Complete Question:
Assume the following: the investor's required rate of return is 17 percent, the expected level of earnings at the end of this year (E1) is $5, the retention ratio is 45 percent, the return on equity (ROE) is 18 percent (that is, it can earn 18 percent on reinvested earnings), and similar shares of stock sell at multiples of 6.180 times earnings per share. Questions a. Determine the expected growth rate for dividends b. Determine the price earnings ratio (PIE1) c. What is the stock price using the P/E ratio valuation method? d. What is the stock price using the dividend discount model?
Answer:
a. The expected growth rate for dividends
= 8.1%
b. The price earnings ratio (P/E1) = Share price/Earnings per share
= 5 x
c. The stock price using the P/E ratio valuation method
= $30.90
d. The stock price using the dividend discount model
= $30.90
Step-by-step explanation:
a) Data and Calculations:
Investor's required rate of return = 17%
Expected level of earnings at the end of this year (E1) = $5
Retention ratio = 45%
Return on equity (ROE) = 18%
(that is, it can earn 18 percent on reinvested earnings)
Price multiples = 6.180 times earnings per share
a. The expected growth rate for dividends
= Return on equity * Retention ratio
= 18% * 45%
= 0.081
= 8.1%
b. The price earnings ratio (P/E1) = Share price/Earnings per share
= $30.90/6.180
= 5 x
c. The stock price using the P/E ratio valuation method
= Share price multiples * Expected level of earnings
= 6.180 * $5
= $30.90
d. The stock price using the dividend discount model
= (Dividend payout ratio * Expected level of earnings) / (Required return - Dividend Growth rate)
= (0.55 * $5)/ (0.17 - 0.081)
= $2.75/ 0.089
= $30.90
(Dividend payout ratio = (1 - Retention ratio) = 1 - 0.45 = 0.55)