Stock Valuation A Discounted Cash Flow Approach

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Stock ValuationA Discounted Cash Flow Approach
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Common Stock

• Provides Ownership in the firm, owners have the
  right to
• Share proportionally in dividends paid
• Vote on stockholder matters
• Share proportionally in assets remaining after
  all liabilities are paid in event of liquidation.
• Dividends are declared by management

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Preferred Stock

• Claim prior to common
• Fixed dividend schedule
• Missing payment does not constitute default

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The Market for Common Stocks

• Secondary Market Transactions
• Outstanding shares are traded between investors,
  transactions do not raise money for the firm
• Sale of additional shares
• If the firm decides to increase the number of
  shares outstanding it sells them in the primary
  market, raising money for the firm
• Initial Public Offering
• The initial sale of shares in a firm that was
  previously privately held.

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A General Valuation Model

• The basic components of the valuation are
• An estimate of the future cash flow stream from
  owning the asset
• The required rate of return for each period based
  upon the riskiness of the asset
• The value is then found by discounting each cash
  flow by its respective discount rate and then
  summing the PVs (Basically the PV of an Uneven
  Cash Flow Stream)

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The Formal Model

• The value of the asset should then be equal to

How do we apply the model to find the value of a
stock?
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All Stocks

• Regardless of type of stock, the return from
  owning the stock is usually earned in one of two
  ways
• Dividends
• Dividends are declared by management and paid on
  a per share basis to the share holder
• Capital Gains
• Capital Gains represent the change in the price
  of the stock

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General Valuation Model Stocks

• Assuming that the firms pays dividends, the
  future expected cash flows received from owning
  the stock are the dividends that the firm is
  expected to pay.
• What about the capital gains?

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Basic Stock Valuation

• The firm is a legal entity that continues
  forever, we are assuming that dividends continue
  forever (t infinity)
• Valuation would then be the PV of the dividends,
  Dt, from t 0 to t infinity.
• The Dividends are discounted at the required rate
  of return for the investor , rs

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What about the future price?

• Let the stock price in one year
• There are two future cash flows Dividend one and
  the future price.
• 0 1

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Valuation

• The valuation would then be
• What is equal to?

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Valuation

• The value of the stock at time 1 must equal the
  PV of the cash flows that come after it. The PV
  of D2, D3, etc. at time t1

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Valuation

• Substitute for in our equation

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• Which leaves our original equation

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Dividends

• The key to valuing the stock then becomes your
  assumption about whether dividends change over
  time.
• If they do change you need to decide how to
  estimate possible future changes in dividends.
• This can in part be determined by the type of
  stock (common or preferred).

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Pref Stock Valuation

• Often it is assumed that the dividends are
  constant for a preferred stock. If there is no
  maturity date the valuation is the same as a
  perpetuity

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Dividends

• For common stock the dividend is usually not
  expected to remain the same amount forever.
• Constant dividends formally were often a goal of
  management, but they represent a decline in real
  income.

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Constant Growth in Dividends

• One possible assumption is that dividends grow at
  a constant rate.
• In this case
• D1D0(1g)
• D2D1(1g) D0(1g)2
• D3D2(1g) D0(1g)3
• etc
• Use this in the basic formula in the valuation
  formula from before.

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Constant Growth in Dividends
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Constant Growth continued
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Constant Growth
Substitute
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Practice Problem

• How much would you be willing to pay for a share
  of stock in Bulldog Industries given the
  following information? Assume that Bulldog just
  paid 1.00 dividend and that the dividend is
  expected to grow at 5 each year forever and that
  the appropriate discount rate for the risk
  associated with the firm is 10.
•  

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Total Return

• The total return earned by the shareholder has
  two components

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Practice Problem Part 2

• Find the the dividend and capital gains yield in
  the previous problem.

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Practice Problem Part 2
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Rates of Return

• The total return for owning the stock is then the
  sum of the capital gains yield and the dividend
  yield.
• In the previous example, we estimated the future
  value of the stock at time t1.
• Therefore the total return found by adding the
  capital gains yield to the divided yield would be
  the expected rate of return,

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Rates of Return

• IF you calculated the return after you observed
  the price at time t1 then you would have found
  the actual or realized rate of return ( ).
  In this case your values for price are not the
  expected value, but the actual observed value.

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Note

• For a constant growth stock. Given the observed
  price of the stock and assuming it is equal to
  value, you can solve for the expected total
  return by rearranging the constant growth
  equation.

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In the case of constant growth, The expected
capital gains yield is equal to the expected
growth rate
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Non Constant Growth

• Assume that the firm grows at a fast rate for a
  short period of time then starts constant growth
• Value would equal the PV of each of the early
  dividends plus the PV of the constant growth
  portion

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• To find the value of this stock,
• Discount the dividend received during each period
  of the supernormal growth period.
• Find the value of the stock in year m assuming
  constant growth, the horizon value (use equation
  above)
• Discount the PV of the stock in year m (found in
  2)) back to the current year.

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Non Constant Growth Valuation

• Assume non constant growth is for two periods

The PV of the Constant Growth From t 2 to
infinity
The PV of the first Two dividends
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Practice Problem-Data

• Assume that the average firm in your companys
  industry is expected to grow at a constant rate
  of 7. Your company is about a risky as the
  average firm in the industry, and investors are
  requiring a 15 return for investing in firms in
  the industry. Your firm has just introduced a
  new product which it expects to increase earnings
  each of the next two years. The expectation is
  that dividends will grow at 40 next year and 20
  the year after that then return to the 7
  constant growth rate of the industry. The last
  dividend paid by the firm was 0.75.

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Practice Problem-questions

• What is the current price of the stock?
• What is the capital gains yield and divined yield
  if the stock was held for the first year?
• What is the capital gains yield and dividend
  yield if the stock was bought following the third
  dividend and held until it paid the fourth
  dividend?
• Explain your answers in b) and c) (Did the
  capital gains yield and dividend yield change
  over time? and if so how? Will you expect it to
  change after year four? why or why not?)