Chapter 9 – Debt V aluation and Interest Rates - Bonds    2005, Pearson Prentice Hall .
Characteristics of Bonds <ul><li>Bonds pay fixed  coupon  (interest) payments at fixed intervals (usually every six months...
Characteristics of Bonds <ul><li>Bonds pay fixed  coupon  (interest) payments at fixed intervals (usually every six months...
<ul><li>Par value  =  $1,000 </li></ul><ul><li>Coupon  =  6.5%  or par value per year, </li></ul><ul><li>or  $65  per year...
<ul><li>Par value  =  $1,000 </li></ul><ul><li>Coupon  =  6.5%  or par value per year, </li></ul><ul><li>or  $65  per year...
<ul><li>Debentures   - unsecured bonds. </li></ul><ul><li>Subordinated debentures   - unsecured “junior” debt. </li></ul><...
<ul><li>Eurobonds   - bonds denominated in one currency and sold in another country. (Borrowing overseas.) </li></ul><ul><...
<ul><li>Eurobonds   - bonds denominated in one currency and sold in another country. (Borrowing overseas.) </li></ul><ul><...
<ul><li>Eurobonds   - bonds denominated in one currency and sold in another country. (Borrowing overseas). </li></ul><ul><...
<ul><li>The  bond contract  between the firm and the trustee representing the bondholders. </li></ul><ul><li>Lists all of ...
<ul><li>Book value:  value of an asset as shown on a firm’s balance sheet; historical cost. </li></ul><ul><li>Liquidation ...
<ul><li>In general, the  intrinsic value  of an asset = the  present value  of the stream of expected cash flows discounte...
<ul><li>C t   = cash flow to be received at time  t . </li></ul><ul><li>k   = the investor’s required rate of return. </li...
<ul><li>Discount the bond’s cash flows at the investor’s required rate of return. </li></ul>
<ul><li>Discount the bond’s cash flows at the investor’s required rate of return. </li></ul><ul><ul><li>The  coupon paymen...
<ul><li>Discount the bond’s cash flows at the investor’s required rate of return. </li></ul><ul><ul><li>The  coupon paymen...
V b  = $I t  (PVIFA  k b , n ) + $M (PVIF  k b , n ) $I t   $M  (1 + k b ) t   (1 + k b ) n V b  =  + n t = 1 
<ul><li>Suppose our firm decides to issue  20-year  bonds with a par value of  $1,000  and annual coupon payments. The ret...
<ul><li>Note :   If the  coupon rate  =  discount rate , the bond will sell for  par value . </li></ul>P/YR = 1  N = 20  I...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Suppose  interest rates fall  immediately after we issue the bonds. The required return on bonds of similar risk d...
<ul><li>P/YR =  1   </li></ul><ul><li>Mode =  end   </li></ul><ul><li>N =  20   </li></ul><ul><li>I%YR =  10   </li></ul><...
<ul><li>P/YR =  1   </li></ul><ul><li>Mode =  end   </li></ul><ul><li>N =  20   </li></ul><ul><li>I%YR =  10   </li></ul><...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Suppose  interest rates rise  immediately after we issue the bonds. The required return on bonds of similar risk r...
<ul><li>P/YR =  1   </li></ul><ul><li>Mode =  end   </li></ul><ul><li>N =  20   </li></ul><ul><li>I%YR =  14   </li></ul><...
<ul><li>P/YR =  1   </li></ul><ul><li>Mode =  end   </li></ul><ul><li>N =  20   </li></ul><ul><li>I%YR =  14   </li></ul><...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 1...
<ul><li>P/YR =  2 </li></ul><ul><li>Mode =  end </li></ul><ul><li>N =  40 </li></ul><ul><li>I%YR =  14 </li></ul><ul><li>P...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 6...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 6...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>PV = 6...
<ul><li>The  expected rate of return  on a bond. </li></ul><ul><li>The rate of return investors earn on a bond if they hol...
<ul><li>The  expected rate of return  on a bond. </li></ul><ul><li>The rate of return investors earn on a bond if they hol...
<ul><li>Suppose we paid  $898.90  for a  $1,000  par  10%  coupon bond with 8 years to maturity and semi-annual coupon pay...
<ul><li>P/YR = 2 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 16 </li></ul><ul><li>PV = -898.90 </li></ul><ul><li>PM...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>898.90...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>898.90...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>898.90...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA  k, n   )  + FV (PVIF  k, n   )  </li></ul><ul><li>898.90...
<ul><li>No coupon interest payments. </li></ul><ul><li>The bond holder’s return is determined entirely by the  price disco...
<ul><li>Suppose you pay  $508  for a zero coupon bond that has  10 years  left to maturity.  </li></ul><ul><li>What is you...
<ul><li>Suppose you pay  $508  for a zero coupon bond that has  10 years  left to maturity.  </li></ul><ul><li>What is you...
<ul><li>P/YR = 1 </li></ul><ul><li>Mode = End </li></ul><ul><li>N = 10 </li></ul><ul><li>PV = -508 </li></ul><ul><li>FV = ...
<ul><li>Mathematical Solution: </li></ul><ul><li>PV = FV (PVIF  i, n   ) </li></ul><ul><li>508 = 1000 (PVIF  i, 10   )  </...
<ul><li>Cur   Net </li></ul><ul><li>Yld  Vol  Close  Chg </li></ul><ul><li>Polaroid 11  1 / 2   06  19.3  395  59  3 / 4  ...
<ul><li>Cur   Net </li></ul><ul><li>Yld  Vol  Close  Chg </li></ul><ul><li>HewlPkd zr  17  ...  20  51  1 / 2   +1 </li></...
<ul><li>  Maturity  Ask </li></ul><ul><li>Rate  Mo/Yr    Bid  Asked    Chg  Yld </li></ul><ul><li>9   Nov  18 139:14  139:...
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Debt valuation and interest rates bonds

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Debt valuation and interest rates bonds

  1. 1. Chapter 9 – Debt V aluation and Interest Rates - Bonds  2005, Pearson Prentice Hall .
  2. 2. Characteristics of Bonds <ul><li>Bonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity . </li></ul>
  3. 3. Characteristics of Bonds <ul><li>Bonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity . </li></ul>0 1 2 . . . n $I $I $I $I $I $I+$M
  4. 4. <ul><li>Par value = $1,000 </li></ul><ul><li>Coupon = 6.5% or par value per year, </li></ul><ul><li>or $65 per year ( $32.50 every six months). </li></ul><ul><li>Maturity = 28 years (matures in 2032). </li></ul><ul><li>Issued by AT&T. </li></ul>
  5. 5. <ul><li>Par value = $1,000 </li></ul><ul><li>Coupon = 6.5% or par value per year, </li></ul><ul><li>or $65 per year ( $32.50 every six months). </li></ul><ul><li>Maturity = 28 years (matures in 2032). </li></ul><ul><li>Issued by AT&T. </li></ul>0 1 2 … 28 $32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000
  6. 6. <ul><li>Debentures - unsecured bonds. </li></ul><ul><li>Subordinated debentures - unsecured “junior” debt. </li></ul><ul><li>Mortgage bonds - secured bonds. </li></ul><ul><li>Zeros - bonds that pay only par value at maturity; no coupons. </li></ul><ul><li>Junk bonds - speculative or below-investment grade bonds; rated BB and below. High-yield bonds. </li></ul>
  7. 7. <ul><li>Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas.) </li></ul><ul><li>example - suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country. Why do this? </li></ul>
  8. 8. <ul><li>Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas.) </li></ul><ul><li>example - suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country. Why do this? </li></ul><ul><ul><li>If borrowing rates are lower in France. </li></ul></ul>
  9. 9. <ul><li>Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas). </li></ul><ul><li>example - suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country. Why do this? </li></ul><ul><ul><li>If borrowing rates are lower in France. </li></ul></ul><ul><ul><li>To avoid SEC regulations. </li></ul></ul>
  10. 10. <ul><li>The bond contract between the firm and the trustee representing the bondholders. </li></ul><ul><li>Lists all of the bond’s features: </li></ul><ul><li>coupon, par value, maturity, etc. </li></ul><ul><li>Lists restrictive provisions which are designed to protect bondholders. </li></ul><ul><li>Describes repayment provisions. </li></ul>
  11. 11. <ul><li>Book value: value of an asset as shown on a firm’s balance sheet; historical cost. </li></ul><ul><li>Liquidation value: amount that could be received if an asset were sold individually. </li></ul><ul><li>Market value: observed value of an asset in the marketplace; determined by supply and demand. </li></ul><ul><li>Intrinsic value: economic or fair value of an asset; the present value of the asset’s expected future cash flows. </li></ul>
  12. 12. <ul><li>In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return . </li></ul><ul><li>Can the intrinsic value of an asset differ from its market value ? </li></ul>
  13. 13. <ul><li>C t = cash flow to be received at time t . </li></ul><ul><li>k = the investor’s required rate of return. </li></ul><ul><li>V = the intrinsic value of the asset. </li></ul>V = t = 1 n  $C t (1 + k) t
  14. 14. <ul><li>Discount the bond’s cash flows at the investor’s required rate of return. </li></ul>
  15. 15. <ul><li>Discount the bond’s cash flows at the investor’s required rate of return. </li></ul><ul><ul><li>The coupon payment stream (an annuity). </li></ul></ul>
  16. 16. <ul><li>Discount the bond’s cash flows at the investor’s required rate of return. </li></ul><ul><ul><li>The coupon payment stream (an annuity). </li></ul></ul><ul><ul><li>The par value payment (a single sum). </li></ul></ul>
  17. 17. V b = $I t (PVIFA k b , n ) + $M (PVIF k b , n ) $I t $M (1 + k b ) t (1 + k b ) n V b = + n t = 1 
  18. 18. <ul><li>Suppose our firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate. </li></ul><ul><li>What would be a fair price for these bonds? </li></ul>
  19. 19. <ul><li>Note : If the coupon rate = discount rate , the bond will sell for par value . </li></ul>P/YR = 1 N = 20 I%YR = 12 FV = 1,000 PMT = 120 Solve PV = - $1,000 0 1 2 3 . . . 20 1000 120 120 120 . . . 120
  20. 20. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 ) </li></ul>
  21. 21. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul>
  22. 22. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul><ul><li> 1 </li></ul><ul><li>PV = 120 1 - (1.12 ) 20 + 1000/ (1.12) 20 = $1000 </li></ul><ul><li> .12 </li></ul>
  23. 23. <ul><li>Suppose interest rates fall immediately after we issue the bonds. The required return on bonds of similar risk drops to 10% . </li></ul><ul><li>What would happen to the bond’s intrinsic value? </li></ul>
  24. 24. <ul><li>P/YR = 1 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 20 </li></ul><ul><li>I%YR = 10 </li></ul><ul><li>PMT = 120 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve PV = - $1,170.27 </li></ul>
  25. 25. <ul><li>P/YR = 1 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 20 </li></ul><ul><li>I%YR = 10 </li></ul><ul><li>PMT = 120 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve PV = - $1,170.27 </li></ul>Note : If the coupon rate > discount rate , the bond will sell for a premium .
  26. 26. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .10, 20 ) + 1000 (PVIF .10, 20 ) </li></ul>
  27. 27. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .10, 20 ) + 1000 (PVIF .10, 20 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul>
  28. 28. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .10, 20 ) + 1000 (PVIF .10, 20 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul><ul><li> 1 </li></ul><ul><li>PV = 120 1 - (1.10 ) 20 + 1000/ (1.10) 20 = $1,170.27 </li></ul><ul><li> .10 </li></ul>
  29. 29. <ul><li>Suppose interest rates rise immediately after we issue the bonds. The required return on bonds of similar risk rises to 14% . </li></ul><ul><li>What would happen to the bond’s intrinsic value? </li></ul>
  30. 30. <ul><li>P/YR = 1 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 20 </li></ul><ul><li>I%YR = 14 </li></ul><ul><li>PMT = 120 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve PV = -$867.54 </li></ul>
  31. 31. <ul><li>P/YR = 1 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 20 </li></ul><ul><li>I%YR = 14 </li></ul><ul><li>PMT = 120 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve PV = - $867.54 </li></ul>Note : If the coupon rate < discount rate , the bond will sell for a discount .
  32. 32. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 ) </li></ul>
  33. 33. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul>
  34. 34. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 120 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul><ul><li> 1 </li></ul><ul><li>PV = 120 1 - (1.14 ) 20 + 1000/ (1.14) 20 = $867.54 </li></ul><ul><li> .14 </li></ul>
  35. 35. <ul><li>P/YR = 2 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 40 </li></ul><ul><li>I%YR = 14 </li></ul><ul><li>PMT = 60 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve PV = - $866.68 </li></ul>
  36. 36. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 60 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 ) </li></ul>
  37. 37. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 60 (PVIFA .07, 40 ) + 1000 (PVIF .07, 40 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul>
  38. 38. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>PV = 60 (PVIFA .07, 40 ) + 1000 (PVIF .07, 40 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul><ul><li> 1 </li></ul><ul><li>PV = 60 1 - (1.07 ) 40 + 1000 / (1.07) 40 = $866.68 </li></ul><ul><li> .07 </li></ul>
  39. 39. <ul><li>The expected rate of return on a bond. </li></ul><ul><li>The rate of return investors earn on a bond if they hold it to maturity. </li></ul>
  40. 40. <ul><li>The expected rate of return on a bond. </li></ul><ul><li>The rate of return investors earn on a bond if they hold it to maturity. </li></ul>$I t $M (1 + k b ) t (1 + k b ) n P 0 = + n t = 1 
  41. 41. <ul><li>Suppose we paid $898.90 for a $1,000 par 10% coupon bond with 8 years to maturity and semi-annual coupon payments. </li></ul><ul><li>What is our yield to maturity ? </li></ul>
  42. 42. <ul><li>P/YR = 2 </li></ul><ul><li>Mode = end </li></ul><ul><li>N = 16 </li></ul><ul><li>PV = -898.90 </li></ul><ul><li>PMT = 50 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve I%YR = 12% </li></ul>YTM Example
  43. 43. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>898.90 = 50 (PVIFA k, 16 ) + 1000 (PVIF k, 16 ) </li></ul>
  44. 44. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>898.90 = 50 (PVIFA k, 16 ) + 1000 (PVIF k, 16 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul>
  45. 45. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>898.90 = 50 (PVIFA k, 16 ) + 1000 (PVIF k, 16 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul><ul><li> 1 </li></ul><ul><li>898.90 = 50 1 - (1 + i ) 16 + 1000 / (1 + i ) 16 </li></ul><ul><li> i </li></ul>
  46. 46. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) </li></ul><ul><li>898.90 = 50 (PVIFA k, 16 ) + 1000 (PVIF k, 16 ) </li></ul><ul><li> 1 </li></ul><ul><li>PV = PMT 1 - (1 + i) n + FV / (1 + i) n </li></ul><ul><li> i </li></ul><ul><li> 1 </li></ul><ul><li>898.90 = 50 1 - (1 + i ) 16 + 1000 / (1 + i ) 16 </li></ul><ul><li> i solve using trial and error </li></ul>
  47. 47. <ul><li>No coupon interest payments. </li></ul><ul><li>The bond holder’s return is determined entirely by the price discount . </li></ul>
  48. 48. <ul><li>Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity. </li></ul><ul><li>What is your yield to maturity ? </li></ul>
  49. 49. <ul><li>Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity. </li></ul><ul><li>What is your yield to maturity ? </li></ul>0 10 -$508 $1000
  50. 50. <ul><li>P/YR = 1 </li></ul><ul><li>Mode = End </li></ul><ul><li>N = 10 </li></ul><ul><li>PV = -508 </li></ul><ul><li>FV = 1000 </li></ul><ul><li>Solve: I%YR = 7% </li></ul>
  51. 51. <ul><li>Mathematical Solution: </li></ul><ul><li>PV = FV (PVIF i, n ) </li></ul><ul><li>508 = 1000 (PVIF i, 10 ) </li></ul><ul><li>.508 = (PVIF i, 10 ) [use PVIF table] </li></ul><ul><li>PV = FV /(1 + i) 10 </li></ul><ul><li>508 = 1000 /(1 + i) 10 </li></ul><ul><li>1.9685 = (1 + i) 10 </li></ul><ul><li>i = 7% </li></ul>0 10 PV = -508 FV = 1000
  52. 52. <ul><li>Cur Net </li></ul><ul><li>Yld Vol Close Chg </li></ul><ul><li>Polaroid 11 1 / 2 06 19.3 395 59 3 / 4 ... </li></ul><ul><li>What is the yield to maturity for this bond? </li></ul><ul><li>P/YR = 2 , N = 10 , FV = 1000 , </li></ul><ul><li>PV = $-597.50 , </li></ul><ul><li>PMT = 57.50 </li></ul><ul><li>Solve: I/YR = 26.48% </li></ul>
  53. 53. <ul><li>Cur Net </li></ul><ul><li>Yld Vol Close Chg </li></ul><ul><li>HewlPkd zr 17 ... 20 51 1 / 2 +1 </li></ul><ul><li>What is the yield to maturity for this bond? </li></ul><ul><li>P/YR = 1 , N = 16, FV = 1000 , </li></ul><ul><li>PV = $-515 , </li></ul><ul><li>PMT = 0 </li></ul><ul><li>Solve: I/YR = 4.24% </li></ul>
  54. 54. <ul><li> Maturity Ask </li></ul><ul><li>Rate Mo/Yr Bid Asked Chg Yld </li></ul><ul><li>9 Nov 18 139:14 139:20 -34 5.46 </li></ul><ul><li>What is the yield to maturity for this Treasury bond? (assume 35 half years) </li></ul><ul><li>P/YR = 2 , N = 35, FV = 1000 , </li></ul><ul><li>PMT = 45 , </li></ul><ul><li>PV = - 1,396.25 (139.625% of par) </li></ul><ul><li>Solve: I/YR = 5.457% </li></ul>
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