Question

Calculate today’s stock price for Deere (DE) if last period’s dividend was $1.32 and its constant growth rate (for its dividend) is projected to be 4% indefinitely (assuming a required rate of return of 8%). (5 pts.)

What would be today’s price if the dividend growth of DE (see above) for the next three years is projected to be 9% in year 1, 11% in year 2, and 7% in year 3....and, after year 3, dividend growth will return to its constant growth rate of 4% (again, assume the required return for shareholders is 8%).

Answer 1

a). P0 = [D0 * (1 + g)] / [r - g]

= [$1.32 * (1 + 0.04)] / [0.08 - 0.04]

= $1.3728 / 0.04 = $34.32

b). P0 = [{D0*(1+g1)}/(1+r)] + [{D0*(1+g1)*(1+g2)}/(1+r)²] + [{D0*(1+g1)*(1+g2)*(1+g3)}/(1+r)³] + [{D0*(1+g1)*(1+g2)*(1+g3)*(1+gC)}/{(r-gC)*(1+r)³}]

= [{$1.32*(1+0.09)}/(1+0.08)] + [{$1.32*(1+0.09)*(1+0.11)}/(1+0.08)²] + [{$1.32*(1+0.09)*(1+0.11)*(1+0.07)}/(1+0.08)³] + [{$1.32*(1+0.09)*(1+0.11)*(1+0.07)*(1+0.04)}/{(0.08-0.04)*(1+0.08)³}]

= $1.33 + $1.37 + $1.36 + $35.27

= $39.33