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CHAPTER SEVENTEEN THE VALUATION OF COMMON STOCK

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

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

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

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CAPITALIZATION OF INCOME METHOD n NET PRESENT VALUE Under or Overpriced? 3 If NPV > 0 underpriced 3 If NPV < 0overpriced

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

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CAPITALIZATION OF INCOME METHOD n 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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THE ZERO GROWTH MODEL n ASSUMPTIONS the future dividends remain constant such that D 1 = D 2 = D 3 = D 4 =... = D N

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THE ZERO GROWTH MODEL n THE ZERO-GROWTH MODEL derivation

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

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THE ZERO GROWTH MODEL n Applying to V

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

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

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

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

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CONSTANT GROWTH MODEL n Substituting

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

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THE MULTIPLE-GROWTH MODEL n ASSUMPTION: future dividend growth is not constant n 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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THE MULTIPLE-GROWTH MODEL find PV of all forecast dividends paid up to and including time T denoted V T-

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THE MULTIPLE-GROWTH MODEL n 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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THE MULTIPLE-GROWTH MODEL

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n Summing V T- and V T+ V = V T- + V T+

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MODELS BASED ON P/E RATIO n PRICE-EARNINGS RATIO MODEL Many investors prefer the earnings multiplier approach since they feel they are ultimately entitled to receive a firm’s earnings

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

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

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

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PRICE-EARNINGS RATIO MODEL n 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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THE ZERO-GROWTH MODEL n ASSUMPTIONS: 3 dividends remain fixed 3 100% payout ration to assure zero-growth

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THE ZERO-GROWTH MODEL n Model:

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THE CONSTANT-GROWTH MODEL n ASSUMPTIONS: 3 growth rate in dividends is constant 3 earnings per share is constant 3 payout ratio is constant

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

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SOURCES OF EARNINGS GROWTH n What causes growth? 3 assume no new capital added 3 retained earnings use to pay firm’s new investment 3 If p t = the payout ratio in year t 3 1-p t = the retention ratio

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SOURCES OF EARNINGS GROWTH n New Investments:

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SOURCES OF EARNINGS GROWTH n 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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SOURCES OF EARNINGS GROWTH n Assume constant rate of return

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SOURCES OF EARNINGS GROWTH n IF n then

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SOURCES OF EARNINGS GROWTH n and

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

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SOURCES OF EARNINGS GROWTH n such that

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END OF CHAPTER 17

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