FIN 301 Dividend Growth Model Examples.docx

FIN 301 Dividend Growth Model Examples Dividend Growth Model Dividends are expected to grow at a constant percent per period Po= D1 / (1+R )+ D2 / (1+R)2 + D3 / (1+R)3? P0 = Do (1+g) / (1+R) + D0 (1+g)2 / (1+R)2 + D0(1+g)3 /(1+R)3? With algebra this will reduce to P0=D0 (1+g)/ (R ? g) P0= D1 / (R ?g) Dividend Growth Model?Example 1 Suppose Big D Inc. just paid a dividend og $0.50 per share. 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? Po= .50(1+.02) / (.15-.02) = $3.92 Dividend Growth Model?Example 2 Suppose TB Pirates Inc is expected to pay a $2 dividend in one year. If the dividend is expected to grow at a 5% per year and the required return is 20%, what is the price? Price = 2 / (.2 - .05) = $13.33 Why isn?t the $2 in the numerator multiplied by (1.05) in this example? Because $2 is the value of the dividend paid in year one. We multiply the dividend in year 0 by 1 + the growth rate in order to get D1 but here we already have it. What happens if g > rs? If g > rs the constant growth formula will lead to a NEGATIVE stock price, which doesn?t make any sense. For this reason; the constant growth model can be used only if g < rs If the stock was expected to have negative growth (g<0), would anyone buy the stock? The firm still has earnings and pays dividends, even though they may be declining, they still have value. Stocks with negative growth may not be as attractive to investors, but if they are offered the right price they are likely to buy them. Stock Price Sensitivity to Dividend Growth, g As dividend growth rate increases stock price becomes exponentially more sensitive to changes in that growth rate Stock Price Sensitivity to Required Return, R Book Example 8.3 Gordon Growth Company 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? Price = 4 / (.16 - .06) = $40 Again, we already have the dividend expected next year, so we don?t multiply the dividend by 1+g Example 8.3?Gordon Growth Company 2 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 Price is assumed to grow at the same rate as the dividends Nonconstant Growth Problem Suppose a firm is expected to increase dividends by 20% in one year, and by 15% in 2 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 Present Value of all expected future dividends Compute the dividends one at a time until growth levels off D1= 1(1.2) = $1.20 D2= 1.20(1.15) = $ 1.38 D3= 1.38(1.05)= $1.45 Find the expected future price P2 = D3 / (R ? g) 1.45/.2-.05 = $9.67