Stock Valuation,Chapter Eight,Key Concepts and Skills,Understand how stock prices depend on future dividends and dividend growth Be able to compute stock prices using the dividend growth model Understand how corporate directors are elected Understand how stock markets work Understand how stock prices are quoted,Chapter Outline,Common Stock Valuation Some Features of Common and Preferred Stocks The Stock Markets,Cash Flows for Stockholders,If you buy a share of stock, you can receive cash in two ways The company pays dividends You sell your shares, either to another investor in the market or back to the company As with bonds, the price of the stock is the present value of these expected cash flows,One Period Example,Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay? Compute the PV of the expected cash flows Price = (14 + 2) / (1.2) = $13.33 Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33,Two Period Example,Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33 Or CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33,Three Period Example,Finally, what if you decide to hold the stock for three periods? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and a stock price of $15.435. Now how much would you be willing to pay? PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33 Or CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64; F03 = 1; NPV; I = 20; CPT NPV = 13.33,Developing The Model,You could continue to push back when you would sell the stock You would find that the price of the stock is really just the present value of all expected future dividends So, how can we estimate all future dividend payments?,Estimating Dividends: Special Cases,Constant dividend The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula Constant dividend growth The firm will increase the dividend by a constant percent every period Supernormal growth Dividend growth is not consistent initially, but settles down to constant growth eventually,Zero Growth,If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity P0 = D / R Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? P0 = .50 / (.1 / 4) = $20,Dividend Growth Model,Dividends are expected to grow at a constant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + With a little algebra, this reduces to:,DGM Example 1,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, how much should the stock be selling for? P0 = .50(1+.02) / (.15 - .02) = $3.92,DGM Example 2,Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? P0 = 2 / (.2 - .05) = $13.33 Why isnt the $2 in the numerator multiplied by (1.05) in this example?,Stock Price Sensitivity to Dividend Growth, g,D1 = $2; R = 20%,Stock Price Sensitivity to Required Return, R,D1 = $2; g = 5%,Example 8.3 Gordon Growth Company - I,Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? P0 = 4 / (.16 - .06) = $40 Remember that we already have the dividend expected next year, so we dont multiply the dividend by 1+g,Example 8.3 Gordon Growth Company - II,What is the price expected to be in year 4? P4 = D4(1 + g) / (R g) = D5 / (R g) P4 = 4(1+.06)4 / (.16 - .06) = 50.50 What is the implied return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6% The price grows at the same rate as the dividends,Nonconstant Growth Problem Statement,Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends.,Nonconstant Growth Example Solution,Compute the dividends until growth levels off D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future price P2 = D3 / (R g) = 1.449 / (.2 - .05) = 9.66 Find the present value of the expected future cash flows P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67,