If a stock has an expected dividend payout ratio of 50 percent, a required rate of return of 13 percent and an expected growth rate for dividends of 9 percent, what is the P/E ratio?
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A. B. C. D.B
The P/E ratio is calculated as: P/E = (D/E)/(k - g). In this case P/E = 0.5/(0.13 - 0.09) = 12.5
To calculate the price-to-earnings (P/E) ratio, we need to use the dividend discount model (DDM). The DDM values a stock by considering the present value of its future dividends.
The formula for the Gordon growth model, which is a variant of the DDM, is as follows:
P = D1 / (r - g)
Where: P = Price of the stock D1 = Expected dividend for the next period r = Required rate of return g = Expected growth rate of dividends
In this case, we know that the expected dividend payout ratio is 50 percent. Therefore, the expected dividend (D1) can be calculated as follows:
D1 = Dividend payout ratio × Earnings = 0.5 × Earnings
To find the earnings, we can use the formula:
Earnings = Dividends / Dividend payout ratio = D1 / Dividend payout ratio = D1 / 0.5
Now, we substitute the values into the Gordon growth model formula:
P/E = (D1 / 0.5) / (r - g)
Given: r = 13% (0.13) g = 9% (0.09)
P/E = (D1 / 0.5) / (0.13 - 0.09) = 2 × D1 / 0.04 = 50 × D1
We need to determine the P/E ratio, so we need to find the value of D1.
Since we don't have specific information about the earnings or dividends of the stock, we can't calculate the exact P/E ratio. Therefore, the correct answer is D. None of these answers.