Lecture 3 Stock Valuation Contact: Natt Koowattanatianchai Email: - - PowerPoint PPT Presentation

Stock Valuation

Lecture 3

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Contact: Natt Koowattanatianchai

 Email:



fbusnwk@ku.ac.th

 Homepage:



http://fin.bus.ku.ac.th/nattawoot.htm

 Phone:



02-9428777 Ext. 1218

 Mobile:



087- 5393525

 Office:



9th Floor, KBS Building, Kasetsart University

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Outline

1 The Present Value of Common Stocks 2 Different growth assumptions

9-3

References

 Ross, S., Westerfield, R. and Jaffe, J.

(2013), Corporate Finance (10th Edition), McGraw Hill/Irvin. (Chapter 9)

 Moyer, R.C., McGuigan, J.R., and Rao,

R.P. (2015), Contemporary Financial Management (13th Edition), Cengage

• Learning. (Chapter 7)

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The PV of Common Stocks

 The value of any asset is the present value of its

expected future cash flows.

 Stock ownership produces cash flows from:

 Dividends  Capital Gains

 Valuation of Different Types of Stocks

 Zero Growth  Constant Growth  Differential Growth

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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

3 3 2 2 1 1

        

   

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:

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Case 2: Constant Growth

) 1 ( Div Div

1

g  

Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value

• f a growing perpetuity:

g R P  

1

Div

Assume that dividends will grow at a constant rate, g, forever, i.e.,

2 1 2

) 1 ( Div ) 1 ( Div Div g g    

3 2 3

) 1 ( Div ) 1 ( Div Div g g    

. . .

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Constant Growth Example

 Suppose Big D, Inc., just paid a dividend of

$.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?

 P0 = .50(1+.02) / (.15 - .02) = $3.92

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Case 3: Differential Growth

 Assume that dividends will grow at different

rates in the foreseeable future and then will grow at a constant rate thereafter.

 To value a Differential Growth Stock, we need

to:

 Estimate future dividends in the foreseeable future.  Estimate the future stock price when the stock

becomes a Constant Growth Stock (case 2).

 Compute the total present value of the estimated

future dividends and future stock price at the appropriate discount rate.

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Case 3: Differential Growth

) (1 Div Div

1 1

g  

 Assume that dividends will grow at rate g1 for N

years and grow at rate g2 thereafter.

2 1 1 1 2

) (1 Div ) (1 Div Div g g    

N N N

g g ) (1 Div ) (1 Div Div

1 1 1

   



) (1 ) (1 Div ) (1 Div Div

2 1 2 1

g g g

N N N

    



. . . . . .

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Case 3: Differential Growth

) (1 Div

1

g 

Dividends will grow at rate g1 for N years and grow at rate g2 thereafter

2 1

) (1 Div g 

N

g ) (1 Div

1

 ) (1 ) (1 Div ) (1 Div

2 1 2

g g g

N N

   

…

1 2

…

N N+1

…

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Case 3: Differential Growth

We can value this as the sum of:

• a T-year annuity growing at rate g1

          

T T A

R g g R C P ) 1 ( ) 1 ( 1

1 1

• plus the discounted value of a perpetuity growing at

rate g2 that starts in year T+1

T B

R g R P ) 1 ( Div

2 1 T

          



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Case 3: Differential Growth

Consolidating gives:

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.

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A Differential Growth Example

A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%.

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With the Formula

3 3 3 3

) 12 . 1 ( 04 . 12 . ) 04 . 1 ( ) 08 . 1 ( 2 $ ) 12 . 1 ( ) 08 . 1 ( 1 08 . 12 . ) 08 . 1 ( 2 $                     P

  



3

) 12 . 1 ( 75 . 32 $ 8966 . 1 54 $     P

31 . 23 $ 58 . 5 $   P 89 . 28 $  P

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With Cash Flows

08) . 2(1 $

2

08) . 2(1 $

…

1 2 3 4

3

08) . 2(1 $ ) 04 . 1 ( 08) . 2(1 $

3

16 . 2 $ 33 . 2 $

1 2 3

04 . 12 . 62 . 2 $ 52 . 2 $   89 . 28 $ ) 12 . 1 ( 75 . 32 $ 52 . 2 $ ) 12 . 1 ( 33 . 2 $ 12 . 1 16 . 2 $

3 2

     P

75 . 32 $ 08 . 62 . 2 $

3

  P

The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.

Questions?