Expected return = (Div1 + P1 – P0)/P0 VALUING COMMON STOCKS Expected return : the percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR) Expected return = (Div1 + P1 – P0)/P0 = Dividen Yield + Capital Appreciation = Div1/P0 + (P1 – P0)/P0 • Dividen Discount Model : Computation of today’s stock price which states that share value equals the present value P0 ={[Div1/(1+r)1] + [Div2/(1+r)2] + . . . +[(DivH+PH)/(1+r)H]}

5.4 The Present Value of Common Stocks Dividends versus Capital Gains Valuation of Different Types of Stocks Zero Growth Constant Growth Differential Growth

Case 1: Zero Growth Assume that dividends will remain at the same level forever L = 3 2 1 Div Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: r P Div ) 1 ( 3 2 = + L

Case 2: Constant Growth g r P - = Div Assume that dividends will grow at a constant rate, g, forever. i.e. ) 1 ( Div g + = 2 1 ) ( Div g + = . 3 2 ) 1 ( Div g + = 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: g r P - = 1 Div

Case 3: Differential Growth Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter ) (1 Div 1 g + = 2 1 ) (1 Div g + = . . . N g ) (1 Div 1 + = - ) (1 Div 2 1 g N + = . . .

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

Case 3: Differential Growth We can value this as the sum of: an N-year annuity growing at rate g1 ú û ù ê ë é + - = T A r g C P ) 1 ( plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1 N B r g P ) 1 ( Div 2 + ÷ ø ö ç è æ - =

Case 3: Differential Growth To value a Differential Growth Stock, we can use N T r g C P ) 1 ( Div 2 + ÷ ø ö ç è æ - ú û ù ê ë é = Or we can cash flow it out.

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 [ ] ( ) r g C P ) 1 ( Div + ÷ ø ö ç è æ - ú û ù ê ë é N T r g C P ) 1 ( Div 2 + ÷ ø ö ç è æ - ú û ù ê ë é = 3 ) 12 . 1 ( 04 08 2 $ ÷ ø ö ç è æ - + ú û ù ê ë é ´ = P [ ] ( ) 3 12 . 1 75 32 $ 8966 54 + - ´ = P 31 . 23 $ 58 5 + = P 89 . 28 $ = P

A Differential Growth Example (continued) 3 08) . 2(1 $ ) 04 . 1 ( 08) 2(1 $ 3 08) . 2(1 $ 2 08) . 2(1 $ … 0 1 2 3 4 The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3. 08 . 62 2 $ 52 + 16 . 2 $ 33 . 2 $ This type of problem separates the “A” students from the rest of the class. 0 1 2 3 89 . 28 $ ) 12 1 ( 75 32 52 2 33 16 3 = + P

VALUING COMMON STOCKS Example : Current forecasts are for XYZ Company to pay dividends of $3, $3.24 and $3,50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? (PV = $75.00) If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. Perpetuity = Po = Div1/r or EPS/r • Constant Growth DDM : A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model)

VALUING COMMON STOCKS GGM,P0 = Div1/(r – g) Example : What is the value of a stock that expects to pay a $3.00 dividend next year, and then increase the dividen at a rate of 8% per year, indefinitely? Assume a 12% expected return.(P0 = $75.00) If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends? (g = .09) If a firm elects to pay a lower dividen, and reinvest the funds, the stock price may increase because future dividends may be higher Payout Ratio : Fraction of earnings paid out as dividends Plowback Ratio : Fraction of earnings retained by the firm g = return on equity x plowback ratio

VALUING COMMON STOCKS Example : Our company forecasts to pay a $5.00 dividen next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plowback 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? (No growth : P0 = 5/.12 = $41.67 ; With growth : g = .20x.40 = .08, and P0 = 3/(.12 - .08) = $75.00) If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00 The difference between these two numbers ($75.00 - $41.67) is called the Present Value of Growth Oppurtunities (PVGO). PVGO : Net Present Value of a firm’s future investment Sustainable Growth Rate : Steady rate at which a firm can grow: plowback ratio x return on equity

KONSEP PENENTUAN HARGA SAHAM Expectation: a) Dividen, b) capital gain Dalam penentuan harga saham  Time value of money concept Harga saham dipengaruhi: a) r (gunakan CAPM) dipengaruhi β dan Rf , b) Div dipengaruhi laba. MODEL BERDASARKAN ARUS KAS Model dengan pertumbuhan konstan, asumsi ; a. Perusahaan mempertahankan DPR sbg dividen yg konstan b. Setiap laba yg diinvestasikan kembali memperoleh tingkat keuntungan yg sama setiap tahunnya. c.Sbg akibatnya maka EPS dan DPS akan meningkat dengan % yg konstan setiap tahunnya : Do = Eo(1 – b), D1= E1(1 – b) PER = (1 – b)/(r - g)

continue 2. Model dengan dua periode pertumbuhan : pertumbuhan tidak diasumsikan konstan selamanya, tetapi akan berubah setelah periode tertentu. 3. Model dengan tiga periode pertumbuhan, perluasan model 2 4. Model Regresi Crossectional Faktor yg mempengaruhi PER;  a. Elton Gruber (1991); PER = a + b (pertumbuhan div atau laba) b. Whitbecker-Kisor (1969) ; i) tingkat pertumbuhan laba, ii) DPR, iii) Deviasi standar tingkat pertumbuhan PER = a + β1a + β2b + β3c