Homework SourseYouve collected the following information from your favorite
You’ve collected the following information from your favorite financial website. 52-Week Price Stock (Div) Div Yld % PE Ratio Close Price Net Chg Hi Lo 77.40 10.43 Palm Coal .36 2.6 6 13.90 –.24 55.81 33.42 Lake Lead Grp 1.54 3.8 10 40.43 –.01 131.01 69.90 SIR 2.40 2.7 10 89.05 3.07 50.24 13.95 DR Dime .80 5.2 6 15.43 –.26 35.00 20.74 Candy Galore .32 1.5 28 ?? .18 According to your research, the growth rate in dividends for SIR for the next five years is expected to be 19.5 percent. Suppose SIR meets this growth rate in dividends for the next five years and then the dividend growth rate falls to 5 percent indefinitely. Assume investors require a return of 14 percent on SIR stock. According to the dividend growth model, what should the stock price be today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Current stock price $ 31.33
Solution
P5 = D6/(R - g)
= D0(1 + g1)5(1 + g2) / (R - g2)
= $2.40(1.195)5(1.05) / (0.14 - 0.05)
= $6.141/0.09 = $68.23
The price of the stock today is the present value of the first five dividends, plus the present value of the Year 5 stock price. The price of the stock today will be:
P0 = D0(1 + g1)/(1 + r)1 + D0(1 + g1)2/(1 + r)2 + D0(1 + g1)3/(1 + r)3
+ D0(1 + g1)4/(1 + r)4 + D0(1 + g1)5/(1 + r)5 + P5/(1 + r)5
= $2.40(1.195)/1.14 + $2.40(1.195)2/1.142 + $2.40(1.195)3/1.143 + $2.40(1.195)4/1.144 + $2.40(1.195)5/1.145 + $68.23/1.145
= $2.52 + $2.64 + $2.76 + $2.90 + $3.04 + $35.44 = $49.29
