A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $37.33 using the DDM where P_o = D₁ / (k − g). We are given D_o = $3.25, g = 3.5%, and k = 12.5%. What we need to find is D₁ which equals D_o × (1 + g) therefore D₁ = $3.25 × 1.035 = $3.36 thus P_o = 3.36 / (0.125 − 0.035) = $37.33.

In the answer choice where the stock value is $18.70, discounting the future cash flows back to the present gives the present value of the stock. the future cash flows are the dividend in year 1 plus the dividend and value of the stock in year 2 thus the equation becomes: V_o = 2.2 / 1.15 + (2.2 + 20) / 1.15² = $18.70

For the answer choice where the stock value is $31.13 use the DDM which is P_o = D₁ / (k − g). We are given k = 0.08, g = 0.04, and what we need to find is next year’s dividend or D₁. D₁ = Expected earnings × payout ratio = $4.15 × 0.3 = $1.245 thus P_o = $1.245 / (0.08 − 0.04) = $31.13