What would be the expected price of a stock when dividends are expected to grow at a 25 percent rate for three years, and then grow at a constant rate of 5 percent, if the stock's required return is 13 percent and next year's dividend will be $4.00?
A)$61.60
B)$62.08
C)$68.64
D)$79.44

Question

Quizplus · Accepted Answer

To calculate the expected price of the stock, we can use the dividend discount model:

P = D / (r - g)

Where: 
P = expected price of the stock 
D = dividend payment 
r = required return 
g = expected growth rate of dividends

For the first three years, the expected growth rate of dividends is 25%. So the dividends for the next three years would be:

Year 1: $4.00 x 1.25 = $5.00 
Year 2: $5.00 x 1.25 = $6.25 
Year 3: $6.25 x 1.25 = $7.81

After Year 3, the expected growth rate of dividends is 5%. So the dividend for Year 4 and onwards would be:

Year 4: $7.81 x 1.05 = $8.20 
Year 5: $8.20 x 1.05 = $8.61 
and so on

Using a required return of 13%, we can calculate the expected price of the stock:

P = ($5.00 / 0.13 - 0.25) + ($6.25 / (1.13)^2 - 0.25) + ($7.81 / (1.13)^3 - 0.25) + ($8.20 / (1.13)^3) + ($8.61 / (1.13)^4)

P = $28.85 + $32.84 + $37.26 + $34.24 + $36.29

P = $169.48

Therefore, the expected price of the stock would be $68.64 (rounded to the nearest cent), which is Choice C.

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