1. 1 Valuation and Characteristics of Bonds Chapter 7

2. 2 Learning Objectives Learning Objectives  Distinguish between different kinds of bonds.  Explain the more popular features of bonds.  Define the term value as used for several different purposes.  Describe the basic process for valuing assets.  Estimate the value of a bond.  Compute a bondholder’s expected rate of return.  Explain five important relationships that exist in bond valuation.

3. 3 General Valuation: The following comments are valid for all kind of assets.  Book Value  Stated value from the firm’s Balance Sheet  Market Value  The price for the asset at any given time--determined by supply and demand in the marketplace. Asset can be bought or sold at this price.  Intrinsic Value  Present value of the asset’s expected cash flow  Investor estimates cash flows  Investor determines required rate based on risk of asset and market conditions.

4. 4 In a perfect market where all investors have the same expectations & risk aversion: In a perfect market where all investors have the same expectations & risk aversion: Market Value = Intrinsic Value

5. 5 Bonds  Debt Instruments  Bondholders are lending to the corporation (or, governments) money for some stated period of time.  Liquid Asset  Corporate Bonds can be traded in the secondary market.  Price at which a given bond trades is determined by market conditions and terms of the bond.

6. 6 Bond Terminology  Par Value  Usually $1,000. Also called the Face Value  Coupon Interest Rate  Borrowers (firms) typically make periodic payments to the bondholders. Coupon rate is the percent of face value paid every year.  Maturity  Time at which the maturity value (Par Value) is paid to the bondholder.  Indenture  Document which details the legal obligation of the corporation to the bondholders. The indenture lists all the terms and conditions of the bond.

7. 7 Types of Bonds  Debentures  Subordinated Debenture  Mortgage Bond  Eurobond  Convertible Bond  Zero Coupon Bonds  Junk Bond

8. 8 Bond Ratings  Moody’s and Standard & Poors regularly monitor issuers’ financial conditions and assign a rating to the debt. Bond rating shows the relative probability of default.  similar to a personal credit report AAATop Quality AA A BBB BB B CCC CCLow Quality CNo interest being paid DCurrently in Default InvestmentGrade Junk

9. 9 Bond Ratings  Bond Ratings can change due to many factors.  Caterpillar Corp debt was recently upgraded due to fact that it appears that current 10 month strike has not affected prospects of firm in any significant manner. Corporate Bond Ratings CiticorpA- GMACBBB+ Bell SouthAAA DuPontAA- Phillip MorrisA KrogerBB+ UnisysBB- Bethlehem SteelB+ Grand UnionD

10. 10 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Company Issuing the Bond

11. 11 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Coupon Interest Rate

12. 12 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Coupon Interest Rate Determines the Investor’s Periodic Cash Flow

13. 13 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Coupon Interest Rate Determines the Investor’s Periodic Cash Flow Cash Flow = Interest Payment = Coupon Rate x Par =.06375 x 1000 = $63.75/Year

14. 14 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Year of Maturity

15. 15 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Year of Maturity Determines the Time frame for the Investment 00 = year 2000, therefore in 1995 this is a 5 year investment

16. 16 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Current Yield (%)

17. 17 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Current Yield (%) Current Yield = Anuual $ Coupon Market Price =.066 = 6.6% 63.75 966.25 =

18. 18 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Daily Trading Volume

19. 19 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Daily Closing Market Price

20. 20 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Daily Closing Market Price Expressed as a % of Par

21. 21 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Daily Closing Market Price $Price = 96 5 / 8 x 10 = $966.25 Expressed as a % of Par

22. 22 Bond Quotes CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Change from Previous Day’s Closing Price

23. 23 Bond Valuation Model  Bond Valuation is an application of Present Value.  The Value of the bond is the present value of all the cash flows the investor receives as a result of holding the bond.  3 Cash Flows  Amount that is paid to purchase the bond (PV)  Periodic Interest Payments made to the bondholders (PMT)  Payment of maturity value at end of Bond’s life.  Other Terminology  Time frame for cash flows (N) = Bond’s Maturity  Interest Rate for Time Value is the rate at which future cash flows are being discounted to present.

24. 24 Bond Valuation Model IBM Bond Timeline: CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal Investor that purchases bond today (1995) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.

25. 25 Bond Valuation Model IBM Bond Timeline: CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Investor that purchases bond today (1995) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.

26. 26 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.

27. 27 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. $59.03$63.75 (1.08)

28. 28 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. $59.03 $63.75 (1.08) 2 $54.66

29. 29 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. $59.03 $54.66 $50.61 $63.75 (1.08) 3

30. 30 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. $59.03 $54.66 $50.61 $46.86 $63.75 (1.08) 4

31. 31 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. $59.03 $54.66 $50.61 $46.86 $43.39 $63.75 (1.08) 5

32. 32 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment. $59.03 $54.66 $50.61 $46.86 $43.39 $935.12 $1000 (1.08) 5 $680.58

33. 33 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years

34. 34 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years $1000 Lump Sum in 5 years

35. 35 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years V b = I (PV of Annuity) + PV of Par $1000 Lump Sum in 5 years

36. 36 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years V b = I (PV of Annuity) + PV of Par $1000 Lump Sum in 5 years Where: I = Periodic Interest Payment k b = Investor’s Required Rate of Return

37. 37 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years V b = I (PV of Annuity) + PV of Par $1000 Lump Sum in 5 years 1.08(1+.08) 5 1.08 = 63.75( ) + 1000 (1+.08) 5

38. 38 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years V b = I (PV of Annuity) + PV of Par $1000 Lump Sum in 5 years 1.08(1+.08) 5 1.08 = 63.75( ) + = 63.75(3.9927) + 680.58 1000 (1+.08) 5

39. 39 Bond Valuation Model Compute Bond’s Intrinsic Value 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 $63.75 Annuity for 5 years V b = I (PV of Annuity) + PV of Par $1000 Lump Sum in 5 years 1.08(1+.08) 5 1.08 = 63.75( ) + = 63.75(3.9927) + 680.58 1000 (1+.08) 5 = 254.54 + 680.58 = 935.12

40. 40 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45

41. 41 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: CurNet BondsYldVolCloseChg AMR6¼24cv691¼-1½ ATT8.35s258.3110102¾+¼ IBM 6 3 / 8 006.622896 5 / 8 - 1 / 8 Kroger 9s998.874101 7 / 8 - ¼ Source: Wall Street Journal 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45 Rather than receiving 4 annual payments of $90, the bondholder will receive 4x2 = 8 semiannual payments of 90÷2=$45.

42. 42 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.

43. 43 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment. Since interest is received every 6 months, need to use semi-annual compounding

44. 44 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment. Since interest is received every 6 months, need to use semi-annual compounding 1.05(1+.05) 8 1.05 V b = 45( ) + 1000 (1+.05) 8 10% 2 10% 2 Semi-Annual Compounding

45. 45 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment. Since interest is received every 6 months, need to use semi-annual compounding 1.05(1+.05) 8 1.05 V b = 45( ) + =45(6.4632) + 676.84 1000 (1+.05) 8

46. 46 Bond Valuation Model Some Bonds Pay Interest Semi-Annually: 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 4545.00 1000.00 45 Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment. Since interest is received every 6 months, need to use semi-annual compounding 1.05(1+.05) 8 1.05 V b = 45( ) + =45(6.4632) + 676.84 1000 (1+.05) 8 = 290.85 + 676.84 = 967.68

47. 47 Yield to Maturity  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned?

48. 48 Yield to Maturity  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? Substitute the Market Price (P 0 ) for V b and solve for k b where k b = Annual YTM Substitute the Market Price (P 0 ) for V b and solve for k b where k b = Annual YTM

49. 49 Yield to Maturity  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? Substitute the Market Price (P 0 ) for V b and solve for k b where k b = Annual YTM Substitute the Market Price (P 0 ) for V b and solve for k b where k b = Annual YTM Cannot Solve Directly

50. 50 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? -966.25 IBM Corporate Bond:

51. 51 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? -966.25 ?? + ?? 966.25 IBM Corporate Bond:

52. 52 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? -966.25 ?? + ?? 966.25 IBM Corporate Bond:

53. 53 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00  Bondholder’s Expected Rate of Return.  If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned? -966.25 ?? + ?? 966.25 IBM Corporate Bond:

54. 54 Yield to Maturity Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:

55. 55 Yield to Maturity Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM: YTM Approximation Formula

56. 56 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 -966.25 IBM Corporate Bond: YTM Approximation Formula

57. 57 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 -966.25 IBM Corporate Bond: YTM Approximation Formula

58. 58 Yield to Maturity 0 1 2 3 4 5 1995 1996 1997 1998 1999 2000 63.75 1000.00 -966.25 IBM Corporate Bond: 70.50 977.50   7.21%  YTM Approximation Formula

59. 59 Interest Rate Risk  Bond Prices fluctuate over Time  As interest rates in the economy change, required rates on bonds will also change resulting in investor’s intrinsic values changing and market prices changing. Interest Rates VbVbVbVb

60. 60 Interest Rate Risk  Bond Prices fluctuate over Time  As interest rates in the economy change, required rates on bonds will also change resulting in investor’s intrinsic values changing and market prices changing. Interest Rates VbVbVbVb VbVbVbVb

61. 61 Interest Rate Risk  Bond Prices fluctuate over Time

62. 62 Interest Rate Risk  Bond Prices fluctuate over Time  When bonds are originally issued, the coupon rate is set to match current prevailing rates.

63. 63 Interest Rate Risk  Bond Prices fluctuate over Time  When bonds are originally issued, the coupon rate is set to match current prevailing rates.  Over time, the prevailing rates may change, but the coupon rate is fixed.

64. 64 Interest Rate Risk  Bond Prices fluctuate over Time  When bonds are originally issued, the coupon rate is set to match current prevailing rates.  Over time, the prevailing rates may change, but the coupon rate is fixed.  Resulting in the actual price of the bond changing.

65. 65 Interest Rate Risk  Bond Prices fluctuate over Time  When bonds are originally issued, the coupon rate is set to match current prevailing rates.  Over time, the prevailing rates may change, but the coupon rate is fixed.  Resulting in the actual price of the bond changing. 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6%

66. 66 Interest Rate Risk  Bond Prices fluctuate over Time  When bonds are originally issued, the coupon rate is set to match current prevailing rates.  Over time, the prevailing rates may change, but the coupon rate is fixed.  Resulting in the actual price of the bond changing. 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6% 1.06(1+.06) 20 1.06 V b = 60( ) + 1000 (1+.06) 20 = $1,000

67. 67 Interest Rate Risk 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6% 1998 If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%) AAA Bonds are currently yielding 9%

68. 68 Interest Rate Risk 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6% 1998 AAA Bonds are currently yielding 9% 1.09(1+.09) 17 1.09 V b = 60( ) + 1000 (1+.09) 17 = $743.69 If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)

69. 69 Interest Rate Risk 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6% 1998 AAA Bonds are currently yielding 9% Market Price for ATT6s2015 is now $743.69 2001 If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%) AAA Bonds are currently yielding 5% If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)

70. 70 Interest Rate Risk 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6% 1998 AAA Bonds are currently yielding 9% Market Price for ATT6s2015 is now $743.69 2001 If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%) AAA Bonds are currently yielding 5% 1.05(1+.05) 14 1.05 V b = 60( ) + 1000 (1+.05) 14 = $1,098.99 If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)

71. 71 Interest Rate Risk 1995 Purchase ATT 6s2015 Bond for $1000.00 AAA Bonds are currently yielding 6% 1998 AAA Bonds are currently yielding 9% Market Price for ATT6s2015 is now $743.69 2001 AAA Bonds are currently yielding 5% Market Price for ATT6s2015 is now $1,098.99 If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%) If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%) Bond Prices fall during periods of rising interest rates and rise during periods of falling interest rates.

72. 72 Bond Relationships

73. 73 Bond Relationships Bond Price changes in the opposite direction of the interest rate changes

74. 74 Bond Relationships Bond Price changes in the opposite direction of the interest rate changes If the coupon rate of a bond is less than the required rate of investors, the bond will sell at a discount. Fig. 7-3. As the maturity date approaches, the market value of the bond approaches its par value. Fig 7-4, Table 7- 2. Everything else being equal, a bond with longer maturity is more price sensitive to changes in interest rates than a bond with shorter maturity.

75. 75 Bond Relationships Bond Price changes in the opposite direction of the interest rate changes. If the coupon rate of a bond is less than the required rate of investors, the bond will sell at a discount. Fig. 7-3. As the maturity date approaches, the market value of the bond approaches its par value. Fig 7-4, Table 7- 2. Everything else being equal, a bond with longer maturity is more price sensitive to changes in interest rates than a bond with shorter maturity. Everything else being equal, a bond with higher coupon is less price sensitive to changes in interest rates than a bond with lower coupon.

76. 76