WilliamsF1 is expected to have earnings per share next year (EPS1) equal to $16.38. Analysts expect WilliamsF1's return on equity (ROE) will equal 6.83% in perpetuity. It is also expected that the company's dividend payout ratio will be equal to 50% in perpetuity. Under the dividend discount model and assuming the intrinsic equity value is equal to the book value of equity, the required rate of return on equity, re, must be equal to what? Do not enter the % sign in your answer.If you solve this problem with algebra, round any intermediate calculations to 6 decimal places.Write your answer as a whole number, not a decimal. In all cases round your final answer to two decimal places, e.g. 8.723456% (0.082734), write 8.72
Question
WilliamsF1 is expected to have earnings per share next year (EPS1) equal to $16.38. Analysts expect WilliamsF1's return on equity (ROE) will equal 6.83% in perpetuity. It is also expected that the company's dividend payout ratio will be equal to 50% in perpetuity. Under the dividend discount model and assuming the intrinsic equity value is equal to the book value of equity, the required rate of return on equity, re, must be equal to what? Do not enter the % sign in your answer.If you solve this problem with algebra, round any intermediate calculations to 6 decimal places.Write your answer as a whole number, not a decimal. In all cases round your final answer to two decimal places, e.g. 8.723456% (0.082734), write 8.72
Solution
To find the required rate of return on equity (re), we can use the Gordon Growth Model, which is a version of the Dividend Discount Model (DDM). The formula is:
re = D1 / P0 + g
Where: re = required rate of return D1 = expected dividend per share one year from now P0 = current price of the stock g = growth rate of dividends
Given that the dividend payout ratio is 50%, the expected dividend per share one year from now (D1) is 50% of the earnings per share next year (EPS1), which is 8.19.
Since the company's return on equity (ROE) is expected to be 6.83% in perpetuity and the dividend payout ratio is 50%, the growth rate of dividends (g) is the retained earnings reinvested back into the company, which is ROE * (1 - dividend payout ratio) = 6.83% * (1 - 0.5) = 3.415%.
Assuming the intrinsic equity value is equal to the book value of equity, the current price of the stock (P0) is the same as the earnings per share next year (EPS1), which is $16.38.
Substituting these values into the Gordon Growth Model, we get:
re = 16.38 + 3.415% re = 50% + 3.415% re = 53.415%
So, the required rate of return on equity (re) must be approximately 53.42%.
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