FormulasToKnow-Chapters4-8-9(and5from8thEd)

# FormulasToKnow-Chapters4-8-9(and5from8thEd) - Formulas to...

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BMGT440 Dr. E F Kiss formulae-1 Formulas to know from Chapters 4, 8, 9 (ch. 5 in 8 th ed.)

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BMGT440 Dr. E F Kiss formulae-2 From chapter 4 Summary and Conclusions We presented five simplifying formulae : r C PV = : Perpetuity g r C PV - = : Perpetuity Growing + - = T r r C PV ) 1 ( 1 1 : Annuity + + - - = T r g g r C PV ) 1 ( 1 1 : Annuity Growing
BMGT440 Dr. E F Kiss formulae-3 Chapter 8 (ch. 5 in 8 th ed) : The Bond-Pricing Equation t t r) (1 F r r) (1 1 - 1 C Value Bond + + + =

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BMGT440 Dr. E F Kiss formulae-4 Case 1: Zero Growth Assume that dividends will remain at the same level forever r P r r r P Div ) 1 ( Div ) 1 ( Div ) 1 ( Div 0 3 3 2 2 1 1 0 = + + + + + + = = = = 3 2 1 Div Div Div Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:
BMGT440 Dr. E F Kiss formulae-5 Case 2: Constant Growth ) 1 ( Div Div 0 1 g + = Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: g R P - = 1 0 Div Assume that dividends will grow at a constant rate, g , forever. i.e. 2 0 1 2 ) 1 ( Div ) 1 ( Div Div g g + = + = 3 0 2 3 ) 1 ( Div ) 1 ( Div Div g g + = + = . . . P = Div /(R-g) = [Div (1+g)]/(R-g)

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BMGT440 Dr. E F Kiss formulae-6 Case 3: Differential Growth We can value this as the sum of: an N -year annuity growing at rate g 1 + + - - = T T A R g g R C P ) 1 ( ) 1 ( 1 1 1 plus the discounted value of a perpetuity growing at rate g 2 that starts in year N +1 N B R g R P ) 1 ( Div 2 1 T + - = +
BMGT440 Dr. E F Kiss formulae-7 Case 3: Differential Growth To value a Differential Growth Stock, we can use T T T R g R R g g R C P ) 1 ( Div ) 1 ( ) 1 ( 1 2 1 T 1 1 + - + + + - - = + Or we can cash flow it out, which is the method that I usually use and will use in the HW problems.

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BMGT440 Dr. E F Kiss formulae-8 Formula for Firm’s Growth Rate g = Retention ratio × Return on retained earnings Retention ratio = 1 – (Dividend Payout ratio)
BMGT440 Dr. E F Kiss

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FormulasToKnow-Chapters4-8-9(and5from8thEd) - Formulas to...

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