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What is the expected growth rate for dividends? 5.25% (Round to two decimal places.) b. What is the price earnings ratio (P/E 1

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) ? (Round to three decimal places.) c. What is the stock price using the P/E ratio valuation method? \$67.10 (Round to the nearest cent.) (Common stock valuation) Assume the following: - the investor's required rate of return is 13 percent, - the expected level of earnings at the end of this year (E 1

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) is $8, - the retention ratio is 35 percent, - the return on equity (ROE) is 15 percent (that is, it can earn 15 percent on reinvested earnings), and - similar shares of stock sell at multiples of 8.388 times earnings per share. Questions: a. Determine the expected growth rate for dividends. b. Determine the price earnings ratio (P/E 1

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). c. What is the stock price using the P/E ratio valuation method? d. What is the stock price using the dividend discount model? e. What would happen to the P/E ratio (P/E 1

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) and stock price if the company increased its retention rate to 70 percent (holding all else constant)? What would happen to the P/E ratio (P/E 1

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) and stock price if the company paid out all its earnings in the form of dividends? f. What have you learned about the relationship between the retention rate and the P/E ratios?

Answer :

The stock price using the P/E ratio valuation method is $6.80. The expected growth rate for dividend is as follows:

a. Expected Growth Rate for dividends:

To calculate the expected growth rate for dividends, we will use the Retention Ratio (RR) and Return on Equity (ROE) as follows:

Expected Growth Rate (g) = RR * ROE g = 0.35 * 0.15g = 0.0525 or 5.25%. Therefore, the expected growth rate for dividends is 5.25%.

b. Price Earnings Ratio (P/E 1)The Price Earnings Ratio (P/E 1) is given as: P/E 1 = Payout Ratio / (k - g)

We know that: Payout Ratio = 1 - RR .And, k = Required Rate of Return = 13%P/E 1 = (1 - 0.35) / (0.13 - 0.0525)P/E 1 = 1.308 or 1.308x. Therefore, the Price Earnings Ratio (P/E 1) is 1.308.

c. Stock Price using the P/E ratio valuation method. The stock price using the P/E ratio valuation method is given as:P0 = EPS × P/E 1Here, EPS = E1 * (1 - RR) = 8 * (1 - 0.35) = 5.2. Therefore,P0 = 5.2 * 1.308P0 = $6.80 Therefore, the stock price using the P/E ratio valuation method is $6.80.

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