# Stock Valuation Chapter 9

Pages: 11 (1617 words) Published: February 14, 2013
Chapter 9
Stock V l ti St k Valuation

McGraw-Hill/Irwin

Key Concepts and Skills
Understand h stock prices depend on future U d d how k i d d f dividends and dividend growth  B able to compute stock prices using the Be bl k i i h dividend growth model U d Understand h growth opportunities affect d how h ii ff stock values U d Understand valuation comparables d l i bl  Understand how stock markets work 

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Chapter Outline
9.1 91 9.2 9.3 9.4 94 9.5 9.6 The P Th Present Value of C V l f Common S k Stocks Estimates of Parameters in the Dividend Discount Model Growth Opportunities Comparables Valuing the Entire Firm The Stock Markets

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9.1 The PV of Common Stocks
 

The value of any asset is the present value of its expected future cash flows. Stock S k ownership produces cash fl hi d h flows from: f  

Dividends Capital Gains Zero Growth Constant Growth Differential Growth e e t a G owt 9-3

Valuation of Different Types of Stocks
  

Case 1: Zero Growth

Assume that di id d will remain at the same level A h dividends ill i h l l forever

Div 1  Div 2  Div 3  

 Since future cash flows are constant, the value of a zero

growth stock is the present value of a perpetuity:

Div 3 Div 1 Div 2 P0     1 2 3 (1  R) (1  R) (1  R) Div P0  R 9-4

Case 2: Constant Growth
Assume that dividends will grow at a constant rate, g, h di id d ill forever, i.e.,

Div 1  Div 0 (1  g )

Div 2  Div 1 (1  g )  Div 0 (1  g ) 2 Div 3  Div 2 (1  g )  Div 0 (1  g ) 3 . . .

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:

Div Di 1 P0  R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 di id d will grow at different A h dividends ill diff rates in the foreseeable future and then will grow at a constant rate thereafter. 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 p p future dividends and future stock price at the appropriate discount rate. 

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Case 3: Differential Growth
 Assume that dividends will grow at rate g1 for N

years and grow at rate g2 thereafter.

Div 1  Div 0 (1  g1 )

Div 2  Div 1 (1  g1 )  Div 0 (1  g1 ) 2 ( (
Div N  Div N 1 (1  g1 )  Div 0 (1  g1 ) N
. . .

Div N 1  Div N (1  g 2 )  Div 0 (1  g1 ) N (1  g 2 ) ( ( ( . . .
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Case 3: Differential Growth
Dividends will grow at rate g1 for N years and grow at rate g2 thereafter

Div 0 (1  g1 ) Div 0 (1  g1 ) 2

0 1 2

Div 0 (1  g1 ) N

Div Di N (1  g 2 )  Div 0 (1  g1 ) N (1  g 2 )

N

N+1

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Case 3: Differential Growth
We W can value this as the sum of: l hi h f  a T-year annuity growing at rate g1

 (1  g1 )T  C PA  1  T  R  g1  (1  R)   plus the discounted value of a perpetuity growing at

rate g2 that starts in year T+1 T 1

 Div T 1    Rg   2  PB   T (1  R)

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Case 3: Differential Growth
Consolidating gives: C lid ti i

 Di T 1  Div   C  (1  g1 )T   R  g 2    P  1  T  T R  g1  (1  R )  (1  R ) 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. perpetuity What is the stock worth? The discount rate is 12%.

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