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# Лекц 5-6 Valuation of stocks

## on Dec 23, 2013

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Лекц 5-6 Valuation of stocks

Лекц 5-6 Valuation of stocks

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## Лекц 5-6 Valuation of stocksPresentation Transcript

• Valuation of Stocks
• The Present Value of Common Stocks  Dividends versus Capital Gains  Valuation of Different Types of Stocks    Zero Growth Constant Growth Differential Growth
• Dividends versus Capital Gains Div1 P 1 P0 = + 1+ r 1+ r Div2 P2 P= + 1 1+ r 1+ r
• Dividends versus Capital Gains (contd.) 1   Div2 + P2  P0 = Div1 +    1+ r   1 + r  Div1 Div2 P2 = + + 2 2 1 + r (1 + r ) (1 + r ) ∞ Div3 Divt Div1 Div2 P0 = + + + ⋅⋅⋅ = ∑ 2 3 t 1 + r (1 + r ) (1 + r ) t =1 (1 + r )
• Case 1: Zero Growth  Assume that dividends will remain at the same level forever Div1 = Div2 = Div3 =  Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: Div1 Div 2 Div 3 + + + P0 = 1 2 3 (1 + r ) (1 + r ) (1 + r ) Div P0 = r
• Case 2: Constant Growth Assume that dividends will grow at a constant rate, g, forever. i.e. Div1 = Div0 (1 + g ) = Div1 (1 + g ) = Div0 (1 + g )2 Div2 = Div2 (1 + g ) = Div0 (1 + g )3 Div3 . . . 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: Div1 P = 0 r −g
• Case 3: Differential Growth  Assume that dividends will grow at different rates in the future    One constant growth rate in the foreseeable future A different constant growth 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 thereafter (case 2). Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.
• Case 3: Differential Growth Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter Div1 = Div0 (1 + g1 ) = Div1 (1 + g1 ) = Div0 (1 + g1 )2 Div2 . . . = DivN −1 (1 + g1 ) = Div0 (1 + g1 )N DivN N DivN +1 = DivN (1 + g2 ) = Div0 (1 + g1 ) (1 + g2 ) . . .
• Case 3: Differential Growth Dividends will grow at rate g1 for N years and grow at rate g2 thereafter + g1 ) Div0 (1 + g1 )2 Div0 (1 … 0 1 Div0 (1 + g1 ) 2 N DivN (1 + g2 ) = Div0 (1 + g1 )N (1 + g2 ) … … N N+1
• Case 3: Differential Growth We can value this as the sum of: an N-year annuity growing at rate g1  (1 + g1 )N  Div1 PA = 1 − N  r − g1  (1 + r )  plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1  DivN +1   −  r g2 P = B + r )N (1    
• Case 3: Differential Growth To value a Differential Growth Stock, we can use  DivN +1   (1 + g1 )N   r − g2 Div1  + P= 1 − N  − g1  (1 + r )  (1 + r )N r    
• 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%.
• With the Formula  DivN +1   (1 + g1 )N   r − g2 Div1 = − + P 1 N  − g1  (1 + r )  (1 + r )N r      \$2(1.08)3 (1.04)     .12 −.04   (1.08)3   \$2 ×(1.08) −  = + P 1 3  3 −.08  (1.12)  .12 (1.12) (\$32.75 ) P = \$54 ×[ −.8966]+ 1 3 (1.12) P = \$5.58 + \$23.31 P = \$28.89
• A Differential Growth Example (continued) \$2(1.08) 0 1 \$2.16 0 1 2 \$2(1.08) 2 \$2.33 2 3 3 \$2(1.08) \$2(1.08) (1.04) … 3 4 The constant \$2.62 \$2.52 + .08 3 growth phase beginning in year 4 can be valued as a growing perpetuity at time 3. \$2.62 P3 = = \$32.75 .08 \$2.16 \$2.33 \$2.52 + \$32.75 + + = \$28.89 P = 0 2 3 1.12 (1.12) (1.12)
• Estimates of Parameters in the Dividend-Discount Model  The value of a firm depends upon its growth rate, g, and its discount rate, r.   Where does g come from? Where does r come from?
• Estimating Growth Rate Earnings next year = Earnings this year + Retained earnings this year × Return on retained earnings Increase in earnings Earnings next year Earnings this year  Retained earnings this year   = +   Earnings this year Earnings this year  Earnings this year  × Return on retained earnings
• Estimating Growth Rate (contd.) 1 + g = 1 + Retention ratio × Return on retained earnings g = Retention ratio × Return on retained earnings
• Estimating Discount Rate  The estimation of discount rate can be broken into two parts.  Dividend yield (Div/P0)  Growth rate of dividends (g)  In practice, there is a great deal of estimation error involved in estimating the discount rate, r
• Estimating Discount Rate (contd.) Div P0 = r−g Div r= +g P0
• Value of Stock when Firm Acts as a Cash Cow Value of a firm that pays out 100% of its earnings as dividends EPS Div Value = = r r
• Price Earnings Ratio  Many analysts frequently relate earnings per share to price  The price earnings ratio or multiple  Calculated as current stock price divided by annual EPS Price per share P/E ratio = EPS