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?
A)$8.99
B)$25.21
C)$40.00
D)$110.00
E)none of the above

Question

Quizplus · Accepted Answer

To calculate the current stock price, we can use the dividend discount model: 
P = D1 / (r - g) 
Where P is the current stock price, D1 is the next year's dividend, r is the required rate of return, and g is the growth rate.

First, we need to calculate the dividends for the next five years:

Year 1: $2.00 x 1.10 = $2.20 
Year 2: $2.20 x 1.10 = $2.42 
Year 3: $2.42 x 1.05 = $2.54 
Year 4: $2.54 x 1.05 = $2.67 
Year 5: $2.67 x 1.05 = $2.80

After year 5, the dividend growth rate becomes 2%.

Using the formula above, we can calculate the current stock price:

P = ($2.20 / 1.12) + ($2.42 / 1.12^2) + ($2.54 / 1.12^3) + ($2.67 / 1.12^4) + ($2.80 / 1.12^5) + ($2.80 x 0.02) / (0.12 - 0.02) 
P = $25.21

Therefore, the best choice is B.

The Growth in Dividends of XYZ,Inc