CHAPTER 17 POWERPOINT PRESENTATION

CHAPTER SEVENTEEN

THE VALUATION OF

COMMON STOCK

CAPITALIZATION OF INCOME METHOD



THE INTRINSIC VALUE OF A STOCK

•

represented by present value of the income stream

CAPITALIZATION OF INCOME METHOD



formula

where

C_t = the expected cash flow t = time

k = the discount rate



^







1

( 1 )

t

k

t

V C

^t

CAPITALIZATION OF INCOME METHOD



NET PRESENT VALUE

•

^FORMULA

NPV = V - P

CAPITALIZATION OF INCOME METHOD



NET PRESENT VALUE

•

Under or Overpriced?



If NPV > 0 underpriced



If NPV < 0 overpriced

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

CAPITALIZATION OF INCOME METHOD



APPLICATION TO COMMON STOCK

•

substituting

determines the “true” value of one share

 

 

 

 

 ... (1 )

) 1

( )

1

( ²

2 1

1

k D k

D k

V D



^

 



1 (1 )

t t

t

k D

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

THE ZERO GROWTH MODEL



ASSUMPTIONS

•

the future dividends remain constant such that

D

₁

= D

₂

= D

₃

= D

₄

= . . . = D

_N

THE ZERO GROWTH MODEL



THE ZERO-GROWTH MODEL

•

^derivation



^

 



1

0

) 1

t ( k t

V D

















^ 

1 0 0

) 1

t ( k t

D D

THE ZERO GROWTH MODEL



Using the infinite series property, the model reduces to



if g = 0

k k

t t

1 )

1 (

1

1

 

 

^



THE ZERO GROWTH MODEL



Applying to V

k

V  D

¹

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?

10 .

 8 V

80

 $

THE ZERO GROWTH MODEL



Example(continued)

If the current market price is $65, the stock is underpriced.

Recommendation:

BUY

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

CONSTANT GROWTH MODEL



In General

D

_t

= D

₀

(1 + g)

^t

CONSTANT GROWTH MODEL



THE MODEL:

D₀ = a fixed amount



^





 

1

0

) 1

(

) 1

(

t t

t

k g V D

 



 





 ^D

⁰



^

⁽ ₍ ¹ ₁  _k ^g ₎ ⁾

^tt

V

CONSTANT GROWTH MODEL



Using the infinite property series,

if k > g, then

g k

g k

g

t t

t



 





^ 



1 )

1 (

) 1

(

1

CONSTANT GROWTH MODEL



Substituting

 

 







 

g k

D g

V 1

0

CONSTANT GROWTH MODEL



since D

₁

= D

₀

(1 + g)

g k

V D

 

¹

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

THE MULTIPLE-GROWTH MODEL

•

find PV of all forecast dividends paid up to and including time T denoted VT-









^T



t t

T

k

V D

1

0

) 1

(

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

 

 







_



g D k

V

_{T T}

1

1

THE MULTIPLE-GROWTH MODEL

 

 





 

 T T

T

V k

V ( 1 )

1

T T

k g

k

D

) 1

)(

(

1



  ^

THE MULTIPLE-GROWTH MODEL



Summing V

_T-

and V

_T+

V = V

_T-

+ V

_T+

T T T

t t

T

k g

k

D k

D

) 1

)(

( )

1 (

1

1

  

 

^





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

MODELS BASED ON P/E RATIO



PRICE-EARNINGS RATIO MODEL

•

EARNINGS MULTIPLIER:

= PRICE - EARNINGS RATIO

= Current Market Price

following 12 months earnings

PRICE-EARNINGS RATIO MODEL



The Model is derived from the Dividend Discount model:

g k

P D

  ¹

0

PRICE-EARNINGS RATIO MODEL



Dividing by the coming year’s earnings

g k

D E E

P

 

¹

1

1 0

PRICE-EARNINGS RATIO MODEL



The P/E Ratio is a function of

•

the expected payout ratio ( D1 / E1 )

•

the required return (k)

•

the expected growth rate of dividends (g)

THE ZERO-GROWTH MODEL



ASSUMPTIONS:



dividends remain fixed



100% payout ration to assure zero-growth

THE ZERO-GROWTH MODEL



Model:

E k

V 1

0 

THE CONSTANT-GROWTH MODEL



ASSUMPTIONS:

 growth rate in dividends is constant

 earnings per share is constant

 payout ratio is constant

THE CONSTANT-GROWTH MODEL



The Model:

where g_e = the growth rate in earnings

 

 







 

e e

g k

P g E

V 1

0

SOURCES OF EARNINGS GROWTH



What causes growth?



assume no new capital added



retained earnings use to pay firm’s new investment

 If p

_t

= the payout ratio in year t

 1-p

_t

= the retention ratio

SOURCES OF EARNINGS GROWTH



New Investments:

t t

t p E

I  ( 1  )

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

SOURCES OF EARNINGS GROWTH



Assume constant rate of return

t t t

t E r I

E _1  

 ¹ _t ^{( 1} _t ⁾ 

t r p

E   



SOURCES OF EARNINGS GROWTH



IF



then

) 1

1 ( et t

t E g

E  _ 

) 1

( ₁

1 

  _t  _et

t E g

E

SOURCES OF EARNINGS GROWTH



and

) 1

1 t

(

t

et

r p

g

_

 

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

SOURCES OF EARNINGS GROWTH



Growth rate depends on

• the retention ratio

• average return on equity

SOURCES OF EARNINGS GROWTH



such that

 

 







 

) 1

( 1

1

k r p

D

V

END OF CHAPTER 17