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1 CHAPTER FIFTEEN DIVIDEND DISCOUNT MODELS

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2 CAPITALIZATION OF INCOME METHOD THE INTRINSIC VALUE OF A STOCK –represented by present value of the income stream

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3 CAPITALIZATION OF INCOME METHOD formula where C t = the expected cash flow t = time k = the discount rate

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4 CAPITALIZATION OF INCOME METHOD NET PRESENT VALUE –FORMULA NPV = V - P

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5 CAPITALIZATION OF INCOME METHOD NET PRESENT VALUE –Under or Overpriced? If NPV > 0 If NPV < 0 underpriced overpriced

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6 CAPITALIZATION OF INCOME METHOD INTERNAL RATE OF RETURN (IRR) –set NPV = 0, solve for IRR, or –the IRR is the discount rate that makes the NPV = 0

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7 CAPITALIZATION OF INCOME METHOD APPLICATION TO COMMON STOCK –substituting determines the “true” value of one share

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8 CAPITALIZATION OF INCOME METHOD A COMPLICATION –the previous model assumes dividends can be forecast indefinitely –a forecasting formula can be written D t = D t -1 ( 1 + g t ) where g t = the dividend growth rate

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9 THE ZERO GROWTH MODEL ASSUMPTIONS –the future dividends remain constant such that D 1 = D 2 = D 3 = D 4 =... = D N

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10 THE ZERO GROWTH MODEL THE ZERO-GROWTH MODEL –derivation

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11 THE ZERO GROWTH MODEL Using the infinite series property, the model reduces to if g = 0

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12 THE ZERO GROWTH MODEL Applying to V

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13 THE ZERO GROWTH MODEL Example –If Zinc Co. is expected to pay cash dividends of $8 per share and the firm has a 10% required rate of return, what is the intrinsic value of the stock?

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14 THE ZERO GROWTH MODEL Example(continued) If the current market price is $65, the stock is underpriced. Recommendation: BUY

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15 CONSTANT GROWTH MODEL ASSUMPTIONS: –Dividends are expected to grow at a fixed rate, g such that D 0 (1 + g) = D 1 and D 1 (1 + g) = D 2 or D 2 = D 0 (1 + g) 2

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16 CONSTANT GROWTH MODEL In General D t = D 0 (1 + g) t

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17 CONSTANT GROWTH MODEL THE MODEL: D 0 = a fixed amount

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18 CONSTANT GROWTH MODEL Using the infinite property series, if k > g, then

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19 CONSTANT GROWTH MODEL Substituting

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20 CONSTANT GROWTH MODEL since D 1 = D 0 (1 + g)

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21 THE MULTIPLE-GROWTH MODEL ASSUMPTION: –future dividend growth is not constant Model Methodology –to find present value of forecast stream of dividends –divide stream into parts –each representing a different value for g

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22 THE MULTIPLE-GROWTH MODEL –find PV of all forecast dividends paid up to and including time T denoted V T-

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23 THE MULTIPLE-GROWTH MODEL Finding PV of all forecast dividends paid after time t –next period dividend D t+1 and all thereafter are expected to grow at rate g

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24 THE MULTIPLE-GROWTH MODEL

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25 THE MULTIPLE-GROWTH MODEL Summing V T- and V T+ V = V T- + V T+

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26 MODELS BASED ON P/E RATIO PRICE-EARNINGS RATIO MODEL –Many investors prefer the earnings multiplier approach since they feel they are ultimately entitled to receive a firm’s earnings –P/E ratio is also known as: “Earnings multiplier” “Capitalization factor”

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27 MODELS BASED ON P/E RATIO PRICE-EARNINGS RATIO MODEL –EARNINGS MULTIPLIER: = PRICE - EARNINGS RATIO = Current Market Price following 12 month earnings

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28 PRICE-EARNINGS RATIO MODEL The Model is derived from the Dividend Discount model:

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29 PRICE-EARNINGS RATIO MODEL Dividing by the coming year’s earnings

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30 PRICE-EARNINGS RATIO MODEL The P/E Ratio is a function of –the expected payout ratio ( D 1 / E 1 ) –the required return (k) –the expected growth rate of dividends (g)

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31 THE ZERO-GROWTH MODEL ASSUMPTIONS: dividends remain fixed 100% payout ratio to assure zero-growth

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32 THE ZERO-GROWTH MODEL Model:

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33 THE CONSTANT-GROWTH MODEL ASSUMPTIONS: growth rate in dividends is constant earnings per share is constant payout ratio is constant

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34 THE CONSTANT-GROWTH MODEL The Model: where g e = the growth rate in earnings

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35 SOURCES OF EARNINGS GROWTH What causes growth? assume no new capital added retained earnings used to pay firm’s new investment If p t = the payout ratio in year t 1-p t = the retention ratio

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36 SOURCES OF EARNINGS GROWTH New Investments:

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37 SOURCES OF EARNINGS GROWTH What about the return on equity? Let r t = return on equity in time t r t I t is added to earnings per share in year t+1 and thereafter

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38 SOURCES OF EARNINGS GROWTH Assume constant rate of return

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39 SOURCES OF EARNINGS GROWTH IF then

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40 SOURCES OF EARNINGS GROWTH and

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41 SOURCES OF EARNINGS GROWTH If the growth rate in earnings per share g et+1 is constant, then r t and p t are constant

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42 SOURCES OF EARNINGS GROWTH Growth rate depends on –the retention ratio –average return on equity

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43 SOURCES OF EARNINGS GROWTH such that

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