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L Pch13

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L Pch13

  1. 1. Investments Chapter 13: Interest Rates and Bond Valuation
  2. 2. Definition: Bonds and Yields <ul><li>Bonds </li></ul><ul><li>Represent a claim on future cash flows (coupon payments and par value). </li></ul><ul><li>Yield to Maturity </li></ul><ul><li>The annualized discount rate that makes the present value of the future cash flows equal to the current price of the bond. </li></ul>
  3. 3. Other Measures of Bond Yields <ul><li>Coupon yield / nominal yield. </li></ul><ul><li>Current yield. </li></ul><ul><li>Yield to call. </li></ul><ul><li>Realised yield. </li></ul>
  4. 4. Yield Curve: I <ul><li>Bond prices are related inversely to market interest rates. </li></ul><ul><li>This relation is NOT tautological, however: </li></ul><ul><li>bond prices and market interest rates are determined simultaneously by the underlying economic forces that drive the supply and demand for money. </li></ul>
  5. 5. Yield Curve: II <ul><li>The market generally has various interest rates for various maturities. </li></ul><ul><li>The relationship between the market interest rate and the time to maturity is known as the yield curve. </li></ul>
  6. 6. Yield Curve: III Exhibit 13.1 Examples of actual yield curves
  7. 7. Spot and Forward Rates <ul><li>The Spot Rate </li></ul><ul><li>The yield to maturity of a zero-coupon bond that has a stated maturity. </li></ul><ul><li>The Forward Rate </li></ul><ul><li>The yield to maturity of a zero-coupon bond that an investor agrees to purchase at some future specified date. </li></ul>
  8. 8. Spot- & forward rates for pure discount bonds Spot rate is the yield (return) of a pure discount bond, which is sold att discount, since discount bonds, P < F. If a one-year pure discount bond, just issued, is sold at P = €90.9 and has an F = €100, the spot rate is :
  9. 9. Spot & forward rates for pure discount bonds Forward rate is the interest rate an investor will pay to buy a bond in the future , no matter its true interest rate (or its bond price), that date. If I sign a forward contract to buy next year a two-years bond at a P = SEK892.9 (with F = SEK1000, to be paid in two years from now), the forward rate is : If the interest rate next year becomes 10%, the price of the bond will be SEK909. In that case, I gain since I buy the bond at SEK892.9 .
  10. 10. Spot- & forward rates for pure discount bonds Forward rates are derived from spot rates and provide a good information on the expected interest rates in the future. Maturity (n) Spot (R m ) Forward (f n ) 1 5 - 2 5.8 6.606 3 6.3 7.307 4 6.4 6.701 5 6.45 6.65
  11. 11. Spot- & forward rates for pure discount bonds If we graph the spot yield curve, it is 5 % for 1-year and 6.45 % for 5-years. But why is it f 2 = 6.606 % ? Strategy 1 : Save 1 $ directly in 2-years and get: 1(1 + R 2 ) 2 = 1(1.058) 2 = 1.11936. Strategy 2 : (a) Save first 1 $ for 1-year, and (b) sign a contract to invest your $ and its return in an implied rate , (i.e. f 2 ), in order to get the same as in strategy 1.
  12. 12. Spot- & forward rates for pure discount bonds [1(1.05)]*[1 + r impl ] = 1.11936 , i.e. 1 + r impl = 1.11936 / 1.05, => r impl = f 2 = 0.06606. Alternatively, R 2 = (R 1 + f 2 ) / 2. The Formula to estimate implied forward rates (f n ) from one periods’ spot rates (R n ) is:
  13. 13. Calculating Spot and Forward Rates Exhibit 13.2 Spot and forward rates for annually compounded, zero-coupon bonds Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  14. 14. Explaining Yield Curves <ul><li>The Expectations Hypothesis: </li></ul><ul><li>- The Local Expectations Hypothesis. </li></ul><ul><li>- The Unbiased Expectations Hypothesis. </li></ul><ul><li>The Liquidity Preference Hypothesis. </li></ul><ul><li>The Market Segmentation Hypothesis. </li></ul><ul><li>- The Preferred Habitat Hypothesis. </li></ul>
  15. 15. Credit Risk <ul><li>The risk that a company issuing bonds fails to pay the coupon payments or par value in a timely manner. </li></ul><ul><li>Firms that assess the credit risk of bonds are known as credit rating agencies. </li></ul>
  16. 16. Bond Ratings Exhibit 13.4 Bond rating categories by company Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  17. 17. Junk Bonds <ul><li>Bonds rated below BBB or Baa (speculative-grade bonds). </li></ul><ul><li>Junk bonds have two attractive features: </li></ul><ul><li>1. They offer relatively high yields (if bankruptcy does not occur). </li></ul><ul><li>2. They have low correlations with changes in overall interest rates. </li></ul>
  18. 18. Embedded Options in Bonds <ul><li>The Call Feature </li></ul><ul><li>The bond issuer has the right to buy bonds back at a stated redemption price. </li></ul><ul><li>The Conversion Feature </li></ul><ul><li>The bond issuer has the right to convert bonds in common or preferred stocks. </li></ul>
  19. 19. Convertible Bonds <ul><li>A convertible bond is similar to a bond with warrants. </li></ul><ul><li>The most important difference is that a bond with warrants can be separated into different securities and a convertible bond cannot. </li></ul><ul><li>Recall that the minimum (floor) value of convertible: </li></ul><ul><ul><li>Straight or “intrinsic” bond value </li></ul></ul><ul><ul><li>Conversion value </li></ul></ul><ul><li>The conversion option has value. </li></ul>
  20. 20. The Value of Convertible Bonds <ul><li>The value of a convertible bond has three components: </li></ul><ul><ul><li>Straight bond value </li></ul></ul><ul><ul><li>Conversion value </li></ul></ul><ul><ul><li>Option value </li></ul></ul>
  21. 21. Convertible Bond Problem <ul><li>Litespeed, Inc., just issued a zero coupon convertible bond due in 10 years. </li></ul><ul><li>The conversion ratio is 25 shares. </li></ul><ul><li>The appropriate interest rate is 10%. </li></ul><ul><li>The current stock price is $12 per share. </li></ul><ul><li>Each convertible is trading at $400 in the market. </li></ul><ul><ul><li>What is the straight bond value? </li></ul></ul><ul><ul><li>What is the conversion value? </li></ul></ul><ul><ul><li>What is the option value of the bond? </li></ul></ul>
  22. 22. Convertible Bond Problem (continued) <ul><ul><li>What is the straight bond value? </li></ul></ul><ul><ul><li>What is the conversion value? </li></ul></ul><ul><ul><li>25 shares × $12/share = $300 </li></ul></ul><ul><ul><li>What is the option value of the bond? </li></ul></ul><ul><ul><li>$400 – 385.54 = $14.46 </li></ul></ul>
  23. 23. The Value of Convertible Bonds Convertible Bond Value Stock Price Conversion Value Straight bond value = conversion ratio floor value floor value Convertible bond values Option value

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