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

Lecture 3 Stock Valuation

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: 9 th Floor, KBS Building, Kasetsart University  9-1

Outline 1 The Present Value of Common Stocks 2 Different growth assumptions 9-2

References  Ross, S., Westerfield, R. and Jaffe, J. (2013), Corporate Finance (10 th Edition), McGraw Hill/Irvin. (Chapter 9)  Moyer, R.C., McGuigan, J.R., and Rao, R.P. (2015), Contemporary Financial Management (13 th Edition), Cengage Learning. (Chapter 7) 9-3

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 9-4

Case 1: Zero Growth  Assume that dividends will remain at the same level forever     Div Div Div 1 2 3  Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: Div Div Div     1 2 3  P    0 1 2 3 ( 1 ) ( 1 ) ( 1 ) R R R Div  P 0 R 9-5

Case 2: Constant Growth Assume that dividends will grow at a constant rate, g , forever, i.e.,   Div Div ( 1 ) g 1 0     2 Div Div ( 1 ) Div ( 1 ) g g 2 1 0     3 Div Div ( 1 ) Div ( 1 ) g g 3 2 0 . . . 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  1 P  0 R g 9-6

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?  P 0 = .50(1+.02) / (.15 - .02) = $3.92 9-7

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. 9-8

Case 3: Differential Growth  Assume that dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter.   Div Div (1 ) g 1 0 1     2 Div Div (1 ) Div (1 ) g g 2 1 1 0 1 . . .     N Div Div (1 ) Div (1 ) g g  1 1 0 1 N N      N Div Div (1 ) Div (1 ) (1 ) g g g  N 1 N 2 0 1 2 . . . 9-9

Case 3: Differential Growth Dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter   2 Div (1 ) Div (1 ) g g 0 1 0 1 … 0 1 2  Div (1 ) g 2 N  N Div (1 g )    N Div (1 ) (1 ) g g 0 1 0 1 2 … … N N +1 9-10

Case 3: Differential Growth We can value this as the sum of:  a T -year annuity growing at rate g 1    T ( 1 ) C g   1  1  P   A T   ( 1 ) R g R 1  plus the discounted value of a perpetuity growing at rate g 2 that starts in year T +1   Div    T 1      R g  2 P  B T ( 1 ) R 9-11

Case 3: Differential Growth Consolidating gives:   Div    T 1       T   R g ( 1 ) C g    2 1  1  P    T T   ( 1 ) ( 1 ) R g R R 1 Or, we can “cash flow” it out. 9-12

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%. 9-13

With the Formula   3 $ 2 ( 1 . 08 ) ( 1 . 04 )          3   . 12 . 04 $ 2 ( 1 . 08 ) ( 1 . 08 )    1  P  3 3   . 12 . 08 ( 1 . 12 ) ( 1 . 12 )     $ 32 . 75     $ 54 1 . 8966 P 3 ( 1 . 12 )    $ 5 . 58 $ 23 . 31 $ 28 . 89 P P 9-14

With Cash Flows 3 3 $ 2(1 . 08) $ 2(1 . 08) ( 1 . 04 ) 2 $ 2(1 . 08) $ 2(1 . 08) … 0 1 2 3 4 The constant $ 2 . 62  $ 2 . 33 $ 2 . 52 $ 2 . 16 growth phase  . 12 . 04 beginning in year 4 can be valued as a 0 1 2 3 growing perpetuity at time 3 .  $ 2 . 16 $ 2 . 33 $ 2 . 52 $ 32 . 75     $ 28 . 89 P 0 2 3 1 . 12 ( 1 . 12 ) ( 1 . 12 ) $ 2 . 62   $ 32 . 75 P 3 . 08 9-15

Questions?