The growth in dividends of XYZ,Inc.is expected to be 10%/year for the next two years,followed by a growth rate of 5%/year for three years;after this five year period,the growth in dividends is expected to be 2%/year,indefinitely.The required rate of return on XYZ,Inc.is 12%.Last year's dividends per share were $2.00.What should the stock sell for today?

Question

Quizplus · Accepted Answer

To calculate the stock price, we need to use the dividend discount model:
P = D / (r - g)
where P is the stock price, D is the dividend per share, r is the required rate of return, and g is the dividend growth rate.

For the first two years, the dividend grows at 10%, so:
D1 = $2.00 x 1.10 = $2.20
D2 = $2.20 x 1.10 = $2.42

For the next three years, the dividend grows at 5%, so:
D3 = $2.42 x 1.05 = $2.54
D4 = $2.54 x 1.05 = $2.67
D5 = $2.67 x 1.05 = $2.80

After year 5, the dividend growth rate drops to 2%, so:
g = 0.02

Plugging in these numbers, we get:

P = $2.20 / (0.12 - 0.10) + $2.42 / (1.12)^2 / (0.12 - 0.10) + $2.54 / (1.12)^3 / (0.12 - 0.05) + $2.67 / (1.12)^4 / (0.12 - 0.05) + $2.80 / (1.12)^5 / (0.12 - 0.05) = $25.21

Therefore, the stock price should be $25.21, which is answer choice B.

The Growth in Dividends of XYZ,Inc