Bonds, equities and interest rates

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Bonds, equities and interest rates

  1. 1. Finance Lecture:Bonds, Equities and Interest Rates Brad Simon
  2. 2. Lecture Overview  Bonds  Definitions  Issuers and holders  Example  Valuation  Interest Rates  Conclusions (bonds and interest rates)  Equities  Definition  Stock Markets  Valuation  Conclusion2
  3. 3. Bonds – Definition3
  4. 4. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)4
  5. 5. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:5
  6. 6. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:  A principal amount to be repaid on a specific date in the future6
  7. 7. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:  A principal amount to be repaid on a specific date in the future  The principal amount is also known as the face value or par value7
  8. 8. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:  A principal amount to be repaid on a specific date in the future  The principal amount is also known as the face value or par value  The payment date is known as the maturity date8
  9. 9. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:  A principal amount to be repaid on a specific date in the future  The principal amount is also known as the face value or par value  The payment date is known as the maturity date  Many bonds have regular coupon payments which are paid-out annually, semi-annually or quarterly.9
  10. 10. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:  A principal amount to be repaid on a specific date in the future  The principal amount is also known as the face value or par value  The payment date is known as the maturity date  Many bonds have regular coupon payments which are paid-out annually, semi-annually or quarterly.  The coupon rate is the interest rate used to calculate the coupon payment and is a percentage of the principal amount10
  11. 11. Bonds – Definition  A bond is a type of security instrument used to raise capital by an issuing party (an issuer)  A bond typically has the following characteristics:  A principal amount to be repaid on a specific date in the future  The principal amount is also known as the face value or par value  The payment date is known as the maturity date  Many bonds have regular coupon payments which are paid-out annually, semi-annually or quarterly.  The coupon rate is the interest rate used to calculate the coupon amount and is a percentage of the principal amount  Coupon Payment = Coupon Rate x Principal11
  12. 12. Bonds – Definition12
  13. 13. Bonds – Definition  A bond is a legal debt obligation. Failure to make payments as required can result in legal recourse by the holders of the bonds.13
  14. 14. Bonds – Definition  A bond is a legal debt obligation. Failure to make payments as required can result in legal recourse by the holders of the bonds.  A bond may be callable by the issuer14
  15. 15. Bonds – Definition  A bond is a legal debt obligation. Failure to make payments as required can result in legal recourse by the holders of the bonds.  A bond may be callable by the issuer  After some specified amount of time or some specified event, the issuer can purchase the bonds back from the market.15
  16. 16. Bonds – Definition  A bond is a legal debt obligation. Failure to make payments as required can result in legal recourse by the holders of the bonds.  A bond may be callable by the issuer  After some specified amount of time or some specified event, the issuer can purchase the bonds back from the market.  Typically the issuer will have to pay some type of penalty for this early re-call.16
  17. 17. Bonds – Definition  A bond is a legal debt obligation. Failure to make payments as required can result in legal recourse by the holders of the bonds.  A bond may be callable by the issuer  After some specified amount of time or some specified event, the issuer can purchase the bonds back from the market.  Typically the issuer will have to pay some type of penalty for this early re-call.  Other features can also exist.17
  18. 18. Bonds – Definition18
  19. 19. Bonds – Definition  Issuing Party or Issuer – the party who has made the payment promises19
  20. 20. Bonds – Definition  Issuing Party or Issuer – the party who has made the payment promises  The issuance of bonds is known as a bond offering20
  21. 21. Bonds – Definition  Issuing Party or Issuer – the party who has made the payment promises  The issuance of bonds is known as a bond offering  Holding Party or Holder – the party who currently has possession of the bond21
  22. 22. Bonds – Definition  Issuing Party or Issuer – the party who has made the payment promises  The issuance of bonds is known as a bond offering  Holding Party or Holder – the party who currently has possession of the bond  The holding party receives the payments from the issuer22
  23. 23. Bonds – Definition  Issuing Party or Issuer – the party who has made the payment promises  The issuance of bonds is known as a bond offering  Holding Party or Holder – the party who currently has possession of the bond  The holding party receives the payments from the issuer  Often, the holding party can freely sell the bond to a third-party and all rights will transfer23
  24. 24. Bonds – Definition  Issuing Party or Issuer – the party who has made the payment promises  The issuance of bonds is known as a bond offering  Holding Party or Holder – the party who currently has possession of the bond  The holding party receives the payments from the issuer  Often, the holding party can freely sell the bond to a third-party and all rights will transfer  Effectively, a bond is a loan.24
  25. 25. Bonds – Definition Recap25
  26. 26. Bonds – Definition Recap  Principal or Face Value26
  27. 27. Bonds – Definition Recap  Principal or Face Value  Maturity Date27
  28. 28. Bonds – Definition Recap  Principal or Face Value  Maturity Date  Coupon Rate, Coupon Payment28
  29. 29. Bonds – Definition Recap  Principal or Face Value  Maturity Date  Coupon Rate, Coupon Payment  Legal debt obligation29
  30. 30. Bonds – Definition Recap  Principal or Face Value  Maturity Date  Coupon Rate, Coupon Payment  Legal debt obligation  Callable30
  31. 31. Bonds – Definition Recap  Principal or Face Value  Maturity Date  Coupon Rate, Coupon Payment  Legal debt obligation  Callable  Issuing Party or Issuer31
  32. 32. Bonds – Definition Recap  Principal or Face Value  Maturity Date  Coupon Rate, Coupon Payment  Legal debt obligation  Callable  Issuing Party or Issuer  Bond offering32
  33. 33. Bonds – Definition Recap  Principal or Face Value  Maturity Date  Coupon Rate, Coupon Payment  Legal debt obligation  Callable  Issuing Party or Issuer  Bond offering  Holding Party or Holder33
  34. 34. Bonds – Issuers34
  35. 35. Bonds – Issuers  Bonds are issued by various types of parties:35
  36. 36. Bonds – Issuers  Bonds are issued by various types of parties:  Federal governments36
  37. 37. Bonds – Issuers  Bonds are issued by various types of parties:  Federal governments  State and municipal governments37
  38. 38. Bonds – Issuers  Bonds are issued by various types of parties:  Federal governments  State and municipal governments  Corporations38
  39. 39. Bonds – Issuers  Bonds are issued by various types of parties:  Federal governments  State and municipal governments  Corporations  Money Markets39
  40. 40. Bonds – Issuers  Bonds are issued by various types of parties:  Federal governments  State and municipal governments  Corporations  Money Markets  Mortgage-backed and Asset-backed securities40
  41. 41. Bonds – Bondholders41
  42. 42. Bonds – Bondholders  Bonds are held by various types of parties:42
  43. 43. Bonds – Bondholders  Bonds are held by various types of parties:  Pension funds43
  44. 44. Bonds – Bondholders  Bonds are held by various types of parties:  Pension funds  Insurance companies44
  45. 45. Bonds – Bondholders  Bonds are held by various types of parties:  Pension funds  Insurance companies  University endowments45
  46. 46. Bonds – Bondholders  Bonds are held by various types of parties:  Pension funds  Insurance companies  University endowments  Bond funds46
  47. 47. Bonds – Bondholders  Bonds are held by various types of parties:  Pension funds  Insurance companies  University endowments  Bond funds  Individuals47
  48. 48. Bonds – Magnitude48
  49. 49. Bonds – Magnitude  The bond market is enormous49
  50. 50. Bonds – Magnitude  The bond market is enormous  As of 2009, the face value of total bonds outstanding globally was $82 trillion. Sources: Asset Allocation Advisor and World Economic Outlook Database50
  51. 51. Bonds – Magnitude  The bond market is enormous  As of 2009, the face value of total bonds outstanding globally was $82 trillion.  By comparison  The total value of all global equities (stocks) was $44 trillion. Sources: Asset Allocation Advisor and World Economic Outlook Database51
  52. 52. Bonds – Magnitude  The bond market is enormous  As of 2009, the face value of total bonds outstanding globally was $82 trillion.  By comparison  The total value of all global equities (stocks) was $44 trillion.  Total global GDP in 2010 was roughly $62 trillion. Sources: Asset Allocation Advisor and World Economic Outlook Database52
  53. 53. Bonds – Magnitude  The bond market is enormous  As of 2009, the face value of total bonds outstanding globally was $82 trillion.  By comparison  The total value of all global equities (stocks) was $44 trillion.  Total global GDP in 2010 was roughly $62 trillion. o US GDP was $14.5 trillion or nearly 25% of total GDP Sources: Asset Allocation Advisor and World Economic Outlook Database53
  54. 54. Bonds – Magnitude54
  55. 55. Bonds – Magnitude Sources: Asset Allocation Advisor and World Economic Outlook Database55
  56. 56. Bonds – An Example56
  57. 57. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds57
  58. 58. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:58
  59. 59. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,00059
  60. 60. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,000  Maturity Date is 5 years from issuance60
  61. 61. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,000  Maturity Date is 5 years from issuance  Coupon Rate is 5%61
  62. 62. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,000  Maturity Date is 5 years from issuance  Coupon Rate is 5%  Coupon Payments are made annually at end of year62
  63. 63. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,000  Maturity Date is 5 years from issuance  Coupon Rate is 5%  Coupon Payments are made annually at end of year  Coupon Payment is:63
  64. 64. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,000  Maturity Date is 5 years from issuance  Coupon Rate is 5%  Coupon Payments are made annually at end of year  Coupon Payment is:  Principal x Coupon Rate64
  65. 65. Bonds – An Example  A company wants to raise money for a new project and decides to do so by issuing bonds  The characteristics of the bonds are as follows:  Principal is $1,000  Maturity Date is 5 years from issuance  Coupon Rate is 5%  Coupon Payments are made annually at end of year  Coupon Payment is:  Principal x Coupon Rate  $1,000 x 5% = $5065
  66. 66. Bonds – An Example66
  67. 67. Bonds – An Example  Note, we are discussing the characteristics at an individual bond level. The company has likely issued a number of these bonds in the offering.67
  68. 68. Bonds – An Example  Note, we are discussing the characteristics at an individual bond level. The company has likely issued a number of these bonds in the offering.  For example, the company may be issuing $1 million of face value bonds of this characteristic.68
  69. 69. Bonds – An Example  Note, we are discussing the characteristics at an individual bond level. The company has likely issued a number of these bonds in the offering.  For example, the company may be issuing $1 million of face value bonds of this characteristic.  This means the company is issuing 1,000 bonds, each with a face value of $1,000.69
  70. 70. Bonds – An Example70
  71. 71. Bonds – An Example  When issued, some bonds simply sell for their face value.71
  72. 72. Bonds – An Example  When issued, some bonds simply sell for their face value.  In this case, the company would convey the bond to the buyer in exchange for receiving $1,000.72
  73. 73. Bonds – An Example  When issued, some bonds simply sell for their face value.  In this case, the company would convey the bond to the buyer in exchange for receiving $1,000.  Assuming the buyer holds the bond to maturity he would receive 5 annual payments of $50 and a final payment of $1,000 after 5 years.73
  74. 74. Bonds – An Example  When issued, some bonds simply sell for their face value.  In this case, the company would convey the bond to the buyer in exchange for receiving $1,000.  Assuming the buyer holds the bond to maturity he would receive 5 annual payments of $50 and a final payment of $1,000 after 5 years.  In other words, the buyer receives annual interest payments and finally the return of his principal.74
  75. 75. Bonds – Valuation75
  76. 76. Bonds – Valuation  In the previous slide I said that some bonds are issued at a price equal to their face value.76
  77. 77. Bonds – Valuation  In the previous slide I said that some bonds are issued at a price equal to their face value.  Many bonds, however, are issued at a price higher or lower than their face value.77
  78. 78. Bonds – Valuation  In the previous slide I said that some bonds are issued at a price equal to their face value.  Many bonds, however, are issued at a price higher or lower than their face value.  Ultimately, the market (i.e. supply and demand) determines a bond’s price. Sometimes it is willing to pay more than face value, other times less.78
  79. 79. Bonds – Valuation  In the previous slide I said that some bonds are issued at a price equal to their face value.  Many bonds, however, are issued at a price higher or lower than their face value.  Ultimately, the market (i.e. supply and demand) determines a bond’s price. Sometimes it is willing to pay more than face value, other times less.  We can make sense of this by applying the Time- Value-of-Money concept:79
  80. 80. Bonds – Valuation  In the previous slide I said that some bonds are issued at a price equal to their face value.  Many bonds, however, are issued at a price higher or lower than their face value.  Ultimately, the market (i.e. supply and demand) determines a bond’s price. Sometimes it is willing to pay more than face value, other times less.  We can make sense of this by applying the Time- Value-of-Money concept:  The issuing party specifies how much and when they will make payments.80
  81. 81. Bonds – Valuation  In the previous slide I said that some bonds are issued at a price equal to their face value.  Many bonds, however, are issued at a price higher or lower than their face value.  Ultimately, the market (i.e. supply and demand) determines a bond’s price. Sometimes it is willing to pay more than face value, other times less.  We can make sense of this by applying the Time- Value-of-Money concept:  The issuing party specifies how much and when they will make payments.  The market then applies an interest rate to discount the specified payments to the present81
  82. 82. Bonds – Valuation82
  83. 83. Bonds – Valuation  Let’s look at our prior example:83
  84. 84. Bonds – Valuation  Let’s look at our prior example:  Face Value of $1,000, payment to be made in 5 years84
  85. 85. Bonds – Valuation  Let’s look at our prior example:  Face Value of $1,000, payment to be made in 5 years  Coupon rate of 5%85
  86. 86. Bonds – Valuation  Let’s look at our prior example:  Face Value of $1,000, payment to be made in 5 years  Coupon rate of 5%  Annual coupon payments of $50 for five years86
  87. 87. Bonds – Valuation  Let’s look at our prior example:  Face Value of $1,000, payment to be made in 5 years  Coupon rate of 5%  Annual coupon payments of $50 for five years Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,05087
  88. 88. Bonds – Valuation88
  89. 89. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,05089
  90. 90. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5%90
  91. 91. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5%91
  92. 92. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5% Year Payment PVIF PV 0 $ - 1 $ 50 0.952 $ 48 2 $ 50 0.907 $ 45 3 $ 50 0.864 $ 43 4 $ 50 0.823 $ 41 5 $ 1,050 0.784 $ 823 Present Value: $ 1,00092
  93. 93. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5% Year Payment PVIF PV 0 $ - 1 $ 50 0.952 $ 48 2 $ 50 0.907 $ 45 3 $ 50 0.864 $ 43 4 $ 50 0.823 $ 41 5 $ 1,050 0.784 $ 823 Present Value: $ 1,00093
  94. 94. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5% Year Payment PVIF PV 0 $ - 1 $ 50 0.952 $ 48 2 $ 50 0.907 $ 45 3 $ 50 0.864 $ 43 4 $ 50 0.823 $ 41 5 $ 1,050 0.784 $ 823 Present Value: $ 1,00094
  95. 95. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5% Year Payment PVIF PV 0 $ - 1 $ 50 0.952 $ 48 2 $ 50 0.907 $ 45 3 $ 50 0.864 $ 43 4 $ 50 0.823 $ 41 5 $ 1,050 0.784 $ 823 Present Value: $ 1,00095
  96. 96. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 5% Year Payment PVIF PV 0 $ - 1 $ 50 0.952 $ 48 2 $ 50 0.907 $ 45 3 $ 50 0.864 $ 43 4 $ 50 0.823 $ 41 5 $ 1,050 0.784 $ 823 Present Value: $ 1,00096
  97. 97. Bonds – Valuation97
  98. 98. Bonds – Valuation  Based on the TVM, we would be willing to pay $1,000 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 5%.98
  99. 99. Bonds – Valuation  Based on the TVM, we would be willing to pay $1,000 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 5%.  When the bond valuation (i.e. the price) is equal to the face value we say the bond is “selling at par value.”99
  100. 100. Bonds – Valuation  Based on the TVM, we would be willing to pay $1,000 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 5%.  When the bond valuation (i.e. the price) is equal to the face value we say the bond is “selling at par value.”  Now, what happens if the market applies an interest rate of 7%? How much would the previous bonds be valued at?100
  101. 101. Bonds – Valuation101
  102. 102. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050102
  103. 103. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 7%103
  104. 104. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 7%104
  105. 105. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Year Payment PVIF PV i = 7% 0 $ - 1 $ 50 0.935 $ 47 2 $ 50 0.873 $ 44 3 $ 50 0.816 $ 41 4 $ 50 0.763 $ 38 5 $ 1,050 0.713 $ 749 Present Value: $ 918105
  106. 106. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Year Payment PVIF PV i = 7% 0 $ - 1 $ 50 0.935 $ 47 2 $ 50 0.873 $ 44 3 $ 50 0.816 $ 41 4 $ 50 0.763 $ 38 5 $ 1,050 0.713 $ 749 Present Value: $ 918106
  107. 107. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Year Payment PVIF PV i = 7% 0 $ - 1 $ 50 0.935 $ 47 2 $ 50 0.873 $ 44 3 $ 50 0.816 $ 41 4 $ 50 0.763 $ 38 5 $ 1,050 0.713 $ 749 Present Value: $ 918107
  108. 108. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Year Payment PVIF PV i = 7% 0 $ - 1 $ 50 0.935 $ 47 2 $ 50 0.873 $ 44 3 $ 50 0.816 $ 41 4 $ 50 0.763 $ 38 5 $ 1,050 0.713 $ 749 Present Value: $ 918108
  109. 109. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Year Payment PVIF PV i = 7% 0 $ - 1 $ 50 0.935 $ 47 2 $ 50 0.873 $ 44 3 $ 50 0.816 $ 41 4 $ 50 0.763 $ 38 5 $ 1,050 0.713 $ 749 Present Value: $ 918109
  110. 110. Bonds – Valuation110
  111. 111. Bonds – Valuation  Based on the TVM, we would be willing to pay $$918 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 7%.111
  112. 112. Bonds – Valuation  Based on the TVM, we would be willing to pay $$918 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 7%.  When the bond valuation is below the face value we say the bond is “selling at discount to par value.”112
  113. 113. Bonds – Valuation  Based on the TVM, we would be willing to pay $$918 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 7%.  When the bond valuation is below the face value we say the bond is “selling at discount to par value.”  Now, what happens if the market decides the interest rate should be 3%? How much would the previous bonds be valued at?113
  114. 114. Bonds – Valuation114
  115. 115. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050115
  116. 116. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 3%116
  117. 117. Bonds – Valuation Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 i = 3% Year Payment PVIF PV 0 $ - 1 $ 50 0.971 $ 49 2 $ 50 0.943 $ 47 3 $ 50 0.915 $ 46 4 $ 50 0.888 $ 44 5 $ 1,050 0.863 $ 906 Present Value: $ 1,092117
  118. 118. Bonds – Valuation118
  119. 119. Bonds – Valuation  Based on the TVM, we would be willing to pay $$1,092 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 3%.119
  120. 120. Bonds – Valuation  Based on the TVM, we would be willing to pay $$1,092 to receive five annual payments of $50 and a final payment of $1,000 after five years, assuming an interest rate of 3%.  When the bond valuation is below the face value we say the bond is “selling at premium to par value.”120
  121. 121. Bonds – Valuation Summary121
  122. 122. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050122
  123. 123. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5%123
  124. 124. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000124
  125. 125. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000 i = 3%125
  126. 126. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000 i = 3% Bond price today is $1,092126
  127. 127. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000 i = 3% i = 5% Bond price today is $1,092127
  128. 128. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000 i = 3% i = 5% Bond price Bond price today is today is $1,092 $1,000128
  129. 129. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000 i = 3% i = 5% i = 7% Bond price Bond price today is today is $1,092 $1,000129
  130. 130. Bonds – Valuation Summary Y 0 ear Y 1 ear Y 2 ear Y 3 ear Y 4 ear Y 5 ear ? $50 $50 $50 $50 $1,050 Coupon Rate = 5% Face Value = $1,000 i = 3% i = 5% i = 7% Bond price Bond price Bond price today is today is today is $918 $1,092 $1,000130
  131. 131. Bonds – Valuation Conclusions131
  132. 132. Bonds – Valuation Conclusions  We use the TVM to value a bond’s price today132
  133. 133. Bonds – Valuation Conclusions  We use the TVM to value a bond’s price today  The time-frame, coupon payments and the final principal payment are specified by the bond issuer. These represents a future cash flow.133
  134. 134. Bonds – Valuation Conclusions  We use the TVM to value a bond’s price today  The time-frame, coupon payments and the final principal payment are specified by the bond issuer. These represents a future cash flow.  The numerator of the TVM134
  135. 135. Bonds – Valuation Conclusions  We use the TVM to value a bond’s price today  The time-frame, coupon payments and the final principal payment are specified by the bond issuer. These represents a future cash flow.  The numerator of the TVM  The market will then apply an interest rate to the above cash flow to calculate their present value (the bond’s price today)135
  136. 136. Bonds – Valuation Observations136
  137. 137. Bonds – Valuation Observations  Valuing a bond is the same as calculating the present value of an annuity + and the PV of a single payment137
  138. 138. Bonds – Valuation Observations  Valuing a bond is the same as calculating the present value of an annuity + and the PV of a single payment  5 annual payments of $50 at a given interest rate138
  139. 139. Bonds – Valuation Observations  Valuing a bond is the same as calculating the present value of an annuity + and the PV of a single payment  5 annual payments of $50 at a given interest rate  A payment of $1,000 in 5 years at a given interest rate139
  140. 140. Bonds – Valuation Observations  Valuing a bond is the same as calculating the present value of an annuity + and the PV of a single payment  5 annual payments of $50 at a given interest rate  A payment of $1,000 in 5 years at a given interest rate  PV(Bond) = PVA(Coupon Payments) + PV(Face Value)140
  141. 141. Interest Rates141
  142. 142. Interest Rates  I keep using the term, “interest rate” and it appears to mean different things depending on the use.142
  143. 143. Interest Rates  I keep using the term, “interest rate” and it appears to mean different things depending on the use.  Unfortunately, there are many terms for the same concept143
  144. 144. Interest Rates  I keep using the term, “interest rate” and it appears to mean different things depending on the use.  Unfortunately, there are many terms for the same concept  And there are many concepts that use the same name144
  145. 145. Interest Rates  I keep using the term, “interest rate” and it appears to mean different things depending on the use.  Unfortunately, there are many terms for the same concept  And there are many concepts that use the same name  Back in our bond calculations, the market interest rate which was the denominator of our TVM analysis is also known as the “yield to maturity” (YTM) or simply “yield”.145
  146. 146. Interest Rates  I keep using the term, “interest rate” and it appears to mean different things depending on the use.  Unfortunately, there are many terms for the same concept  And there are many concepts that use the same name  Back in our bond calculations, the market interest rate which was the denominator of our TVM analysis is also known as the “yield to maturity” (YTM) or simply “yield”.146  People will also use the term “discount rate” or
  147. 147. Interest Rates147
  148. 148. Interest Rates  To make it even more confusing, there are many different interest rates in an economy148
  149. 149. Interest Rates  To make it even more confusing, there are many different interest rates in an economy  The interest rate the government is charged to borrow money is lower than the interest rate I am charged on my credit card149
  150. 150. Interest Rates  To make it even more confusing, there are many different interest rates in an economy  The interest rate the government is charged to borrow money is lower than the interest rate I am charged on my credit card  Companies with good investment opportunities and lots of cash have lower interest rates for their corporate debt than companies few growth opportunities and no cash.150
  151. 151. Interest Rates  To make it even more confusing, there are many different interest rates in an economy  The interest rate the government is charged to borrow money is lower than the interest rate I am charged on my credit card  Companies with good investment opportunities and lots of cash have lower interest rates for their corporate debt than companies few growth opportunities and no cash.  Interest rates for the exact same security will change over time151
  152. 152. Interest Rates  To make it even more confusing, there are many different interest rates in an economy  The interest rate the government is charged to borrow money is lower than the interest rate I am charged on my credit card  Companies with good investment opportunities and lots of cash have lower interest rates for their corporate debt than companies few growth opportunities and no cash.  Interest rates for the exact same security will change over time  Interest rates of identical securities except their152 times to maturity will have different interest rates
  153. 153. Interest Rates153
  154. 154. Interest Rates  But in all these cases, the interest rate will increase when a given risk increases and decrease when a given risk decreases.154
  155. 155. Interest Rates  But in all these cases, the interest rate will increase when a given risk increases and decrease when a given risk decreases.  The logic is simple:155
  156. 156. Interest Rates  But in all these cases, the interest rate will increase when a given risk increases and decrease when a given risk decreases.  The logic is simple:  In the face of multiple investment or lending opportunities, if we are not compensated for additional risk we will always put our money in the least risky opportunity.156
  157. 157. Interest Rates  But in all these cases, the interest rate will increase when a given risk increases and decrease when a given risk decreases.  The logic is simple:  In the face of multiple investment or lending opportunities, if we are not compensated for additional risk we will always put our money in the least risky opportunity.  We need to be induced to invest or lend to the riskier situation by the promise of higher returns.157
  158. 158. Interest Rates158
  159. 159. Interest Rates  The interest rate is a function of a number of factors:159
  160. 160. Interest Rates  The interest rate is a function of a number of factors:  The prevailing market interest rates (including the “real” interest rate)160
  161. 161. Interest Rates  The interest rate is a function of a number of factors:  The prevailing market interest rates (including the “real” interest rate)  Inflation risks161
  162. 162. Interest Rates  The interest rate is a function of a number of factors:  The prevailing market interest rates (including the “real” interest rate)  Inflation risks  Repayment or default risks expectations162
  163. 163. Interest Rates  The interest rate is a function of a number of factors:  The prevailing market interest rates (including the “real” interest rate)  Inflation risks  Repayment or default risks expectations  Liquidity risk163
  164. 164. Interest Rates  The interest rate is a function of a number of factors:  The prevailing market interest rates (including the “real” interest rate)  Inflation risks  Repayment or default risks expectations  Liquidity risk  Other risk factors164
  165. 165. Interest Rates165
  166. 166. Interest Rates  Back in our example of the 5 year bond we calculated the price using three different interest rates, 3%, 5% and 7%.166
  167. 167. Interest Rates  Back in our example of the 5 year bond we calculated the price using three different interest rates, 3%, 5% and 7%.  We can interpret the difference in interest rates as different risk assessments related to the bond’s cash flows.167
  168. 168. Interest Rates  Back in our example of the 5 year bond we calculated the price using three different interest rates, 3%, 5% and 7%.  We can interpret the difference in interest rates as different risk assessments related to the bond’s cash flows.  For example, we might apply a higher rate of 7% if we are concerned the company might not actually make the payments (default risk).168
  169. 169. Interest Rates  Back in our example of the 5 year bond we calculated the price using three different interest rates, 3%, 5% and 7%.  We can interpret the difference in interest rates as different risk assessments related to the bond’s cash flows.  For example, we might apply a higher rate of 7% if we are concerned the company might not actually make the payments (default risk).  Or maybe we are concerned that inflation will increase and so we need extra compensation.169
  170. 170. Conclusions170
  171. 171. Conclusions  The lower the interest rate, the higher a bond’s (or any security’s) price today.171
  172. 172. Conclusions  The lower the interest rate, the higher a bond’s (or any security’s) price today.  Conversely, the higher the interest rate, the lower the bond’s price today.172
  173. 173. Conclusions  The lower the interest rate, the higher a bond’s (or any security’s) price today.  Conversely, the higher the interest rate, the lower the bond’s price today.  Higher interest rates have built-in “additional compensation” compared to lower interest rates.173
  174. 174. Conclusions  The lower the interest rate, the higher a bond’s (or any security’s) price today.  Conversely, the higher the interest rate, the lower the bond’s price today.  Higher interest rates have built-in “additional compensation” compared to lower interest rates.  The additional compensation will relate to some type of additional perceived risk related to the underlying cash flow.174
  175. 175. Equities175
  176. 176. Equities  Equity securities (stocks) represent ownership in a corporation176
  177. 177. Equities  Equity securities (stocks) represent ownership in a corporation  Common stockholders are residual claimants177
  178. 178. Equities  Equity securities (stocks) represent ownership in a corporation  Common stockholders are residual claimants  They have a claim on cash flows only after all other claimants (employees, suppliers, debtholders, the government) have been paid178
  179. 179. Equities  Equity securities (stocks) represent ownership in a corporation  Common stockholders are residual claimants  They have a claim on cash flows only after all other claimants (employees, suppliers, debtholders, the government) have been paid  At any point in time the market value of a firm’s common stock depends on many factors including:179
  180. 180. Equities  Equity securities (stocks) represent ownership in a corporation  Common stockholders are residual claimants  They have a claim on cash flows only after all other claimants (employees, suppliers, debtholders, the government) have been paid  At any point in time the market value of a firm’s common stock depends on many factors including:  The company’s profitability (cash flows)180
  181. 181. Equities  Equity securities (stocks) represent ownership in a corporation  Common stockholders are residual claimants  They have a claim on cash flows only after all other claimants (employees, suppliers, debtholders, the government) have been paid  At any point in time the market value of a firm’s common stock depends on many factors including:  The company’s profitability (cash flows)  The company’s growth potential181
  182. 182. Equities  Equity securities (stocks) represent ownership in a corporation  Common stockholders are residual claimants  They have a claim on cash flows only after all other claimants (employees, suppliers, debtholders, the government) have been paid  At any point in time the market value of a firm’s common stock depends on many factors including:  The company’s profitability (cash flows)  The company’s growth potential  Current market interest rates182
  183. 183. Stock Markets183
  184. 184. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.184
  185. 185. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.  This liquidity allows buyers and sellers the means to transact with each other and gives people the confidence to buy shares in the first place.185
  186. 186. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.  This liquidity allows buyers and sellers the means to transact with each other and gives people the confidence to buy shares in the first place.  New York Stock Exchange (NYSE)186
  187. 187. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.  This liquidity allows buyers and sellers the means to transact with each other and gives people the confidence to buy shares in the first place.  New York Stock Exchange (NYSE)  NASDAQ187
  188. 188. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.  This liquidity allows buyers and sellers the means to transact with each other and gives people the confidence to buy shares in the first place.  New York Stock Exchange (NYSE)  NASDAQ  London Stock Exchange188
  189. 189. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.  This liquidity allows buyers and sellers the means to transact with each other and gives people the confidence to buy shares in the first place.  New York Stock Exchange (NYSE)  NASDAQ  London Stock Exchange  Private trading floors (the major banks).189
  190. 190. Stock Markets  Stock exchanges provide liquidity: the ability for owners of common stock to convert their shares into cash at any time.  This liquidity allows buyers and sellers the means to transact with each other and gives people the confidence to buy shares in the first place.  New York Stock Exchange (NYSE)  NASDAQ  London Stock Exchange  Private trading floors (the major banks).  Largest private trading floor in the world is at UBS (a Swiss Bank), located in Stamford, CT.190
  191. 191. Stock Markets  UBS Trading floor – Stamford, CT191
  192. 192. Stock Markets  UBS Trading floor – Stamford, CT Your Instructor192
  193. 193. Stock Valuation193
  194. 194. Stock Valuation  We would like to use our TVM tool to value stocks.194
  195. 195. Stock Valuation  We would like to use our TVM tool to value stocks.  For example, when valuing bonds we discounted the promised future payments of the bond by an appropriate interest rate (discount rate) to arise at the present value (i.e. the market price) of bond.195
  196. 196. Stock Valuation  We would like to use our TVM tool to value stocks.  For example, when valuing bonds we discounted the promised future payments of the bond by an appropriate interest rate (discount rate) to arise at the present value (i.e. the market price) of bond.  Unfortunately, for stocks the issuer has not promised any specific payments so it is not obvious what values we should use for our future cash flows (i.e. the numerator of the TVM analysis).196
  197. 197. Stock Valuation  We would like to use our TVM tool to value stocks.  For example, when valuing bonds we discounted the promised future payments of the bond by an appropriate interest rate (discount rate) to arise at the present value (i.e. the market price) of bond.  Unfortunately, for stocks the issuer has not promised any specific payments so it is not obvious what values we should use for our future cash flows (i.e. the numerator of the TVM analysis).  This makes it harder to value stocks.197
  198. 198. Stock Valuation  We would like to use our TVM tool to value stocks.  For example, when valuing bonds we discounted the promised future payments of the bond by an appropriate interest rate (discount rate) to arise at the present value (i.e. the market price) of bond.  Unfortunately, for stocks the issuer has not promised any specific payments so it is not obvious what values we should use for our future cash flows (i.e. the numerator of the TVM analysis).  This makes it harder to value stocks.  But not impossible.198
  199. 199. Stock Valuation – A First Cut199
  200. 200. Stock Valuation – A First Cut  Let’s we are trying to value a company’s stock in which we expect a dividend to be paid.200
  201. 201. Stock Valuation – A First Cut  Let’s we are trying to value a company’s stock in which we expect a dividend to be paid.  We can look at historic dividend payments to get a sense of how much the dividend in the future might be.201
  202. 202. Stock Valuation – A First Cut  Let’s we are trying to value a company’s stock in which we expect a dividend to be paid.  We can look at historic dividend payments to get a sense of how much the dividend in the future might be.  Let’s assume the company is “mature” and the dividends are expected to be the same, forever.202
  203. 203. Stock Valuation – A First Cut  Let’s we are trying to value a company’s stock in which we expect a dividend to be paid.  We can look at historic dividend payments to get a sense of how much the dividend in the future might be.  Let’s assume the company is “mature” and the dividends are expected to be the same, forever.  If we assume a dividend of $2.00 (based on our historic analysis of dividends paid-out by this company) then what we are really saying is every year we expect a $2.00 dividend payment,203 forever.
  204. 204. Stock Valuation – Dividend Discount Model204
  205. 205. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity:205
  206. 206. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00206
  207. 207. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00207
  208. 208. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00208
  209. 209. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever209
  210. 210. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:210
  211. 211. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:  PV = Annual Payment / Discount Rate211
  212. 212. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:  PV = Annual Payment / Discount Rate  Let’s Assume a discount rate of 12%212
  213. 213. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:  PV = Annual Payment / Discount Rate  Let’s Assume a discount rate of 12%  PV = $2.00 / 0.12213
  214. 214. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:  PV = Annual Payment / Discount Rate  Let’s Assume a discount rate of 12%  PV = $2.00 / 0.12 = $16.67214
  215. 215. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:  PV = Annual Payment / Discount Rate  Let’s Assume a discount rate of 12%  PV = $2.00 / 0.12 = $16.67  The value of such a stock is $16.67215
  216. 216. Stock Valuation – Dividend Discount Model  A $2.00 dividend in perpetuity: Year 1: $2.00 Year 2: $2.00 Year 3: $2.00 Continue forever  Valuing this is simply valuing a perpetuity:  PV = Annual Payment / Discount Rate  Let’s Assume a discount rate of 12%  PV = $2.00 / 0.12 = $16.67  The value of such a stock is $16.67  The Dividend Discount Model216
  217. 217. Stock Valuation – Dividend Discount Model217
  218. 218. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.218
  219. 219. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.219
  220. 220. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.  If we can estimate (or assume) a constant growth rate (g) we could value the stock using a perpetuity with constant growth:220
  221. 221. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.  If we can estimate (or assume) a constant growth rate (g) we could value the stock using a perpetuity with constant growth:  PV = Dividend this year x (1 + g) / (r – g)221
  222. 222. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.  If we can estimate (or assume) a constant growth rate (g) we could value the stock using a perpetuity with constant growth:  PV = Dividend this year x (1 + g) / (r – g)  Let’s say our growth rate is 3%222
  223. 223. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.  If we can estimate (or assume) a constant growth rate (g) we could value the stock using a perpetuity with constant growth:  PV = Dividend this year x (1 + g) / (r – g)  Let’s say our growth rate is 3%  PV = $2.00 x (1.03) / (12% - 3%)223
  224. 224. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.  If we can estimate (or assume) a constant growth rate (g) we could value the stock using a perpetuity with constant growth:  PV = Dividend this year x (1 + g) / (r – g)  Let’s say our growth rate is 3%  PV = $2.00 x (1.03) / (12% - 3%)  PV = $2.06 / 9%224
  225. 225. Stock Valuation – Dividend Discount Model  We could build on this model to make it more versatile.  For example, we might assume that this is an established but growing company.  If we can estimate (or assume) a constant growth rate (g) we could value the stock using a perpetuity with constant growth:  PV = Dividend this year x (1 + g) / (r – g)  Let’s say our growth rate is 3%  PV = $2.00 x (1.03) / (12% - 3%)  PV = $2.06 / 9%225  PV = $22.89
  226. 226. Stock Valuation – Comparison226
  227. 227. Stock Valuation – Comparison  Let’s compare the values to see the difference:227
  228. 228. Stock Valuation – Comparison  Let’s compare the values to see the difference:  Constant Dividend: $16.67228
  229. 229. Stock Valuation – Comparison  Let’s compare the values to see the difference:  Constant Dividend: $16.67  Constant Growth: $22.89229
  230. 230. Stock Valuation – Comparison  Let’s compare the values to see the difference:  Constant Dividend: $16.67  Constant Growth: $22.89  The growth assumption gave us an extra $6.22 per share of value (or 37% more).230
  231. 231. Stock Valuation – Comparison  Let’s compare the values to see the difference:  Constant Dividend: $16.67  Constant Growth: $22.89  The growth assumption gave us an extra $6.22 per share of value (or 37% more).  Growth is good!231
  232. 232. Stock Valuation – Comparison  Let’s compare the values to see the difference:  Constant Dividend: $16.67  Constant Growth: $22.89  The growth assumption gave us an extra $6.22 per share of value (or 37% more).  Growth is good!  This is why managers of companies are constantly trying (encouraged) to grow their businesses.232
  233. 233. Stock Valuation – Extensions233
  234. 234. Stock Valuation – Extensions  There are many extensions to this basic model.234
  235. 235. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:235
  236. 236. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend236
  237. 237. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend  An estimation of growth237
  238. 238. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend  An estimation of growth  For example, a common extension is to split our time horizon into two parts:238
  239. 239. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend  An estimation of growth  For example, a common extension is to split our time horizon into two parts:  A high-growth phase in the early years239
  240. 240. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend  An estimation of growth  For example, a common extension is to split our time horizon into two parts:  A high-growth phase in the early years  A slow but steady growth phase from then on out240
  241. 241. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend  An estimation of growth  For example, a common extension is to split our time horizon into two parts:  A high-growth phase in the early years  A slow but steady growth phase from then on out  High Growth Period + Steady Growth Period241
  242. 242. Stock Valuation – Extensions  There are many extensions to this basic model.  But the essential ingredients involve what we have just seen:  An estimated dividend  An estimation of growth  For example, a common extension is to split our time horizon into two parts:  A high-growth phase in the early years  A slow but steady growth phase from then on out  High Growth Period + Steady Growth Period  We can value each period separately using the prior242 methods and simply add each component together
  243. 243. Conclusion - Equities243
  244. 244. Conclusion - Equities  If there is any residual value after paying back all outstanding obligations (payroll, taxes, loans, etc.), it is owned by the shareholders.244
  245. 245. Conclusion - Equities  If there is any residual value after paying back all outstanding obligations (payroll, taxes, loans, etc.), it is owned by the shareholders.  Equities are bought and sold in stock markets just like bonds are bought and sold in bond markets.245
  246. 246. Conclusion - Equities  If there is any residual value after paying back all outstanding obligations (payroll, taxes, loans, etc.), it is owned by the shareholders.  Equities are bought and sold in stock markets just like bonds are bought and sold in bond markets.  We can value stocks by taking the present value of any future estimated dividends, accounting for growth, and using an appropriate discount rate.246
  247. 247. Conclusion - Equities  If there is any residual value after paying back all outstanding obligations (payroll, taxes, loans, etc.), it is owned by the shareholders.  Equities are bought and sold in stock markets just like bonds are bought and sold in bond markets.  We can value stocks by taking the present value of any future estimated dividends, accounting for growth, and using an appropriate discount rate.247

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