Question

5. You purchased a stock when the last paid dividend was $4.00. What was the growth rate of dividends if you required a 12% return for the purchase, assumed a constant rate of growth, and paid $44.44 for the stock?

Answer 1

Price of a stock using the costant dividend growth model is given by:
P0 = D0*(1+g)/(r-g)
where
D0 = last paid dividend
g = growth rate, and
r = required return
Substituting available values, we have
44.44 = 4*(1+g)/(0.12-g)
Solving for g, we have
44.44*(0.12-g)/4 = 1+g
11.11*0.12-11.11*g = 1+g
(11.11*0.12-1)/12.11 = g = 2.75%
CHECK:
Share price = 4*1.0275/(0.12-0.0275) =	$          44.43
Answer: Growth rate of dividends =	2.75%