FINANCE 5. Stock valuation - DDM

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FINANCE5. Stock valuation - DDM

• Professor André Farber
• Solvay Business School
• Université Libre de Bruxelles
• Fall 2006

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Stock Valuation

• Objectives for this session
• Introduce the dividend discount model (DDM)
• Understand the sources of dividend growth
• Analyse growth opportunities
• Examine why Price-Earnings ratios vary across
  firms
• Introduce free cash flow model (FCFM)

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DDM one-year holding period

• Review valuing a 1-year 4 coupon bond
• Face value 50
• Coupon 2
• Interest rate 5
• How much would you be ready to pay for a stock
  with the following characteristics
• Expected dividend next year 2
• Expected price next year 50
• Looks like the previous problem. But one crucial
  difference
• Next year dividend and next year price are
  expectations, the realized price might be very
  different. Buying the stock involves some risk.
  The discount rate should be higher.

Bond price P0 (502)/1.05 49.52
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Dividend Discount Model (DDM) 1-year horizon

• 1-year valuation formula
• Back to example. Assume r 10

Dividend yield 2/47.27 4.23
Rate of capital gain (50 47.27)/47.27 5.77
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DDM where does the expected stock price come
from?

• Expected price at forecasting horizon depends on
  expected dividends and expected prices beyond
  forecasting horizon
• To find P2, use 1-year valuation formula again
• Current price can be expressed as
• General formula

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DDM - general formula

• With infinite forecasting horizon
• Forecasting dividends up to infinity is not an
  easy task. So, in practice, simplified versions
  of this general formula are used. One widely used
  formula is the Gordon Growth Model base on the
  assumption that dividends grow at a constant
  rate.
• DDM with constant growth g
• Note g lt r

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DDM with constant growth example
Data Next dividend 6.00Div.growth rate
4Discount rate 10
Year Dividend DiscFac Price
0 100.00
1 6.00 0.9091 104.00
2 6.24 0.8264 108.16
3 6.49 0.7513 112.49
4 6.75 0.6830 116.99
5 7.02 0.6209 121.67
6 7.30 0.5645 126.53
7 7.59 0.5132 131.59
8 7.90 0.4665 136.86
9 8.21 0.4241 142.33
10 8.54 0.3855 148.02
P0 6/(.10-.04)
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Differential growth

• Suppose that r 10
• You have the following data
• P3 3.02 / (0.10 0.05) 60.48

Year 1 2 3 4 to 8
Dividend 2 2.40 2.88 3.02
Growth rate 20 20 5
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A formula for g

• Dividend are paid out of earnings
• Dividend Earnings Payout ratio
• Payout ratios of dividend paying companies tend
  to be stable.
• Growth rate of dividend g Growth rate of
  earnings
• Earnings increase because companies invest.
• Net investment Retained earnings
• Growth rate of earnings is a function of
• Retention ratio 1 Payout ratio
• Return on Retained Earnings

g (Return on Retained Earnings) (Retention
Ratio)
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Example

• Data
• Expected earnings per share year 1 EPS1 10
• Payout ratio 60
• Required rate of return r 10
• Return on Retained Earnings RORE 15
• Valuation
• Expected dividend per share next year div1 10
  60 6
• Retention Ratio 1 60 40
• Growth rate of dividend g (40) (15) 6
• Current stock price
• P0 6 / (0.10 0.06) 150

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Return on Retained Earnings and Debt

• Net investment ?Total Asset
• For a levered firm
• ?Total Asset ?Stockholders equity ?Debt
• RORE is a function of
• Return on net investment (RONI)
• Leverage (L ?D/ ?SE)
• RORE RONI RONI i (1-TC)L

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Growth model example
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Valuing the company

• Assume discount rate r 15
• Step 1 calculate terminal value
• As Earnings Dividend from year 4 on
• V3 503.71/15 3,358
• Step 2 discount expected dividends and terminal
  value

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Valuing Growth Opportunities

• Consider the data
• Expected earnings per share next year EPS1 10
• Required rate of return r 10
• Why is A more valuable than B or C?
• Why do B and C have same value in spite of
  different investment policies

Cy A Cy B Cy C
Payout ratio 60 60 100
Return on Retained Earnings 15 10 -
Next years dividend 6 6 10
g 6 4 0
Price per share P0 150 100 100
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NPVGO

• Cy C is a cash cow company
• Earnings Dividend (Payout 1)
• No net investment
• Cy B does not create value
• Dividend lt Earnings, Payout lt1, Net investment gt0
• But Return on Retained Earnings Cost of
  capital
• NPV of net investment 0
• Cy A is a growth stock
• Return on Retained Earnings gt Cost of capital
• Net investment creates value (NPVgt0)
• Net Present Value of Growth Opportunities (NPVGO)
• NPVGO P0 EPS1/r 150 100 50

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Source of NPVG0 ?

• Additional value if the firm retains earnings in
  order to fund new projects
• where PV(NPVt) represent the present value at
  time 0 of the net present value (calculated at
  time t) of a future investment at time t
• In previous example
• Year 1 EPS1 10 div1 6 ? Net investment 4
• ?EPS 4 15 0.60 (a permanent
  increase)
• NPV1 -4 0.60/0.10 2 (in year
  1)
• PV(NPV1) 2/1.10 1.82

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NPVGO details
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What Do Price-Earnings Ratios mean?

• Definition P/E Stock price / Earnings per
  share
• Why do P/E vary across firms?
• As P0 EPS/r NPVGO ?
• Three factors explain P/E ratios
• Accounting methods
• Accounting conventions vary across countries
• The expected return on shareholdersequity
• Risky companies should have low P/E
• Growth opportunities

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Beyond DDM The Free Cash Flow Model

• Consider an all equity firm.
• If the company
• Does not use external financing (not stock issue,
  shares constant)
• Does not accumulate cash (no change in cash)
• Then, from the cash flow statement
• Free cash flow Dividend
• CF from operation Investment Dividend
• Company financially constrained by CF from
  operation
• If external financing is a possibility
• Free cash flow Dividend Stock Issue
• Market value of company PV(Free Cash Flows)