If the spread between the required rate of return and the anticipated dividend growth rate were to decrease significantly and suddenly while the remaining components of the P/E ratio were to remain unchanged, which of the following would likely occur? Further, a decrease in the retention rate wouldlead to what effect on the earnings multiplier, holding both the required return and expected growth rate constant?
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A. B. C. D. E.B
Remember that the equation used to determine the appropriate earnings multiplier for a stock market series is the following:
P/E = [D/E / (k - g)]
Where: P/E = the earnings multiplier, or Price-to-Earnings ratio, D/E = the dividend payout ratio at t1, k = the required rate of return, and g = the anticipated growth rate of dividends.
As the spread between k and g narrows, the earnings multiplier figure will increase. Indeed, the earnings multiplier is very sensitive to changes in the spread between k and g, and this is the primary reason for the greater relative volatility of the P/E ratio versus the EPS figure for a stock market series.
A decrease in the retention rate will lead to an increase in the earnings multiplier figure, holding everything else equal. Remember that the retention rate is simply
(1 - dividend payout ratio). So said, a decline in the retention rate is analogous to an increase in the dividend payout ratio. An increase in the dividend payout ratio, holding everything else equal, will lead to an increase in the earnings multiplier figure.