FINC 3310

1
FINC 3310

• Chapter Eight
• Stock Valuation

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Symbols and Abbreviations

• P0 the price of a share of stock today
• Dt the dividend at time t
• g the growth rate in dividends over time
• r the appropriate required rate of return

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Characteristics of Equity

• Dividends
• Ownership claims
• Voting
• Maturity

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Valuing a Share of Stock

• Start with a one period horizon
• Buy now at P0
• Expect to receive dividend at end of year D1
• Expect to sell at P1 at end of year
• Required return r
• P0
• Question What is P1?

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Valuation, continued

• P1 and
• P2 and P3 and so on.
• Which gives us
• P0

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Valuation, continued

• We can go on pushing Pt out more and more into
  the future, so that really, P0 is the present
  value of the stream of all future dividends, or
• P0
  ... ...
• P0

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Valuation, continued

• How do we evaluate this infinite sum?
• We must make assumptions about the behavior of
  Dt over time.
• No Growth
• Constant Growth
• Non-constant, or supernormal, Growth

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Dividend Models of Stock Valuation 1

• No growth Dt D "t tÎ1, so that we
  have
• P0 ...
  ...
• This is just a perpetuity, so
• P0 D/r

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No Growth Example

• Wilbur's Proven Best Fertilizers, Inc., pays a
  5 dividend every year. If the required return
  is 8 for such investments, what should the price
  of Wilbur's stock be?
• P0 5/.08 62.50.

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Dividend Models of Stock Valuation 2

• Constant Growth - There is often a stable, even
  predictable, relationship in dividends period
  after period. Some research suggests that
  "smooth" dividends are a corporate goal.
• Denote the growth rate as g. Now, if the most
  recent dividend is D0, then the expected next
  dividend is D1 and D1 D0 (1g). That is, D1
  is D0 increased by g.
• Now our stock model looks like this

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Constant Growth, continued

• P0
  ... ...
• This is true because of the constant rate of
  growth, g. That is, we can write
• D1 D0(1g) D2 D1(1g)
  D0(1g)2
• D3 D2(1g) D0(1g)3
• Generally, Dt D0(1g)t

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Constant Growth, continued

• Now, if r gt g (strictly gt), then we can reduce
  this to
• Note the relationship. P0 is based on the next
  expected dividend D1. In fact, you can find the
  price at any time t using this!

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Constant Growth Example

• Brady Textiles, a polyester manufacturer, just
  paid a 2.50 dividend. All estimates agree
  growth is expected to be constant at 4 per year
  indefinitely. The required return is 10. What
  is the price of Brady Textiles' stock?
• P0 (2.50)(1.04) 2.60 43.33
• .10 - .04 .06

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Constant Growth Example, continued

• What is the price expected to be at the end of
  the fifth year?
• P5
• (2.50)(1.04)6 3.1633 52.72
• .06 .06

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Dividend Models of Stock Valuation 3

• Non-constant Growth How do we value the shares of
  a company that pays no dividends currently, but
  is expected to pay dividends later? Or, what
  about a company with rapidly growing dividends
  (rltg now), and a more stable stream later?
• Treat the non-constant or "supernormal" period
  separately, and then use what we know about the
  constant growth model.

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Non-constant Growth Example

• Blair Tours, a new outdoors/camping vacation
  provider, is experiencing rapid growth of 40 per
  year. This is expected to last 2 years, after
  which time growth will stabilize at 5 per year.
  The current dividend is 3.00. The required
  return is 14.
• 1) Draw a timeline and find the "supernormal"
  dividends
• 1 2 3
• ______________________________________
• 3.00 4.20 5.88 6.17
• 40 40 5 g5

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Non-constant Growth Example

• 2) Locate period of constant growth. D3 is
  first "stable" dividend, so we can use D3 to find
  the present value of the constant growth stream
  of dividends.
• Question If D3 is used, where (in terms of the
  time line) is the price? At t 2!
• P2 D3/(r-g)
• P2 6.17/.09 68.56
• 3) Add up the present values of the cash flows
• P0 4.20/1.14 5.88/(1.14)2 68.56/(1.14)2
• 3.68 4.52 52.75
• 60.95

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Components of the Required Return

• Rearrange the dividend growth model
• solving for the required rate of return
• r g

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Components of the Required Return

• Dividend Yield
• Capital Gains Yield g

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The Stock Markets

• Primary versus Secondary
• Dealers and Brokers
• Trading on the NYSE
• Trading on the NASDAQ