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CHAPTER 9 Stocks and Their Valuation Features of common stock Stock valuations Constant dividend growth model The behavior of dividends and their PV The model Applying the model when g>r, g=0 and g<0 Future stock price Dividend yield and capital gain Non-constant growth model Preferred stock 8-1 Facts about common stock Represents ownership Ownership implies control Stockholders elect directors Directors elect management Receives cash flow in the form of dividend Management’s goal: Maximize the stock price 8-2 Dividend growth model Value of a stock is the present value of the future dividends expected to be generated by the stock. D3 D1 D2 D P0 ... 1 2 3 (1 rs ) (1 rs ) (1 rs ) (1 rs ) ^ 8-3 Constant growth stock A stock whose dividends are expected to grow forever at a constant rate, g. D1 = D0 (1+g)1 D2 = D0 (1+g)2 Dt = D0 (1+g)t 8-4 Constant growth stock If g is constant, the dividend growth formula converges to: D0 (1 g) D1 P0 rs - g rs - g ^ 8-5 What happens if g > rs? If g > rs, the constant growth formula leads to a negative stock price, which does not make sense. The constant growth model can only be used if: rs > g g is expected to be constant forever 8-6 If rRF = 7%, rM = 12%, and β = 1.2, what is the required rate of return on the firm’s stock? Use the SML to calculate the required rate of return (ks): rs = rRF + (rM – rRF)β = 7% + (12% - 7%)1.2 = 13% D0 = $2 and g is a constant 6%, 8-7 What is the stock’s market value? Using the constant growth model: D1 $2.12 P0 rs - g 0.13- 0.06 $2.12 0.07 $30.29 8-8 What would the expected price today be, if g = -5%?, if g=0? When g=-5% D1=1.9, P=1.9/(13%+5%)=10.56 When g=0, The dividend stream would be a perpetuity. 0 rs = 13% 1 2 3 ... 2.00 2.00 2.00 PMT $2.00 P0 $15.38 r 0.13 ^ 8-9 Computing other variables ^ P0 D0 (1 g) D1 rs - g rs - g Computing Ks Computing D Computing g 8-10 What is the expected market price of the stock, one year from now? D1 will have been paid out already. So, P1 is the present value (as of year 1) of D2, D3, D4, etc. D2 $2.247 P1 rs - g 0.13- 0.06 ^ $32.10 8-11 Future stock price What is the expected market price of the stock two years from now? P2, D3 $2.382 P2 rs - g 0.13- 0.06 ^ $34.03 What is the expected market price of the stock years from now? Pn, n D0 (1 g) n 1 Dn 1 Pn rs - g rs - g ^ 8-12 The growth rate of stock price What is the % change of stock price from and from P1 to P2 What is the % change of stock price from Pn+1 P0 to Pn to What is the expected market price of the stock two years from now? P1 P2, P2 =P1 *(1+g)= P0 *(1+g)2 8-13 Dividend Yield and Capital Gain P0=D1/(r-g) k=(D1/P0)+g Total return=dividend yield + Capital gain g is capital gain for constant growth stock 8-14 What is the expected dividend yield, capital gains yield, and total return during the first year? Dividend yield = D1 / P0 = $2.12 / $30.29 = 7.0% Capital gains yield = (P1 – P0) / P0 = ($32.10 - $30.29) / $30.29 = 6.0% Total return (rs) = Dividend Yield + Capital Gains Yield = 7.0% + 6.0% = 13.0% 8-15 Supernormal growth: What if g = 30% for 3 years before achieving long-run growth of 6%? Can no longer use just the constant growth model to find stock value. However, the growth does become constant after 3 years. 8-16 Valuing common stock with nonconstant growth 0 r = 13% 1 s g = 30% D0 = 2.00 2 g = 30% 2.600 3 g = 30% 3.380 4 ... g = 6% 4.394 4.658 2.301 2.647 3.045 P$ 3 46.114 54.107 ^ = P0 4.658 0.13 - 0.06 $66.54 8-17 Nonconstant growth: What if g = 0% for 3 years before longrun growth of 6%? 0 r = 13% 1 s g = 0% 2 g = 0% D0 = 2.00 2.00 3 g = 0% 2.00 4 ... g = 6% 2.00 2.12 1.77 1.57 1.39 P$ 3 20.99 25.72 ^ = P0 2.12 0.13 - 0.06 $30.29 8-18 Preferred stock Hybrid security Like bonds, preferred stockholders receive a fixed dividend that must be paid before dividends are paid to common stockholders. However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy. 8-19 A preferred stock has an annual dividend of $5, what should the preferred stock price be if discount rate is 10%? Vp = D / rp $50 = $5 / 10% 8-20