Principles of Equity Valuation

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Principles of Equity Valuation

• Riccardo Colacito

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Outline

• A framework for asset pricing
• The Gordon Growth Model (GGM)
• Some examples
• Preferred stock
• A company that pays off all the earnings
• A company with a growth opportunity
• Multi-stage GGM
• Some valuation ratios

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The question

• For a given company, consider the distribution of
  next years dividend, D1, and price, P1.
• What should todays price, V0, be?

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Answer

• Find the required rate of return, r, using the
  CAPM.
• Fundamental-value equation at time 0

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Dividend Discount Model

• Assume that the market is efficient so that the
  market price is the fundamental value
• Use the fundamental-value equation repeatedly

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Warren Buffett

• Intrinsic value is an all-important concept that
  offers the only logical approach to evaluate the
  relative attractiveness of investments and
  businesses. Intrinsic value can be defined
  simply it is the discounted value of the cash
  that can be taken out of business during its
  remaining life.

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Gordons Growth Model (GGM)

• Suppose that expected dividends grow at a rate g,
  that is
• Then the dividend-discount model becomes

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Gordons Growth Model (GGM) - Derivation
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Example 1

• What should be the price of a preferred stock?

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Example 2

• The following information is available about GM
• Beta1.14
• E(Rm)10
• Rf3
• Todays Dividend0.20 per share
• Dividends growth rate1 per year
• How much is a share of GM worth?

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Example 2 (contd)

• Figure out the required rate of return using the
  CAPM
• Use the GGM to compute todays price

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Example 3

• After many years in the business, and as a
  consequence of a lot of competition in the
  sector, GM announces that it does not expected
  its earnings to keep growing at the steady rate
  they used to grow.
• That is earnings are expected to remain constant
  at 0.20 per share forever.
• The new policy will consist in distributing all
  earnings in the form of dividends.

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Example 3 (contd)

• How does the price of GM change?
• If dividends are not growing, it should be lower!
  Remember Buffetts quote you are expecting to
  take out less from this business!
• Lets see
• Indeed!

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Example 4

• In order to re-vitalize the business, GM
  announces that has started investing in a growth
  project that yields 15 per year.
• As a consequence, only a share (1-b) of the
  earnings will be distributed as dividend
• The remaining share of b will be reinvested in
  the growth project
• How will GMs price change?

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Example 4 (contd)

• Let b40
• Let ROE be the return on the project
• Say that GMs initial capital is 100mil.

This is the new capital at the end of year 0!
Retained earnings increase total capital
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Example 4 (contd)

• Therefore dividends will grow at a rate
• Can compute price

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Example 4 (contd)

• Remarks
• ROE stands for Return On Equity
• b is called the plowback ratio or earnings
  retention ratio
• 1-b is called the dividend payout ratio
• The price of GM stock is the highest of all
  examples remember Buffetts quote?

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Present Value of Growth Opportunity

• Decompose the last price of GM in two parts

This would have been the price of GM if not
investing in the growth project
This is the extra kick in the price that comes
from the growth opportunity. Call it the Present
Value of Growth Opportunity
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Present Value of Growth Opportunity (contd)

• Decompose the last price of GM in two parts (in
  numbers)

This is the price of example 3
This can be computed as the difference of the
prices of examples 4 and 3
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Present Value of Growth Opportunity (contd)

• Remarks
• In this example the PVGOgt0
• This is because ROEgtr
• That is the rate of return of the growth
  opportunity is greater than the required rate of
  return of GM
• Exercise repeat example 4, assuming that ROE5.
  Show that PVGO-0.46.
• Will GM ever invest in this project? NO
• Why? Because ROEltr, implying PVGOlt0

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Multi-stage GGM

• A company can grow exceptionally for a while, but
  at some point the company matures and its growth
  normalizes.
• Suppose that you estimate that a companys growth
  will reach its long-run level of g after 3
  years.
• Then in year 3 its price is

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Multi-stage GGM (contd)

• Based on estimates of the next 3 years, todays
  value is

For 3 years you expect to get these dividends and
must discount them at the required rate of return
r
This is P3 as computed before, that must be
discounted for 3 years
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Some valuation ratios (according to GGM)

• Price-dividend ratio
• Price-earnings ratio
• D0(1-b)E0 with earnings retention ratio of b
• Other ratios
• Price-to-book ratio
• Price-to-sales ratio