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Lecture on bond

Learn about bonds, long-term debt instruments, their types (fixed rate, floating rate, inflation-linked, etc.), and how to value them. Understand coupon rates, discounts, and differences between stocks and bonds.

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Lecture on bond

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  1. Lecture on bond www.AssignmentPoint.com

  2. A bond is a long-term debt instrument issued by a corporation or a government. It is a fixed-income security. What’s a bond? www.AssignmentPoint.com

  3. A bond is a formal contract to repay borrowed money with interest at fixed intervals. • A bond provides the borrower with external funds to: • finance long term investments (for corporations) • finance current expenditures (for municipal, state or national governments). What’s a bond? www.AssignmentPoint.com

  4. Shares of stockBond Equity stake in the firm Creditor stake in the firm [i.e. owners] [.i.e. lenders] Undefined term Defined term (maturity) (outstanding indefinitely) Difference between stocks and bonds www.AssignmentPoint.com

  5. A non-zero coupon-paying bondis a coupon-paying bond with a finite life. • A zero-coupon bond is a bond that pays no interest but sells at a deep discount from face value. • A perpetual bond is a bond that never matures. It has an infinite life. Types of bonds www.AssignmentPoint.com

  6. A fixed rate bondis a bond whose coupon rate remains constant throughout the life of the bond. • A floating rate bond is a bond with a variable coupon that is linked to a reference rate of interest, such as the LIBOR. [LIBOR + 20 b.p.] • An inflation-linked bond is a bond whose coupon payments and principal are indexed to inflation. • Gilts in the UK • TIPS in the US Types of bonds www.AssignmentPoint.com

  7. A Municipal bond (or muni) is a bond issued by a municipality, city, state or their agencies and is usually tax exempt. • A lottery bond is a bond with coupon payments like fixed-rate bonds, but the issuer will redeem randomly selected individual bonds for a higher value than the bond’s face value. • An asset-backed security (e.g. CDOs, CMOs, MBSs) is a bond whose interest and principal payments are backed by underlying cash flows from other assets. Types of bonds www.AssignmentPoint.com

  8. The maturity value (MV) [or face value] of a bond is the stated value. • In the case of a U.S. bond, the MV is usually $1,000. • In the case of a Bangladeshi prize bond, the MV is usually 100 Taka. The maturity value www.AssignmentPoint.com

  9. The coupon rate [or coupon yield] of a bond is the stated rate of interest. Coupon rate Annual coupon payments (CP) Coupon rate = Maturity value (MV) For example: Annual coupon payments = $80 Face value = $1,000 Coupon rate = $80/$1,000 = 0.08 = 8% www.AssignmentPoint.com

  10. If the annual coupon payments are $70 and the face value of a bond is $1,000, what is its coupon rate? Sample problem #1 Annual coupon payments (CP) Coupon rate = Maturity value (MV) Annual coupon payments = $70 Face value = $1,000 Coupon rate = $70/$1,000 = 0.07 = 7% www.AssignmentPoint.com

  11. If the annual coupon payments are $100 and the face value of a bond is $1,000, what is its coupon rate? Sample problem #2 Annual coupon payments (CP) Coupon rate = Maturity value (MV) Annual coupon payments = $100 Face value = $1,000 Coupon rate = $100/$1,000 = 0.10 = 10% www.AssignmentPoint.com

  12. The discount rate [or capitalization rate] of a bond is dependent on the risk of the bond. • The discount rate (kd) is composed of the risk-free rate plus a premium for risk. The discount rate www.AssignmentPoint.com

  13. Bond value = PV of coupons + PV of MV • Bond value = PV annuity + PV of lump sum Bond valuation Remember: as interest rates increase, the PVs decrease. So, as interest rates increase, bond prices decrease. www.AssignmentPoint.com

  14. Bond value = PV of coupons + PV of MV • Bond value = PV annuity + PV of lump sum Bond valuation V = CP(PVIFA kd, n) + MV(PVIF kd, n) www.AssignmentPoint.com

  15. A bond has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the bond? Bond valuation V = CP(PVIFA kd, n) + MV(PVIF kd, n) www.AssignmentPoint.com

  16. A bond has a $ 1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the bond? Bond valuation V = CP(PVIFA 10%, 30) + MV(PVIF 10%, 30) =$80(9.427) + $1,000 (0.057) = $754.16 + 57.00 = $811.16 www.AssignmentPoint.com

  17. A bond has a $ 1,000 face value and provides a 6% annual coupon for 20 years. The appropriate discount rate is 6%. What is the value of the bond? Sample problem #1 V = CP(PVIFA 6%, 20) + MV(PVIF 6%, 20) =$60(11.4699) + $1,000 (0.3118) = $688.19 + 311.80 = $999.99 www.AssignmentPoint.com

  18. A bond has a $ 1,000 face value and provides a 6% annual coupon for 10 years. The appropriate discount rate is 10%. What is the value of the bond? Sample problem #2 V = CP(PVIFA 10%, 10) + MV(PVIF 10%, 10) =$60(6.1446) + $1,000 (0.3855) = $368.68 + 385.50 = $754.18 www.AssignmentPoint.com

  19. Most bonds pay coupon payments twice a year. • They pay ½ of the annual coupon payments. Semi-annual compounding Adjustments neededfor semi-annual compounding: (1) Divide kd by 2 (2) Multiply n by 2 (3) Divide CP by 2 www.AssignmentPoint.com

  20. Semi-annual compounding A non-zero coupon bondadjusted for semi-annual compounding: V = CP/2(PVIFA kd/2, n*2) + MV(PVIF kd/2, n*2) www.AssignmentPoint.com

  21. A bond has a $ 1,000 face value and provides an 8% semi-annual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond? Sample problem #1 V = CP/2(PVIFA 10%/2, 15*2) + MV(PVIF 10%/2, 15*2) =$40(15.3725) + $1,000 (0.2314) = $614.90 + 231.40 = $846.30 www.AssignmentPoint.com

  22. A bond has a $ 1,000 face value and provides a 6% semi-annual coupon for 15 years. The appropriate discount rate is 6% (annual rate). What is the value of the coupon bond? Sample problem #2 V = CP/2(PVIFA 6%/2, 15*2) + MV(PVIF 6%/2, 15*2) =$30(19.6004) + $1,000 (0.4120) = $588.01 + 412.00 = $1,000.01 www.AssignmentPoint.com

  23. A zero-coupon bond is a bond that pays no interest but sells at a deep discount from its face value. Zero-coupon bond valuation V = MV(PVIF kd, n) www.AssignmentPoint.com

  24. A bond has a $1,000 face value and a 30-year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond? Zero-coupon bond example V = MV(PVIF kd, n) www.AssignmentPoint.com

  25. A bond has a $1,000 face value and a 30-year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond? Zero-coupon bond example V = MV(PVIF 10%, 30) = $1,000 (0.057) = $57.00 www.AssignmentPoint.com

  26. A bond has a $1,000 face value and a 30-year life. The appropriate discount rate is 6%. What is the value of the zero-coupon bond? Zero-coupon bond example #2 V = MV(PVIF 6%, 30) = $1,000 (0.1741) = $174.10 www.AssignmentPoint.com

  27. A bond has a $1,000 face value and a 10-year life. The appropriate discount rate is 6%. What is the value of the zero-coupon bond? Zero-coupon bond example #3 V = MV(PVIF 6%, 10) = $1,000 (0.5584) = $558.40 www.AssignmentPoint.com

  28. A perpetual bond is a bond that never matures. It has an infinite life. Perpetual bond valuation V = CP / kd www.AssignmentPoint.com

  29. A bond has a $1,000 face value and provides an 8% coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? Perpetual bond example V = CP / kd www.AssignmentPoint.com

  30. A bond has a $1,000 face value and provides an 8% coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond? Perpetual bond example CP = $1,000 * (8%) = $80 kd = 10% = 0.10 V = CP /kd =$80/ 0.10 =$800 www.AssignmentPoint.com

  31. A bond has a $1,000 face value and provides a 6% coupon. The appropriate discount rate is 20%. What is the value of the perpetual bond? Perpetual bond example #2 CP = $1,000 * (6%) = $60 kd = 20% = 0.20 V = CP /kd =$60/ 0.20 =$300 www.AssignmentPoint.com

  32. A bond has a $1,000 face value and provides a 5% coupon. The appropriate discount rate is 8%. What is the value of the perpetual bond? Perpetual bond example #3 CP = $1,000 * (5%) = $50 kd = 8% = 0.08 V = CP /kd =$50/ 0.08 =$625 www.AssignmentPoint.com

  33. The yield to maturity (YTM) of a bond is the discount rate which returns the market price of the bond. • YTM is often used to price a bond. • Bond prices are often quoted in terms of YTM. Yield to maturity (YTM) www.AssignmentPoint.com

  34. You want to determine the YTM for an issue of outstanding bonds at your firm. • Your firm has an issue of 10% annual coupon bonds with 15 years left to maturity. • The bonds have a current market value of $1,250. • What is the YTM? YTM calculations www.AssignmentPoint.com

  35. $1,250 = $100 (PVIFA 9%, 15) + $1,000 (PVIF 9%, 15) $1,250 = $100 (8.061) + $1,000 (.275) $1,250 = $806.10 + $275.00 = $1,081.10 [Rate is too high] YTM solution (9%) www.AssignmentPoint.com

  36. $1,250 = $100 (PVIFA 7%, 15) + $1,000 (PVIF 7%, 15) $1,250 = $100 (9.108) + $1,000 (.362) $1,250 = $910.80 + $362.00 = $1,272.80 [Rate is too low] YTM solution (7%) www.AssignmentPoint.com

  37. .07 $1,273 .02IRR$1,250$192 .09 $1,081 X$23 .02$192 YTM solution (interpolate) $23 X = www.AssignmentPoint.com

  38. .07 $1,273 .02IRR$1,250$192 .09 $1,081 X$23.02$192 YTM solution (interpolate) $23 X = www.AssignmentPoint.com

  39. .07 $1,273 .02 YTM $1,250 $192 .09 $1,081 ($23)(0.02) $192 YTM solution (interpolate) $23 X X = X = .0024 YTM = .07 + .0024 = .0724 or 7.24% www.AssignmentPoint.com

  40. Your firm has an issue of 8% annual coupon bonds with 10 years left to maturity. • The bonds have a current market value of $1,100. • What is the YTM? YTM problem #1 www.AssignmentPoint.com

  41. Your firm has an issue of 9% annual coupon bonds with 12 years left to maturity. • The bonds have a current market value of $1,310. • What is the YTM? YTM problem #2 www.AssignmentPoint.com

  42. A bond selling for more than its face value is called a premium bond. • A bond selling for less than its face value is called a discount bond. Premium vs. discount bond www.AssignmentPoint.com

  43. The current yield is the coupon payment (CP) as a percentage of the current bond price (P0). Current yield = CP / P0 Current vs. coupon yield • The coupon yield of a bond is the stated rate of interest. Annual coupon payments (CP) Coupon yield = Maturity value (MV) www.AssignmentPoint.com

  44. When a bond sells at a discount • YTM > current yield > coupon yield • When a bond sells at a premium • Coupon yield > current yield > YTM • When a bond sells at par • YTM = current yield = coupon yield YTM, current & coupon yield www.AssignmentPoint.com

  45. Bangladesh’s bond market is TINY. • It accounts for only 12% of the GDP. • In South Asian countries, bonds account for an average of 34% of the GDP. • In USA, the bond market accounts for 21% of the GDP, in Korea 29%, in Japan 16% and for select OECD countries 16%. The Bangladeshi bond market www.AssignmentPoint.com

  46. The bond market is dominated by short and long term government securities. • The Bangladesh Bank sells 28-day, 91-day, 182-day and 364-day treasury bills and five, ten, fifteen and twenty year treasury bonds. • The central bank holds auctions every week and any investor can bid for bonds through any bank. The Bangladeshi bond market www.AssignmentPoint.com

  47. An auction committee fixes the coupon rate which is applicable throughout the instrument’s life. • These government bonds pay interest or coupon payments every six months. • Generally, these bonds are of 100,000 (or 1 Lakh) Taka denomination or their multiples. The Bangladeshi bond market www.AssignmentPoint.com

  48. There is a secondary bond market; however, the trading activity is very limited. • Government paper has been traded since 2005. • Corporate bonds are far and few in between. The Bangladeshi bond market www.AssignmentPoint.com

  49. The corporate bond market is highly under-developed and has only nine bonds. • All corporate bonds are issued through private placement. • Notable corporate bonds include the Islamic Bank Bangladesh Limited (IBBL) Mudaraba Perpetual bond. <- Perpetual bond The Bangladeshi bond market www.AssignmentPoint.com

  50. Grameenphone issued 540-day and 720-day bonds worth US $62 million via Citi. (coupon: 14.5%) <- Fixed rate bond • Bangladesh Petroleum (BPC) closed a US $250 million 360-day facility via Standard Chartered. (coupon: LIBOR + 160 b.p.). <- Floating rate bond The Bangladeshi bond market www.AssignmentPoint.com

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