Chapter 5 How to Value Bonds and Stocks

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Chapter 5 How to Value Bonds and Stocks

• 5.1 Definition and Example of a Bond
• 5.2 How to Value Bonds
• 5.3 Bond Concepts
• 5.4 The Present Value of Common Stocks
• 5.5 Estimates of Parameters in the Dividend
  Discount Model
• 5.6 Growth Opportunities
• 5.7 The Dividend Growth Model and the NPVGO Model
  (Advanced)
• 5.8 Price Earnings Ratio
• 5.9 Summary and Conclusions
• Appendix 5A The Term Structure of Interest Rates

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Valuation of Bonds and Stock

• First Principles
• Value of financial securities PV of expected
  future cash flows
• To value bonds and stocks we need to
• Estimate future cash flows size (how much) and
  timing (when)
• Discount future cash flows at an appropriate
  rate

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Pure Discount Bonds

• Information needed for valuing pure discount
  bonds
• Time to maturity (T) Maturity date - todays
  date
• Face value (F)
• Discount rate (r)
• 0 1 2 T
• --------------------------------------------
  ------
• F
• Value of a pure discount bond
• PV F / (1 r)T

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Level-Coupon Bonds

• Information needed to value level-coupon bonds
• Coupon payment dates and Time to maturity (T)
• Coupon (C) per payment period and Face value (F)
• Discount rate
• 0 1 2 T
• -----------------------------------------
  ------
• Coupon Coupon Coupon F
• Value of a Level-coupon bond
• PV F / (1 r)T C x 1/r - 1 / r x (1
  r)T
• PV of face value PV of coupon payments

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YTM, Bond Value, and Discount Rate
Bond Value and Discount Rate
1800
1600
1400
Bond Value
1200
1000
993.12
800
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Discount Rate
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Some Tips on Bond Pricing

• 1. Bond prices and market interest rates move in
  opposite directions.
• 2. When coupon rate YTM, price par value.
• When coupon rate gt YTM, price gt par value
  (premium bond)
• When coupon rate lt YTM, price lt par value
  (discount bond)
• 3. A bond with longer maturity has higher
  relative () price change than one with shorter
  maturity when interest rate (YTM) changes. All
  other features are identical.
• 4. A lower coupon bond has a higher relative ()
  price change than a higher coupon bond when
  interest rate (YTM) changes. All other features
  are identical.

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Common Stock Valuation

• Information needed to value common stocks
• Common Stock Dividends (Dt)
• Discount rate
• PV0 D1/(1 r)1 D2/(1 r)2 D3/(1 r)3
  . . . forever. .

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Case 1 Zero Growth

• Assume that dividends will remain at the same
  level forever, i.e. D1 D2 Dt
• Since future cash flows are constant, the value
  of a zero growth stock is the present value of a
  perpetuity
• Pt Dt1 / r

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Case 2 Constant Growth

• Assume that dividends will grow at a constant
  rate, g, forever, i. e.,
• D1 D0 x (1g)
• D2 D1 x (1g), etc., etc.. and
• Dt D0 x (1g)t
• Since future cash flows grow at a constant rate
  forever, the value of a constant growth stock is
  the present value of a growing perpetuity
• Pt Dt1 / (r - g)

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Case 3 Differential Growth

• Assume that dividends will grow at different
  rates in the foreseeable future and then will
  grow at a constant rate thereafter.
• To value a Differential Growth Stock, we need to
• Estimate future dividends in the foreseeable
  future.
• Estimate the future stock price when the stock
  becomes a Constant Growth Stock (case 2).
• Compute the total present value of the estimated
  future dividends and future stock price at the
  appropriate discount rate.

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A Differential Growth Example (Problem 5.13)

• r 12 (required return)
• g1 g2 g3 8
• D0 2
• D1 2 x 1.08 2.16, D2 2.33, D3 2.52
• g4 gn 4
• Constant growth rate applies to D4
• -gt use Case 2 (constant growth) to compute P3
• D4 2.52 x 1.04 2.62
• P3 2.62 / (.12 - .04) 32.75

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Problem 5.13 (concluded)

• Expected future cash flows of this stock
• 0 1 2 3
• ---------------------------- (r 12)
• D1 D2 D3 P3
• 2.16 2.33 2.52 32.75
• P0 2.16/1.12 2.33/1.122 35.27/1.123
  28.89