the interest rate goes down by 0.75% (points) then the price of the bond: A. decreases by 10% B. decreases by 7.5% C. increases by 7.5% D. increases by 0.75% Change in bond price = (Volatility) * (change in interest rates) = 10 * 0.75 = 7.5%

Type: Difficult

20. If a bond's volatility is 5% and the interest rate changes by 0.5% (points) then the price of the bond: A. changes by 5% B. changes by 2.5% C. changes by 7.5% D. none of the above 5 * 0.5 = 2.5%

Type: Medium

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21. Volatility of a bond is given by: I) Duration/ (1 + yield) II) Slope of the curve relating the bond price to the interest rate III) Yield to maturity A. I only B. II only C. III only D. I and II only

Type: Difficult

22. The term structure of interest rates can be described as the: A. Relationship between the spot interest rates and the bond prices B. Relationship between spot interest rates and stock prices C. Relationship between spot interest rates and maturity of a bond D. None of the above

Type: Difficult

23. Which of the following statements is true? I) The spot interest rate is a weighted average of yields to maturity II) Yield to maturity is the weighted average of spot interest rates and estimated forward rates III) The yield to maturity is always higher than the spot rates A. I only B. II only C. III only D. I and III only

Type: Difficult

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24. A forward rate prevailing from period three through to period four can be: I) readily observed in the market place II) extracted from spot interest rate with 3 and 4 years to maturity III) extracted from 1 and 2 year spot interest rates A. I only B. II only C. III only D. I and III only

Type: Difficult

25. If the 3-year spot rate is 10.5% and the 2-year spot rate is 10%, what is the one-year forward rate of interest two years from now? A. 3.7% B. 9.5% C. 11.5% D. None of the above forward rate = [(1.105^3)/(1.1^2)] -1 = 11.5%

Type: Difficult

26. If the 5-year spot rate is 10% and the 4-year spot rate is 9%, what is the one-year forward rate of interest four years from now? A. 14.1% B. 9.5% C. 1.0% D. 11.0% forward rate = [(1.1^5)/(1.09^4)] -1 = 14.1%

Type: Difficult

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27. If the 4-year spot rate is 7% and the 3-year spot rate is 6%, what is the one-year forward rate of interest three years from now? A. 10.0% B. 6.5% C. 9.6% D. None of the above f = [(1.07^4)/(1.06^3)] -1 = 10%

Type: Difficult

28. Interest represented by "r2" is: A. Spot rate on a one-year investment (APR) B. Spot rate on a two-year investment (APR) C. Expected spot rate 2 years from today D. Expected spot rate one year from today

Type: Easy

29. How can one invest today at the 2-year forward rate of interest? I) By buying a 2-year bond and selling a 1-year bond with the same coupon II) By buying a 1-year bond and selling a 2-year bond with the same coupon III) By buying a 1-year bond and then after a year reinvesting in a further 1-year bond A. I only B. II only C. III only D. II and III only

Type: Difficult

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30. The expectations hypothesis states that the forward interest rate is the: I) expected future spot rate II) always greater than the spot rate III) yield to maturity A. I only B. II only C. III only D. II and III only

Type: Difficult

31. If the nominal interest rate per year is 10% and the inflation rate is 4%, what is the real rate of interest? A. 10% B. 4% C. 5.8% D. None of the above 1 + rreal = (1 + rnominal)/(1 + rinflation) = 1.1/1.04 = 1.058; r real = 5.8%

Type: Easy

32. Mr. X invests $1000 at 10% nominal rate for one year. If the inflation rate is 4%, what is the real value of the investment at the end of one year? A. $1100 B. $1000 C. $1058 D. None of the above Real investment = (1000 * 1.1)/(1.04) = $1058

Type: Medium

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33. What forward rate is embedded in a two year zero coupon bonds with a yield to maturity of 6% and a three year zero coupon bond and a yield to maturity of 6.5%? Assume both bonds are currently priced at par. A. 5.50% B. 6.00% C. 6.50% D. 7.50% First calculate the future value of $1 at each YTM. You get 1.1236 for the 2 year bond and 1.1910 for the 3 year bond. Now determine the IRR over between years 2 and 3.

Type: Difficult

34. Which bond is more sensitive to an interest rate change of 0.75%? Bond A: YTM = 4.00%, Maturity = 8 years, Coupon = 6% or $60, Par Value = $1,000 Bond B: YTM = 3.50%, Maturity = 5 years, Coupon = 7% or $70, Par Value = $1,000 A. A B. B C. Both the same D. Cannot be determined The price of bond A decreases from 1134 to 1108. Bond B decreases in price from 1158 to 1121. A drops by 4.67% and B drops by 3.15%.

Type: Difficult

True / False Questions

35. The yield to maturity on a bond is really its internal rate of return. TRUE

Type: Easy

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36. In the US, most bonds make coupon payments annually. FALSE

Type: Easy

37. The duration of any bond is the same as its maturity. FALSE

Type: Difficult

38. The duration of a zero coupon bond is the same as its maturity. TRUE

Type: Medium

39. The longer a bond's duration greater is its volatility. TRUE

Type: Medium

40. The term structure of interest rate is the relationship between yield to maturity and maturity. TRUE

Type: Medium

41. If the term structure of interest rate is flat the nine-year interest rate is equal to the ten-year interest rate. TRUE

Type: Medium

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42. Short-term and long-term interest rates always move in parallel. FALSE

Type: Difficult

43. The expectations theory implies that the only reason for a declining term structure is that investors expect spot interest rates to fall. TRUE

Type: Difficult

44. The relationship between nominal interest rate and real interest rate is given by: (1 + rnominal) = (1 + rreal)(1 + inflation rate) TRUE

Type: Medium

45. Treasury bonds do not have default risk, but are subject to inflation risk. TRUE

Type: Medium

46. Indexed bonds were completely unknown in the U.S. before 1997. FALSE

Type: Medium

47. The U.S. Treasury issues inflation-indexed bonds known as TIPs. TRUE

Type: Medium

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48. Forward rates are always higher than spot rates. FALSE

Type: Difficult

49. Defaulted bonds often pay some level of residual? TRUE

Type: Difficult

Short Answer Questions

50. Briefly explain the cash flows associated with a bond to the investor. Bonds provide two types of cash flows: interest payments and the principal payment. Interest payments occur each period, usually annually or semi-annually. Periodic interest payments are also called coupon payments. Thus this forms an annuity. Principal payment occurs at the time of maturity of the bond and is a lump sum payment.

Type: Easy

51. Briefly explain the term "yield to maturity." The yield to maturity is the single discount rate that is used to calculate the present value of cash flows received from buying a bond. It is used for calculating the bond value. Conceptually it is the same as the internal rate of return (IRR). It is also stock-in-trade of any bond dealer.

Type: Medium

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52. What is the relationship between interest rates and bond prices? Interest rates and bond prices are inversely related. High interest rates cause bond prices to fall and vice-versa. For a given change in interest rates, prices of long-term bonds fluctuate more than for short-term bonds. Similarly, for a given change in interest rates low coupon bond prices fluctuate more than for high coupon bonds.

Type: Medium

53. Discuss the concept of duration. Duration can be thought of as the weighted average time of a bond's cash flow. The weights are determined by the present value factors. Duration is expressed in units of time. Duration is an important concept for two reasons. First, the volatility of a bond is directly related to its duration. Second, one way to hedge interest rate risk is through a strategy of duration matching.

Type: Difficult

54. Briefly discuss the concept of volatility. Volatility is calculated as Duration/ (1 + yield). Bonds with longer duration also have greater volatility. Bond's volatility is directly related to duration. Volatility is also the slope of the curve relating the bond price to the interest rate.

Type: Medium

55. Briefly explain what is meant by "the term structure of interest rates." The term structure of interest rates is the plot of interest rates on the y-axis and the maturity on the x-axis. It is also called the yield curve. It shows how interest rates and maturity are related. Economists have developed several theories to explain the shape of the yield curve.

Type: Medium

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56. Briefly explain the expectations theory. This theory postulates that the current forward rates are the expected value of the corresponding future spot rates.

Type: Medium

57. What is the relationship between real and nominal rates of interest? The exact relationship is given by: (1 + nominal rate ) = (1 + real rate) * (1 + expected Inflation rate). It can also be written as: nominal rate = real rate + Inflation rate + (real rate) * (Inflation rate)

Type: Easy

58. Define the term, "real interest rate." Real interest rate is the inflation adjusted nominal interest rate. We do not observe it directly. The relationship between the two is given by: 1 + rnominal = (1 + rreal rate)(1 + inflation rate). (An approximate formula that works for low values is: rnominal = rreal rate + Inflation rate)

Type: Medium

59. What are TIPs? Briefly explain. TIPs(Treasury Inflation-Protected Securities) are issued by the U.S. Treasury. The U.S. Treasury began issuing TIPs in 1997. These are also known as Inflation-indexed bonds. The real cash flows on TIPs are fixed, but the nominal cash flows, which includes interest and principal, are increased as the Consumer Price Index (CPI) increases. Thus the buying power of the lender in protected.

Type: Medium

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60. What is the relationship between spot and forward rates? A forward rate is the internal rate of return derived from the future value of bonds given spot rates from two different maturity bonds.

Type: Difficult

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