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Chapter 11

Chapter 11. Bond Prices and Yields. Chapter Summary. Objective:To review the principles of bond pricing and to examine the determinants of credit risk. Bond Characteristics Bond Pricing and YTM Taxation Issues Default Risk and Ratings. Bond Characteristics. Face or par value Coupon rate

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Chapter 11

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  1. Chapter 11 Bond Prices and Yields

  2. Chapter Summary • Objective:To review the principles of bond pricing and to examine the determinants of credit risk. • Bond Characteristics • Bond Pricing and YTM • Taxation Issues • Default Risk and Ratings

  3. Bond Characteristics • Face or par value • Coupon rate • Zero coupon bond • Compounding and payments • Accrued Interest, “dirty price” • Indenture

  4. Different Issuers of Bonds • Canada bonds • Provincial government bonds • Corporations • Municipalities • International Governments and Corporations • Innovative Bonds • Indexed Bonds • Floaters and Reverse Floaters

  5. Provisions of Bonds • Secured or unsecured • Registered or bearer bonds (Canada) • Call provision • Convertible provision • Retractable and extendible (putable) bonds • Floating rate bond

  6. Summary Reminder • Objective:To review the principles of bond pricing and to examine the determinants of credit risk. • Bond Characteristics • Bond Pricing and YTM • Taxation Issues • Default Risk and Ratings

  7. Bond Pricing PB = price of the bond Ct = interest or coupon payments T = number of periods to maturity r = the appropriate semi-annual discount rate

  8. Solving for Price: 10-yr, 8% Coupon Bond, FV = $1,000 Ct = 40 (SA) P = 1000 T = 60 periods r = 5% (SA) PB = $810.71

  9. Bond Prices and Interest Rates • Prices and market interest rates have an inverse relationship • When interest rates get very high the value of the bond will be very low • When rates approach zero, the value of the bond approaches the sum of the cash flows

  10. Price Interest Rate Prices and Interest Rates

  11. Yield to Maturity • Interest rate that makes the present value of the bond’s payments equal to its price Solve the bond price formula for r

  12. Yield to Maturity Example 10 yr Maturity Coupon Rate = 7% Price = $950 Solve for r = semiannual rate r = 3.8635%

  13. Yield Measures Bond Equivalent Yield 3.86% x 2 = 7.72% Effective Annual Yield (1.0386)2 - 1 = 7.88% Current Yield (Annual Interest/Market Price) $70 / $950 = 7.37 %

  14. Realized Yield versus YTM • Reinvestment Assumptions • Holding Period Return • Changes in rates affects returns • Reinvestment of coupon payments • Change in price of the bond

  15. Holding-Period Return: Single Period where I = interest payment P1 = price in one period P0 = purchase price

  16. Holding-Period Example CR = 8% ; YTM = 8%; N=10 years Semiannual Compounding P0 = $1000 In 6M the rate falls to 7%; P1 =$1068.55 HPR = 10.85% (semiannual)

  17. Realized Compound Yield vs. YTM • Requires actual calculation of reinvestment income • Solve for the Internal Rate of Return using the following: • Future Value: sale price + future value of coupons • Investment: purchase price

  18. Example • Two-year bond selling at par, 10% coupon paid once a year. First coupon is reinvested at 8%. Then:

  19. Price Premium bond 1,000 Discount bond Time 0 Maturity date Price Paths of Coupon Bonds

  20. Summary Reminder • Objective:To review the principles of bond pricing and to examine the determinants of credit risk. • Bond Characteristics • Bond Pricing and YTM • Taxation Issues • Default Risk and Ratings

  21. Zero-Coupon Bonds and Taxation Issues • For constant yields, discount bond prices rise over time and premium bond prices decline over time • Original issue discount bonds’ price appreciation (based on constant yield) is taxed as ordinary income • Price changes stemming from yield changes are taxed as capital gains if the bond is sold

  22. Example • 30-year bond with 4% coupon rate, issued at an 8% YTM; if sold one year later, when YTM=7%, for a 36% income tax and a 20% capital gains tax: P0=549.69; P1(8%)=553.66; P1(7%)=631.67

  23. Example (continued)

  24. Summary Reminder • Objective:To review the principles of bond pricing and to examine the determinants of credit risk. • Bond Characteristics • Bond Pricing and YTM • Taxation Issues • Default Risk and Ratings

  25. Default Risk and Ratings • Rating companies • Moody’s Investor Service • Standard & Poor’s • Fitch IBCA • Canadian Bond Rating Service (CBRS) • Rating Categories • Investment grade • Speculative grade

  26. Factors Used by Rating Companies • Coverage ratios • Leverage ratio • Liquidity ratios • Profitability ratios • Cash flow to debt

  27. Financial Ratios by Rating Class

  28. The Altman Discriminant Analysis Method • Observe a sample of bankrupt firms one year prior to default • Observe a sample of similar solvent firms • Find a function of ROE and coverage ratios that separates the bankrupt from the solvent firms • Use the function to predict default/solvency for any off-sample firm (high/low values)

  29. Example of the Altman Method (Canada) • Predicting equation: • Firms with Z>1.626 were “safe”, and firms with Z<1.626 were in risk of default

  30. Protection Against Default • Sinking funds • Subordination of future debt • Dividend restrictions • Collateral

  31. Default Risk and Yield • Risk structure of interest rates • Default premiums • Yields compared to ratings • Yield spreads over business cycles • Flight to quality

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