# CHAPTER SEVENTEEN THE VALUATION OF COMMON STOCK. CAPITALIZATION OF INCOME METHOD n THE INTRINSIC VALUE OF A STOCK represented by present value of the.

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CHAPTER SEVENTEEN THE VALUATION OF COMMON STOCK

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

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

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

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

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

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

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

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

THE ZERO GROWTH MODEL n THE ZERO-GROWTH MODEL derivation

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

THE ZERO GROWTH MODEL n Applying to V

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?

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

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

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

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

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

CONSTANT GROWTH MODEL n Substituting

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

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

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

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

THE MULTIPLE-GROWTH MODEL

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

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

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

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

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

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)

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

THE ZERO-GROWTH MODEL n Model:

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

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

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

SOURCES OF EARNINGS GROWTH n New Investments:

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

SOURCES OF EARNINGS GROWTH n Assume constant rate of return

SOURCES OF EARNINGS GROWTH n IF n then

SOURCES OF EARNINGS GROWTH n and

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

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

SOURCES OF EARNINGS GROWTH n such that

END OF CHAPTER 17

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