VIP Corporation has just paid a dividend of $1.50.Dividends are expected to grow at 20% for the first three years and 10% for the following two years.What is the expected growth rate for the subsequent years, assuming that the rate would be constant for all subsequent years if the share is selling for $24.86 today and the required return is 17%?

Question

Quizplus · Accepted Answer

First, calculate the expected dividends for the next five years:
Year 1: $1.50 x 1.20 = $1.80
Year 2: $1.80 x 1.20 = $2.16
Year 3: $2.16 x 1.20 = $2.59
Year 4: $2.59 x 1.10 = $2.85
Year 5: $2.85 x 1.10 = $3.14

Next, calculate the present value of these dividends:
PV = ($1.80 / 1.17) + ($2.16 / 1.17^2) + ($2.59 / 1.17^3) + ($2.85 / 1.17^4) + ($3.14 / 1.17^5)
PV = $7.98

Finally, use the constant growth model to solve for the expected growth rate for the subsequent years:
$24.86 = ($7.98 x (1 + g) / (0.17 - g))
$24.86(0.17 - g) = $7.98(1 + g)
0.017 - 0.17g = 0.1254 + 0.07992g
0.24992g = -0.10854
g = -0.10854 / 0.24992
g = -0.434
g = -1.07%

Therefore, the correct answer is (C) 8.00%.

VIP Corporation Has Just Paid a Dividend of $1