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CHAPTER 6 Bonds and Their Valuation

CHAPTER 6 Bonds and Their Valuation. Bonds are simply long-term IOUs that represent claims against a firm’s assets. Bonds are a form of debt Bonds are often referred to as fixed -income investments. Bond Basics. Key Features of a Bond. Debt instrument issued by a corp. or government.

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CHAPTER 6 Bonds and Their Valuation

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  1. CHAPTER 6Bonds and Their Valuation

  2. Bonds are simply long-term IOUs that represent claims against a firm’s assets. Bonds are a form of debt Bonds are often referred to as fixed-income investments. Bond Basics

  3. Key Features of a Bond • Debt instrument issued by a corp. or government.

  4. Key Features of a Bond • Par value = face amount of the bond, which is paid at maturity (assume $1,000). =

  5. Key Features of a Bond • Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.

  6. Key Features of a Bond • Maturity date – when the bond must be repaid. • Yield to maturity - rate of return earned on a bond held until maturity.

  7. What is interest rate risk? • Interest rate risk is the concern that interest rates will change, and therefore, a reduction in the value/price of a security.

  8. Interest rate risk example Suppose you just inherited $500,000. You intend to invest the money and live off the interest.

  9. Interest rate risk example • You may invest in either a: • 10-year bond • series of ten 1-year bonds • Both bonds currently yield 5%.

  10. If you choose the 1-year bond strategy: • After year 1, you receive $25,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. • If you choose the 10-year bond strategy: • You can lock in a 5% interest rate, and $25,000 annual income.

  11. Interest Rate Risk • Price Risk • Change in price due to changes in interest rates • Long-term bonds have more price risk than short-term bonds • Low coupon rate bonds have more price risk than high coupon rate bonds

  12. Bond Value • Bond Value = PV(coupons) + PV(par) • Bond Value = PV(annuity) + PV(lump sum) • Remember: • As interest rates increase present values decrease • ( r → PV  ) • As interest rates increase, bond prices decrease and vice versa

  13. Bond Valuation Compute the value for an IBM Bond with a 6.375% coupon that will mature in 5 years given that you require an 8% return on your investment. What are the annual interest payments ($)?

  14. 2009 2010 2011 2012 2013 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1,000.00 IBM Bond Timeline:

  15. 2009 2010 2011 2012 2013 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1000.00 IBM Bond Timeline: $1000 Lump Sum in 5 years $63.75 Annuity for 5 years

  16. IBM Bond Timeline: $1000 Lump Sum in 5 years $63.75 Annuity for 5 years 2009 2010 2011 2012 2013 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 1000.00 = 63.75 PMT 1000 FV 8% I 5 N = PV = 935.12

  17. Most Bonds Pay Interest Semi-Annually: What is the value of a bond with a semi-annual coupon with 5 years to maturity, 9% (nominal) coupon rate if an investor desires a 10% (nominal) return?

  18. 2013 2014 2015 2016 2017 0 1 2 3 4 5 45.00 1000.00 45 45 45 45 45 45 45 45 45 Most Bonds Pay Interest Semi-Annually: e.g. semiannual coupon bond with 5 years to maturity, 9% annual coupon rate. Instead of 5 annual payments of $90, the bondholderreceives 10 semiannual payments of $45.

  19. 2013 2014 2015 2016 2017 0 1 2 3 4 5 45.00 1000.00 45 45 45 45 45 45 45 45 45 Most Bonds Pay Interest Semi-Annually: Compute the value of the bond given that you require a 10% s-a. return on your investment. Since interest is received every 6 months, we need to use semiannual compounding VB = 45 - PMT 1000 - FV 5% - I 10 - N

  20. Compute the value of the bond given that you require a 10% s-a. return on your investment. 2013 2014 2015 2016 2017 Since interest is received every 6 months, we need to use semiannual compounding 0 1 2 3 4 5 45 1,000 45 45 45 45 45 45 45 45 45 Most Bonds Pay Interest Semi-Annually: = PV = 961.39

  21. Semiannual Bonds • Coupon rate = 14% - Semiannual • YTM = 16% (APR) • Maturity = 7 years • Value of bond? • Number of coupon payments? (2t or N) • 14 = 2 x 7 years • Semiannual coupon payment? (C/2 or PMT) • $70 = (14% x Face Value)/2 • Semiannual yield? (YTM/2 or I/Y) • 8% = 16%/2

  22. Semiannual Bonds • Semiannual coupon = $70 • Semiannual yield = 8% • Periods to maturity = 14 • Bond value = • 70[1 – 1/(1.08)14] / .08 + 1000 / (1.08)14 = 917.56 Using the calculator: 14 N 8 I/Y 70 PMT 1000 FV CPT PV = -917.56 Using Excel: =PV(0.08, 14, 70, 1000, 0)

  23. -1,000 2013 2014 2015 2016 2017 012345 80 80 80 80 80 1,000 Yield to Maturity • If bond Sells at a DISCOUNT (less than $1,000) then YTM > Coupon Rate • If bond Sells at a PREMIUM (more than $1,000) then YTM < Coupon Rate

  24. Valuing a Discount Bond with Annual Coupons • Coupon rate = 10% • Annual coupons • Par = $1,000 • Maturity = 5 years • YTM = 11% • Price= ?

  25. Valuing a Discount Bond with Annual Coupons • Coupon rate = 10% • Annual coupons • Par = $1,000 • Maturity = 5 years • YTM = 11% Using the calculator: 5 N 11 I/Y 100 PMT 1000 FV CPT PV = -963.04 Using the formula: B = PV(annuity) + PV(lump sum) B = 369.59 + 593.45 = 963.04 Using Excel: =PV(0.11, 5, 100, 1000, 0) Note: When YTM > Coupon rate  Price < Par = “Discount Bond”

  26. Valuing a Premium Bond with Annual Coupons • Coupon rate = 10% • Annual coupons • Par = $1,000 • Maturity = 20 years • YTM = 8% • Price = ?

  27. Valuing a Premium Bond with Annual Coupons • Coupon rate = 10% • Annual coupons • Par = $1,000 • Maturity = 20 years • YTM = 8% Using the calculator: 20 N 8 I/Y 100 PMT 1000 FV CPT PV = -1196.36 Using the formula: B = PV(annuity) + PV(lump sum) B = 981.81 + 214.55 = 1196.36 Using Excel: =PV(0.08, 20, 100, 1000, 0) Note: When YTM < Coupon rate  Price > Par = “Premium Bond”

  28. 2013 2014 2015 2016 2017 0 1 2 3 4 5 Yield to Maturity • If an investor purchases a 6.375% annual coupon bond today for $900 and holds it until maturity (5 years), what is the expected annual rate of return (YTM)? 63.75 63.75 63.75 63.75 63.75 -900 1000.00 ?? + ?? 900

  29. If an investor purchases a 6.375% annual coupon bond today for $900 and holds it until maturity (5 years), what is the expected annual rate of return ? Will it be >< than 6.375%? 2013 2014 2015 2016 2017 0 1 2 3 4 5 63.75 63.75 63.75 63.75 63.75 -900 1000.00 ?? + ?? 900 Yield to Maturity YTMB = 63.75 PMT 1000 FV 5 N -900 PV I = ?

  30. What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 0 1 9 10 rd=? ... 90 90 90 1,000 PV1 . . . PV10 PVM Find rd that “works”! 887

  31. 10 -887 90 1000 N I/YR PV PMT FV 10.91 INPUTS OUTPUT

  32. Types of Bonds • Vanilla – fixed coupons, repaid at maturity • Zero Coupon – pay no explicit interest but instead, sell at a deep discount • Convertible – can be converted into to stock

  33. Types of Bonds • Junk Bonds – below investment grade

  34. Government Bonds • Treasury Securities = Federal government debt • Treasury Bills (T-bills) • Pure discount bonds • Original maturity of one year or less • Treasury notes (T-notes) • Coupon debt • Original maturity between one and ten years • Treasury bonds (T-bonds) • Coupon debt • Original maturity greaterthan ten years

  35. Tax Consequences A taxable bond has a yield of 8% and a municipal bond has a yield of 6% • If you are in a 40% tax bracket, which bond do you prefer? • 8%(1 - .4) = 4.8% • The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal • At what tax rate would you be indifferent between the two bonds? • 8%(1 – T) = 6% • T = 25%

  36. AAA Best Quality AA High Quality A Upper Medium Grade BBB Medium Grade BB Speculative B Very Speculative CCC Very Very Speculative CC C No Interest Being Paid D Currently in Default Bond Ratings • Moody’s , Standard & Poor’s and Fitch regularly monitor issuer’s financial condition and assign a rating to the debt Investment Grade Below Investment Grade (Junk)

  37. Bond Ratings – Investment Quality • High Grade • Moody’s Aaa and S&P AAA – capacity to pay is extremely strong • Moody’s Aa and S&P AA – capacity to pay is very strong • Medium Grade • Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances • Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

  38. Bond Ratings - Speculative • Low Grade • Moody’s Ba, B, Caa and Ca • S&P BB, B, CCC, CC • Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation. • Very Low Grade • Moody’s C and S&P C – income bonds with no interest being paid • Moody’s D and S&P D – in default with principal and interest in arrears

  39. What affects Bond prices? • Risk • Interest rates

  40. What is the “term structure of interest rates”? What is a “yield curve”? • Term structure: the relationship between interest rates (or yields) and maturities. • A graph of the term structure is called the yield curve.

  41. Draw a normal yield curve

  42. Hypothetical Treasury Yield Curve Interest Rate (%) 1 yr 8.0% 10 yr 11.4% 20 yr 12.65% 15 Maturity risk premium 10 Inflation premium 5 Real risk-free rate Years to Maturity 0 1 20 10

  43. What factors can explain the shape of this yield curve? • This constructed yield curve is upward sloping. • This is due to increasing expected inflation and an increasing maturity risk premium.

  44. Current Yield Curve • Bloomberg

  45. Default risk • If an issuer defaults, investors receive less than the promised return. • Influenced by the issuer’s financial strength and the terms of the bond contract.

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