A firm has an expected dividend payout ratio of 40%, and an expected dividend growth rate of 4% per year. What is the firm's Price/Earnings ratio if the appropriate discount rate is 8% per year?
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A. B. C. D.A
Value = 0.40/(0.08-0.04) = 10.
To calculate the Price/Earnings (P/E) ratio, we need to know the expected dividend payout ratio, the expected dividend growth rate, and the appropriate discount rate.
The P/E ratio is calculated by dividing the market price per share by the earnings per share (EPS). It reflects how much investors are willing to pay for each dollar of earnings generated by the company.
Given data:
To calculate the P/E ratio, we need to find the EPS. We can start by determining the dividend per share (DPS). The DPS can be calculated by multiplying the expected dividend payout ratio by the earnings per share (DPS = Dividend Payout Ratio * EPS).
Since we know that the expected dividend payout ratio is 40%, it means that the DPS is 40% of the EPS.
Next, we need to find the growth rate of dividends per share (DPS growth rate). The DPS growth rate is equal to the expected dividend growth rate. In this case, the DPS growth rate is 4%.
Using these values, we can write the following equation to find the EPS:
EPS = DPS / (Discount Rate - DPS Growth Rate)
Substituting the known values: EPS = (Dividend Payout Ratio * EPS) / (Discount Rate - DPS Growth Rate)
We can rearrange this equation to solve for EPS:
EPS * (Discount Rate - DPS Growth Rate) = Dividend Payout Ratio * EPS
EPS * Discount Rate - EPS * DPS Growth Rate = Dividend Payout Ratio * EPS
EPS * (Discount Rate - DPS Growth Rate) - Dividend Payout Ratio * EPS = 0
EPS * (Discount Rate - DPS Growth Rate - Dividend Payout Ratio) = 0
Since EPS cannot be zero, we can cancel out EPS from both sides of the equation:
Discount Rate - DPS Growth Rate - Dividend Payout Ratio = 0
Rearranging this equation to solve for the DPS Growth Rate:
DPS Growth Rate = Discount Rate - Dividend Payout Ratio
DPS Growth Rate = 8% - 40% = -32%
It is not possible for the DPS growth rate to be negative, as it implies a decline in dividends over time. Therefore, the above data is not consistent, and we cannot compute the P/E ratio with the given information.
Hence, the correct answer is B. Not able to compute with the above data.