Bond Valuation

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Bond valuation is the determination of the fair price of a bond

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Bond Valuation

  1. 1. Corporate Finance Bond Valuation – Session 2
  2. 2. Bonds – Fixed Income Securities “ Fixed income securities, promises to pay a stream of semiannual or annual payments for a given number of years and then repay the loan amount at the maturity date.”
  3. 3. Types of Financial Instruments  Treasury Bonds  Corporate Bonds or TFC  Treasury Bills
  4. 4. Key Characteristics of Bonds        Par Value Coupon payment Coupon interest rate Floating Rate Bond Zero coupon bond Original issue discount / premium bonds Maturity Date
  5. 5. Bond Indenture  The bond indenture is the contract between the issuer and the holder. It specifies:      Details regarding payment terms Collateral Positive & negative covenants Par or face value (usually increments of $1,000) Bond pricing – usually shown as the price per $100 of par value, which is equal to the percentage of the bond’s face value
  6. 6. Security & Protective Provisions  Covenants  Positive covenants – things the firm agrees to do    Supply periodic financial statements Maintain certain ratios Negative covenants – things the firm agrees not to do   Restrictions on the amount of debt the firm can take on Prevents the firm from acquiring or disposing of assets
  7. 7. Bond Valuation  Kd = The bond market rate of interest. Discount to use to calculate the present value of bond.  N = The number of years before the bond matures.  INT = Rupee amount of interest paid annually or semiannually.  M or FV = the or maturity value of the bond.
  8. 8. Bond Valuation Bond Value = VB = INT + INT + … + INT + M (1+Kd) ⁿ (1+Kd) ⁿ (1+Kd)¹ (1+Kd)² [ or ] 1 PV = C 1 − r (1+ r ) n + (1FV) n r +r
  9. 9. Bond Valuation       N=3 Kd = 12% INT = 10 M or FV = 100 Find out Bond value. Semi annual coupon.
  10. 10. Current Yield  It is the yield based on bond’s annual coupon payment.  It does not reflect the total return on bond.  It does not reflect the capital gain or loss on bond.
  11. 11. Current Yield  Current Yield = Annual Coupon Payment Current Price of Bond Example: A semi annual bond with a FV = 100, market price Rs.98 and coupon rate of 9.50%. Compute current yield.
  12. 12. Yield to Maturity    The rate of return earned on a bond if it is held till maturity. It is the total rate of return on a bond. YTM equals the expected rate of return only if: 1. The probability of default is ZERO. 2. The bond cannot be called.
  13. 13. Yield to Maturity  YTM approx. = Annual Cpn + (FV – PV ) / N (FV + PV ) / 2 E.g. N = 10, annual coupon 10%, FV = Rs.100, PV = Rs.105. Find out YTM.
  14. 14. Yield to Call  The rate of return earned on a bond if it is called before its maturity.  Can be called if interest rates falls below the bond coupon rate.
  15. 15. Yield to Call YTC = Annual Cpn + (Call price – PV ) / N (Call price + PV ) / 2 E.g. N = 10, FV = 100, PV = 105, Coupon rate = 10%, Call price = 108, Kd = 5%. The bond can be called after 5 Years.
  16. 16. Factors Affecting Bond Prices  There are three factors that affect the price volatility of a bond  Yield to maturity  Time to maturity  Size of coupon
  17. 17. Coupon Rate Relationship to Yield-toMaturity  The relationship between the coupon rate and the bond’s yieldto-maturity (YTM) determines if the bond will sell at a premium, at a discount or at par If Then Bond Sells at a: Coupon < YTM Market < Face Discount Coupon = YTM Market = Face Par Coupon > YTM Market > Face Premium 6 - 17 CHAPTER 6 – Bond Valuation and Interest Rates
  18. 18. Other Types of Bonds/Debt Instruments
  19. 19. Treasury Bills     Short-term obligations of government with an initial term to maturity of one year or less Issued at a discount & mature at face value The difference between the issue price and the face value is treated as interest income To calculate the price of a T bill, use the following formula: P Bill T 6 - 19 Where: P = market price of the T Bill F = F = face value of the T Bill n BEY = the bond equivalent yield 1 + BEY  ÷ n = the number of days until maturity B B = the annual basis (365 days in Pakistan) CHAPTER 6 – Bond Valuation and Interest Rates
  20. 20. Solving for Yield on a T Bill   To solve for the yield on a T bill, rearrange the previous formula and solve for BEY. Example: What is the yield on a Rs.100 T-bill with 180 days to maturity and a market price of Rs.98.20? 6 - 20 CHAPTER 6 – Bond Valuation and Interest Rates
  21. 21. Zero Coupon Bonds    A zero coupon bond is a bond issued at a discount that matures at par or face value A zero coupon bond has no reinvestment rate risk, since there are no coupons to be reinvested To calculate the price of a zero coupon bond, solve for the PV of the face amount 6 - 21 CHAPTER 6 – Bond Valuation and Interest
  22. 22. Zero Coupon Bonds  Example: What is the market price of a Rs.100 zero coupon bond with 25 years to maturity that is currently yielding 14%? 6 - 22 CHAPTER 6 – Bond Valuation and Interest Rates

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